From 2feb6c4d98c0c891e2b0fd1a8399d37723d28176 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Tue, 25 Nov 2025 19:53:42 +0100 Subject: [PATCH 01/12] Update Python test --- examples/test_r.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 examples/test_r.ipynb diff --git a/examples/test_r.ipynb b/examples/test_r.ipynb new file mode 100644 index 0000000..e69de29 From 0d48f6291f3e2dd1f569138b8fe3e7840485a495 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Wed, 3 Dec 2025 02:02:33 +0100 Subject: [PATCH 02/12] Update R --- examples/test_r.ipynb | 1446 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1446 insertions(+) diff --git a/examples/test_r.ipynb b/examples/test_r.ipynb index e69de29..116f107 100644 --- a/examples/test_r.ipynb +++ b/examples/test_r.ipynb @@ -0,0 +1,1446 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "8443073c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3f4527cc", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e4b77c16", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n", + "also installing the dependencies 'igraph', 'numDeriv'\n", + "\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'igraph' successfully unpacked and MD5 sums checked\n", + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpaOiKF4\\downloaded_packages\n" + ] + } + ], + "source": [ + "# Download and install\n", + "install.packages(\"LoopDetectR\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "37148f24", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpaOiKF4\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpaOiKF4\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5af1f007", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")" + ] + }, + { + "cell_type": "markdown", + "id": "7821beca", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **In brief and quick start**\n", + "The package LoopDetectR enables determining all feedback loops of an ordinary differential equation (ODE) system at user-defined values of the model parameters and of the modelled variables.\n", + "\n", + "The following call reports (up to 10) feedback loops for an ODE system determined by a function, here the example function `func_POSm4`, at variable values s_star (here, these are all equal to 1). Additional arguments to the example function are supplied." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "452aaf33", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
3, 31-1
4, 41-1
3, 4, 1,....4-1
3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 6 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 3, 4, 1,.... & 4 & -1\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 3, 4, 1,.... | 4 | -1 |\n", + "| 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 4, 4 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Load example ODE system with function func_POSm4, 4 variables\n", + "data(\"func_POSm4\")\n", + "# Example variable values\n", + "s_star <- rep(1,4)\n", + "# Further arguments of func_POSm4, in addition: time t as argument\n", + "klin <- rep(1,8)\n", + "knonlin <- c(2.5,3)\n", + "\n", + "# compute loops\n", + "res_tab <- find_loops_vset(func_POSm4,vset=list(s_star),t=1,klin=klin,\n", + " knonlin=knonlin,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]]" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "eedcc059", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\n", + "
A data.frame: 1 × 3
looplengthsign
<I<list>><dbl><dbl>
63, 4, 2, 331
\n" + ], + "text/latex": [ + "A data.frame: 1 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t6 & 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 1 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 6 | 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# This is the sixth loop of the list. It is a positive feedback loop (sign in \n", + "# the loop list equals +1) of length 3 in that variable 3 regulates variable 4, \n", + "# variable 4 regulates variable 2, and variable 2 regulates variable 3. \n", + "res_tab$loop_rep[[1]][6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "441d7e21", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1 0 0-1
1-1 0 1
0 1-1 0
0 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & 0 & 0 & -1\\\\\n", + "\t 1 & -1 & 0 & 1\\\\\n", + "\t 0 & 1 & -1 & 0\\\\\n", + "\t 0 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | 0 | 0 | -1 |\n", + "| 1 | -1 | 0 | 1 |\n", + "| 0 | 1 | -1 | 0 |\n", + "| 0 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 0 0 -1 \n", + "[2,] 1 -1 0 1 \n", + "[3,] 0 1 -1 0 \n", + "[4,] 0 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "69850e68", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "aaa76790", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Load example ODE system with function func_POSm4, \n", + "# Positive feedback chain model from [Baum et al., 2016], 4 variables\n", + "data(func_POSm4)\n", + "# The function func_POSm4 returns a vector, but deSolve needs the vector within\n", + "# a list as output. Therefore, we define a function that simply puts the output \n", + "# of func_POSm4 into a list:\n", + "func_POSm4_list <- function(t,x,klin,knonlin){list(func_POSm4(t,x,klin,knonlin))}\n", + "# Kinetic parameters of the model, supplied as arguments to func_POSm4\n", + "klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1)\n", + "knonlin <- c(0.3,2)\n", + "# Solve the system using deSolve\n", + "sol <- deSolve::ode(y = rep(1,4), times = seq(0,15,0.1), func = func_POSm4_list, \n", + " parms=klin, knonlin=knonlin)\n", + "# The solution of the 4-variable system is oscillatory, showing only the first \n", + "# variable here\n", + "plot(sol[,1],sol[,2],type='l',xlab='Time',ylab ='Variable 1')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e363256e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n", + "also installing the dependencies 'rematch', 'blob', 'DBI', 'gargle', 'cellranger', 'ids', 'rematch2', 'timechange', 'systemfonts', 'textshaping', 'selectr', 'conflicted', 'dbplyr', 'dtplyr', 'forcats', 'googledrive', 'googlesheets4', 'haven', 'lubridate', 'modelr', 'ragg', 'readxl', 'reprex', 'rstudioapi', 'rvest'\n", + "\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " There is a binary version available but the source version is later:\n", + " binary source needs_compilation\n", + "selectr 0.4-2 0.5-0 FALSE\n", + "\n", + "package 'rematch' successfully unpacked and MD5 sums checked\n", + "package 'blob' successfully unpacked and MD5 sums checked\n", + "package 'DBI' successfully unpacked and MD5 sums checked\n", + "package 'gargle' successfully unpacked and MD5 sums checked\n", + "package 'cellranger' successfully unpacked and MD5 sums checked\n", + "package 'ids' successfully unpacked and MD5 sums checked\n", + "package 'rematch2' successfully unpacked and MD5 sums checked\n", + "package 'timechange' successfully unpacked and MD5 sums checked\n", + "package 'systemfonts' successfully unpacked and MD5 sums checked\n", + "package 'textshaping' successfully unpacked and MD5 sums checked\n", + "package 'conflicted' successfully unpacked and MD5 sums checked\n", + "package 'dbplyr' successfully unpacked and MD5 sums checked\n", + "package 'dtplyr' successfully unpacked and MD5 sums checked\n", + "package 'forcats' successfully unpacked and MD5 sums checked\n", + "package 'googledrive' successfully unpacked and MD5 sums checked\n", + "package 'googlesheets4' successfully unpacked and MD5 sums checked\n", + "package 'haven' successfully unpacked and MD5 sums checked\n", + "package 'lubridate' successfully unpacked and MD5 sums checked\n", + "package 'modelr' successfully unpacked and MD5 sums checked\n", + "package 'ragg' successfully unpacked and MD5 sums checked\n", + "package 'readxl' successfully unpacked and MD5 sums checked\n", + "package 'reprex' successfully unpacked and MD5 sums checked\n", + "package 'rstudioapi' successfully unpacked and MD5 sums checked\n", + "package 'rvest' successfully unpacked and MD5 sums checked\n", + "package 'tidyverse' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpYFGT5P\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "installing the source package 'selectr'\n", + "\n", + "\n", + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + }, + { + "ename": "ERROR", + "evalue": "Error: object 'sol_long' not found\n", + "output_type": "error", + "traceback": [ + "Error: object 'sol_long' not found\nTraceback:\n", + "1. .handleSimpleError(function (cnd) \n . {\n . watcher$capture_plot_and_output()\n . cnd <- sanitize_call(cnd)\n . watcher$push(cnd)\n . switch(on_error, continue = invokeRestart(\"eval_continue\"), \n . stop = invokeRestart(\"eval_stop\"), error = NULL)\n . }, \"object 'sol_long' not found\", base::quote(eval(expr, envir)))" + ] + } + ], + "source": [ + "# Make beautiful plot using ggplot2 / tidyverse\n", + "install.packages(\"tidyverse\") # if not already installed\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e7722a33", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "library(deSolve)\n", + "library(tidyverse)\n", + "\n", + "# solve system\n", + "sol_for_plot <- as.data.frame(\n", + " ode(\n", + " y = rep(1,4),\n", + " times = seq(0, 15, 0.1),\n", + " func = func_POSm4_list,\n", + " parms = klin,\n", + " knonlin = knonlin\n", + " )\n", + ")\n", + "\n", + "# rename columns for clarity\n", + "colnames(sol_for_plot) <- c(\"time\", \"X1\", \"X2\", \"X3\", \"X4\")\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = X1:X4, names_to = \"species\", values_to = \"value\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "079c187f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + "# geom_line(size = 1.1) +\n", + "# scale_colour_brewer(palette = \"Dark2\") +\n", + "# labs(\n", + "# title = \"Dynamics of the 4-Variable Positive Feedback Chain\",\n", + "# x = \"Time\",\n", + "# y = \"Concentration\",\n", + "# colour = \"Species\"\n", + "# ) +\n", + "# theme_minimal(base_size = 16) +\n", + "# theme(\n", + "# plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + "# legend.position = \"right\",\n", + "# panel.grid.minor = element_blank()\n", + "# )\n", + "\n", + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(size = 1.1) +\n", + " scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_y_log10(\n", + " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", + " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", + " ) + # ← log₁₀ transformation\n", + " labs(\n", + " title = \"Dynamics of the 4-Variable Positive Feedback Chain\",\n", + " x = \"Time\",\n", + " y = \"Concentration (log scale)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " panel.grid.minor = element_blank()\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "90aac4e1", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "dir.create(\"results\", showWarnings = FALSE)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "5da4476d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "agg_record_757164869: 2" + ], + "text/latex": [ + "\\textbf{agg\\textbackslash{}\\_record\\textbackslash{}\\_757164869:} 2" + ], + "text/markdown": [ + "**agg_record_757164869:** 2" + ], + "text/plain": [ + "agg_record_757164869 \n", + " 2 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "svg(\"results/posm4.svg\", width = 10, height = 8)\n", + "print(plot1)\n", + "dev.off()" + ] + }, + { + "cell_type": "markdown", + "id": "834f11c6", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **Calculating the Jacobian matrix**\n", + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003].\n", + "\n", + "The input function, in the example `func_POSm4` (positive feedback chain model from [Baum et al., 2016]) defines the time derivatives of the modelled variables as a vector: \n", + "$f_i(s)=dS_i/dt$. Note that only those input arguments to the function that encode the modelled variables (and hence in whose direction the partial derivatives are taken) are allowed to be called `x`." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "7a7e6226", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
1
63.9008547597954
2
0.0111646237998349
3
0.0748170189314118
4
1.37597224802616
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[1] 63.9008547597954\n", + "\\item[2] 0.0111646237998349\n", + "\\item[3] 0.0748170189314118\n", + "\\item[4] 1.37597224802616\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "1\n", + ": 63.90085475979542\n", + ": 0.01116462379983493\n", + ": 0.07481701893141184\n", + ": 1.37597224802616\n", + "\n" + ], + "text/plain": [ + " 1 2 3 4 \n", + "63.90085476 0.01116462 0.07481702 1.37597225 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "bdad5d8b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1.2396132 0 0.0-85.9719
0.9696132-5550 0.0 85.9719
0.0000000 550-82.4 0.0000
0.0000000 0 78.0 -5.1000
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1.2396132 & 0 & 0.0 & -85.9719\\\\\n", + "\t 0.9696132 & -5550 & 0.0 & 85.9719\\\\\n", + "\t 0.0000000 & 550 & -82.4 & 0.0000\\\\\n", + "\t 0.0000000 & 0 & 78.0 & -5.1000\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1.2396132 | 0 | 0.0 | -85.9719 |\n", + "| 0.9696132 | -5550 | 0.0 | 85.9719 |\n", + "| 0.0000000 | 550 | -82.4 | 0.0000 |\n", + "| 0.0000000 | 0 | 78.0 | -5.1000 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] \n", + "[1,] -1.2396132 0 0.0 -85.9719\n", + "[2,] 0.9696132 -5550 0.0 85.9719\n", + "[3,] 0.0000000 550 -82.4 0.0000\n", + "[4,] 0.0000000 0 78.0 -5.1000" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1)\n", + "knonlin <- c(0.3,2)\n", + "j_matrix <- numDeriv::jacobian(func_POSm4,s_star,method=\"complex\",\n", + " t=1,klin=klin,knonlin=knonlin,)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "39c1a233", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1 0 0-1
1-1 0 1
0 1-1 0
0 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & 0 & 0 & -1\\\\\n", + "\t 1 & -1 & 0 & 1\\\\\n", + "\t 0 & 1 & -1 & 0\\\\\n", + "\t 0 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | 0 | 0 | -1 |\n", + "| 1 | -1 | 0 | 1 |\n", + "| 0 | 1 | -1 | 0 |\n", + "| 0 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 0 0 -1 \n", + "[2,] 1 -1 0 1 \n", + "[3,] 0 1 -1 0 \n", + "[4,] 0 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "f50e0305", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **Computing all feedback loops and useful functions for loop search**\n", + "The Jacobian matrix is used to compute feedback loops in the generated interaction graph. The default function for this is `find_loops`, in that strongly connected components are determined to reduce runtime. For smaller systems, the function `find_loops_noscc` skips this step and thus can be faster. The optional second input argument, `max_num_loops`, sets an upper limit to the number of detected and reported loops and thus can prevent overly long runtime (but also potentially not all loops are returned)." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "cfc29fc4", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
3, 31-1
4, 41-1
3, 4, 1,....4-1
3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 6 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 3, 4, 1,.... & 4 & -1\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 3, 4, 1,.... | 4 | -1 |\n", + "| 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 4, 4 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Determine the loop_list from Jacobian matrix j_matrix\n", + "loop_list <- find_loops(j_matrix)\n", + "loop_list" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "54d49c90", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
3, 31-1
4, 41-1
3, 4, 1,....4-1
3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 6 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 3, 4, 1,.... & 4 & -1\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 3, 4, 1,.... | 4 | -1 |\n", + "| 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 4, 4 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Use the signed Jacobian matrix to determine the loop_list give the same result\n", + "loop_list <- find_loops(signed_jacobian)\n", + "loop_list" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "a4336c7f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[[1]]\n", + "[1] 3 4 1 2 3\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Retrieve fifth loop\n", + "loop_list[5,1] " + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "3b862f3d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 3
  2. 4
  3. 1
  4. 2
  5. 3
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 3\n", + "\\item 4\n", + "\\item 1\n", + "\\item 2\n", + "\\item 3\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 3\n", + "2. 4\n", + "3. 1\n", + "4. 2\n", + "5. 3\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 3 4 1 2 3" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# In order to obtain the vector of the order of variables of a loop, you have to \n", + "# call the list element\n", + "loop_list[5,1][[1]]" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "e28abdc5", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\n", + "
A data.frame: 1 × 3
looplengthsign
<I<list>><dbl><dbl>
53, 4, 1,....4-1
\n" + ], + "text/latex": [ + "A data.frame: 1 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t5 & 3, 4, 1,.... & 4 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 1 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 5 | 3, 4, 1,.... | 4 | -1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "5 3, 4, 1,.... 4 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Retrieve all loops of length 4\n", + "loop_list[loop_list$length==4,]" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e3dc787d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 4
len_1len_2len_3len_4
<dbl><dbl><dbl><dbl>
all4011
pos0010
neg4001
\n" + ], + "text/latex": [ + "A data.frame: 3 × 4\n", + "\\begin{tabular}{r|llll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\tall & 4 & 0 & 1 & 1\\\\\n", + "\tpos & 0 & 0 & 1 & 0\\\\\n", + "\tneg & 4 & 0 & 0 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 4\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> |\n", + "|---|---|---|---|---|\n", + "| all | 4 | 0 | 1 | 1 |\n", + "| pos | 0 | 0 | 1 | 0 |\n", + "| neg | 4 | 0 | 0 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4\n", + "all 4 0 1 1 \n", + "pos 0 0 1 0 \n", + "neg 4 0 0 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(loop_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "9cb66750", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
53, 4, 1,....4-1
6 3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 3 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t5 & 3, 4, 1,.... & 4 & -1\\\\\n", + "\t6 & 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 5 | 3, 4, 1,.... | 4 | -1 |\n", + "| 6 | 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2\n", + "# Return all loops from loop_list containing node 2\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "3291b3cc", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "The `LoopDetectR` function `find_edge` can be used to search a loop list for loops containing specific edges defined by the indices of the ingoing and outgoing nodes. This example returns the indices of all loops with a regulation of node 3 by node 2. These are only two here." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "d736f376", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 2 × 3
looplengthsign
<I<list>><dbl><dbl>
53, 4, 1,....4-1
6 3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 2 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t5 & 3, 4, 1,.... & 4 & -1\\\\\n", + "\t6 & 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 2 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 5 | 3, 4, 1,.... | 4 | -1 |\n", + "| 6 | 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Obtain the indices of the loops with edge '2 regulates 3' in loop_list \n", + "loop_edge_ind <- find_edge(loop_list,source_node=2,target_node=3);\n", + "loops_with_edge_2_to_3 <- loop_list[loop_edge_ind,]\n", + "loops_with_edge_2_to_3" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "a0151df7", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "'C:\\\\Users\\\\Admin\\\\AppData\\\\Local\\\\Temp\\\\RtmpaOiKF4'" + ], + "text/latex": [ + "'C:\\textbackslash{}\\textbackslash{}Users\\textbackslash{}\\textbackslash{}Admin\\textbackslash{}\\textbackslash{}AppData\\textbackslash{}\\textbackslash{}Local\\textbackslash{}\\textbackslash{}Temp\\textbackslash{}\\textbackslash{}RtmpaOiKF4'" + ], + "text/markdown": [ + "'C:\\\\Users\\\\Admin\\\\AppData\\\\Local\\\\Temp\\\\RtmpaOiKF4'" + ], + "text/plain": [ + "[1] \"C:\\\\Users\\\\Admin\\\\AppData\\\\Local\\\\Temp\\\\RtmpaOiKF4\"" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "tempdir()" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "ed4a5e03", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# This writes a file 'looplist_func_POSm4.RData'\n", + "save(loop_list,file=file.path(tempdir(),'looplist_func_POSm4.RData')) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bb9080e6", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# This loads the object 'loop_list' into the workspace\n", + "load(file.path(tempdir(),'looplist_func_POSm4.RData'))\n", + "\n", + "# This saves the loop list into a table with separation by tab\n", + "write.table(loop_list,file=file.path(tempdir(),'looplist_func_POSm4.txt'),\n", + " sep='\\t',quote=F,row.names=F)\n", + "# This reads the loop list back into the R session, as object ll\n", + "ll <- read.table(file.path(tempdir(),'looplist_func_POSm4.txt'),\n", + " header=T,sep='\\t')\n", + "ll" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 91726cfa7722bf7a151e19ec4e9c465ee0e02664 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Thu, 11 Dec 2025 14:01:30 +0100 Subject: [PATCH 03/12] Update examples python --- examples/test_r.ipynb | 111 ++++++++++++++++++++---------------------- 1 file changed, 53 insertions(+), 58 deletions(-) diff --git a/examples/test_r.ipynb b/examples/test_r.ipynb index 116f107..95b276e 100644 --- a/examples/test_r.ipynb +++ b/examples/test_r.ipynb @@ -155,7 +155,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 2, "id": "452aaf33", "metadata": { "vscode": { @@ -371,7 +371,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 3, "id": "aaa76790", "metadata": { "vscode": { @@ -381,15 +381,15 @@ "outputs": [ { "data": { - "image/png": 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DL53oOl43MbkT4/y0RungisfAzd5KqRZwuvtH0/EE3Gr42gJu+FZK536lA3bePFtvM7xibvlWmr2VUi3g/88znp/u/Ml6vFQFvidmfQE3W4KA74yTqsD3R5OGWyfglse3nu8bsPKXB9eAW552Am55fOP5/76k5jredbrw1m2nOz+tUTE3fsDuO5QKWPnLQ9PhQluvGkvAzglI30+FKnDduvOXzZqxpTtJafGbrQhYZbpwBY1Pu37AewJePM1wAeUvD7oBO3/ZrBpbvJPjdP+XCA2WMDi6+Qo/DZO5KwlXILz1urHlOznefwOlxRL1RzdfwTdg32/vvuN1h3uf9qqpFRvZp2X/ISUCZvrPk0S27vxTVd3U8M9Ch9/g36Nc70lU8Nsgja3XTg3fR/gN/j1K+H4qUoHr1p2/bFZOjd5Hg/05fw9TuZ8ScI/h1VMJWCfgHl8erMa3T0xkeu1QAibgu3OGD9j3vFQPJWD372FWCzjfk1zHC39lI2ACJmDd4QRctUSLfgn43hiBvfcYTsD+xzZf5Nc5Jgs435Ncx+sOJ2AClr6fCuy9y3AC9j+29SK/j4l/P/W9o67wqwMB+x/behHfgJ3vSboB9/nqQMDeh7ZfpVPAytPDb935pyqDoQTs/j3MZIU7EwavQHjrFkMJmIC9x+sO9z7tBjMJmICl995rOAE7H9p6lbtDqldwvie5jl/nVwcCdj2y/TLKAQvvvdtwAnY9sv0ywhH47l34xBBw5RJCAd+fETsCAi4ZQMCeRzZfRjlg4b33G07Ajgd2WEc4At+9C58YAq5cQijgv0bULeF8T+oYcOgTQ8CVSxDwoqN976fjBux7XqxmErD7s0D1SwgHLPyVjYBrlyDgZQdHvqO67r3nVwcCdjuuw0LKAQtP1x1uN5OA3Z8Fql5ixYkFPjEEXLsEAS88dtSAhb862M0k4MEDFp6uO9xwJgG7P41bu8SaE4t7Ygi4dolm/QYPuPMD7LgBC391MJxJwGMHLLz3zsM97qAE3GOlJYdHvZ/63lFX/dWBgH0Oa7+Sb8C9H2CH3Xvvrw4E7HNY+5WUAxbee+/hBOxxVBnfZ4HqVhAO2PfMELDXLmyWWFfAvq+lBb2juu69+1cHAvY4qsywAQtP1x1uO5KAK9daeGzMu1L/CmKeGAKuX4KAlx82YMDCXx1sR0YNuGW/wwYsPF13uPFIAq5cjIDrDot4Ygi4fgmVgJce6vo4Qjgx4RNDwOYHlSJgtem6w61HEnDdYgRceVTAE0PA9Us07bditcVHun4VE05M+MQQsPEx5QhYbLrucPORBFy1mnDAMbYufGII2PiYcsWrLT/Q9SQ4P8sQbu9BToz91gm4jHrAytPDbb3neVlNwG37HTLgjEPEKqic3nN4zFRi7spiuSgRKE9n664TLcTclcVyUe5JBdNzjhCroG5619s0Zioxd2WxHAHXHyF8YuyHx0wl5q4MlgsTgfJ0tl41MWbAjfsdMOCsA4T3Hms4ATtpEHCwu1KcrQufGPvhBFymbL28o3LXiBNBsOlxtk7AdkfUGS5g360H2nuo4QTshYDXOl1s+EoCbt1v2YKZB7n+deHEhE8MAVsdUGu0gH3/eqS9RxpOwG4IeK1/XWx404CfH3fp1W5+Nl5CImDhb0vKf33de2kY8HmTPm1tlyBgtcdu7f56pBMjHfCcpqfj9dLpMKXZconm/RJwz+nCJ8Z8eMOAp3T8uHxMk+USEgHHikB5Olsv30DZIW/Hpd/+UL0EAftOz7+2WhUUH9D/NuU7cBkC7jhd+MSYD2/7GPhwul4a8jFwsAiUp7P1ih1U1LL98iz05my4RPt+xwrY+U7Sv4LSIwLcpi0DvjzP19eBp92j7evAHQJu8UqX8P1UrILSIwIMbxqw1xIKAUeLQHk6W6/Zglcu6asQOzJdM9o9KeOQktOrVUHhIRFu0/YB7zcp7Q6mSxBwtPupWAWFh0QY3jDgt++rt2ey7j4JnblEj35bfI0RTizK9HBblw94TvP5cjnNaW+3xFoDDnI/9d16vL3HGB414CldXz86p43dEgQc7n6qPF1reOuA35+fsnwrpUDAZVt0vBGlExM+MfIBP7wHbPhWSgION3yEgGN8dWga8O5xf0hPLxfPs+FbKbv0S8Crna41vGnAH6/xpjTZvZVSIODCLfo9j+E+PUTAAU+McsCX43G/3+2uT2XNd/sl4KzDXKf7bl044CBf2FoG7LQEAXtOL/55y3O68ImxHk7AhXJWDRmB8nS2XrONYAH36XeUgIvPrlQFBcdFuU0JuBABd5wufGKshxNwId9znHHgiNPZes0+CDhz2Zj3pEUHlp9cqQryDwxzmxJwIQLuOF34xFgPlw+4U7++TzNkHDnkdLZesxECzls36D1pyZEVJ1eqguwj49ymBFyIgDtOFz4x1sMJuNDidaNGoDydrZf95eJDHJcgYL/pNedWeO+dh48VcK9+gwTsm5jw9LBbtx5OwIWWLly1Qd37ae/pYbdOwKV/09gAAdedW929+54Y4+kEXGjhwr4RRLon5R7tuvfAJ8Z46wRcSD9g5elsvfCvFx7itkS3fgcIuPLcuk4XPjHGwwm40LKVI0egPJ2tl/79skPcliBgt+m1p1apgqzDY92mBFyIgHtOFz4xxsMJuNCilUNHoDydrRcfECrgfv2uPuDqU6tUQc7xwW5TAi61ZO3Q9yTl6Wy9/AgCXrx27HuS8nS2Xn4EAS9eO/Y96e4AgzPrOV75xNhOJ+BSf68d7bZuO/3eiKESy5jQpsY4Affsd90BW5zZVQYc7gsbAZci4OLxY58Y2/NCwKX+XDzcF+u203sFHP7EEHDuX/Ox5oBNTuyvQwY/MbbnhYBL9Q04+rfIe0PiVbB4RrytKwfctd8/Vx/tntR2vO5wAs78W15aBNzpruQb8OgnxnY4AZf6Y3WBCH6bYnRehSpYOCXibUrApQi453ThE2M7nIBL9QxYITGlCppOJ+Ccv+Tn/vIK96RfxpidV8/xyifGdDoBl+oYcMh70sJBnBjb80LApe4uP+A9qe145RNDwBl/yQ8Bl4znxBifFwIudW/5mF+sG09vH7DIiSHgjL/kZ6UBG57VH0ZxYn6eVD5cN+DO/d5bX+ObmHTAzYdH3ToBl1pnwJZndVUBR/3CRsClfl8/6m3dePoPs1z3LnNiTLdOwKWaBCwcgfLefU8MAS/+O55+Xd83grD3pAXjXfeuc2JMty4bcO9+Vxmw8Un9/zjXMyN0Yiy3TsClfttA3Nv6z+HOAbueGaUTY7l1Ai7VJmDdCLzH6w4n4Ea7KNqAbwSB70l/jnfdu9SJsdw6AZdaX8Dmp1R3774nhoAD9PvLDnwjiHxP+mu86961Tozl1gm41OoCtj+lvuPTL5etZ8e+TQm41I87cNhW+vGi+WzvgF2ni50Yy/NCwKXWFrDv1oUDjv2FjYBL/bQDj12lHy7Zz5b72qN8YizPCwGXah6wXGGuiSmfGMvzIhpw/35/2oPLrjzvp86J+e79Y6jeiTE8LwRc7J89OG0qOU73Lcw1MeUTY3heCLjYGgL2Ha48XWU4ARf7/x689pQ8p7sOV56uMpyAizUN2O0KJ+/hnJifZw8dcIR+/78Jvz2lS3K8wskzgiuv6bonxvC8EHCxdOdPtgu5Xt0U42yW4MQQcIX06x88F5Ib74gTQ8AV0i+XgXYIuBgBoz/JgGPkkn68CLREwMXSD5eAtgi4mPPbEIEFCLjY+/vhYuwGYyLgYr5vMwKWaBrw8+Pu+haU3fxctUSMaK7vtYuxFQyrYcDnTfq0rVgiSDS+b+QDlmgY8Jymp+P10ukwpbl8iSDZkC/6axjwlI4fl49pKl+CcICbhgF/+47177ev9FXhEsBgFL8DA7hp+xj4cLpeqnwMDOCm5ctI2y8/I2/OLksAY2n7OvB8fR142j3WvQ4M4I3kO7EAvCFgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBAWNGAAixTUZR+s2Aa6GfeaD3zVza9591PZfQPdjHvNB77qBLwe417zga86Aa/HuNd84KtOwOsx7jUf+KoT8HqMe80HvuoEvB7jXvOBrzoBr8e413zgq07A6zHuNR/4qhPweox7zQe+6gS8HuNe84GvOgGvx7jXfOCrvr6AAZQjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWEEDAgjYEAYAQPCCBgQRsCAMAIGhBEwIIyAAWF9A56nNM3nrlvoo/i/ZaVu/36dh7vp36+58U3f9T60vV6VTc8t9HEcNeDj+3Ue7qZ/v+bWN33P+9Bzmo6X45SeO+6hj2Pa9d5CFy839tsdbrib/uOaW9/0PQOe0+Hln0/pseMe+tgPeJ0vr1d7e7sbj3bTf15z65u+Z8C7dLqM+d1on/a9t9BDmi+3u/FoN/3nNbe+6XsGfLtKAz4U3KXDQ5rm3tto7fj/23yYm/7zmlvf9ATcw+7tiYxt7320N2jAly8B2970BNxDSk+Xy3ke8Afp4QO2vukJuJ/zSC+j3Awf8Bu7m77nGZzGuxW/G/Ca367ygDf99+tqds37Pwt9GuapyH+MdP+9+fYs9FA3/QoDfry+GHhIwz0b+/IN6PVNhEPdf29ud9wBb/qPnz1sb3reidXD/HrPPb+9m2Eso74T6+OaW9/0XX+I24z6Ysp5ul7zgb7/vHv/0XG8m/52za1v+q4Bn6+/ktJzB728XvPNeC8ifQY83k3/9Zob3vTjPY0CrAgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBA8IIGBBGwIAwAgaEETAgjIABYQQMCCNgQBgBr1364uM/E4+14AZdOwJeNW7QIRDuWnHDDoGA14obdgjvAb/+++V/j2l6vFzmlObr/7vfpGnfcXcoR8BD+B7w4+vj4cP29Z+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4FScV6W15cdVucegS4gGGa6vxKs4q0tvr+nQfaVo9O7iPRFtlT0A13ri7v637CpFSxWsWabs6XoBb7YXyqYXownBtNV7FoURanjd+l+lukzaLUlZb8aweZbi2Gq/iSCJtyvJwFGlTnv4edxr4ccXh9m5XRIofzzwD3XCNIk3lcBbkjt9HOj1lXdaHt7f9umyEs3qQ4dpqvIpDiXQ6rHtEpKN57xzKQjirBxmurcarOJRIi493pN1tMc7jLoX7LV63X7etJ9M9grcMRqvYv7aVc6TtdPtQ7TzuOPDpUyTjLUKjtZWDghHp1pDVXb9fdB5XVs+bbXl5f3hYG28RGq6txqvY//r+vo9UVi/3jPt/2FbKZLtFaLi2Gq7iAEfOs1Pc7Tab1ep0yWF906MhRMrdVzVSFzzmFiEPbZW7r2qkLrhBpMAfEOmhrXL3VY3UBSOSGan7qoZmDhE2YHFoJ0PqvqqRuuAhRXLRVrn7qkbqgptFejld/v5jN/d53P2HgogUONZVFJPQr7dVpM9fH1/9Pe6BD91HpLChbpC64EaRjh9o8v7PdirPfw+8/0P3+66Dj7bK3Vc1UhfcKNLnR2z98fFaH9z9ofuIFDbUDVIX3CjS1xHafZe/7/3QfUQKGukmqQtuPrT7fEcS/QMviBQ00k1SF9y8+/t0jvQ6/f2b5rNDSOOkrXL3VY3UBQ+4s8FJW+XuqxpqaVjUi0hmpO6rGqkLHm9ng5e2yt1XNVIXjEhmpO6rGqkLlhLp9Y6tDY0hAsz9EFqJULDToN+GrMOdI9FXVqQuuPk+0if3bFudFUIYN22Vu69qpC64eYvQy9uy7PfL8scfapkfQhg3bZW7r2ooJWJTr8AWoef3d6PdPZ/HNS+EMG7aKndf1UhdsIBI2+OHQ0Y5R/LTVrn7qkbqghtFWr0f2u3L4u0VkR4mdV/VSF1wo0jbo0CnX+4T3WyHSMGi3EXqglsvfz8fv3r66+8dNYUIMvPDpO6rGqkLHmxng6O2yt1XNVIXjEhmpO6rGqkLbtr9/W0HuHFWxhPPQCUXClYCkcxI3Vc1Uhc81qGdp7bK3Vc1Uhfceh9J9mpdLUSEeWehkcxwBUcVqdNfe0WkQDHuJnXBjSItyu2/GDYTRAoU425SF9wo0mG1FN32XQnhf9qZpO6rGqkLbj60i3TVzlVbRb5oMw9Euj4EkeaDSCFDyEWOux70lSmpCx5JJF9tpZDOcAUnECnCpwgN11fDFRxYpEifIjRcX1GwHo0ihfoUIfrKltQFN4oU6VOEnLVV/3yGKziwSJE+RWi4vhqu4OAiRfkUoeH6ioIVad39HehThOgrY1IX3ChSoE8R8tZW3TNyVzAi3RgS51OE3PUVIoULIBv7c4joBe96CO9ztoFIseaXDv45pEzrvWguv0N4n7ONvhmNVm9ckRbvZ0bLPm9LHZbEX18hUrD5pYN/Ddmvp3eX1jvJfH6EcD1lK4gUa37p4JdDXp/eVVpspH/fHJG8zz6H1OeE7bu/X45Xv59kD/EQyffk80CkP4Ycnt9PlyaJbK6GcDhjO4gUaXr56LUhW+87Gxz2FSKFml4+Ou9IQiBSnNl7hA95juSwr7rmNFq95hW37rULctXOY18NJ1Lqt+AWkV6P95GmEPeRhusrClZmkJ0N1stcpWNSLutFpPqQMj13+eDvN0TyPHUDiFQd0uNDv3+E8DqfDIgUZO5O8RVSRiS/UzeQuWBEsqNfVj7rRaTmIdYhzJe5CiKFmLpbAvFEMl/lOogUYupuCSCSEIgUYOaOGSCSEN3SclovIjUPMQ5hv8xVECnAzB0zCCeS/SrXQST3E3dNAZGE6JWX13oRqXmIbQgHy1wFkdxP3DWFaCI5WOU6iOR+4q4pIJIQiOR83kdAJDs6Jea2XkRqHmIawsMyV0Ek5/M+Qn6RPKxyHURyPu8jIJIdiOR62sdAJDv6ZOa3XkRqHmIZwsUyV0Ek19M+RnqRXKxyHURyPOujIJIdmfuqSuaCEcmOLqk5rheRmod88Pq8Ov4B9LJa//EJRIjka1IhEKl1yInDovxn2SVEz5nkQSS3kz6OokjrMr2cP954v53KukeInjPJk7mvqmQuWFGkqfz/lPDd7T8Dg0ie5hQDkVqHnMeVa1+Iheg5kzyI5HbSx0n+juRklesgktM556B7jrTdnx7pnSN5WeYqmfuqSuaCNS9/Ly+u2i1u/iELRPI0pxiZC9a9j7Q+3UeaVs9a95G8LHOVDsm5rjd1wbl3NrhZ5jry6fkuGJFah1iFcLPMdRDJ45TzyL1FyM0y10Ekj1POI/UWITerfAVE8jfjXFJvEfKzzHXE83NeMCK1Djmhf0PWzzLXQSR/M87FzxahcsnMED+nlJmmG4jkb8a5ZH5H8rPKV0AkbxPOJ/MWIUfLXEc6Qe8FI1LrkDPaW4QcLXMdRPI24XwybxFytMx1EMnbhPNJvLPB0SpfAZF8zdcCIhkinKH7ghGpdYhJCE/LXAeRfM3XAiIZgki+5mshr0ieVvkKiORpujZUdzbcvXkBkcxn6wEitQ45sUGkHyCSp+na0Dy02023f3lCIITwHJ1BJE/TtaF6jrS7vTFIIoTkFN1BJD+ztaJ7sWFzsW+1UwjBKbojmmOAghGpdYhBCF/LXAeR/MzWCiIZgkheJmsnq0jOlrlO5saqkbleRDJEMskIBSNS6xD9EM6WuQ4ieZmsHUQyBJF8zCUBIhmSubFqZK43qUjelrmOYJYhCkak1iHqIbwtcx1E8jGXBIhkCCJ5mEoGRDIkc2PVyFxvTpHcLXMduTRjFIxIrUO0Q7hb5jqI5GEqGRDJEESyn0kKRDJELM3R6nVYcEqR/C1zHUSyn0kKRDIEkexnkgKRDEEk64nkQCRDpPIcrV6PBWcUyeEy10Ek64nkQCRDEMl6IjkQyRBEsp1HEkQyRCjR0ep1WXBCkTwucx1Esp1HEkQyBJEsp5EFkQzJ3Fg1MteLSJaIpBqnXkRqHaIZwuUyXwGRDKeRBZEsQSSzWaRBJEsQyWwWaRDJEolcA9WLSK1DNEP4XOc6iGQ2izTpRPK5zFdAJKNJ5EEkSxDJaBJ5EMkSgWQj1YtIrUMUQzhd5zqIZDSJPIhkCSKZzNGDbCJ5Xec67dmGqheRWofohfC6znUQyWSOHiCSJYhkMkcPEMkSRDKYog+IZElztoOV67jgZCK5Xec6g4mU+R0YkSxBJP0ZOoFIliCS9gTdQCRLWtMNVi4itQ5RC+F3oasgkvYE3UAkSxBJe4Ju5BLJ7zrXacw3WrmZXzgQyRJE0h3fEUSyBJF0x3cEkSxBJN3xHUEkS9ryjVZt6heOVCJ5XugqiKQ5vCuIZAkiaQ7vCiJZgkiaw7uCSJY0JRyu2tQvHIhkCSLpje5MJpFcL3QVRNIb3RlEsqQl43jVIlLzEJ0Qrhe6CiLpje4MIlmCSFqDu5NIJN8LXQWRtAZ3B5EsaUg5YLWI1DxEJYTvha6CSFqDu4NIliCSzlgF8ojkfKGrIJLOWAUQyZL5OUesFpGah2iEcL7QVRBJZ6wCiGQJImkMVQGRLJmdc8Ri3xCpeYhCCO8LXQWRNIaq4LNlfWYlDyJpDFXBZ8v6zKoDc7OOWW3mc0KfLeszqw7MzDpmsYjUPKR/CPcLXQeRuo9UApFMQaTOA9VAJFMQqfNANRDJlHlpBy0WkZqHfPD6vCpHVutX4RD+F7oOInUeqIaiSIdF+c9SNoT/ha6DSF3HKaIo0rpML7vTo/12KmvREAFWusqsvKMWi0jNQ05MZff1eFcm0RABVroKInUdp4iiSKVc+6I9RICVroJIHYepkuMdKcJKV0GkjsNU0T1H2u5Pj8TPkSKsdJVRfl/kA0RqHHJmeXHVbnGQDBFhpasgUsdhqujeR1qf7iNNq2fh+0gRVroKInUbpUyKnQ0hVrqKz+XvBiI1Drlr2ktcZKSAn+VXAZEah1yyWZSy2oqGCLHSVRCp0yB11O8jfVxxuHnRDpFkh7gBkRqHnMcdB67L+vD2tl+XjVyIGCtdZZht7mcQqXHIedxx4FRO170PZSEXIsZKV0GkToPU0Rbp8zqC5BahGCtdBZG6jDFAW6SnT5EEtwgFWeoaw2wqPINIjUPO48rqebMtL+8PD2vJLUJBlroGInUZY4CqSF/3iEqZ5LYIBVnpKojUYYgJmqXtdpvNanW65LC+6REiyQ1wBSI1DukaIspS1xhmU+EZn90mgs/SEEno+c7w2W0i+CztkRBRVroKIomPMAKRTBlmL9QZRGoc0jNEmKWugUjiI4xAJFMQSXiAGeFFirPUNRBJeIAZiGTKMFs4ziBS45COIeIsdQ1EEh5gBiKZgkiizzcEkUxBJNHnGxJdpEBLXWOYLRxnEKlxSL8QgZa6BiIJPt0URDIFkQSfbgoimYJIgk83JbhIkZa6xjBbOM4kvraCSKYgktizjUEkUxBJ7NnGIJIpiCT0ZHMQyZRh7jyfQaTGIb1CxFrrCogk9GRzEMmWYS70n0h8JItItgxzEHsCkRqH9AoRbLErIJLEcx0QWqRga10Dkdqf6gJEsmWc994jiNQ4pFOIaItdAZHan+oCRLIFkVqf6QREsmWcSo8gUuOQPiHCLXYFRGp9phMQyRZEanuiGxDJlnEqPYJIjUP6hIi32r8Zp9IjiNQ4pEuIeItdAZFanucIRLJlnEqPIFLjkC4hAq72b8ap9AgiNQ7pEiLgav9mnEqPJL5GiUi23FNEikJPIFLjkB4hIq72b8ap9EjiSyuIZMs4lR5BpMYhPUKEXO5f3FFFjkJPIFLjkB4hQi73LxBp3pPcEVakmMv9i7/LSFLombyvkIhkCyLNeo4/EMkWRJrxFI8gki1/lpGkzg/y/mARyRZEmvEUj0QVKehy/+KvOrLU+UHeHywi2YJIDz/DJ4hkCyI9/AyfIJItf9SRpcxP8p4SBhUp7Hr/BJEefIJXEMmW24WkKfOTvEeyiGQLIj30fb8gki2I9ND3/YJIttwsJE2VX+Q9JYwpUuAF/wEiPfBtzyCSLbcqyVPlF4jUNkQ6ROAF/wEi3f1d3yCSLTcqyVPkfxCpbYhwiMgL/gNEuvOb3kEkW66XkqjI/yBS2xDhEKFX/DuIdNf3/INItlwtJVGNFyBS2xDhELGX/BuIdMe3IhBRpOBL/o1rtWSq8QJEahsiGyL4kn8Dkf78TgwQyZYrtWQq8RJEahsiGyL6mn+jXkyqEi/Ie0qISMZUi0lV4SWI1DZENET4Nf8GIt36/+OASMbUqslV4SWI1DZENET8Rb+kUk2uAr+R99oKIhmDSNf/70ggkjG/q8lV33fyXqOMJ1KGVb8AkXIUjEjG/ConWX3fQaS2IZIhUiz7f36Wk6y8H+S9RolIxgwvUpKCw4mUZN2/KDe/zAYitQ0RDJFk3b8oN77KR95LK4hkTLn6RUbyXlpBJGPGFilPwYhkTLnyOCd5zwijiZRo6c+U6sOs5D0jRCRjvgoq6UqrkPdAFpGMKT/+zU3eA1lEMqZ8+yc7/8vM9gaMSMacCsrWVVcpvx5kQVWk1+dVObJav84MkW79jxUNo9H/9998FSuKdFiU/yznhUj4A0jYVNc5vWykrFhRpHWZXnanR/vtVNazQuT7EeSr6BY5JTqiKNJUdl+Pd2XqEQLACEWRvr0Y/X5lKpfMDAFgBO9IAALoniNt96dH88+RAHyiefl7eXHstjh0CQFgg+59pPXpPtK0ep57HwnAJ9F2NgC4BJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAARAIQAJEABEAkAAEQCUAApyIBBGNGl8uL4zu2RVAKTRazAiIljTlMoYhEf6ULOkrMCoiUNOYwhSIS/ZUu6CgxKyBS0pjDFIpI9Fe6oKPErIBISWMOUygi0V/pgo4SswIiJY05TKGIRH+lCzpKzAqIlDTmMIUiEkAeEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAAQwE2k9lWl9UA66WRgEfXt7VV/l3VMpT3vVkAf1n+jmc1lNeukHViItTx2nWxEAAAOrSURBVB/6v9ANuj4FnbSX/DBpr/JWv9D9dI6pZ+/u849GmPTST4xEei3T7m03lVfNoLvydDi+jj1pBn1nNefPhDQxva/uYVXWiiGfTtHWeov73j3nZTXppV8YibQu2/f/vpRnzaCrc7Habf0y6+/ttEU8NvWhTIoxi/LibsryI5ZJL/3CSKRVOR4C7MrKILZyW++/fuJqPJWdbsB3Pg5f1eR9f634WFbLXrrIxyiszZvDkUNZqsZblr12mYvy9jydjmP1eP44tNN6X9j9bCKLXrpgPJE2pyMBNZ7Li3qZpaxOJ/6qQTfHqw3TRjEiIlkWv59UDwFORxz6Ih0vNjzpnjU8n66daYZEJMPiD5Pugd3ieA1aX6TjOdJe9Yrw5nho9y6v4lsSIv0/NVUPv9S93fB0Oo7UF+nyHx0W5XhKdtCU96M+s176hulVu732lZb9Yql7u7/lD87Px+I6v4G8367aqffSz2Rswj6fXqm3qrcMj/F0j+usRDqv7l612vP7guq9q49FtemlX8nYhDW5G63bWRdoH3W8nx0djucrL4ox1+W4222t2c7sbHg7HlIf0W3sJ4t3hyPqEZ8NVnepHvNzWS166XcyRnHPe4V1Y5ocZp0Da0fcLtVX9039J/q5rBa99At+HwlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAEQCEACRAARAJAABEAlAAESKQLnA4O//wd/wQ4kAIrmHH0oYEMgz/HDCgEie4YcThk+Rjv++/++5TM9vb+tSzn/Pe7Mo08Ywu9FBpDB8F+n5eL60XR7/ezRpdTp/WpomODSIFIbvIi0Pb5uP/05vb9vjo8OybG1THBhECsN3kV5Pj/YfX6/K4f3RoawM8xsbRArDj3Okt8v//r84Djaw8mFAJM+w8mG4LZJdXnCEH0AYbom04jKDMYgUhlsivZRp9/a24WKDGYgUhlsivZ1uKJVpb5bd6CBSGG6KdNzZUJ7wyAxEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAARAJQABEAhAAkQAEQCQAAf4BHTzOzE5sZCsAAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { - "height": 360, - "width": 480 + "height": 420, + "width": 420 } }, "output_type": "display_data" @@ -404,10 +404,11 @@ "# of func_POSm4 into a list:\n", "func_POSm4_list <- function(t,x,klin,knonlin){list(func_POSm4(t,x,klin,knonlin))}\n", "# Kinetic parameters of the model, supplied as arguments to func_POSm4\n", - "klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1)\n", + "# klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1)\n", + "klin <- c(150, 0.04, 0.3, 500, 5000, 80, 4, 5)\n", "knonlin <- c(0.3,2)\n", "# Solve the system using deSolve\n", - "sol <- deSolve::ode(y = rep(1,4), times = seq(0,15,0.1), func = func_POSm4_list, \n", + "sol <- deSolve::ode(y = rep(1,4), times = seq(0,11,0.1), func = func_POSm4_list, \n", " parms=klin, knonlin=knonlin)\n", "# The solution of the 4-variable system is oscillatory, showing only the first \n", "# variable here\n", @@ -416,7 +417,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "id": "e363256e", "metadata": { "vscode": { @@ -430,9 +431,6 @@ "text": [ "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", "(as 'lib' is unspecified)\n", - "\n", - "also installing the dependencies 'rematch', 'blob', 'DBI', 'gargle', 'cellranger', 'ids', 'rematch2', 'timechange', 'systemfonts', 'textshaping', 'selectr', 'conflicted', 'dbplyr', 'dtplyr', 'forcats', 'googledrive', 'googlesheets4', 'haven', 'lubridate', 'modelr', 'ragg', 'readxl', 'reprex', 'rstudioapi', 'rvest'\n", - "\n", "\n" ] }, @@ -440,48 +438,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "\n", - " There is a binary version available but the source version is later:\n", - " binary source needs_compilation\n", - "selectr 0.4-2 0.5-0 FALSE\n", - "\n", - "package 'rematch' successfully unpacked and MD5 sums checked\n", - "package 'blob' successfully unpacked and MD5 sums checked\n", - "package 'DBI' successfully unpacked and MD5 sums checked\n", - "package 'gargle' successfully unpacked and MD5 sums checked\n", - "package 'cellranger' successfully unpacked and MD5 sums checked\n", - "package 'ids' successfully unpacked and MD5 sums checked\n", - "package 'rematch2' successfully unpacked and MD5 sums checked\n", - "package 'timechange' successfully unpacked and MD5 sums checked\n", - "package 'systemfonts' successfully unpacked and MD5 sums checked\n", - "package 'textshaping' successfully unpacked and MD5 sums checked\n", - "package 'conflicted' successfully unpacked and MD5 sums checked\n", - "package 'dbplyr' successfully unpacked and MD5 sums checked\n", - "package 'dtplyr' successfully unpacked and MD5 sums checked\n", - "package 'forcats' successfully unpacked and MD5 sums checked\n", - "package 'googledrive' successfully unpacked and MD5 sums checked\n", - "package 'googlesheets4' successfully unpacked and MD5 sums checked\n", - "package 'haven' successfully unpacked and MD5 sums checked\n", - "package 'lubridate' successfully unpacked and MD5 sums checked\n", - "package 'modelr' successfully unpacked and MD5 sums checked\n", - "package 'ragg' successfully unpacked and MD5 sums checked\n", - "package 'readxl' successfully unpacked and MD5 sums checked\n", - "package 'reprex' successfully unpacked and MD5 sums checked\n", - "package 'rstudioapi' successfully unpacked and MD5 sums checked\n", - "package 'rvest' successfully unpacked and MD5 sums checked\n", "package 'tidyverse' successfully unpacked and MD5 sums checked\n", "\n", "The downloaded binary packages are in\n", - "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpYFGT5P\\downloaded_packages\n" + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\RtmpcZaHJz\\downloaded_packages\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "installing the source package 'selectr'\n", - "\n", - "\n", "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", @@ -493,26 +459,17 @@ "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" ] - }, - { - "ename": "ERROR", - "evalue": "Error: object 'sol_long' not found\n", - "output_type": "error", - "traceback": [ - "Error: object 'sol_long' not found\nTraceback:\n", - "1. .handleSimpleError(function (cnd) \n . {\n . watcher$capture_plot_and_output()\n . cnd <- sanitize_call(cnd)\n . watcher$push(cnd)\n . switch(on_error, continue = invokeRestart(\"eval_continue\"), \n . stop = invokeRestart(\"eval_stop\"), error = NULL)\n . }, \"object 'sol_long' not found\", base::quote(eval(expr, envir)))" - ] } ], "source": [ "# Make beautiful plot using ggplot2 / tidyverse\n", - "install.packages(\"tidyverse\") # if not already installed\n", + "# install.packages(\"tidyverse\") # if not already installed\n", "library(tidyverse)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "e7722a33", "metadata": { "vscode": { @@ -528,7 +485,7 @@ "sol_for_plot <- as.data.frame(\n", " ode(\n", " y = rep(1,4),\n", - " times = seq(0, 15, 0.1),\n", + " times = seq(0, 11, 0.1),\n", " func = func_POSm4_list,\n", " parms = klin,\n", " knonlin = knonlin\n", @@ -545,7 +502,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 7, "id": "079c187f", "metadata": { "vscode": { @@ -553,9 +510,18 @@ } }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Warning message:\n", + "\"\u001b[1m\u001b[22mUsing `size` aesthetic for lines was deprecated in ggplot2 3.4.0.\n", + "\u001b[36mℹ\u001b[39m Please use `linewidth` instead.\"\n" + ] + }, { "data": { - "image/png": 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", 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", "text/plain": [ "plot without title" ] @@ -1424,6 +1390,35 @@ " header=T,sep='\\t')\n", "ll" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9c2c967f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# ** Example 2: Negative feedback loop model from [Novak and Tyson, 2008], 3 variables" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7c994137", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Example 3: MAPK cascade model from [Huang and Ferrell, 1996], 3 variables\n", + "data(\"func_MAPK3\")" + ] } ], "metadata": { From cfc9fc94fd47c0295d13cf0c4cd4d7bce13d8450 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Thu, 15 Jan 2026 12:31:54 +0100 Subject: [PATCH 04/12] Update Python, MATLAB and R notebooks (all results have not yet reproduced in R and MATLAB) --- .../model_3_complex_formation_extend_R.ipynb | 832 ++++++++++++++++++ examples/test_r.ipynb | 30 +- 2 files changed, 861 insertions(+), 1 deletion(-) create mode 100644 examples/model_3_complex_formation_extend_R.ipynb diff --git a/examples/model_3_complex_formation_extend_R.ipynb b/examples/model_3_complex_formation_extend_R.ipynb new file mode 100644 index 0000000..bc14c67 --- /dev/null +++ b/examples/model_3_complex_formation_extend_R.ipynb @@ -0,0 +1,832 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "53d51c8d", + "metadata": {}, + "source": [ + "## 0. Libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "b54689cf", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "suppressPackageStartupMessages({\n", + " library(deSolve) # ODE solver\n", + " library(numDeriv) # numerical Jacobian (jacobian)\n", + " library(dplyr)\n", + " library(tidyr)\n", + " library(purrr)\n", + " library(LoopDetectR)\n", + "})" + ] + }, + { + "cell_type": "markdown", + "id": "bf752a71", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "## 1. Configuration" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "2185219a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "colors <- c(\"#EE7733\", \"#0077BB\", \"#33BBEE\", \"#EE3377\", \"#CC3311\", \"#009988\", \"#BBBBBB\")" + ] + }, + { + "cell_type": "markdown", + "id": "a184ae0d", + "metadata": {}, + "source": [ + "## 2. Main reproduction" + ] + }, + { + "cell_type": "markdown", + "id": "39347b82", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **Example 3: Model of complex formation with activation-deactivation cycle**\n", + "\n", + "The model of complex formation with activation-deactivation cycle has also been investigated in [4]. It is composed of the basic model of complex formation in that A\n", + "and B bind to form complex AB as described in section 1.2, together with an activation and deactivation of one of the complex-forming species, B and B∗. In addition\n", + "to the two reactions of complex formation and complex decomposition, the activating\n", + "reaction and the deactivation reaction are modelled using Michaelis-Menten reaction\n", + "kinetics. Thereby, the activation of B to B∗\n", + "is in addition stimulus-dependent (the\n", + "stimulus is modelled as a parameter, kn3), while the deactivation of B∗\n", + "to B depends\n", + "linearly on species A. The model contains four species, A, B, AB, B∗\n", + ", four rate coefficients, k1 . . . , k4, two activation constants, kn1, kn2, and a stimulus parameter, kn3." + ] + }, + { + "cell_type": "markdown", + "id": "480bf021", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{aligned}\n", + "\\frac{dA}{dt} &= -k_1\\,A\\,B + k_2\\,AB ,\\\\[6pt]\n", + "\\frac{dB}{dt} &= -k_1\\,A\\,B + k_2\\,AB + k_3\\,A\\,\\frac{B^*}{B^* + kn_1} - k_4\\,kn_3\\,\\frac{B}{B + kn_2} ,\\\\[6pt]\n", + "\\frac{d(AB)}{dt} &= k_1\\,A\\,B - k_2\\,AB ,\\\\[6pt]\n", + "\\frac{dB^*}{dt} &= -k_3\\,A\\,\\frac{B^*}{B^* + kn_1} + k_4\\,kn_3\\,\\frac{B}{B + kn_2} .\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "We employed the following parameter set for the analyses: k1 = 0.021458, k2 =\n", + "0.000227335, k3 = 663.297, k4 = 0.000139797, kn1 = 55.5913, kn2 = 10.2194, and\n", + "values for the stimulus of kn3 = 1 (unstimulated) or kn3 = 20 (stimulated). The initial\n", + "conditions were set as A = 5, B = 300, AB = 0.0001, B∗ = 0.01.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f17d4fdf", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "#### " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "dc85fe5e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "model_complex_formation_act_deact_cycle <- function(t, y, params) {\n", + " A <- y[1]\n", + " B <- y[2]\n", + " AB <- y[3]\n", + " B_star <- y[4]\n", + "\n", + " k1 <- params[1]\n", + " k2 <- params[2]\n", + " k3 <- params[3]\n", + " k4 <- params[4]\n", + " kn1 <- params[5]\n", + " kn2 <- params[6]\n", + " kn3 <- params[7]\n", + "\n", + " dAdt <- -k1 * A * B + k2 * AB\n", + " dBdt <- -k1 * A * B + k2 * AB + k3 * A * (B_star / (B_star + kn1)) - k4 * kn3 * (B / (B + kn2))\n", + " dABdt <- k1 * A * B - k2 * AB\n", + " dB_stardt <- -k3 * A * (B_star / (B_star + kn1)) + k4 * kn3 * (B / (B + kn2))\n", + "\n", + " list(c(dAdt, dBdt, dABdt, dB_stardt))\n", + "}\n", + "\n", + "solve_complex_formation_act_deact_cycle <- function(initial_conditions, time_points, params) {\n", + " y0 <- c(A = initial_conditions[1],\n", + " B = initial_conditions[2],\n", + " AB = initial_conditions[3],\n", + " B_star = initial_conditions[4])\n", + "\n", + " out <- deSolve::ode(\n", + " y = y0,\n", + " times = time_points,\n", + " func = model_complex_formation_act_deact_cycle,\n", + " parms = params,\n", + " method = \"lsoda\"\n", + " )\n", + " out <- as.data.frame(out)\n", + " out\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1e74389f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "res_tab <- find_loops_vset(func_POSm4,vset=list(s_star),t=1,klin=klin,\n", + " knonlin=knonlin,max_num_loops=10)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4ff19c48", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Parameters from supplementary material\n", + "initial_conditions_act_deact <- c(5, 300, 0.0001, 0.01)\n", + "\n", + "k1 <- 0.021458\n", + "k2 <- 0.000227335\n", + "k3 <- 663.297\n", + "k4 <- 0.000139797\n", + "kn1 <- 55.5913\n", + "kn2 <- 10.2194\n", + "kn3_unstimulated <- 1.0\n", + "kn3_stimulated <- 20.0\n", + "\n", + "params_act_deact_unstimulated <- c(k1, k2, k3, k4, kn1, kn2, kn3_unstimulated)\n", + "params_act_deact_stimulated <- c(k1, k2, k3, k4, kn1, kn2, kn3_stimulated)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "1857ac28", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "time_points_act_deact <- seq(0, 5000, length.out = 1001)\n", + "sol_act_deact <- solve_complex_formation_act_deact_cycle(\n", + " initial_conditions = initial_conditions_act_deact,\n", + " time_points = time_points_act_deact,\n", + " params = params_act_deact_unstimulated\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "e20ac2df", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Concentration vs Time for Activation-Deactivation Cycle Model\"" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol_act_deact$time,\n", + " sol_act_deact[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", + " type = \"l\", lwd = 2, log = \"y\",\n", + " xlab = \"Time\", ylab = \"Concentration\",\n", + " main = \"Concentration vs Time for Activation-Deactivation Cycle Model\"\n", + ")\n", + "legend(\"left\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c824b68e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "time_1 <- seq(-1000, 0, length.out = 500)\n", + "time_2 <- seq(0, 2000, length.out = 1000)\n", + "\n", + "# Continue from stabilized final state\n", + "y_stable <- as.numeric(sol_act_deact[nrow(sol_act_deact), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "\n", + "sol_unstimulated <- solve_complex_formation_act_deact_cycle(\n", + " initial_conditions = y_stable,\n", + " time_points = time_1,\n", + " params = params_act_deact_unstimulated\n", + ")\n", + "\n", + "y_at_0 <- as.numeric(sol_unstimulated[nrow(sol_unstimulated), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "\n", + "sol_stimulated <- solve_complex_formation_act_deact_cycle(\n", + " initial_conditions = y_at_0,\n", + " time_points = time_2,\n", + " params = params_act_deact_stimulated\n", + ")\n", + "\n", + "# Combine full trajectory\n", + "time_full <- c(time_1, time_2)\n", + "sol_full <- bind_rows(sol_unstimulated, sol_stimulated) %>%\n", + " select(time, A, B, AB, B_star)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c5272ed2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Concentration vs Time (Unstimulated then Stimulated)\"" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol_full$time,\n", + " sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", + " type = \"l\", lwd = 2, log = \"y\",\n", + " xlab = \"Time\", ylab = \"Concentration\",\n", + " main = \"Concentration vs Time (Unstimulated then Stimulated)\"\n", + ")\n", + "legend(\"topleft\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "0ab26b0c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Unstimulated conditions:\n", + "Jacobian matrix:\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -6.3289739 -3.853766e-06 0.000227335 0.000000000\n", + "[2,] -5.5766599 -3.869107e-06 0.000227335 0.002138019\n", + "[3,] 6.3289739 3.853766e-06 -0.000227335 0.000000000\n", + "[4,] -0.7523141 1.534086e-08 0.000000000 -0.002138019\n", + "Signed Jacobian matrix:\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0\n", + "[2,] -1 -1 1 1\n", + "[3,] 1 1 -1 0\n", + "[4,] -1 1 0 -1\n" + ] + } + ], + "source": [ + "# Numerical Jacobian + signed Jacobian\n", + "vf <- function(y, params) {\n", + " # deSolve model returns list(c(...)); unwrap\n", + " model_complex_formation_act_deact_cycle(t = 0, y = y, params = params)[[1]]\n", + "}\n", + "\n", + "# Evaluate Jacobian at the stabilized endpoint (same as Python: sol_act_deact.y[:, -1])\n", + "y_eval_un <- as.numeric(sol_act_deact[nrow(sol_act_deact), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "J_un <- numDeriv::jacobian(func = function(x) vf(x, params_act_deact_unstimulated), x = y_eval_un)\n", + "Jsign_un <- sign(J_un)\n", + "\n", + "# Evaluate Jacobian at end of sol_unstimulated (t=0-) for stimulated params (Python used sol_unstimulated.y[:, -1])\n", + "y_eval_st <- as.numeric(sol_unstimulated[nrow(sol_unstimulated), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "J_st <- numDeriv::jacobian(func = function(x) vf(x, params_act_deact_stimulated), x = y_eval_st)\n", + "Jsign_st <- sign(J_st)\n", + "\n", + "cat(\"Unstimulated conditions:\\n\")\n", + "cat(\"Jacobian matrix:\\n\"); print(J_un)\n", + "cat(\"Signed Jacobian matrix:\\n\"); print(Jsign_un)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b7ddb306", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "find_loops_signed <- function(Jsign, max_len = 4) {\n", + " n <- nrow(Jsign)\n", + " nodes <- 0:(n - 1)\n", + "\n", + " has_edge <- function(i, j) Jsign[i + 1, j + 1] != 0\n", + " edge_sign <- function(i, j) Jsign[i + 1, j + 1]\n", + "\n", + " loops <- list()\n", + "\n", + " # length 1: self loops\n", + " for (i in nodes) {\n", + " if (has_edge(i, i)) {\n", + " loops <- append(loops, list(list(loop = c(i, i), length = 1L, sign = as.integer(edge_sign(i, i)))))\n", + " }\n", + " }\n", + "\n", + " # length 2..max_len\n", + " if (max_len >= 2) {\n", + " # length 2: i -> j -> i, i!=j\n", + " for (i in nodes) for (j in nodes) if (i != j) {\n", + " if (has_edge(i, j) && has_edge(j, i)) {\n", + " s <- edge_sign(i, j) * edge_sign(j, i)\n", + " loops <- append(loops, list(list(loop = c(i, j, i), length = 2L, sign = as.integer(s))))\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (max_len >= 3) {\n", + " # length 3: i -> j -> k -> i, all distinct\n", + " for (i in nodes) for (j in nodes) for (k in nodes) {\n", + " if (length(unique(c(i, j, k))) == 3) {\n", + " if (has_edge(i, j) && has_edge(j, k) && has_edge(k, i)) {\n", + " s <- edge_sign(i, j) * edge_sign(j, k) * edge_sign(k, i)\n", + " loops <- append(loops, list(list(loop = c(i, j, k, i), length = 3L, sign = as.integer(s))))\n", + " }\n", + " }\n", + " }\n", + " }\n", + "\n", + " if (max_len >= 4) {\n", + " # length 4: i -> j -> k -> l -> i, all distinct\n", + " for (i in nodes) for (j in nodes) for (k in nodes) for (l in nodes) {\n", + " if (length(unique(c(i, j, k, l))) == 4) {\n", + " if (has_edge(i, j) && has_edge(j, k) && has_edge(k, l) && has_edge(l, i)) {\n", + " s <- edge_sign(i, j) * edge_sign(j, k) * edge_sign(k, l) * edge_sign(l, i)\n", + " loops <- append(loops, list(list(loop = c(i, j, k, l, i), length = 4L, sign = as.integer(s))))\n", + " }\n", + " }\n", + " }\n", + " }\n", + "\n", + " # Deduplicate cycles up to rotation/reversal can be non-trivial.\n", + " # For n=4 and this example, we keep as-is and then distinct by exact sequence.\n", + " df <- tibble(\n", + " loop = map(loops, \"loop\"),\n", + " length = map_int(loops, \"length\"),\n", + " sign = map_int(loops, \"sign\")\n", + " ) %>%\n", + " distinct(loop, length, sign) %>%\n", + " arrange(length, loop)\n", + "\n", + " df\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "010b9be1", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "loop_summary_table <- function(loop_df) {\n", + " loop_df %>%\n", + " mutate(length = as.integer(length),\n", + " pos = sign > 0,\n", + " neg = sign < 0) %>%\n", + " group_by(length) %>%\n", + " summarise(\n", + " total = n(),\n", + " pos = sum(pos),\n", + " neg = sum(neg),\n", + " .groups = \"drop\"\n", + " ) %>%\n", + " arrange(length)\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "1a5a32c8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Unstimulated conditions:\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[90m# A tibble: 25 × 3\u001b[39m\n", + " loop length sign\n", + " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", + "\u001b[90m 1\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", + "\u001b[90m 2\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", + "\u001b[90m 3\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", + "\u001b[90m 4\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", + "\u001b[90m 5\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m 6\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m 7\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m 8\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m 9\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m10\u001b[39m \u001b[90m\u001b[39m 2 1\n", + "\u001b[90m# ℹ 15 more rows\u001b[39m\n", + "\n", + "Loop summary for unstimulated conditions:\n", + "\u001b[90m# A tibble: 4 × 4\u001b[39m\n", + " length total pos neg\n", + " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", + "\u001b[90m1\u001b[39m 1 4 0 4\n", + "\u001b[90m2\u001b[39m 2 8 8 0\n", + "\u001b[90m3\u001b[39m 3 9 3 6\n", + "\u001b[90m4\u001b[39m 4 4 0 4\n" + ] + } + ], + "source": [ + "cat(\"\\nUnstimulated conditions:\\n\")\n", + "res_tab_complex_loop_rep <- find_loops_signed(Jsign_un, max_len = 4)\n", + "print(res_tab_complex_loop_rep)\n", + "\n", + "cat(\"\\nLoop summary for unstimulated conditions:\\n\")\n", + "print(loop_summary_table(res_tab_complex_loop_rep))" + ] + }, + { + "cell_type": "markdown", + "id": "c5046567", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **2.7. Search time where signed Jacobian structure changes**" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "602f9742", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "At time 234.23 after the stimulus, the signed Jacobian structure changes.\n", + "Jacobian matrix at this time:\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -6.31881288 -3.859960e-06 0.000227335 0.000000000\n", + "[2,] 0.02316377 -4.167731e-06 0.000227335 0.002105474\n", + "[3,] 6.31881288 3.859960e-06 -0.000227335 0.000000000\n", + "[4,] -6.34197665 3.077716e-07 0.000000000 -0.002105474\n", + "Signed Jacobian matrix at this time:\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0\n", + "[2,] 1 -1 1 1\n", + "[3,] 1 1 -1 0\n", + "[4,] -1 1 0 -1\n", + "Loop summary at this time:\n", + "\u001b[90m# A tibble: 4 × 4\u001b[39m\n", + " length total pos neg\n", + " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", + "\u001b[90m1\u001b[39m 1 4 0 4\n", + "\u001b[90m2\u001b[39m 2 8 6 2\n", + "\u001b[90m3\u001b[39m 3 9 6 3\n", + "\u001b[90m4\u001b[39m 4 4 0 4\n" + ] + } + ], + "source": [ + "Jsign_ref_un <- Jsign_un\n", + "Jsign_ref_st <- Jsign_st\n", + "\n", + "t_change <- NA_real_\n", + "J_change <- NULL\n", + "Jsign_change <- NULL\n", + "summary_change <- NULL\n", + "\n", + "# Use a modest stride to avoid heavy computation; set stride=1 for exact match (slower).\n", + "stride <- 1L\n", + "\n", + "for (idx in seq(1, nrow(sol_full), by = stride)) {\n", + " t_now <- sol_full$time[idx]\n", + " y_now <- as.numeric(sol_full[idx, c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "\n", + " params_now <- if (t_now < 0) params_act_deact_unstimulated else params_act_deact_stimulated\n", + " J_now <- numDeriv::jacobian(func = function(x) vf(x, params_now), x = y_now)\n", + " Jsign_now <- sign(J_now)\n", + "\n", + " Jsign_ref <- if (t_now < 0) Jsign_ref_un else Jsign_ref_st\n", + "\n", + " if (!isTRUE(all.equal(Jsign_now, Jsign_ref))) {\n", + " t_change <- t_now\n", + " J_change <- J_now\n", + " Jsign_change <- Jsign_now\n", + " summary_change <- loop_summary_table(find_loops_signed(Jsign_now, max_len = 4))\n", + " break\n", + " }\n", + "}\n", + "\n", + "if (!is.na(t_change)) {\n", + " cat(sprintf(\"\\nAt time %.2f after the stimulus, the signed Jacobian structure changes.\\n\", t_change))\n", + " cat(\"Jacobian matrix at this time:\\n\"); print(J_change)\n", + " cat(\"Signed Jacobian matrix at this time:\\n\"); print(Jsign_change)\n", + " cat(\"Loop summary at this time:\\n\"); print(summary_change)\n", + "} else {\n", + " cat(\"\\nNo signed Jacobian structure change detected on the scanned grid.\\n\")\n", + "}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cae9464f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + 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", + "text/plain": [ + "Plot with title \"Concentration vs Time (before/after Jacobian sign change)\"" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "if (!is.na(t_change)) {\n", + " matplot(\n", + " sol_full$time,\n", + " sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", + " type = \"l\", lwd = 2, log = \"y\",\n", + " xlab = \"Time\", ylab = \"Concentration\",\n", + " main = \"Concentration vs Time (before/after Jacobian sign change)\"\n", + " )\n", + " usr <- par(\"usr\")\n", + " rect(xleft = min(sol_full$time), ybottom = usr[3], xright = t_change, ytop = usr[4],\n", + " border = NA, col = rgb(0, 0, 1, alpha = 0.1))\n", + " rect(xleft = t_change, ybottom = usr[3], xright = max(sol_full$time), ytop = usr[4],\n", + " border = NA, col = rgb(1, 0, 0, alpha = 0.1))\n", + " matlines(sol_full$time, sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")], lwd = 2)\n", + " legend(\"topleft\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "7f0b9cdd", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Dynamics of B\"" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plot(sol_full$time, sol_full$B, type = \"l\", lwd = 2,\n", + " xlim = c(-999, 2000),\n", + " xlab = \"Time\", ylab = \"Concentration\",\n", + " main = \"Dynamics of B\")\n", + "axis(1, at = c(0, 2000))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24150e8f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "ce89ef50", + "metadata": {}, + "source": [ + "## 3. Additional features" + ] + }, + { + "cell_type": "markdown", + "id": "3a0acda4", + "metadata": {}, + "source": [ + "### 3.1. Add subject ID to make the loop result more comprehensible" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "5d78b4f6", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\u001b[90m# A tibble: 25 × 4\u001b[39m\n", + " loop length sign loop_subject\n", + " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \n", + "\u001b[90m 1\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", + "\u001b[90m 2\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", + "\u001b[90m 3\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", + "\u001b[90m 4\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", + "\u001b[90m 5\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m 6\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m 7\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m 8\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m 9\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m10\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", + "\u001b[90m# ℹ 15 more rows\u001b[39m\n" + ] + } + ], + "source": [ + "id_to_subject <- c(\"A\", \"B\", \"AB\", \"B*\")\n", + "names(id_to_subject) <- as.character(0:3)\n", + "\n", + "df_loops <- res_tab_complex_loop_rep %>%\n", + " mutate(\n", + " loop_subject = map(loop, ~ unname(id_to_subject[as.character(.x)]))\n", + " ) %>%\n", + " arrange(length, loop)\n", + "\n", + "print(df_loops)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "24878ee0", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/test_r.ipynb b/examples/test_r.ipynb index 95b276e..6172825 100644 --- a/examples/test_r.ipynb +++ b/examples/test_r.ipynb @@ -155,7 +155,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "id": "452aaf33", "metadata": { "vscode": { @@ -240,6 +240,34 @@ "res_tab$loop_rep[[1]]" ] }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1ad58566", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " loop length sign\n", + "1 1, 1 1 -1\n", + "2 2, 2 1 -1\n", + "3 3, 3 1 -1\n", + "4 4, 4 1 -1\n", + "5 3, 4, 1,.... 4 -1\n", + "6 3, 4, 2, 3 3 1\n" + ] + } + ], + "source": [ + "print(res_tab$loop_rep[[1]])" + ] + }, { "cell_type": "code", "execution_count": 20, From 985b4e8fbb4e5f2dcbfd4efc0b9aa3686cf9bd8c Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Wed, 28 Jan 2026 18:36:34 +0100 Subject: [PATCH 05/12] Update R reproduction (including pertubation + additional scripts) for model 1; Fix typo at 3.3 addtional function on extended loop summary for Python (Model 1) --- examples/model_1_POSm4_R.ipynb | 1497 ++++++++++++++++++++ examples/model_1_perturbation.png | Bin 0 -> 58791 bytes examples/model_2_complex_formation_R.ipynb | 0 3 files changed, 1497 insertions(+) create mode 100644 examples/model_1_POSm4_R.ipynb create mode 100644 examples/model_1_perturbation.png create mode 100644 examples/model_2_complex_formation_R.ipynb diff --git a/examples/model_1_POSm4_R.ipynb b/examples/model_1_POSm4_R.ipynb new file mode 100644 index 0000000..1f8c36d --- /dev/null +++ b/examples/model_1_POSm4_R.ipynb @@ -0,0 +1,1497 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "846fd1a6", + "metadata": {}, + "source": [ + "## **0. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "fc391249", + "metadata": {}, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a4619679", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4ea4fa08", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "# Download and install\n", + "install.packages(\"LoopDetectR\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "adf81c8c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "16dc790d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + } + ], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")\n", + "library(deSolve)\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "b677961f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "colors <- c('#EE7733', '#0077BB', '#33BBEE', '#EE3377', '#CC3311', '#009988', '#BBBBBB')" + ] + }, + { + "cell_type": "markdown", + "id": "bc602c8d", + "metadata": {}, + "source": [ + "## **1. Model definition**" + ] + }, + { + "cell_type": "markdown", + "id": "2b148688", + "metadata": {}, + "source": [ + "Model POSm4 with 4 positive feedbacks can be loaded from the library" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "12108b07", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Load example ODE system with function func_POSm4, 4 variables\n", + "data(\"func_POSm4\")" + ] + }, + { + "cell_type": "markdown", + "id": "1903c5dc", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "## **2. Result reproduction**" + ] + }, + { + "cell_type": "markdown", + "id": "5fc586ee", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **2.1. Loop structures**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5ab687a9", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Parameters from supplementary material\n", + "klin <- c(150, 0.04, 0.3, 500, 5000, 80, 4, 5)\n", + "knonlin <- c(0.3,2)\n", + "s_star <- c(1,2,3,4) # Dummy steady state for initialization\n", + "\n", + "# Parameters not yet in supplement data\n", + "perturbation_point <- 8.6" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "81b11f06", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
3, 31-1
4, 41-1
3, 4, 1,....4-1
3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 6 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 3, 4, 1,.... & 4 & -1\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 3, 4, 1,.... | 4 | -1 |\n", + "| 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 4, 4 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute loops\n", + "res_tab <- find_loops_vset(func_POSm4,vset=list(s_star),t=1,klin=klin,\n", + " knonlin=knonlin,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]] \n", + "# To access a specific loop representation: e.g., the sixth loop, add [6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "b1bccacc", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 4
len_1len_2len_3len_4
<dbl><dbl><dbl><dbl>
all4011
pos0010
neg4001
\n" + ], + "text/latex": [ + "A data.frame: 3 × 4\n", + "\\begin{tabular}{r|llll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\tall & 4 & 0 & 1 & 1\\\\\n", + "\tpos & 0 & 0 & 1 & 0\\\\\n", + "\tneg & 4 & 0 & 0 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 4\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> |\n", + "|---|---|---|---|---|\n", + "| all | 4 | 0 | 1 | 1 |\n", + "| pos | 0 | 0 | 1 | 0 |\n", + "| neg | 4 | 0 | 0 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4\n", + "all 4 0 1 1 \n", + "pos 0 0 1 0 \n", + "neg 4 0 0 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f1f8c98c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
53, 4, 1,....4-1
6 3, 4, 2, 33 1
\n" + ], + "text/latex": [ + "A data.frame: 3 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t5 & 3, 4, 1,.... & 4 & -1\\\\\n", + "\t6 & 3, 4, 2, 3 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 5 | 3, 4, 1,.... | 4 | -1 |\n", + "| 6 | 3, 4, 2, 3 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "5 3, 4, 1,.... 4 -1 \n", + "6 3, 4, 2, 3 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2\n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "c3a1aa95", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **2.2. Calculating the Jacobian matrix**\n", + "\n", + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "9e3795b8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1 0 0-1
1-1 0 1
0 1-1 0
0 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & 0 & 0 & -1\\\\\n", + "\t 1 & -1 & 0 & 1\\\\\n", + "\t 0 & 1 & -1 & 0\\\\\n", + "\t 0 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | 0 | 0 | -1 |\n", + "| 1 | -1 | 0 | 1 |\n", + "| 0 | 1 | -1 | 0 |\n", + "| 0 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 0 0 -1 \n", + "[2,] 1 -1 0 1 \n", + "[3,] 0 1 -1 0 \n", + "[4,] 0 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "52610797", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003].\n", + "\n", + "The input function, in the example `func_POSm4` (positive feedback chain model from [Baum et al., 2016]) defines the time derivatives of the modelled variables as a vector: \n", + "$f_i(s)=dS_i/dt$. Note that only those input arguments to the function that encode the modelled variables (and hence in whose direction the partial derivatives are taken) are allowed to be called `x`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c261caec", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
1
259.243116830199
2
0.00371448194657896
3
0.0218301587733568
4
0.295548075392272
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[1] 259.243116830199\n", + "\\item[2] 0.00371448194657896\n", + "\\item[3] 0.0218301587733568\n", + "\\item[4] 0.295548075392272\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "1\n", + ": 259.2431168301992\n", + ": 0.003714481946578963\n", + ": 0.02183015877335684\n", + ": 0.295548075392272\n", + "\n" + ], + "text/plain": [ + " 1 2 3 4 \n", + "2.592431e+02 3.714482e-03 2.183016e-02 2.955481e-01 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The function func_POSm4 returns a vector, but deSolve needs the vector within\n", + "# a list as output. Therefore, we define a function that simply puts the output \n", + "# of func_POSm4 into a list:\n", + "func_POSm4_list <- function(t,x,klin,knonlin){list(func_POSm4(t,x,klin,knonlin))}\n", + "sol <- deSolve::ode(y = rep(1,4), times = seq(0,11,0.1), func = func_POSm4_list, \n", + " parms=klin, knonlin=knonlin)\n", + "\n", + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "8b4155db", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-0.37882163 0 0-68.1056
0.07882163-5500 0 68.1056
0.00000000 500-84 0.0000
0.00000000 0 80 -5.0000
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -0.37882163 & 0 & 0 & -68.1056\\\\\n", + "\t 0.07882163 & -5500 & 0 & 68.1056\\\\\n", + "\t 0.00000000 & 500 & -84 & 0.0000\\\\\n", + "\t 0.00000000 & 0 & 80 & -5.0000\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -0.37882163 | 0 | 0 | -68.1056 |\n", + "| 0.07882163 | -5500 | 0 | 68.1056 |\n", + "| 0.00000000 | 500 | -84 | 0.0000 |\n", + "| 0.00000000 | 0 | 80 | -5.0000 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] \n", + "[1,] -0.37882163 0 0 -68.1056\n", + "[2,] 0.07882163 -5500 0 68.1056\n", + "[3,] 0.00000000 500 -84 0.0000\n", + "[4,] 0.00000000 0 80 -5.0000" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "j_matrix <- numDeriv::jacobian(func_POSm4,s_star,method=\"complex\",\n", + " t=1,klin=klin,knonlin=knonlin,)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "71c0bc77", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1 0 0-1
1-1 0 1
0 1-1 0
0 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & 0 & 0 & -1\\\\\n", + "\t 1 & -1 & 0 & 1\\\\\n", + "\t 0 & 1 & -1 & 0\\\\\n", + "\t 0 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | 0 | 0 | -1 |\n", + "| 1 | -1 | 0 | 1 |\n", + "| 0 | 1 | -1 | 0 |\n", + "| 0 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 0 0 -1 \n", + "[2,] 1 -1 0 1 \n", + "[3,] 0 1 -1 0 \n", + "[4,] 0 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "e6ed3518", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **2.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "bee71136", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol[,1], sol[,2:5],\n", + " type = \"l\",\n", + " lty = 1,\n", + " log = \"y\",\n", + " xlab = \"Time\",\n", + " ylab = \"Variables\"\n", + ")\n", + "\n", + "legend(\n", + " \"topright\",\n", + " legend = paste(\"Variable\", 1:4),\n", + " col = 1:4,\n", + " lty = 1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "b014adcb", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Continue simulation to observe stability\n", + "sol <- deSolve::ode(y = as.numeric(sol[95,2:5]), times = seq(0,11,0.1), func = func_POSm4_list, \n", + " parms=klin, knonlin=knonlin)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "21bbad0e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_for_plot <- as.data.frame(sol)\n", + "\n", + "# rename columns for clarity\n", + "colnames(sol_for_plot) <- c(\"time\", \"S1\", \"S2\", \"S3\", \"S4\")\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = S1:S4, names_to = \"species\", values_to = \"value\")" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "4b596080", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "colors <- c(\n", + " S1 = \"#EE7733\",\n", + " S2 = \"#0077BB\",\n", + " S3 = \"#33BBEE\",\n", + " S4 = \"#EE3377\"\n", + ")\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(size = 1.5) +\n", + " ## vertical dashed line\n", + " geom_vline(\n", + " xintercept = perturbation_point,\n", + " linetype = \"dashed\",\n", + " colour = \"black\",\n", + " linewidth = 0.7\n", + " ) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = 0:11,\n", + " minor_breaks = seq(0, 11, 0.5),\n", + " limits = c(0, 11),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 11), clip = \"on\") +\n", + " scale_y_log10(\n", + " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", + " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", + " ) + # ← log₁₀ transformation\n", + " labs(\n", + " title = \"Dynamics of the 4-Variable Positive Feedback Chain\",\n", + " x = \"Time\",\n", + " y = \"Concentration (log scale)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + "\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "markdown", + "id": "24c09faa", + "metadata": {}, + "source": [ + "### **2.4. Pertubation Analysis**" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "70a2312f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "t0 <- 8.6 # perturbation time in original time axis\n", + "idx0 <- 86\n", + "cap <- 0.05 # window half-width (before/after), like Python cap_range\n", + "dt <- 0.001" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "id": "831ef59a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# pre-perturbation window from the already-simulated sol\n", + "k <- round(cap / dt)\n", + "pre <- sol[(idx0 - k):idx0, 2:5, drop = FALSE]\n", + "tpre <- seq(-cap, 0, by = dt)\n", + "\n", + "# perturbed IC and forward simulation on local time [0, cap]\n", + "y0 <- as.numeric(sol[idx0, 2:5])\n", + "y0[4] <- 0.75" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "07e45a5a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "s_star_pertubation_1 <- as.numeric(sol[81,2:5])\n", + "tpre = seq(-cap, 0, by = dt)\n", + "sol_pertubation_1_pre <- deSolve::ode(y = s_star_pertubation_1, times = tpre, func = func_POSm4_list, \n", + " parms=klin, knonlin=knonlin)\n", + "\n", + "s_star_pertubation_1 <- as.numeric(sol[86,2:5])\n", + "# Change the 4th position to 0.75\n", + "s_star_pertubation_1[4] <- 0.75\n", + "\n", + "tpost <- seq(0, cap, by = dt)\n", + "sol_pertubation_1_post <- deSolve::ode(y = s_star_pertubation_1, times = tpost, func = func_POSm4_list, \n", + " parms=klin, knonlin=knonlin)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ef4f5f4b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Perturbation Analysis: S4 when S4 is perturbed\"" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "t_all <- c(tpre, tpost[-1])\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[-1, , drop = FALSE]) # avoid duplicating t=0 row\n", + "\n", + "# Plot: 4 stacked panels (base graphics)\n", + "\n", + "# To save as PNG file, uncomment the following lines, and the dev.off() line at the end\n", + "\n", + "# png(\n", + "# filename = \"model_1_perturbation.png\",\n", + "# width = 8, height = 8, units = \"in\",\n", + "# res = 300 # ← DPI\n", + "# )\n", + "\n", + "op <- par(mfrow = c(4,1), mar = c(4,5,3,1))\n", + "for (j in 1:4) {\n", + " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j],\n", + " xlab = \"Time\", ylab = paste(\"Concentration of S\", j, sep=\"\"),\n", + " xlim = c(-0.05, 0.05), xaxt = \"n\", xaxs = \"i\",\n", + " main = paste(\"Perturbation Analysis: S\", j, \" when S4 is perturbed\", sep=\"\"))\n", + " axis(\n", + " 1,\n", + " at = seq(-0.05, 0.05, by = 0.01)\n", + " )\n", + " abline(v = 0, lty = 2, lwd = 2)\n", + " box(lwd = 2) # black outer box\n", + "}\n", + "\n", + "# dev.off()\n", + "par(op)" + ] + }, + { + "cell_type": "markdown", + "id": "dc7729e7", + "metadata": {}, + "source": [ + "## **3. Additional features**" + ] + }, + { + "cell_type": "markdown", + "id": "6aa20302", + "metadata": {}, + "source": [ + "### **3.1. Add subject ID to make the loop result more comprehensible**" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "id": "b8a59f66", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "id_to_subject <- c(\n", + " \"S1\", \"S2\", \"S3\", \"S4\"\n", + ")\n", + "names(id_to_subject) <- 1:4" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "a9a0ae03", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "df <- res_tab$loop_rep[[1]]" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "id": "2cce91f7", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "df$loop_subject <- lapply(\n", + " df$loop,\n", + " function(t) unname(id_to_subject[as.character(t)])\n", + ")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "id": "44a698ce", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
\n" + ], + "text/latex": [ + "A data.frame: 6 × 4\n", + "\\begin{tabular}{llll}\n", + " loop & length & sign & loop\\_subject\\\\\n", + " > & & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", + "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", + "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", + "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", + "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 4\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", + "|---|---|---|---|\n", + "| 1, 1 | 1 | -1 | S1, S1 |\n", + "| 2, 2 | 1 | -1 | S2, S2 |\n", + "| 3, 3 | 1 | -1 | S3, S3 |\n", + "| 4, 4 | 1 | -1 | S4, S4 |\n", + "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", + "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "\n" + ], + "text/plain": [ + " loop length sign loop_subject \n", + "1 1, 1 1 -1 S1, S1 \n", + "2 2, 2 1 -1 S2, S2 \n", + "3 3, 3 1 -1 S3, S3 \n", + "4 4, 4 1 -1 S4, S4 \n", + "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", + "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "markdown", + "id": "14c9f240", + "metadata": {}, + "source": [ + "### **3.2. Represent regulation relationship from Jacobian matrix**" + ] + }, + { + "cell_type": "code", + "execution_count": 136, + "id": "080c0f16", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 9 × 4
fromtoregulationregulation_words
<chr><chr><dbl><chr>
S1S1-1inhibition (negative)
S1S4-1inhibition (negative)
S2S1 1activation (positive)
S2S2-1inhibition (negative)
S2S4 1activation (positive)
S3S2 1activation (positive)
S3S3-1inhibition (negative)
S4S3 1activation (positive)
S4S4-1inhibition (negative)
\n" + ], + "text/latex": [ + "A tibble: 9 × 4\n", + "\\begin{tabular}{llll}\n", + " from & to & regulation & regulation\\_words\\\\\n", + " & & & \\\\\n", + "\\hline\n", + "\t S1 & S1 & -1 & inhibition (negative)\\\\\n", + "\t S1 & S4 & -1 & inhibition (negative)\\\\\n", + "\t S2 & S1 & 1 & activation (positive)\\\\\n", + "\t S2 & S2 & -1 & inhibition (negative)\\\\\n", + "\t S2 & S4 & 1 & activation (positive)\\\\\n", + "\t S3 & S2 & 1 & activation (positive)\\\\\n", + "\t S3 & S3 & -1 & inhibition (negative)\\\\\n", + "\t S4 & S3 & 1 & activation (positive)\\\\\n", + "\t S4 & S4 & -1 & inhibition (negative)\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 9 × 4\n", + "\n", + "| from <chr> | to <chr> | regulation <dbl> | regulation_words <chr> |\n", + "|---|---|---|---|\n", + "| S1 | S1 | -1 | inhibition (negative) |\n", + "| S1 | S4 | -1 | inhibition (negative) |\n", + "| S2 | S1 | 1 | activation (positive) |\n", + "| S2 | S2 | -1 | inhibition (negative) |\n", + "| S2 | S4 | 1 | activation (positive) |\n", + "| S3 | S2 | 1 | activation (positive) |\n", + "| S3 | S3 | -1 | inhibition (negative) |\n", + "| S4 | S3 | 1 | activation (positive) |\n", + "| S4 | S4 | -1 | inhibition (negative) |\n", + "\n" + ], + "text/plain": [ + " from to regulation regulation_words \n", + "1 S1 S1 -1 inhibition (negative)\n", + "2 S1 S4 -1 inhibition (negative)\n", + "3 S2 S1 1 activation (positive)\n", + "4 S2 S2 -1 inhibition (negative)\n", + "5 S2 S4 1 activation (positive)\n", + "6 S3 S2 1 activation (positive)\n", + "7 S3 S3 -1 inhibition (negative)\n", + "8 S4 S3 1 activation (positive)\n", + "9 S4 S4 -1 inhibition (negative)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sign_J <- sign(j_matrix)\n", + "labs <- paste0(\"S\", 1:nrow(sign_J))\n", + "rownames(sign_J) <- labs\n", + "colnames(sign_J) <- labs\n", + "\n", + "regulation_info <- sign_J %>%\n", + " as.data.frame() %>%\n", + " mutate(from = rownames(.)) %>%\n", + " pivot_longer(\n", + " -from,\n", + " names_to = \"to\",\n", + " values_to = \"regulation\"\n", + " ) %>%\n", + " mutate(\n", + " regulation_words = case_when(\n", + " regulation == -1 ~ \"inhibition (negative)\",\n", + " regulation == 1 ~ \"activation (positive)\",\n", + " TRUE ~ \"no regulation\"\n", + " )\n", + " )\n", + "regulation_info[regulation_info$regulation != 0, ]" + ] + }, + { + "cell_type": "markdown", + "id": "066927c1", + "metadata": {}, + "source": [ + "### **3.3. Loop Summary in more detail**" + ] + }, + { + "cell_type": "code", + "execution_count": 161, + "id": "e3dddce3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
\n" + ], + "text/latex": [ + "A data.frame: 6 × 4\n", + "\\begin{tabular}{llll}\n", + " loop & length & sign & loop\\_subject\\\\\n", + " > & & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", + "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", + "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", + "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", + "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 4\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", + "|---|---|---|---|\n", + "| 1, 1 | 1 | -1 | S1, S1 |\n", + "| 2, 2 | 1 | -1 | S2, S2 |\n", + "| 3, 3 | 1 | -1 | S3, S3 |\n", + "| 4, 4 | 1 | -1 | S4, S4 |\n", + "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", + "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "\n" + ], + "text/plain": [ + " loop length sign loop_subject \n", + "1 1, 1 1 -1 S1, S1 \n", + "2 2, 2 1 -1 S2, S2 \n", + "3 3, 3 1 -1 S3, S3 \n", + "4 4, 4 1 -1 S4, S4 \n", + "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", + "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "code", + "execution_count": 162, + "id": "9733249d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 7
lengthnum_loopsnum_loops_positivenum_loops_negativeloopsloops_positiveloops_negative
<dbl><int><int><int><I<named list>><I<named list>><I<named list>>
11404c(\"S1\", .... c(\"S1\", ....
33110c(\"S3\", ....c(\"S3\", ....
44101c(\"S3\", .... c(\"S3\", ....
\n" + ], + "text/latex": [ + "A data.frame: 3 × 7\n", + "\\begin{tabular}{r|lllllll}\n", + " & length & num\\_loops & num\\_loops\\_positive & num\\_loops\\_negative & loops & loops\\_positive & loops\\_negative\\\\\n", + " & & & & & > & > & >\\\\\n", + "\\hline\n", + "\t1 & 1 & 4 & 0 & 4 & c(\"S1\", .... & & c(\"S1\", ....\\\\\n", + "\t3 & 3 & 1 & 1 & 0 & c(\"S3\", .... & c(\"S3\", .... & \\\\\n", + "\t4 & 4 & 1 & 0 & 1 & c(\"S3\", .... & & c(\"S3\", ....\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 7\n", + "\n", + "| | length <dbl> | num_loops <int> | num_loops_positive <int> | num_loops_negative <int> | loops <I<named list>> | loops_positive <I<named list>> | loops_negative <I<named list>> |\n", + "|---|---|---|---|---|---|---|---|\n", + "| 1 | 1 | 4 | 0 | 4 | c(\"S1\", .... | | c(\"S1\", .... |\n", + "| 3 | 3 | 1 | 1 | 0 | c(\"S3\", .... | c(\"S3\", .... | |\n", + "| 4 | 4 | 1 | 0 | 1 | c(\"S3\", .... | | c(\"S3\", .... |\n", + "\n" + ], + "text/plain": [ + " length num_loops num_loops_positive num_loops_negative loops \n", + "1 1 4 0 4 c(\"S1\", ....\n", + "3 3 1 1 0 c(\"S3\", ....\n", + "4 4 1 0 1 c(\"S3\", ....\n", + " loops_positive loops_negative\n", + "1 c(\"S1\", .... \n", + "3 c(\"S3\", .... \n", + "4 c(\"S3\", .... " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "split_by_len <- split(df, df$length)\n", + "\n", + "loop_summary_extended <- data.frame(\n", + " length = as.numeric(names(split_by_len)),\n", + " num_loops = vapply(split_by_len, nrow, integer(1)),\n", + " loops = I(lapply(split_by_len, function(x) x$loop_subject)),\n", + " stringsAsFactors = FALSE\n", + ")\n", + "\n", + "loop_summary_extended$num_loops_positive <- vapply(\n", + " split_by_len,\n", + " function(x) sum(x$sign > 0),\n", + " integer(1)\n", + ")\n", + "\n", + "loop_summary_extended$num_loops_negative <- vapply(\n", + " split_by_len,\n", + " function(x) sum(x$sign < 0),\n", + " integer(1)\n", + ")\n", + "\n", + "loop_summary_extended$loops_positive <- I(lapply(\n", + " split_by_len,\n", + " function(x) x$loop_subject[x$sign > 0]\n", + "))\n", + "\n", + "loop_summary_extended$loops_negative <- I(lapply(\n", + " split_by_len,\n", + " function(x) x$loop_subject[x$sign < 0]\n", + "))\n", + "\n", + "loop_summary_extended <- loop_summary_extended[\n", + " order(loop_summary_extended$length),\n", + " c(\"length\",\"num_loops\",\"num_loops_positive\",\"num_loops_negative\",\n", + " \"loops\",\"loops_positive\",\"loops_negative\")\n", + "]\n", + "\n", + "loop_summary_extended\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bb0f25f8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/model_1_perturbation.png b/examples/model_1_perturbation.png new file mode 100644 index 0000000000000000000000000000000000000000..b68a8052694f272aaaf35660fa73ef8a7e9221e8 GIT binary patch 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zc^K^0odNXBBtaoqA^(>anh2ww0v1aMp?41v6NjG_2wv4iG$<}y6%ZsuNrEh@MoOCR4aNOO}9w)|HIkAVI1*os(pe*?A>KN@J~TT^+~}a Hg#Z5o$UO2q literal 0 HcmV?d00001 diff --git a/examples/model_2_complex_formation_R.ipynb b/examples/model_2_complex_formation_R.ipynb new file mode 100644 index 0000000..e69de29 From 61baac01299179fb699e1a07970b9d5876cc8f7f Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Sat, 31 Jan 2026 18:37:00 +0100 Subject: [PATCH 06/12] Fix bug --- examples/model_1_POSm4_R.ipynb | 401 ++++- examples/model_2_complex_formation_R.ipynb | 1624 ++++++++++++++++++++ examples/model_2_perturbation_A.png | Bin 0 -> 47200 bytes 3 files changed, 1976 insertions(+), 49 deletions(-) create mode 100644 examples/model_2_perturbation_A.png diff --git a/examples/model_1_POSm4_R.ipynb b/examples/model_1_POSm4_R.ipynb index 1f8c36d..ed2228d 100644 --- a/examples/model_1_POSm4_R.ipynb +++ b/examples/model_1_POSm4_R.ipynb @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 2, "id": "b677961f", "metadata": { "vscode": { @@ -188,7 +188,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "12108b07", "metadata": { "vscode": { @@ -227,7 +227,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "id": "5ab687a9", "metadata": { "vscode": { @@ -247,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "id": "81b11f06", "metadata": { "vscode": { @@ -327,7 +327,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "id": "b1bccacc", "metadata": { "vscode": { @@ -390,7 +390,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "id": "f1f8c98c", "metadata": { "vscode": { @@ -471,7 +471,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "id": "9e3795b8", "metadata": { "vscode": { @@ -545,7 +545,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "id": "c261caec", "metadata": { "vscode": { @@ -604,7 +604,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "id": "8b4155db", "metadata": { "vscode": { @@ -664,7 +664,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "id": "71c0bc77", "metadata": { "vscode": { @@ -735,7 +735,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 12, "id": "bee71136", "metadata": { "vscode": { @@ -779,7 +779,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 13, "id": "b014adcb", "metadata": { "vscode": { @@ -795,7 +795,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 14, "id": "21bbad0e", "metadata": { "vscode": { @@ -816,7 +816,7 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 15, "id": "4b596080", "metadata": { "vscode": { @@ -824,6 +824,15 @@ } }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Warning message:\n", + "\"\u001b[1m\u001b[22mUsing `size` aesthetic for lines was deprecated in ggplot2 3.4.0.\n", + "\u001b[36mℹ\u001b[39m Please use `linewidth` instead.\"\n" + ] + }, { "data": { "image/png": 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", @@ -869,7 +878,7 @@ " scale_y_log10(\n", " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", - " ) + # ← log₁₀ transformation\n", + " ) + # ← log10 transformation\n", " labs(\n", " title = \"Dynamics of the 4-Variable Positive Feedback Chain\",\n", " x = \"Time\",\n", @@ -904,7 +913,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 16, "id": "70a2312f", "metadata": { "vscode": { @@ -916,33 +925,12 @@ "t0 <- 8.6 # perturbation time in original time axis\n", "idx0 <- 86\n", "cap <- 0.05 # window half-width (before/after), like Python cap_range\n", - "dt <- 0.001" + "dt <- 0.0001" ] }, { "cell_type": "code", - "execution_count": 62, - "id": "831ef59a", - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "# pre-perturbation window from the already-simulated sol\n", - "k <- round(cap / dt)\n", - "pre <- sol[(idx0 - k):idx0, 2:5, drop = FALSE]\n", - "tpre <- seq(-cap, 0, by = dt)\n", - "\n", - "# perturbed IC and forward simulation on local time [0, cap]\n", - "y0 <- as.numeric(sol[idx0, 2:5])\n", - "y0[4] <- 0.75" - ] - }, - { - "cell_type": "code", - "execution_count": 74, + "execution_count": 18, "id": "07e45a5a", "metadata": { "vscode": { @@ -967,7 +955,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, + "id": "b89c6113", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "t_all <- c(tpre, tpost)\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[, , drop = FALSE])" + ] + }, + { + "cell_type": "code", + "execution_count": 22, "id": "ef4f5f4b", "metadata": { "vscode": { @@ -977,7 +980,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "Plot with title \"Perturbation Analysis: S4 when S4 is perturbed\"" ] @@ -992,8 +995,8 @@ } ], "source": [ - "t_all <- c(tpre, tpost[-1])\n", - "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[-1, , drop = FALSE]) # avoid duplicating t=0 row\n", + "t_all <- c(tpre, tpost)\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[, , drop = FALSE])\n", "\n", "# Plot: 4 stacked panels (base graphics)\n", "\n", @@ -1002,18 +1005,25 @@ "# png(\n", "# filename = \"model_1_perturbation.png\",\n", "# width = 8, height = 8, units = \"in\",\n", - "# res = 300 # ← DPI\n", + "# res = 300 # DPI\n", "# )\n", "\n", "op <- par(mfrow = c(4,1), mar = c(4,5,3,1))\n", - "for (j in 1:4) {\n", - " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j],\n", + "for (j in 2:5) {\n", + " if (j==3) {\n", + " xlim_vals <- c(-0.005, 0.005)\n", + " ticks_seq <- seq(-0.005, 0.005, by = 0.001)\n", + " } else {\n", + " xlim_vals <- c(-0.05, 0.05)\n", + " ticks_seq <- seq(-0.05, 0.05, by = 0.01)\n", + " }\n", + " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j-1],\n", " xlab = \"Time\", ylab = paste(\"Concentration of S\", j, sep=\"\"),\n", - " xlim = c(-0.05, 0.05), xaxt = \"n\", xaxs = \"i\",\n", - " main = paste(\"Perturbation Analysis: S\", j, \" when S4 is perturbed\", sep=\"\"))\n", + " xlim = xlim_vals, xaxt = \"n\", xaxs = \"i\",\n", + " main = paste(\"Perturbation Analysis: S\", j-1, \" when S4 is perturbed\", sep=\"\"))\n", " axis(\n", " 1,\n", - " at = seq(-0.05, 0.05, by = 0.01)\n", + " at = ticks_seq\n", " )\n", " abline(v = 0, lty = 2, lwd = 2)\n", " box(lwd = 2) # black outer box\n", @@ -1023,6 +1033,299 @@ "par(op)" ] }, + { + "cell_type": "code", + "execution_count": 23, + "id": "a0e05ddf", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + 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A matrix: 1002 × 5 of type dbl
time1234
-0.0500105.49530.0016576520.010075820.3230939
-0.0499105.50630.0016573760.010074060.3230130
-0.0498105.51720.0016571000.010072310.3229321
-0.0497105.52810.0016568250.010070560.3228512
-0.0496105.53900.0016565510.010068810.3227704
-0.0495105.54990.0016562770.010067060.3226896
-0.0494105.56090.0016560030.010065310.3226088
-0.0493105.57180.0016557290.010063560.3225280
-0.0492105.58270.0016554560.010061810.3224473
-0.0491105.59360.0016551830.010060070.3223665
-0.0490105.60460.0016549100.010058320.3222859
-0.0489105.61550.0016546370.010056580.3222052
-0.0488105.62640.0016543640.010054830.3221246
-0.0487105.63730.0016540910.010053090.3220439
-0.0486105.64820.0016538190.010051350.3219634
-0.0485105.65920.0016535470.010049610.3218828
-0.0484105.67010.0016532750.010047870.3218023
-0.0483105.68100.0016530030.010046140.3217218
-0.0482105.69190.0016527310.010044400.3216413
-0.0481105.70290.0016524590.010042660.3215608
-0.0480105.71380.0016521880.010040930.3214804
-0.0479105.72470.0016519170.010039190.3214000
-0.0478105.73560.0016516460.010037460.3213196
-0.0477105.74650.0016513750.010035730.3212393
-0.0476105.75750.0016511040.010034000.3211590
-0.0475105.76840.0016508330.010032270.3210787
-0.0474105.77930.0016505630.010030540.3209984
-0.0473105.79020.0016502930.010028810.3209182
-0.0472105.80110.0016500220.010027080.3208379
-0.0471105.81200.0016497520.010025360.3207578
⋮⋮⋮⋮⋮
0.0471159.64920.0078411530.045823200.7196214
0.0472159.65510.0078415670.045830320.7196282
0.0473159.66100.0078419820.045837400.7196350
0.0474159.66690.0078423980.045844450.7196419
0.0475159.67280.0078428150.045851460.7196489
0.0476159.67870.0078432330.045858430.7196559
0.0477159.68460.0078436520.045865360.7196630
0.0478159.69050.0078440720.045872250.7196701
0.0479159.69640.0078444930.045879110.7196772
0.0480159.70230.0078449150.045885930.7196845
0.0481159.70820.0078453380.045892720.7196917
0.0482159.71410.0078457620.045899470.7196991
0.0483159.72000.0078461870.045906190.7197064
0.0484159.72590.0078466130.045912870.7197138
0.0485159.73180.0078470390.045919510.7197213
0.0486159.73770.0078474670.045926120.7197288
0.0487159.74350.0078478950.045932700.7197364
0.0488159.74940.0078483240.045939240.7197440
0.0489159.75530.0078487550.045945750.7197517
0.0490159.76120.0078491860.045952230.7197594
0.0491159.76710.0078496180.045958670.7197672
0.0492159.77300.0078500510.045965080.7197750
0.0493159.77890.0078504850.045971460.7197828
0.0494159.78480.0078509190.045977810.7197907
0.0495159.79070.0078513550.045984130.7197987
0.0496159.79650.0078517910.045990410.7198067
0.0497159.80240.0078522280.045996670.7198147
0.0498159.80830.0078526660.046002890.7198228
0.0499159.81420.0078531050.046009090.7198310
0.0500159.82010.0078535450.046015250.7198391
\n" + ], + "text/latex": [ + "A matrix: 1002 × 5 of type dbl\n", + "\\begin{tabular}{lllll}\n", + " time & 1 & 2 & 3 & 4\\\\\n", + "\\hline\n", + "\t -0.0500 & 105.4953 & 0.001657652 & 0.01007582 & 0.3230939\\\\\n", + "\t -0.0499 & 105.5063 & 0.001657376 & 0.01007406 & 0.3230130\\\\\n", + "\t -0.0498 & 105.5172 & 0.001657100 & 0.01007231 & 0.3229321\\\\\n", + "\t -0.0497 & 105.5281 & 0.001656825 & 0.01007056 & 0.3228512\\\\\n", + "\t -0.0496 & 105.5390 & 0.001656551 & 0.01006881 & 0.3227704\\\\\n", + "\t -0.0495 & 105.5499 & 0.001656277 & 0.01006706 & 0.3226896\\\\\n", + "\t -0.0494 & 105.5609 & 0.001656003 & 0.01006531 & 0.3226088\\\\\n", + "\t -0.0493 & 105.5718 & 0.001655729 & 0.01006356 & 0.3225280\\\\\n", + "\t -0.0492 & 105.5827 & 0.001655456 & 0.01006181 & 0.3224473\\\\\n", + "\t -0.0491 & 105.5936 & 0.001655183 & 0.01006007 & 0.3223665\\\\\n", + "\t -0.0490 & 105.6046 & 0.001654910 & 0.01005832 & 0.3222859\\\\\n", + "\t -0.0489 & 105.6155 & 0.001654637 & 0.01005658 & 0.3222052\\\\\n", + "\t -0.0488 & 105.6264 & 0.001654364 & 0.01005483 & 0.3221246\\\\\n", + "\t -0.0487 & 105.6373 & 0.001654091 & 0.01005309 & 0.3220439\\\\\n", + "\t -0.0486 & 105.6482 & 0.001653819 & 0.01005135 & 0.3219634\\\\\n", + "\t -0.0485 & 105.6592 & 0.001653547 & 0.01004961 & 0.3218828\\\\\n", + "\t -0.0484 & 105.6701 & 0.001653275 & 0.01004787 & 0.3218023\\\\\n", + "\t -0.0483 & 105.6810 & 0.001653003 & 0.01004614 & 0.3217218\\\\\n", + "\t -0.0482 & 105.6919 & 0.001652731 & 0.01004440 & 0.3216413\\\\\n", + "\t -0.0481 & 105.7029 & 0.001652459 & 0.01004266 & 0.3215608\\\\\n", + "\t -0.0480 & 105.7138 & 0.001652188 & 0.01004093 & 0.3214804\\\\\n", + "\t -0.0479 & 105.7247 & 0.001651917 & 0.01003919 & 0.3214000\\\\\n", + "\t -0.0478 & 105.7356 & 0.001651646 & 0.01003746 & 0.3213196\\\\\n", + "\t -0.0477 & 105.7465 & 0.001651375 & 0.01003573 & 0.3212393\\\\\n", + "\t -0.0476 & 105.7575 & 0.001651104 & 0.01003400 & 0.3211590\\\\\n", + "\t -0.0475 & 105.7684 & 0.001650833 & 0.01003227 & 0.3210787\\\\\n", + "\t -0.0474 & 105.7793 & 0.001650563 & 0.01003054 & 0.3209984\\\\\n", + "\t -0.0473 & 105.7902 & 0.001650293 & 0.01002881 & 0.3209182\\\\\n", + "\t -0.0472 & 105.8011 & 0.001650022 & 0.01002708 & 0.3208379\\\\\n", + "\t -0.0471 & 105.8120 & 0.001649752 & 0.01002536 & 0.3207578\\\\\n", + "\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n", + "\t 0.0471 & 159.6492 & 0.007841153 & 0.04582320 & 0.7196214\\\\\n", + "\t 0.0472 & 159.6551 & 0.007841567 & 0.04583032 & 0.7196282\\\\\n", + "\t 0.0473 & 159.6610 & 0.007841982 & 0.04583740 & 0.7196350\\\\\n", + "\t 0.0474 & 159.6669 & 0.007842398 & 0.04584445 & 0.7196419\\\\\n", + "\t 0.0475 & 159.6728 & 0.007842815 & 0.04585146 & 0.7196489\\\\\n", + "\t 0.0476 & 159.6787 & 0.007843233 & 0.04585843 & 0.7196559\\\\\n", + "\t 0.0477 & 159.6846 & 0.007843652 & 0.04586536 & 0.7196630\\\\\n", + "\t 0.0478 & 159.6905 & 0.007844072 & 0.04587225 & 0.7196701\\\\\n", + "\t 0.0479 & 159.6964 & 0.007844493 & 0.04587911 & 0.7196772\\\\\n", + "\t 0.0480 & 159.7023 & 0.007844915 & 0.04588593 & 0.7196845\\\\\n", + "\t 0.0481 & 159.7082 & 0.007845338 & 0.04589272 & 0.7196917\\\\\n", + "\t 0.0482 & 159.7141 & 0.007845762 & 0.04589947 & 0.7196991\\\\\n", + "\t 0.0483 & 159.7200 & 0.007846187 & 0.04590619 & 0.7197064\\\\\n", + "\t 0.0484 & 159.7259 & 0.007846613 & 0.04591287 & 0.7197138\\\\\n", + "\t 0.0485 & 159.7318 & 0.007847039 & 0.04591951 & 0.7197213\\\\\n", + "\t 0.0486 & 159.7377 & 0.007847467 & 0.04592612 & 0.7197288\\\\\n", + "\t 0.0487 & 159.7435 & 0.007847895 & 0.04593270 & 0.7197364\\\\\n", + "\t 0.0488 & 159.7494 & 0.007848324 & 0.04593924 & 0.7197440\\\\\n", + "\t 0.0489 & 159.7553 & 0.007848755 & 0.04594575 & 0.7197517\\\\\n", + "\t 0.0490 & 159.7612 & 0.007849186 & 0.04595223 & 0.7197594\\\\\n", + "\t 0.0491 & 159.7671 & 0.007849618 & 0.04595867 & 0.7197672\\\\\n", + "\t 0.0492 & 159.7730 & 0.007850051 & 0.04596508 & 0.7197750\\\\\n", + "\t 0.0493 & 159.7789 & 0.007850485 & 0.04597146 & 0.7197828\\\\\n", + "\t 0.0494 & 159.7848 & 0.007850919 & 0.04597781 & 0.7197907\\\\\n", + "\t 0.0495 & 159.7907 & 0.007851355 & 0.04598413 & 0.7197987\\\\\n", + "\t 0.0496 & 159.7965 & 0.007851791 & 0.04599041 & 0.7198067\\\\\n", + "\t 0.0497 & 159.8024 & 0.007852228 & 0.04599667 & 0.7198147\\\\\n", + "\t 0.0498 & 159.8083 & 0.007852666 & 0.04600289 & 0.7198228\\\\\n", + "\t 0.0499 & 159.8142 & 0.007853105 & 0.04600909 & 0.7198310\\\\\n", + "\t 0.0500 & 159.8201 & 0.007853545 & 0.04601525 & 0.7198391\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 1002 × 5 of type dbl\n", + "\n", + "| time | 1 | 2 | 3 | 4 |\n", + "|---|---|---|---|---|\n", + "| -0.0500 | 105.4953 | 0.001657652 | 0.01007582 | 0.3230939 |\n", + "| -0.0499 | 105.5063 | 0.001657376 | 0.01007406 | 0.3230130 |\n", + "| -0.0498 | 105.5172 | 0.001657100 | 0.01007231 | 0.3229321 |\n", + "| -0.0497 | 105.5281 | 0.001656825 | 0.01007056 | 0.3228512 |\n", + "| -0.0496 | 105.5390 | 0.001656551 | 0.01006881 | 0.3227704 |\n", + "| -0.0495 | 105.5499 | 0.001656277 | 0.01006706 | 0.3226896 |\n", + "| -0.0494 | 105.5609 | 0.001656003 | 0.01006531 | 0.3226088 |\n", + "| -0.0493 | 105.5718 | 0.001655729 | 0.01006356 | 0.3225280 |\n", + "| -0.0492 | 105.5827 | 0.001655456 | 0.01006181 | 0.3224473 |\n", + "| -0.0491 | 105.5936 | 0.001655183 | 0.01006007 | 0.3223665 |\n", + "| -0.0490 | 105.6046 | 0.001654910 | 0.01005832 | 0.3222859 |\n", + "| -0.0489 | 105.6155 | 0.001654637 | 0.01005658 | 0.3222052 |\n", + "| -0.0488 | 105.6264 | 0.001654364 | 0.01005483 | 0.3221246 |\n", + "| -0.0487 | 105.6373 | 0.001654091 | 0.01005309 | 0.3220439 |\n", + "| -0.0486 | 105.6482 | 0.001653819 | 0.01005135 | 0.3219634 |\n", + "| -0.0485 | 105.6592 | 0.001653547 | 0.01004961 | 0.3218828 |\n", + "| -0.0484 | 105.6701 | 0.001653275 | 0.01004787 | 0.3218023 |\n", + "| -0.0483 | 105.6810 | 0.001653003 | 0.01004614 | 0.3217218 |\n", + "| -0.0482 | 105.6919 | 0.001652731 | 0.01004440 | 0.3216413 |\n", + "| -0.0481 | 105.7029 | 0.001652459 | 0.01004266 | 0.3215608 |\n", + "| -0.0480 | 105.7138 | 0.001652188 | 0.01004093 | 0.3214804 |\n", + "| -0.0479 | 105.7247 | 0.001651917 | 0.01003919 | 0.3214000 |\n", + "| -0.0478 | 105.7356 | 0.001651646 | 0.01003746 | 0.3213196 |\n", + "| -0.0477 | 105.7465 | 0.001651375 | 0.01003573 | 0.3212393 |\n", + "| -0.0476 | 105.7575 | 0.001651104 | 0.01003400 | 0.3211590 |\n", + "| -0.0475 | 105.7684 | 0.001650833 | 0.01003227 | 0.3210787 |\n", + "| -0.0474 | 105.7793 | 0.001650563 | 0.01003054 | 0.3209984 |\n", + "| -0.0473 | 105.7902 | 0.001650293 | 0.01002881 | 0.3209182 |\n", + "| -0.0472 | 105.8011 | 0.001650022 | 0.01002708 | 0.3208379 |\n", + "| -0.0471 | 105.8120 | 0.001649752 | 0.01002536 | 0.3207578 |\n", + "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n", + "| 0.0471 | 159.6492 | 0.007841153 | 0.04582320 | 0.7196214 |\n", + "| 0.0472 | 159.6551 | 0.007841567 | 0.04583032 | 0.7196282 |\n", + "| 0.0473 | 159.6610 | 0.007841982 | 0.04583740 | 0.7196350 |\n", + "| 0.0474 | 159.6669 | 0.007842398 | 0.04584445 | 0.7196419 |\n", + "| 0.0475 | 159.6728 | 0.007842815 | 0.04585146 | 0.7196489 |\n", + "| 0.0476 | 159.6787 | 0.007843233 | 0.04585843 | 0.7196559 |\n", + "| 0.0477 | 159.6846 | 0.007843652 | 0.04586536 | 0.7196630 |\n", + "| 0.0478 | 159.6905 | 0.007844072 | 0.04587225 | 0.7196701 |\n", + "| 0.0479 | 159.6964 | 0.007844493 | 0.04587911 | 0.7196772 |\n", + "| 0.0480 | 159.7023 | 0.007844915 | 0.04588593 | 0.7196845 |\n", + "| 0.0481 | 159.7082 | 0.007845338 | 0.04589272 | 0.7196917 |\n", + "| 0.0482 | 159.7141 | 0.007845762 | 0.04589947 | 0.7196991 |\n", + "| 0.0483 | 159.7200 | 0.007846187 | 0.04590619 | 0.7197064 |\n", + "| 0.0484 | 159.7259 | 0.007846613 | 0.04591287 | 0.7197138 |\n", + "| 0.0485 | 159.7318 | 0.007847039 | 0.04591951 | 0.7197213 |\n", + "| 0.0486 | 159.7377 | 0.007847467 | 0.04592612 | 0.7197288 |\n", + "| 0.0487 | 159.7435 | 0.007847895 | 0.04593270 | 0.7197364 |\n", + "| 0.0488 | 159.7494 | 0.007848324 | 0.04593924 | 0.7197440 |\n", + "| 0.0489 | 159.7553 | 0.007848755 | 0.04594575 | 0.7197517 |\n", + "| 0.0490 | 159.7612 | 0.007849186 | 0.04595223 | 0.7197594 |\n", + "| 0.0491 | 159.7671 | 0.007849618 | 0.04595867 | 0.7197672 |\n", + "| 0.0492 | 159.7730 | 0.007850051 | 0.04596508 | 0.7197750 |\n", + "| 0.0493 | 159.7789 | 0.007850485 | 0.04597146 | 0.7197828 |\n", + "| 0.0494 | 159.7848 | 0.007850919 | 0.04597781 | 0.7197907 |\n", + "| 0.0495 | 159.7907 | 0.007851355 | 0.04598413 | 0.7197987 |\n", + "| 0.0496 | 159.7965 | 0.007851791 | 0.04599041 | 0.7198067 |\n", + "| 0.0497 | 159.8024 | 0.007852228 | 0.04599667 | 0.7198147 |\n", + "| 0.0498 | 159.8083 | 0.007852666 | 0.04600289 | 0.7198228 |\n", + "| 0.0499 | 159.8142 | 0.007853105 | 0.04600909 | 0.7198310 |\n", + "| 0.0500 | 159.8201 | 0.007853545 | 0.04601525 | 0.7198391 |\n", + "\n" + ], + "text/plain": [ + " time 1 2 3 4 \n", + " [1,] -0.0500 105.4953 0.001657652 0.01007582 0.3230939\n", + " [2,] -0.0499 105.5063 0.001657376 0.01007406 0.3230130\n", + " [3,] -0.0498 105.5172 0.001657100 0.01007231 0.3229321\n", + " [4,] -0.0497 105.5281 0.001656825 0.01007056 0.3228512\n", + " [5,] -0.0496 105.5390 0.001656551 0.01006881 0.3227704\n", + " [6,] -0.0495 105.5499 0.001656277 0.01006706 0.3226896\n", + " [7,] -0.0494 105.5609 0.001656003 0.01006531 0.3226088\n", + " [8,] -0.0493 105.5718 0.001655729 0.01006356 0.3225280\n", + " [9,] -0.0492 105.5827 0.001655456 0.01006181 0.3224473\n", + "[10,] -0.0491 105.5936 0.001655183 0.01006007 0.3223665\n", + "[11,] -0.0490 105.6046 0.001654910 0.01005832 0.3222859\n", + "[12,] -0.0489 105.6155 0.001654637 0.01005658 0.3222052\n", + "[13,] -0.0488 105.6264 0.001654364 0.01005483 0.3221246\n", + "[14,] -0.0487 105.6373 0.001654091 0.01005309 0.3220439\n", + "[15,] -0.0486 105.6482 0.001653819 0.01005135 0.3219634\n", + "[16,] -0.0485 105.6592 0.001653547 0.01004961 0.3218828\n", + "[17,] -0.0484 105.6701 0.001653275 0.01004787 0.3218023\n", + "[18,] -0.0483 105.6810 0.001653003 0.01004614 0.3217218\n", + "[19,] -0.0482 105.6919 0.001652731 0.01004440 0.3216413\n", + "[20,] -0.0481 105.7029 0.001652459 0.01004266 0.3215608\n", + "[21,] -0.0480 105.7138 0.001652188 0.01004093 0.3214804\n", + "[22,] -0.0479 105.7247 0.001651917 0.01003919 0.3214000\n", + "[23,] -0.0478 105.7356 0.001651646 0.01003746 0.3213196\n", + "[24,] -0.0477 105.7465 0.001651375 0.01003573 0.3212393\n", + "[25,] -0.0476 105.7575 0.001651104 0.01003400 0.3211590\n", + "[26,] -0.0475 105.7684 0.001650833 0.01003227 0.3210787\n", + "[27,] -0.0474 105.7793 0.001650563 0.01003054 0.3209984\n", + "[28,] -0.0473 105.7902 0.001650293 0.01002881 0.3209182\n", + "[29,] -0.0472 105.8011 0.001650022 0.01002708 0.3208379\n", + "[30,] -0.0471 105.8120 0.001649752 0.01002536 0.3207578\n", + "[31,] ⋮ ⋮ ⋮ ⋮ ⋮ \n", + "[32,] 0.0471 159.6492 0.007841153 0.04582320 0.7196214\n", + "[33,] 0.0472 159.6551 0.007841567 0.04583032 0.7196282\n", + "[34,] 0.0473 159.6610 0.007841982 0.04583740 0.7196350\n", + "[35,] 0.0474 159.6669 0.007842398 0.04584445 0.7196419\n", + "[36,] 0.0475 159.6728 0.007842815 0.04585146 0.7196489\n", + "[37,] 0.0476 159.6787 0.007843233 0.04585843 0.7196559\n", + "[38,] 0.0477 159.6846 0.007843652 0.04586536 0.7196630\n", + "[39,] 0.0478 159.6905 0.007844072 0.04587225 0.7196701\n", + "[40,] 0.0479 159.6964 0.007844493 0.04587911 0.7196772\n", + "[41,] 0.0480 159.7023 0.007844915 0.04588593 0.7196845\n", + "[42,] 0.0481 159.7082 0.007845338 0.04589272 0.7196917\n", + "[43,] 0.0482 159.7141 0.007845762 0.04589947 0.7196991\n", + "[44,] 0.0483 159.7200 0.007846187 0.04590619 0.7197064\n", + "[45,] 0.0484 159.7259 0.007846613 0.04591287 0.7197138\n", + "[46,] 0.0485 159.7318 0.007847039 0.04591951 0.7197213\n", + "[47,] 0.0486 159.7377 0.007847467 0.04592612 0.7197288\n", + "[48,] 0.0487 159.7435 0.007847895 0.04593270 0.7197364\n", + "[49,] 0.0488 159.7494 0.007848324 0.04593924 0.7197440\n", + "[50,] 0.0489 159.7553 0.007848755 0.04594575 0.7197517\n", + "[51,] 0.0490 159.7612 0.007849186 0.04595223 0.7197594\n", + "[52,] 0.0491 159.7671 0.007849618 0.04595867 0.7197672\n", + "[53,] 0.0492 159.7730 0.007850051 0.04596508 0.7197750\n", + "[54,] 0.0493 159.7789 0.007850485 0.04597146 0.7197828\n", + "[55,] 0.0494 159.7848 0.007850919 0.04597781 0.7197907\n", + "[56,] 0.0495 159.7907 0.007851355 0.04598413 0.7197987\n", + "[57,] 0.0496 159.7965 0.007851791 0.04599041 0.7198067\n", + "[58,] 0.0497 159.8024 0.007852228 0.04599667 0.7198147\n", + "[59,] 0.0498 159.8083 0.007852666 0.04600289 0.7198228\n", + "[60,] 0.0499 159.8142 0.007853105 0.04600909 0.7198310\n", + "[61,] 0.0500 159.8201 0.007853545 0.04601525 0.7198391" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "y_all" + ] + }, { "cell_type": "markdown", "id": "dc7729e7", diff --git a/examples/model_2_complex_formation_R.ipynb b/examples/model_2_complex_formation_R.ipynb index e69de29..400177a 100644 --- a/examples/model_2_complex_formation_R.ipynb +++ b/examples/model_2_complex_formation_R.ipynb @@ -0,0 +1,1624 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c1123f2d", + "metadata": {}, + "source": [ + "## **0. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "3aa06e65", + "metadata": {}, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5aaaa97", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "357901cd", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "# Download and install\n", + "install.packages(\"LoopDetectR\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cbf8efe3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5bc2137e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + } + ], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")\n", + "library(deSolve)\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9dd37926", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "colors <- c('#EE7733', '#0077BB', '#33BBEE', '#EE3377', '#CC3311', '#009988', '#BBBBBB')" + ] + }, + { + "cell_type": "markdown", + "id": "ef9fc41b", + "metadata": {}, + "source": [ + "## **1. Model definition**" + ] + }, + { + "cell_type": "markdown", + "id": "b1adc5c3", + "metadata": {}, + "source": [ + "Model 2: Model for Complex Formation \n", + "\n", + "Varusai TM, Kolch W, Kholodenko BN, Nguyen LK (2015) Protein-protein interactions\n", + "generate hidden feedback and feed-forward loops to trigger bistable switches, oscillations\n", + "and biphasic dose-responses. Molecular bioSystems 11: 2750-2762.\n", + "\n", + "Supplement Data Table S4 is for Model 3.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "cf9c4c03", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "func_varusai15_simple <- function(t,x,params){\n", + " # function: Complex Formation [Varusai et al., 2015]\n", + " #\n", + " # Varusai TM, Kolch W, Kholodenko BN, Nguyen LK (2015) Protein-protein interactions\n", + " # generate hidden feedback and feed-forward loops to trigger bistable switches, oscillations\n", + " # and biphasic dose-responses. Molecular bioSystems 11: 2750-2762.\n", + " #\n", + " dx <- rep(0,3)\n", + " dx[1] <- -params[1] * x[1] * x[2] + params[2]* x[3];\n", + " dx[2] <- -params[1] * x[1] * x[2] + params[2]* x[3];\n", + " dx[3] <- params[1] * x[1] * x[2] - params[2]* x[3];\n", + " return(dx)\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "dae5e300", + "metadata": {}, + "source": [ + "## **2. Result reproduction**" + ] + }, + { + "cell_type": "markdown", + "id": "58ea4a5b", + "metadata": {}, + "source": [ + "### **2.1. Loop structures**" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "d9f19514", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Parameters from supplementary material\n", + "params <- c(1.0, 2.0)\n", + "s_star <- c(10.0, 5.0, 2.0) # Dummy steady state for initialization\n", + "\n", + "# Parameters not yet in supplement data\n", + "perturbation_point <- 0.2" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "4f929c59", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 8 × 3
looplengthsign
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1, 11-1
2, 21-1
3, 31-1
1, 2, 12 1
1, 3, 12 1
1, 3, 2, 13-1
2, 3, 1, 23-1
2, 3, 22 1
\n" + ], + "text/latex": [ + "A data.frame: 8 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 1, 3, 1 & 2 & 1\\\\\n", + "\t 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t 2, 3, 2 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 8 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "| 1, 3, 1 | 2 | 1 |\n", + "| 1, 3, 2, 1 | 3 | -1 |\n", + "| 2, 3, 1, 2 | 3 | -1 |\n", + "| 2, 3, 2 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 1, 2, 1 2 1 \n", + "5 1, 3, 1 2 1 \n", + "6 1, 3, 2, 1 3 -1 \n", + "7 2, 3, 1, 2 3 -1 \n", + "8 2, 3, 2 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute loops\n", + "res_tab <- find_loops_vset(func_varusai15_simple,vset=list(s_star),t=1,params=params,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]] \n", + "# To access a specific loop representation: e.g., the sixth loop, add [6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "54b7b1a3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 3
len_1len_2len_3
<dbl><dbl><dbl>
all332
pos030
neg302
\n" + ], + "text/latex": [ + "A data.frame: 3 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & len\\_1 & len\\_2 & len\\_3\\\\\n", + " & & & \\\\\n", + "\\hline\n", + "\tall & 3 & 3 & 2\\\\\n", + "\tpos & 0 & 3 & 0\\\\\n", + "\tneg & 3 & 0 & 2\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 3\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> |\n", + "|---|---|---|---|\n", + "| all | 3 | 3 | 2 |\n", + "| pos | 0 | 3 | 0 |\n", + "| neg | 3 | 0 | 2 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3\n", + "all 3 3 2 \n", + "pos 0 3 0 \n", + "neg 3 0 2 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "2631d303", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 5 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
4 1, 2, 12 1
61, 3, 2, 13-1
72, 3, 1, 23-1
8 2, 3, 22 1
\n" + ], + "text/latex": [ + "A data.frame: 5 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t4 & 1, 2, 1 & 2 & 1\\\\\n", + "\t6 & 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t7 & 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t8 & 2, 3, 2 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 5 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 4 | 1, 2, 1 | 2 | 1 |\n", + "| 6 | 1, 3, 2, 1 | 3 | -1 |\n", + "| 7 | 2, 3, 1, 2 | 3 | -1 |\n", + "| 8 | 2, 3, 2 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "4 1, 2, 1 2 1 \n", + "6 1, 3, 2, 1 3 -1 \n", + "7 2, 3, 1, 2 3 -1 \n", + "8 2, 3, 2 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2 \n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "adee57fb", + "metadata": {}, + "source": [ + "### **2.2. Calculating the Jacobian matrix**\n", + "\n", + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "a3bf2b5d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n" + ], + "text/latex": [ + "\\begin{description}\n", + "\\item[\\$loop\\_rep] \\begin{enumerate}\n", + "\\item A data.frame: 8 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 1, 3, 1 & 2 & 1\\\\\n", + "\t 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t 2, 3, 2 & 2 & 1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$loop\\_rep\\_index] 1\n", + "\\item[\\$jac\\_rep] \\begin{enumerate}\n", + "\\item A matrix: 3 × 3 of type dbl\n", + "\\begin{tabular}{lll}\n", + "\t -1 & -1 & 1\\\\\n", + "\t -1 & -1 & 1\\\\\n", + "\t 1 & 1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$jac\\_rep\\_index] 1\n", + "\\end{description}\n" + ], + "text/markdown": [ + "$loop_rep\n", + ": 1. \n", + "A data.frame: 8 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "| 1, 3, 1 | 2 | 1 |\n", + "| 1, 3, 2, 1 | 3 | -1 |\n", + "| 2, 3, 1, 2 | 3 | -1 |\n", + "| 2, 3, 2 | 2 | 1 |\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "$loop_rep_index\n", + ": 1\n", + "$jac_rep\n", + ": 1. \n", + "A matrix: 3 × 3 of type dbl\n", + "\n", + "| -1 | -1 | 1 |\n", + "| -1 | -1 | 1 |\n", + "| 1 | 1 | -1 |\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "$jac_rep_index\n", + ": 1\n", + "\n", + "\n" + ], + "text/plain": [ + "$loop_rep\n", + "$loop_rep[[1]]\n", + " loop length sign\n", + "1 1, 1 1 -1\n", + "2 2, 2 1 -1\n", + "3 3, 3 1 -1\n", + "4 1, 2, 1 2 1\n", + "5 1, 3, 1 2 1\n", + "6 1, 3, 2, 1 3 -1\n", + "7 2, 3, 1, 2 3 -1\n", + "8 2, 3, 2 2 1\n", + "\n", + "\n", + "$loop_rep_index\n", + "[1] 1\n", + "\n", + "$jac_rep\n", + "$jac_rep[[1]]\n", + " [,1] [,2] [,3]\n", + "[1,] -1 -1 1\n", + "[2,] -1 -1 1\n", + "[3,] 1 1 -1\n", + "\n", + "\n", + "$jac_rep_index\n", + "[1] 1\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res_tab" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "f43813a7", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 3 × 3 of type dbl
-1-1 1
-1-1 1
1 1-1
\n" + ], + "text/latex": [ + "A matrix: 3 × 3 of type dbl\n", + "\\begin{tabular}{lll}\n", + "\t -1 & -1 & 1\\\\\n", + "\t -1 & -1 & 1\\\\\n", + "\t 1 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 3 × 3 of type dbl\n", + "\n", + "| -1 | -1 | 1 |\n", + "| -1 | -1 | 1 |\n", + "| 1 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3]\n", + "[1,] -1 -1 1 \n", + "[2,] -1 -1 1 \n", + "[3,] 1 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "f9454da1", + "metadata": {}, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003].\n", + "\n", + "The input function, in the example `func_POSm4` (positive feedback chain model from [Baum et al., 2016]) defines the time derivatives of the modelled variables as a vector: \n", + "$f_i(s)=dS_i/dt$. Note that only those input arguments to the function that encode the modelled variables (and hence in whose direction the partial derivatives are taken) are allowed to be called `x`." + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "dbd42fd2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
1
6.62356545421023
2
1.62356545421025
3
5.37643454578977
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[1] 6.62356545421023\n", + "\\item[2] 1.62356545421025\n", + "\\item[3] 5.37643454578977\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "1\n", + ": 6.623565454210232\n", + ": 1.623565454210253\n", + ": 5.37643454578977\n", + "\n" + ], + "text/plain": [ + " 1 2 3 \n", + "6.623565 1.623565 5.376435 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The function func_POSm4 returns a vector, but deSolve needs the vector within\n", + "# a list as output. Therefore, we define a function that simply puts the output \n", + "# of func_POSm4 into a list:\n", + "func_list <- function(t,x,params){list(func_varusai15_simple(t,x,params))}\n", + "sol <- deSolve::ode(y = s_star, times = seq(0,1,0.001), func = func_list, \n", + " parms=params)\n", + "\n", + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star_end <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star_end" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "2f3d21ac", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 3 × 3 of type dbl
-1.233223-1.233223 2
-1.233223-1.233223 2
1.233223 1.233223-2
\n" + ], + "text/latex": [ + "A matrix: 3 × 3 of type dbl\n", + "\\begin{tabular}{lll}\n", + "\t -1.233223 & -1.233223 & 2\\\\\n", + "\t -1.233223 & -1.233223 & 2\\\\\n", + "\t 1.233223 & 1.233223 & -2\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 3 × 3 of type dbl\n", + "\n", + "| -1.233223 | -1.233223 | 2 |\n", + "| -1.233223 | -1.233223 | 2 |\n", + "| 1.233223 | 1.233223 | -2 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3]\n", + "[1,] -1.233223 -1.233223 2 \n", + "[2,] -1.233223 -1.233223 2 \n", + "[3,] 1.233223 1.233223 -2 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "j_matrix <- numDeriv::jacobian(func_varusai15_simple,s_star,method=\"complex\",\n", + " t=1,params=params)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "67868589", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 3 × 3 of type dbl
-1-1 1
-1-1 1
1 1-1
\n" + ], + "text/latex": [ + "A matrix: 3 × 3 of type dbl\n", + "\\begin{tabular}{lll}\n", + "\t -1 & -1 & 1\\\\\n", + "\t -1 & -1 & 1\\\\\n", + "\t 1 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 3 × 3 of type dbl\n", + "\n", + "| -1 | -1 | 1 |\n", + "| -1 | -1 | 1 |\n", + "| 1 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3]\n", + "[1,] -1 -1 1 \n", + "[2,] -1 -1 1 \n", + "[3,] 1 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "fb34cf9c", + "metadata": {}, + "source": [ + "### **2.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "e8883776", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol[,1], sol[,2:4],\n", + " type = \"l\",\n", + " lty = 1,\n", + " xlab = \"Time\",\n", + " ylab = \"Concentration\",\n", + ")\n", + "\n", + "legend(\n", + " \"topright\",\n", + " legend = c(\"A\", \"B\", \"AB\"),\n", + " col = 1:3,\n", + " lty = 1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "3beedbcf", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_for_plot <- as.data.frame(sol)\n", + "\n", + "# rename columns for clarity\n", + "colnames(sol_for_plot) <- c(\"time\", \"A\", \"B\", \"AB\")\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = A:AB, names_to = \"species\", values_to = \"value\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "26027184", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "colors <- c(\n", + " A = \"#EE7733\",\n", + " B = \"#0077BB\",\n", + " AB = \"#33BBEE\"\n", + ")\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(size = 3) +\n", + " ## vertical dashed line\n", + " geom_vline(\n", + " xintercept = perturbation_point,\n", + " linetype = \"dashed\",\n", + " colour = \"black\",\n", + " linewidth = 0.7\n", + " ) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 1, 0.2),\n", + " minor_breaks = seq(0, 1, 0.1),\n", + " limits = c(0, 1),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 1), clip = \"on\") +\n", + " scale_y_continuous(\n", + " minor_breaks = seq(0, 11, 2),\n", + " ) +\n", + " labs(\n", + " title = \"Dynamics of the 3-Variable Complex Formation Model\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + "\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "markdown", + "id": "d005f29c", + "metadata": {}, + "source": [ + "### **2.4. Pertubation Analysis**" + ] + }, + { + "cell_type": "markdown", + "id": "688d7e9a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **2.4.1. Partubation in A**" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "id": "1c922b3c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 1001
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\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 1001\n", + "\\item 4\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 1001\n", + "2. 4\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] 1001 4" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "33904 bytes" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Size of variable sol (how many rows and columns)\n", + "dim(sol)\n", + "object.size(sol)" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "6539db9a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "t0 <- 0.2 # perturbation time in original time axis\n", + "idx0 <- 200\n", + "cap <- 0.05 # window half-width (before/after), like Python cap_range\n", + "dt <- 0.001" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "id": "55b33b49", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# pre-perturbation window from the already-simulated sol\n", + "k <- round(cap / dt)\n", + "pre <- sol[(idx0 - k):idx0, 2:4, drop = FALSE]\n", + "tpre <- seq(-cap, 0, by = dt)\n", + "\n", + "# perturbed IC and forward simulation on local time [0, cap]\n", + "y0 <- as.numeric(sol[idx0, 2:4])\n", + "y0[1] <- 40.0" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "id": "1ced98df", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "150" + ], + "text/latex": [ + "150" + ], + "text/markdown": [ + "150" + ], + "text/plain": [ + "[1] 150" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "200-cap/dt" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "55b3ff5e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "s_star_pertubation_1 <- as.numeric(sol[(200-cap/dt),2:4])\n", + "tpre = seq(-cap, 0, by = dt)\n", + "sol_pertubation_1_pre <- deSolve::ode(y = s_star_pertubation_1, times = tpre, func = func_list, \n", + " parms=params)\n", + "\n", + "s_star_pertubation_1 <- as.numeric(sol[200,2:4])\n", + "# Change the 1st position to 40.0\n", + "s_star_pertubation_1[1] <- 40.0\n", + "\n", + "tpost <- seq(0, cap, by = dt)\n", + "sol_pertubation_1_post <- deSolve::ode(y = s_star_pertubation_1, times = tpost, func = func_list, \n", + " parms=params)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "382eba5f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Perturbation Analysis: S3 when S4 is perturbed\"" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "t_all <- c(tpre, tpost[-1])\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[-1, , drop = FALSE]) # avoid duplicating t=0 row\n", + "\n", + "# Plot: 4 stacked panels (base graphics)\n", + "\n", + "# To save as PNG file, uncomment the following lines, and the dev.off() line at the end\n", + "\n", + "# png(\n", + "# filename = \"model_2_perturbation_A.png\",\n", + "# width = 8, height = 8, units = \"in\",\n", + "# res = 300 # DPI\n", + "# )\n", + "\n", + "op <- par(mfrow = c(3,1), mar = c(4,5,3,1))\n", + "for (j in 1:3) {\n", + " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j],\n", + " xlab = \"Time\", ylab = paste(\"Concentration of S\", j, sep=\"\"),\n", + " xlim = c(-0.05, 0.05), xaxt = \"n\", xaxs = \"i\",\n", + " main = paste(\"Perturbation Analysis: S\", j, \" when S4 is perturbed\", sep=\"\"))\n", + " axis(\n", + " 1,\n", + " at = seq(-0.05, 0.05, by = 0.01)\n", + " )\n", + " abline(v = 0, lty = 2, lwd = 2)\n", + " box(lwd = 2) # black outer box\n", + "}\n", + "\n", + "# dev.off()\n", + "par(op)" + ] + }, + { + "cell_type": "markdown", + "id": "ea05a483", + "metadata": {}, + "source": [ + "## **3. Additional features**" + ] + }, + { + "cell_type": "markdown", + "id": "14073aff", + "metadata": {}, + "source": [ + "### **3.1. Add subject ID to make the loop result more comprehensible**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5d29bc2a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "id_to_subject <- c(\n", + " \"S1\", \"S2\", \"S3\", \"S4\"\n", + ")\n", + "names(id_to_subject) <- 1:4" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "796b8fb4", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "df <- res_tab$loop_rep[[1]]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cab114e7", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "df$loop_subject <- lapply(\n", + " df$loop,\n", + " function(t) unname(id_to_subject[as.character(t)])\n", + ")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "fe72c366", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
\n" + ], + "text/latex": [ + "A data.frame: 6 × 4\n", + "\\begin{tabular}{llll}\n", + " loop & length & sign & loop\\_subject\\\\\n", + " > & & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", + "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", + "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", + "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", + "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 4\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", + "|---|---|---|---|\n", + "| 1, 1 | 1 | -1 | S1, S1 |\n", + "| 2, 2 | 1 | -1 | S2, S2 |\n", + "| 3, 3 | 1 | -1 | S3, S3 |\n", + "| 4, 4 | 1 | -1 | S4, S4 |\n", + "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", + "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "\n" + ], + "text/plain": [ + " loop length sign loop_subject \n", + "1 1, 1 1 -1 S1, S1 \n", + "2 2, 2 1 -1 S2, S2 \n", + "3 3, 3 1 -1 S3, S3 \n", + "4 4, 4 1 -1 S4, S4 \n", + "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", + "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df" + ] + }, + { + "cell_type": "markdown", + "id": "a2beb7e7", + "metadata": {}, + "source": [ + "### **3.2. Represent regulation relationship from Jacobian matrix**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8703ce8b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A tibble: 9 × 4
fromtoregulationregulation_words
<chr><chr><dbl><chr>
S1S1-1inhibition (negative)
S1S4-1inhibition (negative)
S2S1 1activation (positive)
S2S2-1inhibition (negative)
S2S4 1activation (positive)
S3S2 1activation (positive)
S3S3-1inhibition (negative)
S4S3 1activation (positive)
S4S4-1inhibition (negative)
\n" + ], + "text/latex": [ + "A tibble: 9 × 4\n", + "\\begin{tabular}{llll}\n", + " from & to & regulation & regulation\\_words\\\\\n", + " & & & \\\\\n", + "\\hline\n", + "\t S1 & S1 & -1 & inhibition (negative)\\\\\n", + "\t S1 & S4 & -1 & inhibition (negative)\\\\\n", + "\t S2 & S1 & 1 & activation (positive)\\\\\n", + "\t S2 & S2 & -1 & inhibition (negative)\\\\\n", + "\t S2 & S4 & 1 & activation (positive)\\\\\n", + "\t S3 & S2 & 1 & activation (positive)\\\\\n", + "\t S3 & S3 & -1 & inhibition (negative)\\\\\n", + "\t S4 & S3 & 1 & activation (positive)\\\\\n", + "\t S4 & S4 & -1 & inhibition (negative)\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A tibble: 9 × 4\n", + "\n", + "| from <chr> | to <chr> | regulation <dbl> | regulation_words <chr> |\n", + "|---|---|---|---|\n", + "| S1 | S1 | -1 | inhibition (negative) |\n", + "| S1 | S4 | -1 | inhibition (negative) |\n", + "| S2 | S1 | 1 | activation (positive) |\n", + "| S2 | S2 | -1 | inhibition (negative) |\n", + "| S2 | S4 | 1 | activation (positive) |\n", + "| S3 | S2 | 1 | activation (positive) |\n", + "| S3 | S3 | -1 | inhibition (negative) |\n", + "| S4 | S3 | 1 | activation (positive) |\n", + "| S4 | S4 | -1 | inhibition (negative) |\n", + "\n" + ], + "text/plain": [ + " from to regulation regulation_words \n", + "1 S1 S1 -1 inhibition (negative)\n", + "2 S1 S4 -1 inhibition (negative)\n", + "3 S2 S1 1 activation (positive)\n", + "4 S2 S2 -1 inhibition (negative)\n", + "5 S2 S4 1 activation (positive)\n", + "6 S3 S2 1 activation (positive)\n", + "7 S3 S3 -1 inhibition (negative)\n", + "8 S4 S3 1 activation (positive)\n", + "9 S4 S4 -1 inhibition (negative)" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sign_J <- sign(j_matrix)\n", + "labs <- paste0(\"S\", 1:nrow(sign_J))\n", + "rownames(sign_J) <- labs\n", + "colnames(sign_J) <- labs\n", + "\n", + "regulation_info <- sign_J %>%\n", + " as.data.frame() %>%\n", + " mutate(from = rownames(.)) %>%\n", + " pivot_longer(\n", + " -from,\n", + " names_to = \"to\",\n", + " values_to = \"regulation\"\n", + " ) %>%\n", + " mutate(\n", + " regulation_words = case_when(\n", + " regulation == -1 ~ \"inhibition (negative)\",\n", + " regulation == 1 ~ \"activation (positive)\",\n", + " TRUE ~ \"no regulation\"\n", + " )\n", + " )\n", + "regulation_info[regulation_info$regulation != 0, ]" + ] + }, + { + "cell_type": "markdown", + "id": "fbe99d74", + "metadata": {}, + "source": [ + "### **3.3. Loop Summary in more detail**" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d57b2e96", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
\n" + ], + "text/latex": [ + "A data.frame: 6 × 4\n", + "\\begin{tabular}{llll}\n", + " loop & length & sign & loop\\_subject\\\\\n", + " > & & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", + "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", + "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", + "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", + "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", + "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 4\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", + "|---|---|---|---|\n", + "| 1, 1 | 1 | -1 | S1, S1 |\n", + "| 2, 2 | 1 | -1 | S2, S2 |\n", + "| 3, 3 | 1 | -1 | S3, S3 |\n", + "| 4, 4 | 1 | -1 | S4, S4 |\n", + "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", + "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "\n" + ], + "text/plain": [ + " loop length sign loop_subject \n", + "1 1, 1 1 -1 S1, S1 \n", + "2 2, 2 1 -1 S2, S2 \n", + "3 3, 3 1 -1 S3, S3 \n", + "4 4, 4 1 -1 S4, S4 \n", + "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", + "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "df" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/model_2_perturbation_A.png b/examples/model_2_perturbation_A.png new file mode 100644 index 0000000000000000000000000000000000000000..01906a0df5067c242c4bcafa22a7af42ffaeb528 GIT binary patch literal 47200 zcmeFZ2UL^Y(=VFPrK$)h2#8XYsuV%0sEB}opoGw)0@8agA&ST=h#-gvNN)lGBE1vf zMGQr1=tX*OhS1C1!T0}t|L>l&&bsTabJsa%t;>pud3Jeb&oeW7X7>E@_K}t<11&o( 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07/12] Fix bug 2 --- examples/model_1_POSm4_R.ipynb | 352 ++------------- examples/model_1_perturbation.png | Bin 58791 -> 59191 bytes examples/model_2_complex_formation_R.ipynb | 500 +++++++++++++++------ examples/model_2_perturbation_A.png | Bin 47200 -> 42925 bytes 4 files changed, 378 insertions(+), 474 deletions(-) diff --git a/examples/model_1_POSm4_R.ipynb b/examples/model_1_POSm4_R.ipynb index ed2228d..be2833e 100644 --- a/examples/model_1_POSm4_R.ipynb +++ b/examples/model_1_POSm4_R.ipynb @@ -188,7 +188,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 34, "id": "12108b07", "metadata": { "vscode": { @@ -227,7 +227,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 35, "id": "5ab687a9", "metadata": { "vscode": { @@ -247,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 36, "id": "81b11f06", "metadata": { "vscode": { @@ -327,7 +327,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 37, "id": "b1bccacc", "metadata": { "vscode": { @@ -390,7 +390,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 38, "id": "f1f8c98c", "metadata": { "vscode": { @@ -471,7 +471,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 39, "id": "9e3795b8", "metadata": { "vscode": { @@ -545,7 +545,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 40, "id": "c261caec", "metadata": { "vscode": { @@ -604,7 +604,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 41, "id": "8b4155db", "metadata": { "vscode": { @@ -664,7 +664,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 42, "id": "71c0bc77", "metadata": { "vscode": { @@ -735,7 +735,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 43, "id": "bee71136", "metadata": { "vscode": { @@ -745,15 +745,15 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "plot without title" ] }, "metadata": { "image/png": { - "height": 420, - "width": 420 + "height": 360, + "width": 480 } }, "output_type": "display_data" @@ -779,7 +779,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 44, "id": "b014adcb", "metadata": { "vscode": { @@ -789,13 +789,13 @@ "outputs": [], "source": [ "# Continue simulation to observe stability\n", - "sol <- deSolve::ode(y = as.numeric(sol[95,2:5]), times = seq(0,11,0.1), func = func_POSm4_list, \n", + "sol <- deSolve::ode(y = as.numeric(sol[95,2:5]), times = seq(0,11,0.01), func = func_POSm4_list, \n", " parms=klin, knonlin=knonlin)" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 45, "id": "21bbad0e", "metadata": { "vscode": { @@ -816,7 +816,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 46, "id": "4b596080", "metadata": { "vscode": { @@ -824,18 +824,9 @@ } }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Warning message:\n", - "\"\u001b[1m\u001b[22mUsing `size` aesthetic for lines was deprecated in ggplot2 3.4.0.\n", - "\u001b[36mℹ\u001b[39m Please use `linewidth` instead.\"\n" - ] - }, { "data": { - "image/png": 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", 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", "text/plain": [ "plot without title" ] @@ -913,7 +904,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 47, "id": "70a2312f", "metadata": { "vscode": { @@ -930,7 +921,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 48, "id": "07e45a5a", "metadata": { "vscode": { @@ -939,12 +930,12 @@ }, "outputs": [], "source": [ - "s_star_pertubation_1 <- as.numeric(sol[81,2:5])\n", + "s_star_pertubation_1 <- as.numeric(sol[855,2:5])\n", "tpre = seq(-cap, 0, by = dt)\n", "sol_pertubation_1_pre <- deSolve::ode(y = s_star_pertubation_1, times = tpre, func = func_POSm4_list, \n", " parms=klin, knonlin=knonlin)\n", "\n", - "s_star_pertubation_1 <- as.numeric(sol[86,2:5])\n", + "s_star_pertubation_1 <- as.numeric(sol[860,2:5])\n", "# Change the 4th position to 0.75\n", "s_star_pertubation_1[4] <- 0.75\n", "\n", @@ -955,7 +946,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 49, "id": "b89c6113", "metadata": { "vscode": { @@ -970,7 +961,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 52, "id": "ef4f5f4b", "metadata": { "vscode": { @@ -980,7 +971,7 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "Plot with title \"Perturbation Analysis: S4 when S4 is perturbed\"" ] @@ -1033,299 +1024,6 @@ "par(op)" ] }, - { - "cell_type": "code", - "execution_count": 23, - "id": "a0e05ddf", - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [ - { - "data": { - "text/html": [ - "\n", - "\n", - "\n", - "\t\n", - "\n", - "\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\n", - "
A matrix: 1002 × 5 of type dbl
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-0.0475105.76840.0016508330.010032270.3210787
-0.0474105.77930.0016505630.010030540.3209984
-0.0473105.79020.0016502930.010028810.3209182
-0.0472105.80110.0016500220.010027080.3208379
-0.0471105.81200.0016497520.010025360.3207578
⋮⋮⋮⋮⋮
0.0471159.64920.0078411530.045823200.7196214
0.0472159.65510.0078415670.045830320.7196282
0.0473159.66100.0078419820.045837400.7196350
0.0474159.66690.0078423980.045844450.7196419
0.0475159.67280.0078428150.045851460.7196489
0.0476159.67870.0078432330.045858430.7196559
0.0477159.68460.0078436520.045865360.7196630
0.0478159.69050.0078440720.045872250.7196701
0.0479159.69640.0078444930.045879110.7196772
0.0480159.70230.0078449150.045885930.7196845
0.0481159.70820.0078453380.045892720.7196917
0.0482159.71410.0078457620.045899470.7196991
0.0483159.72000.0078461870.045906190.7197064
0.0484159.72590.0078466130.045912870.7197138
0.0485159.73180.0078470390.045919510.7197213
0.0486159.73770.0078474670.045926120.7197288
0.0487159.74350.0078478950.045932700.7197364
0.0488159.74940.0078483240.045939240.7197440
0.0489159.75530.0078487550.045945750.7197517
0.0490159.76120.0078491860.045952230.7197594
0.0491159.76710.0078496180.045958670.7197672
0.0492159.77300.0078500510.045965080.7197750
0.0493159.77890.0078504850.045971460.7197828
0.0494159.78480.0078509190.045977810.7197907
0.0495159.79070.0078513550.045984130.7197987
0.0496159.79650.0078517910.045990410.7198067
0.0497159.80240.0078522280.045996670.7198147
0.0498159.80830.0078526660.046002890.7198228
0.0499159.81420.0078531050.046009090.7198310
0.0500159.82010.0078535450.046015250.7198391
\n" - ], - "text/latex": [ - "A matrix: 1002 × 5 of type dbl\n", - "\\begin{tabular}{lllll}\n", - " time & 1 & 2 & 3 & 4\\\\\n", - "\\hline\n", - "\t -0.0500 & 105.4953 & 0.001657652 & 0.01007582 & 0.3230939\\\\\n", - "\t -0.0499 & 105.5063 & 0.001657376 & 0.01007406 & 0.3230130\\\\\n", - "\t -0.0498 & 105.5172 & 0.001657100 & 0.01007231 & 0.3229321\\\\\n", - "\t -0.0497 & 105.5281 & 0.001656825 & 0.01007056 & 0.3228512\\\\\n", - "\t -0.0496 & 105.5390 & 0.001656551 & 0.01006881 & 0.3227704\\\\\n", - "\t -0.0495 & 105.5499 & 0.001656277 & 0.01006706 & 0.3226896\\\\\n", - "\t -0.0494 & 105.5609 & 0.001656003 & 0.01006531 & 0.3226088\\\\\n", - "\t -0.0493 & 105.5718 & 0.001655729 & 0.01006356 & 0.3225280\\\\\n", - "\t -0.0492 & 105.5827 & 0.001655456 & 0.01006181 & 0.3224473\\\\\n", - "\t -0.0491 & 105.5936 & 0.001655183 & 0.01006007 & 0.3223665\\\\\n", - "\t -0.0490 & 105.6046 & 0.001654910 & 0.01005832 & 0.3222859\\\\\n", - "\t -0.0489 & 105.6155 & 0.001654637 & 0.01005658 & 0.3222052\\\\\n", - "\t -0.0488 & 105.6264 & 0.001654364 & 0.01005483 & 0.3221246\\\\\n", - "\t -0.0487 & 105.6373 & 0.001654091 & 0.01005309 & 0.3220439\\\\\n", - "\t -0.0486 & 105.6482 & 0.001653819 & 0.01005135 & 0.3219634\\\\\n", - "\t -0.0485 & 105.6592 & 0.001653547 & 0.01004961 & 0.3218828\\\\\n", - "\t -0.0484 & 105.6701 & 0.001653275 & 0.01004787 & 0.3218023\\\\\n", - "\t -0.0483 & 105.6810 & 0.001653003 & 0.01004614 & 0.3217218\\\\\n", - "\t -0.0482 & 105.6919 & 0.001652731 & 0.01004440 & 0.3216413\\\\\n", - "\t -0.0481 & 105.7029 & 0.001652459 & 0.01004266 & 0.3215608\\\\\n", - "\t -0.0480 & 105.7138 & 0.001652188 & 0.01004093 & 0.3214804\\\\\n", - "\t -0.0479 & 105.7247 & 0.001651917 & 0.01003919 & 0.3214000\\\\\n", - "\t -0.0478 & 105.7356 & 0.001651646 & 0.01003746 & 0.3213196\\\\\n", - "\t -0.0477 & 105.7465 & 0.001651375 & 0.01003573 & 0.3212393\\\\\n", - "\t -0.0476 & 105.7575 & 0.001651104 & 0.01003400 & 0.3211590\\\\\n", - "\t -0.0475 & 105.7684 & 0.001650833 & 0.01003227 & 0.3210787\\\\\n", - "\t -0.0474 & 105.7793 & 0.001650563 & 0.01003054 & 0.3209984\\\\\n", - "\t -0.0473 & 105.7902 & 0.001650293 & 0.01002881 & 0.3209182\\\\\n", - "\t -0.0472 & 105.8011 & 0.001650022 & 0.01002708 & 0.3208379\\\\\n", - "\t -0.0471 & 105.8120 & 0.001649752 & 0.01002536 & 0.3207578\\\\\n", - "\t ⋮ & ⋮ & ⋮ & ⋮ & ⋮\\\\\n", - "\t 0.0471 & 159.6492 & 0.007841153 & 0.04582320 & 0.7196214\\\\\n", - "\t 0.0472 & 159.6551 & 0.007841567 & 0.04583032 & 0.7196282\\\\\n", - "\t 0.0473 & 159.6610 & 0.007841982 & 0.04583740 & 0.7196350\\\\\n", - "\t 0.0474 & 159.6669 & 0.007842398 & 0.04584445 & 0.7196419\\\\\n", - "\t 0.0475 & 159.6728 & 0.007842815 & 0.04585146 & 0.7196489\\\\\n", - "\t 0.0476 & 159.6787 & 0.007843233 & 0.04585843 & 0.7196559\\\\\n", - "\t 0.0477 & 159.6846 & 0.007843652 & 0.04586536 & 0.7196630\\\\\n", - "\t 0.0478 & 159.6905 & 0.007844072 & 0.04587225 & 0.7196701\\\\\n", - "\t 0.0479 & 159.6964 & 0.007844493 & 0.04587911 & 0.7196772\\\\\n", - "\t 0.0480 & 159.7023 & 0.007844915 & 0.04588593 & 0.7196845\\\\\n", - "\t 0.0481 & 159.7082 & 0.007845338 & 0.04589272 & 0.7196917\\\\\n", - "\t 0.0482 & 159.7141 & 0.007845762 & 0.04589947 & 0.7196991\\\\\n", - "\t 0.0483 & 159.7200 & 0.007846187 & 0.04590619 & 0.7197064\\\\\n", - "\t 0.0484 & 159.7259 & 0.007846613 & 0.04591287 & 0.7197138\\\\\n", - "\t 0.0485 & 159.7318 & 0.007847039 & 0.04591951 & 0.7197213\\\\\n", - "\t 0.0486 & 159.7377 & 0.007847467 & 0.04592612 & 0.7197288\\\\\n", - "\t 0.0487 & 159.7435 & 0.007847895 & 0.04593270 & 0.7197364\\\\\n", - "\t 0.0488 & 159.7494 & 0.007848324 & 0.04593924 & 0.7197440\\\\\n", - "\t 0.0489 & 159.7553 & 0.007848755 & 0.04594575 & 0.7197517\\\\\n", - "\t 0.0490 & 159.7612 & 0.007849186 & 0.04595223 & 0.7197594\\\\\n", - "\t 0.0491 & 159.7671 & 0.007849618 & 0.04595867 & 0.7197672\\\\\n", - "\t 0.0492 & 159.7730 & 0.007850051 & 0.04596508 & 0.7197750\\\\\n", - "\t 0.0493 & 159.7789 & 0.007850485 & 0.04597146 & 0.7197828\\\\\n", - "\t 0.0494 & 159.7848 & 0.007850919 & 0.04597781 & 0.7197907\\\\\n", - "\t 0.0495 & 159.7907 & 0.007851355 & 0.04598413 & 0.7197987\\\\\n", - "\t 0.0496 & 159.7965 & 0.007851791 & 0.04599041 & 0.7198067\\\\\n", - "\t 0.0497 & 159.8024 & 0.007852228 & 0.04599667 & 0.7198147\\\\\n", - "\t 0.0498 & 159.8083 & 0.007852666 & 0.04600289 & 0.7198228\\\\\n", - "\t 0.0499 & 159.8142 & 0.007853105 & 0.04600909 & 0.7198310\\\\\n", - "\t 0.0500 & 159.8201 & 0.007853545 & 0.04601525 & 0.7198391\\\\\n", - "\\end{tabular}\n" - ], - "text/markdown": [ - "\n", - "A matrix: 1002 × 5 of type dbl\n", - "\n", - "| time | 1 | 2 | 3 | 4 |\n", - "|---|---|---|---|---|\n", - "| -0.0500 | 105.4953 | 0.001657652 | 0.01007582 | 0.3230939 |\n", - "| -0.0499 | 105.5063 | 0.001657376 | 0.01007406 | 0.3230130 |\n", - "| -0.0498 | 105.5172 | 0.001657100 | 0.01007231 | 0.3229321 |\n", - "| -0.0497 | 105.5281 | 0.001656825 | 0.01007056 | 0.3228512 |\n", - "| -0.0496 | 105.5390 | 0.001656551 | 0.01006881 | 0.3227704 |\n", - "| -0.0495 | 105.5499 | 0.001656277 | 0.01006706 | 0.3226896 |\n", - "| -0.0494 | 105.5609 | 0.001656003 | 0.01006531 | 0.3226088 |\n", - "| -0.0493 | 105.5718 | 0.001655729 | 0.01006356 | 0.3225280 |\n", - "| -0.0492 | 105.5827 | 0.001655456 | 0.01006181 | 0.3224473 |\n", - "| -0.0491 | 105.5936 | 0.001655183 | 0.01006007 | 0.3223665 |\n", - "| -0.0490 | 105.6046 | 0.001654910 | 0.01005832 | 0.3222859 |\n", - "| -0.0489 | 105.6155 | 0.001654637 | 0.01005658 | 0.3222052 |\n", - "| -0.0488 | 105.6264 | 0.001654364 | 0.01005483 | 0.3221246 |\n", - "| -0.0487 | 105.6373 | 0.001654091 | 0.01005309 | 0.3220439 |\n", - "| -0.0486 | 105.6482 | 0.001653819 | 0.01005135 | 0.3219634 |\n", - "| -0.0485 | 105.6592 | 0.001653547 | 0.01004961 | 0.3218828 |\n", - "| -0.0484 | 105.6701 | 0.001653275 | 0.01004787 | 0.3218023 |\n", - "| -0.0483 | 105.6810 | 0.001653003 | 0.01004614 | 0.3217218 |\n", - "| -0.0482 | 105.6919 | 0.001652731 | 0.01004440 | 0.3216413 |\n", - "| -0.0481 | 105.7029 | 0.001652459 | 0.01004266 | 0.3215608 |\n", - "| -0.0480 | 105.7138 | 0.001652188 | 0.01004093 | 0.3214804 |\n", - "| -0.0479 | 105.7247 | 0.001651917 | 0.01003919 | 0.3214000 |\n", - "| -0.0478 | 105.7356 | 0.001651646 | 0.01003746 | 0.3213196 |\n", - "| -0.0477 | 105.7465 | 0.001651375 | 0.01003573 | 0.3212393 |\n", - "| -0.0476 | 105.7575 | 0.001651104 | 0.01003400 | 0.3211590 |\n", - "| -0.0475 | 105.7684 | 0.001650833 | 0.01003227 | 0.3210787 |\n", - "| -0.0474 | 105.7793 | 0.001650563 | 0.01003054 | 0.3209984 |\n", - "| -0.0473 | 105.7902 | 0.001650293 | 0.01002881 | 0.3209182 |\n", - "| -0.0472 | 105.8011 | 0.001650022 | 0.01002708 | 0.3208379 |\n", - "| -0.0471 | 105.8120 | 0.001649752 | 0.01002536 | 0.3207578 |\n", - "| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |\n", - "| 0.0471 | 159.6492 | 0.007841153 | 0.04582320 | 0.7196214 |\n", - "| 0.0472 | 159.6551 | 0.007841567 | 0.04583032 | 0.7196282 |\n", - "| 0.0473 | 159.6610 | 0.007841982 | 0.04583740 | 0.7196350 |\n", - "| 0.0474 | 159.6669 | 0.007842398 | 0.04584445 | 0.7196419 |\n", - "| 0.0475 | 159.6728 | 0.007842815 | 0.04585146 | 0.7196489 |\n", - "| 0.0476 | 159.6787 | 0.007843233 | 0.04585843 | 0.7196559 |\n", - "| 0.0477 | 159.6846 | 0.007843652 | 0.04586536 | 0.7196630 |\n", - "| 0.0478 | 159.6905 | 0.007844072 | 0.04587225 | 0.7196701 |\n", - "| 0.0479 | 159.6964 | 0.007844493 | 0.04587911 | 0.7196772 |\n", - "| 0.0480 | 159.7023 | 0.007844915 | 0.04588593 | 0.7196845 |\n", - "| 0.0481 | 159.7082 | 0.007845338 | 0.04589272 | 0.7196917 |\n", - "| 0.0482 | 159.7141 | 0.007845762 | 0.04589947 | 0.7196991 |\n", - "| 0.0483 | 159.7200 | 0.007846187 | 0.04590619 | 0.7197064 |\n", - "| 0.0484 | 159.7259 | 0.007846613 | 0.04591287 | 0.7197138 |\n", - "| 0.0485 | 159.7318 | 0.007847039 | 0.04591951 | 0.7197213 |\n", - "| 0.0486 | 159.7377 | 0.007847467 | 0.04592612 | 0.7197288 |\n", - "| 0.0487 | 159.7435 | 0.007847895 | 0.04593270 | 0.7197364 |\n", - "| 0.0488 | 159.7494 | 0.007848324 | 0.04593924 | 0.7197440 |\n", - "| 0.0489 | 159.7553 | 0.007848755 | 0.04594575 | 0.7197517 |\n", - "| 0.0490 | 159.7612 | 0.007849186 | 0.04595223 | 0.7197594 |\n", - "| 0.0491 | 159.7671 | 0.007849618 | 0.04595867 | 0.7197672 |\n", - "| 0.0492 | 159.7730 | 0.007850051 | 0.04596508 | 0.7197750 |\n", - "| 0.0493 | 159.7789 | 0.007850485 | 0.04597146 | 0.7197828 |\n", - "| 0.0494 | 159.7848 | 0.007850919 | 0.04597781 | 0.7197907 |\n", - "| 0.0495 | 159.7907 | 0.007851355 | 0.04598413 | 0.7197987 |\n", - "| 0.0496 | 159.7965 | 0.007851791 | 0.04599041 | 0.7198067 |\n", - "| 0.0497 | 159.8024 | 0.007852228 | 0.04599667 | 0.7198147 |\n", - "| 0.0498 | 159.8083 | 0.007852666 | 0.04600289 | 0.7198228 |\n", - "| 0.0499 | 159.8142 | 0.007853105 | 0.04600909 | 0.7198310 |\n", - "| 0.0500 | 159.8201 | 0.007853545 | 0.04601525 | 0.7198391 |\n", - "\n" - ], - "text/plain": [ - " time 1 2 3 4 \n", - " [1,] -0.0500 105.4953 0.001657652 0.01007582 0.3230939\n", - " [2,] -0.0499 105.5063 0.001657376 0.01007406 0.3230130\n", - " [3,] -0.0498 105.5172 0.001657100 0.01007231 0.3229321\n", - " [4,] -0.0497 105.5281 0.001656825 0.01007056 0.3228512\n", - " [5,] -0.0496 105.5390 0.001656551 0.01006881 0.3227704\n", - " [6,] -0.0495 105.5499 0.001656277 0.01006706 0.3226896\n", - " [7,] -0.0494 105.5609 0.001656003 0.01006531 0.3226088\n", - " [8,] -0.0493 105.5718 0.001655729 0.01006356 0.3225280\n", - " [9,] -0.0492 105.5827 0.001655456 0.01006181 0.3224473\n", - "[10,] -0.0491 105.5936 0.001655183 0.01006007 0.3223665\n", - "[11,] -0.0490 105.6046 0.001654910 0.01005832 0.3222859\n", - "[12,] -0.0489 105.6155 0.001654637 0.01005658 0.3222052\n", - "[13,] -0.0488 105.6264 0.001654364 0.01005483 0.3221246\n", - "[14,] -0.0487 105.6373 0.001654091 0.01005309 0.3220439\n", - "[15,] -0.0486 105.6482 0.001653819 0.01005135 0.3219634\n", - "[16,] -0.0485 105.6592 0.001653547 0.01004961 0.3218828\n", - "[17,] -0.0484 105.6701 0.001653275 0.01004787 0.3218023\n", - "[18,] -0.0483 105.6810 0.001653003 0.01004614 0.3217218\n", - "[19,] -0.0482 105.6919 0.001652731 0.01004440 0.3216413\n", - "[20,] -0.0481 105.7029 0.001652459 0.01004266 0.3215608\n", - "[21,] -0.0480 105.7138 0.001652188 0.01004093 0.3214804\n", - "[22,] -0.0479 105.7247 0.001651917 0.01003919 0.3214000\n", - "[23,] -0.0478 105.7356 0.001651646 0.01003746 0.3213196\n", - "[24,] -0.0477 105.7465 0.001651375 0.01003573 0.3212393\n", - "[25,] -0.0476 105.7575 0.001651104 0.01003400 0.3211590\n", - "[26,] -0.0475 105.7684 0.001650833 0.01003227 0.3210787\n", - "[27,] -0.0474 105.7793 0.001650563 0.01003054 0.3209984\n", - "[28,] -0.0473 105.7902 0.001650293 0.01002881 0.3209182\n", - "[29,] -0.0472 105.8011 0.001650022 0.01002708 0.3208379\n", - "[30,] -0.0471 105.8120 0.001649752 0.01002536 0.3207578\n", - "[31,] ⋮ ⋮ ⋮ ⋮ ⋮ \n", - "[32,] 0.0471 159.6492 0.007841153 0.04582320 0.7196214\n", - "[33,] 0.0472 159.6551 0.007841567 0.04583032 0.7196282\n", - "[34,] 0.0473 159.6610 0.007841982 0.04583740 0.7196350\n", - "[35,] 0.0474 159.6669 0.007842398 0.04584445 0.7196419\n", - "[36,] 0.0475 159.6728 0.007842815 0.04585146 0.7196489\n", - "[37,] 0.0476 159.6787 0.007843233 0.04585843 0.7196559\n", - "[38,] 0.0477 159.6846 0.007843652 0.04586536 0.7196630\n", - "[39,] 0.0478 159.6905 0.007844072 0.04587225 0.7196701\n", - "[40,] 0.0479 159.6964 0.007844493 0.04587911 0.7196772\n", - "[41,] 0.0480 159.7023 0.007844915 0.04588593 0.7196845\n", - "[42,] 0.0481 159.7082 0.007845338 0.04589272 0.7196917\n", - "[43,] 0.0482 159.7141 0.007845762 0.04589947 0.7196991\n", - "[44,] 0.0483 159.7200 0.007846187 0.04590619 0.7197064\n", - "[45,] 0.0484 159.7259 0.007846613 0.04591287 0.7197138\n", - "[46,] 0.0485 159.7318 0.007847039 0.04591951 0.7197213\n", - "[47,] 0.0486 159.7377 0.007847467 0.04592612 0.7197288\n", - "[48,] 0.0487 159.7435 0.007847895 0.04593270 0.7197364\n", - "[49,] 0.0488 159.7494 0.007848324 0.04593924 0.7197440\n", - "[50,] 0.0489 159.7553 0.007848755 0.04594575 0.7197517\n", - "[51,] 0.0490 159.7612 0.007849186 0.04595223 0.7197594\n", - "[52,] 0.0491 159.7671 0.007849618 0.04595867 0.7197672\n", - "[53,] 0.0492 159.7730 0.007850051 0.04596508 0.7197750\n", - "[54,] 0.0493 159.7789 0.007850485 0.04597146 0.7197828\n", - "[55,] 0.0494 159.7848 0.007850919 0.04597781 0.7197907\n", - "[56,] 0.0495 159.7907 0.007851355 0.04598413 0.7197987\n", - "[57,] 0.0496 159.7965 0.007851791 0.04599041 0.7198067\n", - "[58,] 0.0497 159.8024 0.007852228 0.04599667 0.7198147\n", - "[59,] 0.0498 159.8083 0.007852666 0.04600289 0.7198228\n", - "[60,] 0.0499 159.8142 0.007853105 0.04600909 0.7198310\n", - "[61,] 0.0500 159.8201 0.007853545 0.04601525 0.7198391" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "y_all" - ] - }, { "cell_type": "markdown", "id": "dc7729e7", diff --git a/examples/model_1_perturbation.png b/examples/model_1_perturbation.png index b68a8052694f272aaaf35660fa73ef8a7e9221e8..4db29821b85565a7ab6fdb131d899f20953d94e2 100644 GIT binary patch literal 59191 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zqn@65GBH#Oz(4pUe$Qe(ZB51K$kk`?Rx)(hi+(~O`_4*<0A=N_9Y6MSdba+$Tq;Gt zUzC+qQ}<39oA-to-~ROx0by|$2}yMq;lpVs-|3$l?%*O&fO!Kzl;9O&3{m5uj%ATZ z0-&rkom!UZ&n4Xf>rnvzhZHz5p2~FuhdOZIgq$WUJzW4m4>YzK97Ha-5L*9}%u%p| zc^K^0odNXBBtaoqA^(>anh2ww0v1aMp?41v6NjG_2wv4iG$<}y6%ZsuNrEh@MoOCR4aNOO}9w)|HIkAVI1*os(pe*?A>KN@J~TT^+~}a Hg#Z5o$UO2q diff --git a/examples/model_2_complex_formation_R.ipynb b/examples/model_2_complex_formation_R.ipynb index 400177a..4892932 100644 --- a/examples/model_2_complex_formation_R.ipynb +++ b/examples/model_2_complex_formation_R.ipynb @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "id": "9dd37926", "metadata": { "vscode": { @@ -194,7 +194,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 3, "id": "cf9c4c03", "metadata": { "vscode": { @@ -236,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 68, "id": "d9f19514", "metadata": { "vscode": { @@ -255,7 +255,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 69, "id": "4f929c59", "metadata": { "vscode": { @@ -342,7 +342,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 6, "id": "54b7b1a3", "metadata": { "vscode": { @@ -405,7 +405,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 7, "id": "2631d303", "metadata": { "vscode": { @@ -490,7 +490,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 8, "id": "a3bf2b5d", "metadata": { "vscode": { @@ -655,7 +655,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 9, "id": "f43813a7", "metadata": { "vscode": { @@ -713,15 +713,12 @@ "id": "f9454da1", "metadata": {}, "source": [ - "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003].\n", - "\n", - "The input function, in the example `func_POSm4` (positive feedback chain model from [Baum et al., 2016]) defines the time derivatives of the modelled variables as a vector: \n", - "$f_i(s)=dS_i/dt$. Note that only those input arguments to the function that encode the modelled variables (and hence in whose direction the partial derivatives are taken) are allowed to be called `x`." + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003]." ] }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 37, "id": "dbd42fd2", "metadata": { "vscode": { @@ -778,7 +775,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 11, "id": "2f3d21ac", "metadata": { "vscode": { @@ -792,34 +789,34 @@ "\n", "\n", "\n", - "\t\n", - "\t\n", - "\t\n", + "\t\n", + "\t\n", + "\t\n", "\n", "
A matrix: 3 × 3 of type dbl
-1.233223-1.233223 2
-1.233223-1.233223 2
1.233223 1.233223-2
-5-10 2
-5-10 2
5 10-2
\n" ], "text/latex": [ "A matrix: 3 × 3 of type dbl\n", "\\begin{tabular}{lll}\n", - "\t -1.233223 & -1.233223 & 2\\\\\n", - "\t -1.233223 & -1.233223 & 2\\\\\n", - "\t 1.233223 & 1.233223 & -2\\\\\n", + "\t -5 & -10 & 2\\\\\n", + "\t -5 & -10 & 2\\\\\n", + "\t 5 & 10 & -2\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A matrix: 3 × 3 of type dbl\n", "\n", - "| -1.233223 | -1.233223 | 2 |\n", - "| -1.233223 | -1.233223 | 2 |\n", - "| 1.233223 | 1.233223 | -2 |\n", + "| -5 | -10 | 2 |\n", + "| -5 | -10 | 2 |\n", + "| 5 | 10 | -2 |\n", "\n" ], "text/plain": [ - " [,1] [,2] [,3]\n", - "[1,] -1.233223 -1.233223 2 \n", - "[2,] -1.233223 -1.233223 2 \n", - "[3,] 1.233223 1.233223 -2 " + " [,1] [,2] [,3]\n", + "[1,] -5 -10 2 \n", + "[2,] -5 -10 2 \n", + "[3,] 5 10 -2 " ] }, "metadata": {}, @@ -834,7 +831,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 12, "id": "67868589", "metadata": { "vscode": { @@ -897,7 +894,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 13, "id": "e8883776", "metadata": { "vscode": { @@ -940,7 +937,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 38, "id": "3beedbcf", "metadata": { "vscode": { @@ -961,7 +958,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 39, "id": "26027184", "metadata": { "vscode": { @@ -1059,7 +1056,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 48, "id": "1c922b3c", "metadata": { "vscode": { @@ -1114,7 +1111,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 49, "id": "6539db9a", "metadata": { "vscode": { @@ -1131,7 +1128,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 41, "id": "55b33b49", "metadata": { "vscode": { @@ -1152,7 +1149,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 42, "id": "1ced98df", "metadata": { "vscode": { @@ -1185,7 +1182,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 43, "id": "55b3ff5e", "metadata": { "vscode": { @@ -1220,9 +1217,97 @@ "outputs": [ { "data": { - "image/png": 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", + "text/html": [ + "agg_record_1372292667: 2" + ], + "text/latex": [ + "\\textbf{agg\\textbackslash{}\\_record\\textbackslash{}\\_1372292667:} 2" + ], + "text/markdown": [ + "**agg_record_1372292667:** 2" + ], "text/plain": [ - "Plot with title \"Perturbation Analysis: S3 when S4 is perturbed\"" + "agg_record_1372292667 \n", + " 2 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t_all <- c(tpre, tpost)\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post) # avoid duplicating t=0 row\n", + "labels <- c(\"A\", \"B\", \"AB\")\n", + "\n", + "# Plot: 4 stacked panels (base graphics)\n", + "\n", + "# To save as PNG file, uncomment the following lines, and the dev.off() line at the end\n", + "\n", + "# png(\n", + "# filename = \"model_2_perturbation_A.png\",\n", + "# width = 8, height = 6, units = \"in\",\n", + "# res = 300 # DPI\n", + "# )\n", + "\n", + "op <- par(mfrow = c(3,1), mar = c(4,5,3,1))\n", + "for (j in 2:4) {\n", + " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j-1],\n", + " xlab = \"Time\", ylab = paste(\"Concentration of\", labels[j-1], sep=\"\"),\n", + " xlim = c(-0.05, 0.05), xaxt = \"n\", xaxs = \"i\",\n", + " main = paste(\"Perturbation Analysis: \", labels[j-1], \" when A is perturbed\", sep=\"\"))\n", + " axis(\n", + " 1,\n", + " at = seq(-0.05, 0.05, by = 0.01)\n", + " )\n", + " abline(v = 0, lty = 2, lwd = 2)\n", + " box(lwd = 2) # black outer box\n", + "}\n", + "\n", + "# dev.off()\n", + "par(op)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "dd297c4b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "s_star_pertubation_1 <- as.numeric(sol[(200-cap/dt),2:4])\n", + "tpre = seq(-cap, 0, by = dt)\n", + "sol_pertubation_1_pre <- deSolve::ode(y = s_star_pertubation_1, times = tpre, func = func_list, \n", + " parms=params)\n", + "\n", + "s_star_pertubation_1 <- as.numeric(sol[200,2:4])\n", + "# Change the 2nd position to 10.0\n", + "s_star_pertubation_1[2] <- 10.0\n", + "\n", + "tpost <- seq(0, cap, by = dt)\n", + "sol_pertubation_1_post <- deSolve::ode(y = s_star_pertubation_1, times = tpost, func = func_list, \n", + " parms=params)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "b4a463ad", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "Plot with title \"Perturbation Analysis: AB when A is perturbed\"" ] }, "metadata": { @@ -1235,25 +1320,26 @@ } ], "source": [ - "t_all <- c(tpre, tpost[-1])\n", - "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post[-1, , drop = FALSE]) # avoid duplicating t=0 row\n", + "t_all <- c(tpre, tpost)\n", + "y_all <- rbind(sol_pertubation_1_pre, sol_pertubation_1_post) # avoid duplicating t=0 row\n", + "labels <- c(\"A\", \"B\", \"AB\")\n", "\n", "# Plot: 4 stacked panels (base graphics)\n", "\n", "# To save as PNG file, uncomment the following lines, and the dev.off() line at the end\n", "\n", "# png(\n", - "# filename = \"model_2_perturbation_A.png\",\n", - "# width = 8, height = 8, units = \"in\",\n", + "# filename = \"model_2_perturbation_B.png\",\n", + "# width = 8, height = 6, units = \"in\",\n", "# res = 300 # DPI\n", "# )\n", "\n", "op <- par(mfrow = c(3,1), mar = c(4,5,3,1))\n", - "for (j in 1:3) {\n", - " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j],\n", - " xlab = \"Time\", ylab = paste(\"Concentration of S\", j, sep=\"\"),\n", + "for (j in 2:4) {\n", + " plot(t_all, y_all[,j], type = \"l\", lwd = 4, col = colors[j-1],\n", + " xlab = \"Time\", ylab = paste(\"Concentration of\", labels[j-1], sep=\"\"),\n", " xlim = c(-0.05, 0.05), xaxt = \"n\", xaxs = \"i\",\n", - " main = paste(\"Perturbation Analysis: S\", j, \" when S4 is perturbed\", sep=\"\"))\n", + " main = paste(\"Perturbation Analysis: \", labels[j-1], \" when A is perturbed\", sep=\"\"))\n", " axis(\n", " 1,\n", " at = seq(-0.05, 0.05, by = 0.01)\n", @@ -1284,7 +1370,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 57, "id": "5d29bc2a", "metadata": { "vscode": { @@ -1294,14 +1380,14 @@ "outputs": [], "source": [ "id_to_subject <- c(\n", - " \"S1\", \"S2\", \"S3\", \"S4\"\n", + " \"A\", \"B\", \"AB\"\n", ")\n", - "names(id_to_subject) <- 1:4" + "names(id_to_subject) <- 1:3" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 58, "id": "796b8fb4", "metadata": { "vscode": { @@ -1315,7 +1401,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 59, "id": "cab114e7", "metadata": { "vscode": { @@ -1332,7 +1418,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 60, "id": "fe72c366", "metadata": { "vscode": { @@ -1344,57 +1430,65 @@ "data": { "text/html": [ "\n", - "\n", + "\n", "\n", "\t\n", "\t\n", "\n", "\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", "\n", "
A data.frame: 6 × 4A data.frame: 8 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
1, 11-1A, A
2, 21-1B, B
3, 31-1AB, AB
1, 2, 12 1A, B, A
1, 3, 12 1A , AB, A
1, 3, 2, 13-1A , AB, B , A
2, 3, 1, 23-1B , AB, A , B
2, 3, 22 1B , AB, B
\n" ], "text/latex": [ - "A data.frame: 6 × 4\n", + "A data.frame: 8 × 4\n", "\\begin{tabular}{llll}\n", " loop & length & sign & loop\\_subject\\\\\n", " > & & & \\\\\n", "\\hline\n", - "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", - "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", - "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", - "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", - "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", - "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\t 1, 1 & 1 & -1 & A, A\\\\\n", + "\t 2, 2 & 1 & -1 & B, B\\\\\n", + "\t 3, 3 & 1 & -1 & AB, AB\\\\\n", + "\t 1, 2, 1 & 2 & 1 & A, B, A\\\\\n", + "\t 1, 3, 1 & 2 & 1 & A , AB, A \\\\\n", + "\t 1, 3, 2, 1 & 3 & -1 & A , AB, B , A \\\\\n", + "\t 2, 3, 1, 2 & 3 & -1 & B , AB, A , B \\\\\n", + "\t 2, 3, 2 & 2 & 1 & B , AB, B \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", - "A data.frame: 6 × 4\n", + "A data.frame: 8 × 4\n", "\n", "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", "|---|---|---|---|\n", - "| 1, 1 | 1 | -1 | S1, S1 |\n", - "| 2, 2 | 1 | -1 | S2, S2 |\n", - "| 3, 3 | 1 | -1 | S3, S3 |\n", - "| 4, 4 | 1 | -1 | S4, S4 |\n", - "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", - "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "| 1, 1 | 1 | -1 | A, A |\n", + "| 2, 2 | 1 | -1 | B, B |\n", + "| 3, 3 | 1 | -1 | AB, AB |\n", + "| 1, 2, 1 | 2 | 1 | A, B, A |\n", + "| 1, 3, 1 | 2 | 1 | A , AB, A |\n", + "| 1, 3, 2, 1 | 3 | -1 | A , AB, B , A |\n", + "| 2, 3, 1, 2 | 3 | -1 | B , AB, A , B |\n", + "| 2, 3, 2 | 2 | 1 | B , AB, B |\n", "\n" ], "text/plain": [ - " loop length sign loop_subject \n", - "1 1, 1 1 -1 S1, S1 \n", - "2 2, 2 1 -1 S2, S2 \n", - "3 3, 3 1 -1 S3, S3 \n", - "4 4, 4 1 -1 S4, S4 \n", - "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", - "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + " loop length sign loop_subject \n", + "1 1, 1 1 -1 A, A \n", + "2 2, 2 1 -1 B, B \n", + "3 3, 3 1 -1 AB, AB \n", + "4 1, 2, 1 2 1 A, B, A \n", + "5 1, 3, 1 2 1 A , AB, A \n", + "6 1, 3, 2, 1 3 -1 A , AB, B , A \n", + "7 2, 3, 1, 2 3 -1 B , AB, A , B \n", + "8 2, 3, 2 2 1 B , AB, B " ] }, "metadata": {}, @@ -1415,7 +1509,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 63, "id": "8703ce8b", "metadata": { "vscode": { @@ -1433,15 +1527,15 @@ "\t<chr><chr><dbl><chr>\n", "\n", "\n", - "\tS1S1-1inhibition (negative)\n", - "\tS1S4-1inhibition (negative)\n", - "\tS2S1 1activation (positive)\n", - "\tS2S2-1inhibition (negative)\n", - "\tS2S4 1activation (positive)\n", - "\tS3S2 1activation (positive)\n", - "\tS3S3-1inhibition (negative)\n", - "\tS4S3 1activation (positive)\n", - "\tS4S4-1inhibition (negative)\n", + "\tA A -1inhibition (negative)\n", + "\tA B -1inhibition (negative)\n", + "\tA AB 1activation (positive)\n", + "\tB A -1inhibition (negative)\n", + "\tB B -1inhibition (negative)\n", + "\tB AB 1activation (positive)\n", + "\tABA 1activation (positive)\n", + "\tABB 1activation (positive)\n", + "\tABAB-1inhibition (negative)\n", "\n", "\n" ], @@ -1451,15 +1545,15 @@ " from & to & regulation & regulation\\_words\\\\\n", " & & & \\\\\n", "\\hline\n", - "\t S1 & S1 & -1 & inhibition (negative)\\\\\n", - "\t S1 & S4 & -1 & inhibition (negative)\\\\\n", - "\t S2 & S1 & 1 & activation (positive)\\\\\n", - "\t S2 & S2 & -1 & inhibition (negative)\\\\\n", - "\t S2 & S4 & 1 & activation (positive)\\\\\n", - "\t S3 & S2 & 1 & activation (positive)\\\\\n", - "\t S3 & S3 & -1 & inhibition (negative)\\\\\n", - "\t S4 & S3 & 1 & activation (positive)\\\\\n", - "\t S4 & S4 & -1 & inhibition (negative)\\\\\n", + "\t A & A & -1 & inhibition (negative)\\\\\n", + "\t A & B & -1 & inhibition (negative)\\\\\n", + "\t A & AB & 1 & activation (positive)\\\\\n", + "\t B & A & -1 & inhibition (negative)\\\\\n", + "\t B & B & -1 & inhibition (negative)\\\\\n", + "\t B & AB & 1 & activation (positive)\\\\\n", + "\t AB & A & 1 & activation (positive)\\\\\n", + "\t AB & B & 1 & activation (positive)\\\\\n", + "\t AB & AB & -1 & inhibition (negative)\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ @@ -1468,28 +1562,28 @@ "\n", "| from <chr> | to <chr> | regulation <dbl> | regulation_words <chr> |\n", "|---|---|---|---|\n", - "| S1 | S1 | -1 | inhibition (negative) |\n", - "| S1 | S4 | -1 | inhibition (negative) |\n", - "| S2 | S1 | 1 | activation (positive) |\n", - "| S2 | S2 | -1 | inhibition (negative) |\n", - "| S2 | S4 | 1 | activation (positive) |\n", - "| S3 | S2 | 1 | activation (positive) |\n", - "| S3 | S3 | -1 | inhibition (negative) |\n", - "| S4 | S3 | 1 | activation (positive) |\n", - "| S4 | S4 | -1 | inhibition (negative) |\n", + "| A | A | -1 | inhibition (negative) |\n", + "| A | B | -1 | inhibition (negative) |\n", + "| A | AB | 1 | activation (positive) |\n", + "| B | A | -1 | inhibition (negative) |\n", + "| B | B | -1 | inhibition (negative) |\n", + "| B | AB | 1 | activation (positive) |\n", + "| AB | A | 1 | activation (positive) |\n", + "| AB | B | 1 | activation (positive) |\n", + "| AB | AB | -1 | inhibition (negative) |\n", "\n" ], "text/plain": [ " from to regulation regulation_words \n", - "1 S1 S1 -1 inhibition (negative)\n", - "2 S1 S4 -1 inhibition (negative)\n", - "3 S2 S1 1 activation (positive)\n", - "4 S2 S2 -1 inhibition (negative)\n", - "5 S2 S4 1 activation (positive)\n", - "6 S3 S2 1 activation (positive)\n", - "7 S3 S3 -1 inhibition (negative)\n", - "8 S4 S3 1 activation (positive)\n", - "9 S4 S4 -1 inhibition (negative)" + "1 A A -1 inhibition (negative)\n", + "2 A B -1 inhibition (negative)\n", + "3 A AB 1 activation (positive)\n", + "4 B A -1 inhibition (negative)\n", + "5 B B -1 inhibition (negative)\n", + "6 B AB 1 activation (positive)\n", + "7 AB A 1 activation (positive)\n", + "8 AB B 1 activation (positive)\n", + "9 AB AB -1 inhibition (negative)" ] }, "metadata": {}, @@ -1498,7 +1592,7 @@ ], "source": [ "sign_J <- sign(j_matrix)\n", - "labs <- paste0(\"S\", 1:nrow(sign_J))\n", + "labs <- paste0(c(\"A\", \"B\", \"AB\"))\n", "rownames(sign_J) <- labs\n", "colnames(sign_J) <- labs\n", "\n", @@ -1530,7 +1624,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 64, "id": "d57b2e96", "metadata": { "vscode": { @@ -1542,57 +1636,65 @@ "data": { "text/html": [ "\n", - "\n", + "\n", "\n", "\t\n", "\t\n", "\n", "\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", - "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", "\n", "
A data.frame: 6 × 4A data.frame: 8 × 4
looplengthsignloop_subject
<I<list>><dbl><dbl><list>
1, 11-1S1, S1
2, 21-1S2, S2
3, 31-1S3, S3
4, 41-1S4, S4
3, 4, 1,....4-1S3, S4, S1, S2, S3
3, 4, 2, 33 1S3, S4, S2, S3
1, 11-1A, A
2, 21-1B, B
3, 31-1AB, AB
1, 2, 12 1A, B, A
1, 3, 12 1A , AB, A
1, 3, 2, 13-1A , AB, B , A
2, 3, 1, 23-1B , AB, A , B
2, 3, 22 1B , AB, B
\n" ], "text/latex": [ - "A data.frame: 6 × 4\n", + "A data.frame: 8 × 4\n", "\\begin{tabular}{llll}\n", " loop & length & sign & loop\\_subject\\\\\n", " > & & & \\\\\n", "\\hline\n", - "\t 1, 1 & 1 & -1 & S1, S1\\\\\n", - "\t 2, 2 & 1 & -1 & S2, S2\\\\\n", - "\t 3, 3 & 1 & -1 & S3, S3\\\\\n", - "\t 4, 4 & 1 & -1 & S4, S4\\\\\n", - "\t 3, 4, 1,.... & 4 & -1 & S3, S4, S1, S2, S3\\\\\n", - "\t 3, 4, 2, 3 & 3 & 1 & S3, S4, S2, S3\\\\\n", + "\t 1, 1 & 1 & -1 & A, A\\\\\n", + "\t 2, 2 & 1 & -1 & B, B\\\\\n", + "\t 3, 3 & 1 & -1 & AB, AB\\\\\n", + "\t 1, 2, 1 & 2 & 1 & A, B, A\\\\\n", + "\t 1, 3, 1 & 2 & 1 & A , AB, A \\\\\n", + "\t 1, 3, 2, 1 & 3 & -1 & A , AB, B , A \\\\\n", + "\t 2, 3, 1, 2 & 3 & -1 & B , AB, A , B \\\\\n", + "\t 2, 3, 2 & 2 & 1 & B , AB, B \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", - "A data.frame: 6 × 4\n", + "A data.frame: 8 × 4\n", "\n", "| loop <I<list>> | length <dbl> | sign <dbl> | loop_subject <list> |\n", "|---|---|---|---|\n", - "| 1, 1 | 1 | -1 | S1, S1 |\n", - "| 2, 2 | 1 | -1 | S2, S2 |\n", - "| 3, 3 | 1 | -1 | S3, S3 |\n", - "| 4, 4 | 1 | -1 | S4, S4 |\n", - "| 3, 4, 1,.... | 4 | -1 | S3, S4, S1, S2, S3 |\n", - "| 3, 4, 2, 3 | 3 | 1 | S3, S4, S2, S3 |\n", + "| 1, 1 | 1 | -1 | A, A |\n", + "| 2, 2 | 1 | -1 | B, B |\n", + "| 3, 3 | 1 | -1 | AB, AB |\n", + "| 1, 2, 1 | 2 | 1 | A, B, A |\n", + "| 1, 3, 1 | 2 | 1 | A , AB, A |\n", + "| 1, 3, 2, 1 | 3 | -1 | A , AB, B , A |\n", + "| 2, 3, 1, 2 | 3 | -1 | B , AB, A , B |\n", + "| 2, 3, 2 | 2 | 1 | B , AB, B |\n", "\n" ], "text/plain": [ - " loop length sign loop_subject \n", - "1 1, 1 1 -1 S1, S1 \n", - "2 2, 2 1 -1 S2, S2 \n", - "3 3, 3 1 -1 S3, S3 \n", - "4 4, 4 1 -1 S4, S4 \n", - "5 3, 4, 1,.... 4 -1 S3, S4, S1, S2, S3\n", - "6 3, 4, 2, 3 3 1 S3, S4, S2, S3 " + " loop length sign loop_subject \n", + "1 1, 1 1 -1 A, A \n", + "2 2, 2 1 -1 B, B \n", + "3 3, 3 1 -1 AB, AB \n", + "4 1, 2, 1 2 1 A, B, A \n", + "5 1, 3, 1 2 1 A , AB, A \n", + "6 1, 3, 2, 1 3 -1 A , AB, B , A \n", + "7 2, 3, 1, 2 3 -1 B , AB, A , B \n", + "8 2, 3, 2 2 1 B , AB, B " ] }, "metadata": {}, @@ -1602,6 +1704,110 @@ "source": [ "df" ] + }, + { + "cell_type": "code", + "execution_count": 65, + "id": "ec36d7d7", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 7
lengthnum_loopsnum_loops_positivenum_loops_negativeloopsloops_positiveloops_negative
<dbl><int><int><int><I<named list>><I<named list>><I<named list>>
11303c(\"A\", \".... c(\"A\", \"....
22330c(\"A\", \"....c(\"A\", \"....
33202c(\"A\", \".... c(\"A\", \"....
\n" + ], + "text/latex": [ + "A data.frame: 3 × 7\n", + "\\begin{tabular}{r|lllllll}\n", + " & length & num\\_loops & num\\_loops\\_positive & num\\_loops\\_negative & loops & loops\\_positive & loops\\_negative\\\\\n", + " & & & & & > & > & >\\\\\n", + "\\hline\n", + "\t1 & 1 & 3 & 0 & 3 & c(\"A\", \".... & & c(\"A\", \"....\\\\\n", + "\t2 & 2 & 3 & 3 & 0 & c(\"A\", \".... & c(\"A\", \".... & \\\\\n", + "\t3 & 3 & 2 & 0 & 2 & c(\"A\", \".... & & c(\"A\", \"....\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 7\n", + "\n", + "| | length <dbl> | num_loops <int> | num_loops_positive <int> | num_loops_negative <int> | loops <I<named list>> | loops_positive <I<named list>> | loops_negative <I<named list>> |\n", + "|---|---|---|---|---|---|---|---|\n", + "| 1 | 1 | 3 | 0 | 3 | c(\"A\", \".... | | c(\"A\", \".... |\n", + "| 2 | 2 | 3 | 3 | 0 | c(\"A\", \".... | c(\"A\", \".... | |\n", + "| 3 | 3 | 2 | 0 | 2 | c(\"A\", \".... | | c(\"A\", \".... |\n", + "\n" + ], + "text/plain": [ + " length num_loops num_loops_positive num_loops_negative loops \n", + "1 1 3 0 3 c(\"A\", \"....\n", + "2 2 3 3 0 c(\"A\", \"....\n", + "3 3 2 0 2 c(\"A\", \"....\n", + " loops_positive loops_negative\n", + "1 c(\"A\", \".... \n", + "2 c(\"A\", \".... \n", + "3 c(\"A\", \".... " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "split_by_len <- split(df, df$length)\n", + "\n", + "loop_summary_extended <- data.frame(\n", + " length = as.numeric(names(split_by_len)),\n", + " num_loops = vapply(split_by_len, nrow, integer(1)),\n", + " loops = I(lapply(split_by_len, function(x) x$loop_subject)),\n", + " stringsAsFactors = FALSE\n", + ")\n", + "\n", + "loop_summary_extended$num_loops_positive <- vapply(\n", + " split_by_len,\n", + " function(x) sum(x$sign > 0),\n", + " integer(1)\n", + ")\n", + "\n", + "loop_summary_extended$num_loops_negative <- vapply(\n", + " split_by_len,\n", + " function(x) sum(x$sign < 0),\n", + " integer(1)\n", + ")\n", + "\n", + "loop_summary_extended$loops_positive <- I(lapply(\n", + " split_by_len,\n", + " function(x) x$loop_subject[x$sign > 0]\n", + "))\n", + "\n", + "loop_summary_extended$loops_negative <- I(lapply(\n", + " split_by_len,\n", + " function(x) x$loop_subject[x$sign < 0]\n", + "))\n", + "\n", + "loop_summary_extended <- loop_summary_extended[\n", + " order(loop_summary_extended$length),\n", + " c(\"length\",\"num_loops\",\"num_loops_positive\",\"num_loops_negative\",\n", + " \"loops\",\"loops_positive\",\"loops_negative\")\n", + "]\n", + "\n", + "loop_summary_extended\n" + ] } ], "metadata": { diff --git a/examples/model_2_perturbation_A.png b/examples/model_2_perturbation_A.png index 01906a0df5067c242c4bcafa22a7af42ffaeb528..7923386af100998971d7ad171db2ade47cb91ccc 100644 GIT binary patch literal 42925 zcmdqJc{tSV`#&tZgjR}>RPM4&izVwM;VwxV#yUgU8hiF-#<3q5q@$m9;fG3gsTb0?^w(wrQcwHC#$i}9|#%9l^rpBfQKBL&|?b+8a9b@J@}*p7oOT1^yGo`mncGvj_hvP>TZJ-S(jWdL!_Z)qDLPd;2Kx$36;t7TAL} z1>l<*rN$NohOlRgvIn267Ew`ZtR_(fQ3c?;JF2@NsvCSV3+&kn?9~dQz_)z?c+Gkb zzPdq^f^P81EMOKCFuMzw%0(0YAG%i7J#VY9Djb&7)pTX{AJI=1gBy6BmZd3CC$NJup*g zurlk?R4={gK+$*fMEj_U&GvS1dF_GGGX3I-CH6_?(@_g{d{tN-_SwW`Lgp* z3`G;If@c}dE4+r&jh7sT=)-Ye|D)3stJC3)PS+6kr;@aw0$Q;q 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results in R (Model 1,2,3,5,6). Fix some minor bugs in Python. Add literatures. --- examples/model_1_POSm4_R.ipynb | 4 +- .../model_3_complex_formation_extend_R.ipynb | 1797 ++++-- examples/model_5_MAPK_reduced_R.ipynb | 5735 +++++++++++++++++ examples/model_6_calcium_oscillations_R.ipynb | 3491 ++++++++++ 4 files changed, 10585 insertions(+), 442 deletions(-) create mode 100644 examples/model_5_MAPK_reduced_R.ipynb create mode 100644 examples/model_6_calcium_oscillations_R.ipynb diff --git a/examples/model_1_POSm4_R.ipynb b/examples/model_1_POSm4_R.ipynb index be2833e..2a3862c 100644 --- a/examples/model_1_POSm4_R.ipynb +++ b/examples/model_1_POSm4_R.ipynb @@ -816,7 +816,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": null, "id": "4b596080", "metadata": { "vscode": { @@ -869,7 +869,7 @@ " scale_y_log10(\n", " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", - " ) + # ← log10 transformation\n", + " ) + # log10 transformation\n", " labs(\n", " title = \"Dynamics of the 4-Variable Positive Feedback Chain\",\n", " x = \"Time\",\n", diff --git a/examples/model_3_complex_formation_extend_R.ipynb b/examples/model_3_complex_formation_extend_R.ipynb index bc14c67..e5f61fe 100644 --- a/examples/model_3_complex_formation_extend_R.ipynb +++ b/examples/model_3_complex_formation_extend_R.ipynb @@ -2,16 +2,25 @@ "cells": [ { "cell_type": "markdown", - "id": "53d51c8d", + "id": "5c5107a0", "metadata": {}, "source": [ - "## 0. Libraries" + "## **0. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "0aa853b2", + "metadata": {}, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" ] }, { "cell_type": "code", - "execution_count": 25, - "id": "b54689cf", + "execution_count": null, + "id": "ad430870", "metadata": { "vscode": { "languageId": "r" @@ -19,32 +28,138 @@ }, "outputs": [], "source": [ - "suppressPackageStartupMessages({\n", - " library(deSolve) # ODE solver\n", - " library(numDeriv) # numerical Jacobian (jacobian)\n", - " library(dplyr)\n", - " library(tidyr)\n", - " library(purrr)\n", - " library(LoopDetectR)\n", - "})" + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" ] }, { - "cell_type": "markdown", - "id": "bf752a71", + "cell_type": "code", + "execution_count": null, + "id": "f2d7c70f", "metadata": { "vscode": { "languageId": "r" } }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], "source": [ - "## 1. Configuration" + "# Download and install\n", + "install.packages(\"LoopDetectR\")" ] }, { "cell_type": "code", - "execution_count": 24, - "id": "2185219a", + "execution_count": null, + "id": "1c741284", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1d32152b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + } + ], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")\n", + "library(deSolve)\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3eb6dbbb", "metadata": { "vscode": { "languageId": "r" @@ -52,15 +167,15 @@ }, "outputs": [], "source": [ - "colors <- c(\"#EE7733\", \"#0077BB\", \"#33BBEE\", \"#EE3377\", \"#CC3311\", \"#009988\", \"#BBBBBB\")" + "colors <- c('#EE7733', '#0077BB', '#33BBEE', '#EE3377', '#CC3311', '#009988', '#BBBBBB')" ] }, { "cell_type": "markdown", - "id": "a184ae0d", + "id": "de63ff1e", "metadata": {}, "source": [ - "## 2. Main reproduction" + "## **1. Model definition**" ] }, { @@ -107,20 +222,6 @@ "\n" ] }, - { - "cell_type": "code", - "execution_count": null, - "id": "f17d4fdf", - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], - "source": [ - "#### " - ] - }, { "cell_type": "code", "execution_count": 3, @@ -132,7 +233,7 @@ }, "outputs": [], "source": [ - "model_complex_formation_act_deact_cycle <- function(t, y, params) {\n", + "func_varusai15 <- function(t, y, params) {\n", " A <- y[1]\n", " B <- y[2]\n", " AB <- y[3]\n", @@ -146,51 +247,34 @@ " kn2 <- params[6]\n", " kn3 <- params[7]\n", "\n", + " dx <- rep(0,4)\n", + "\n", " dAdt <- -k1 * A * B + k2 * AB\n", " dBdt <- -k1 * A * B + k2 * AB + k3 * A * (B_star / (B_star + kn1)) - k4 * kn3 * (B / (B + kn2))\n", " dABdt <- k1 * A * B - k2 * AB\n", " dB_stardt <- -k3 * A * (B_star / (B_star + kn1)) + k4 * kn3 * (B / (B + kn2))\n", "\n", - " list(c(dAdt, dBdt, dABdt, dB_stardt))\n", - "}\n", - "\n", - "solve_complex_formation_act_deact_cycle <- function(initial_conditions, time_points, params) {\n", - " y0 <- c(A = initial_conditions[1],\n", - " B = initial_conditions[2],\n", - " AB = initial_conditions[3],\n", - " B_star = initial_conditions[4])\n", - "\n", - " out <- deSolve::ode(\n", - " y = y0,\n", - " times = time_points,\n", - " func = model_complex_formation_act_deact_cycle,\n", - " parms = params,\n", - " method = \"lsoda\"\n", - " )\n", - " out <- as.data.frame(out)\n", - " out\n", + " # list(c(dAdt, dBdt, dABdt, dB_stardt))\n", + " dx[1] <- dAdt\n", + " dx[2] <- dBdt\n", + " dx[3] <- dABdt\n", + " dx[4] <- dB_stardt\n", + " return(dx)\n", "}" ] }, { - "cell_type": "code", - "execution_count": null, - "id": "1e74389f", - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [], + "cell_type": "markdown", + "id": "44e7e155", + "metadata": {}, "source": [ - "res_tab <- find_loops_vset(func_POSm4,vset=list(s_star),t=1,klin=klin,\n", - " knonlin=knonlin,max_num_loops=10)" + "## **2. Result reproduction**" ] }, { "cell_type": "code", - "execution_count": null, - "id": "4ff19c48", + "execution_count": 4, + "id": "4e5b9062", "metadata": { "vscode": { "languageId": "r" @@ -215,28 +299,29 @@ ] }, { - "cell_type": "code", - "execution_count": 5, - "id": "1857ac28", + "cell_type": "markdown", + "id": "b927c538", + "metadata": {}, + "source": [ + "### **2.1. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "b9c9522a", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], "source": [ - "time_points_act_deact <- seq(0, 5000, length.out = 1001)\n", - "sol_act_deact <- solve_complex_formation_act_deact_cycle(\n", - " initial_conditions = initial_conditions_act_deact,\n", - " time_points = time_points_act_deact,\n", - " params = params_act_deact_unstimulated\n", - ")" + "#### **2.1.1. Loop structure**" ] }, { "cell_type": "code", - "execution_count": 6, - "id": "e20ac2df", + "execution_count": 113, + "id": "6c2540e5", "metadata": { "vscode": { "languageId": "r" @@ -245,72 +330,245 @@ "outputs": [ { "data": { - "image/png": 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", + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 10 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
3, 31-1
4, 41-1
1, 2, 12 1
1, 3, 12 1
1, 3, 2, 13-1
2, 3, 1, 23-1
2, 3, 22 1
1, 4, 2, 13 1
\n" + ], + "text/latex": [ + "A data.frame: 10 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 1, 3, 1 & 2 & 1\\\\\n", + "\t 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t 2, 3, 2 & 2 & 1\\\\\n", + "\t 1, 4, 2, 1 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 10 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "| 1, 3, 1 | 2 | 1 |\n", + "| 1, 3, 2, 1 | 3 | -1 |\n", + "| 2, 3, 1, 2 | 3 | -1 |\n", + "| 2, 3, 2 | 2 | 1 |\n", + "| 1, 4, 2, 1 | 3 | 1 |\n", + "\n" + ], "text/plain": [ - "Plot with title \"Concentration vs Time for Activation-Deactivation Cycle Model\"" + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 3, 3 1 -1 \n", + "4 4, 4 1 -1 \n", + "5 1, 2, 1 2 1 \n", + "6 1, 3, 1 2 1 \n", + "7 1, 3, 2, 1 3 -1 \n", + "8 2, 3, 1, 2 3 -1 \n", + "9 2, 3, 2 2 1 \n", + "10 1, 4, 2, 1 3 1 " ] }, - "metadata": { - "image/png": { - "height": 420, - "width": 420 - } + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute loops\n", + "res_tab <- find_loops_vset(func_varusai15,vset=list(initial_conditions_act_deact),t=1,params=params_act_deact_unstimulated,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]] \n", + "# To access a specific loop representation: e.g., the sixth loop, add [6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "3d056cc3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 3
len_1len_2len_3
<dbl><dbl><dbl>
all433
pos031
neg402
\n" + ], + "text/latex": [ + "A data.frame: 3 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & len\\_1 & len\\_2 & len\\_3\\\\\n", + " & & & \\\\\n", + "\\hline\n", + "\tall & 4 & 3 & 3\\\\\n", + "\tpos & 0 & 3 & 1\\\\\n", + "\tneg & 4 & 0 & 2\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 3\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> |\n", + "|---|---|---|---|\n", + "| all | 4 | 3 | 3 |\n", + "| pos | 0 | 3 | 1 |\n", + "| neg | 4 | 0 | 2 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3\n", + "all 4 3 3 \n", + "pos 0 3 1 \n", + "neg 4 0 2 " + ] }, + "metadata": {}, "output_type": "display_data" } ], "source": [ - "matplot(\n", - " sol_act_deact$time,\n", - " sol_act_deact[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", - " type = \"l\", lwd = 2, log = \"y\",\n", - " xlab = \"Time\", ylab = \"Concentration\",\n", - " main = \"Concentration vs Time for Activation-Deactivation Cycle Model\"\n", - ")\n", - "legend(\"left\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")" + "loop_summary(res_tab$loop_rep[[1]])" ] }, { "cell_type": "code", - "execution_count": 7, - "id": "c824b68e", + "execution_count": 33, + "id": "e9a5ecf2", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 6 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
5 1, 2, 12 1
71, 3, 2, 13-1
82, 3, 1, 23-1
9 2, 3, 22 1
101, 4, 2, 13 1
\n" + ], + "text/latex": [ + "A data.frame: 6 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t5 & 1, 2, 1 & 2 & 1\\\\\n", + "\t7 & 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t8 & 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t9 & 2, 3, 2 & 2 & 1\\\\\n", + "\t10 & 1, 4, 2, 1 & 3 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 6 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 5 | 1, 2, 1 | 2 | 1 |\n", + "| 7 | 1, 3, 2, 1 | 3 | -1 |\n", + "| 8 | 2, 3, 1, 2 | 3 | -1 |\n", + "| 9 | 2, 3, 2 | 2 | 1 |\n", + "| 10 | 1, 4, 2, 1 | 3 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "5 1, 2, 1 2 1 \n", + "7 1, 3, 2, 1 3 -1 \n", + "8 2, 3, 1, 2 3 -1 \n", + "9 2, 3, 2 2 1 \n", + "10 1, 4, 2, 1 3 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "time_1 <- seq(-1000, 0, length.out = 500)\n", - "time_2 <- seq(0, 2000, length.out = 1000)\n", - "\n", - "# Continue from stabilized final state\n", - "y_stable <- as.numeric(sol_act_deact[nrow(sol_act_deact), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", - "\n", - "sol_unstimulated <- solve_complex_formation_act_deact_cycle(\n", - " initial_conditions = y_stable,\n", - " time_points = time_1,\n", - " params = params_act_deact_unstimulated\n", - ")\n", - "\n", - "y_at_0 <- as.numeric(sol_unstimulated[nrow(sol_unstimulated), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", - "\n", - "sol_stimulated <- solve_complex_formation_act_deact_cycle(\n", - " initial_conditions = y_at_0,\n", - " time_points = time_2,\n", - " params = params_act_deact_stimulated\n", - ")\n", + "# Index of node of interest\n", + "noi <- 2 \n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "9f0fc026", + "metadata": {}, + "source": [ + "#### **2.1.2. Calculating the Jacobian matrix**\n", "\n", - "# Combine full trajectory\n", - "time_full <- c(time_1, time_2)\n", - "sol_full <- bind_rows(sol_unstimulated, sol_stimulated) %>%\n", - " select(time, A, B, AB, B_star)" + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" ] }, { "cell_type": "code", - "execution_count": 8, - "id": "c5272ed2", + "execution_count": 20, + "id": "eefb6816", "metadata": { "vscode": { "languageId": "r" @@ -319,35 +577,175 @@ "outputs": [ { "data": { - "image/png": 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    A data.frame: 10 × 3
    looplengthsign
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    1, 11-1
    2, 21-1
    3, 31-1
    4, 41-1
    1, 2, 12 1
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    A matrix: 4 × 4 of type dbl
    -1-1 1 0
    -1-1 1 1
    1 1-1 0
    -1 1 0-1
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\n" + ], + "text/latex": [ + "\\begin{description}\n", + "\\item[\\$loop\\_rep] \\begin{enumerate}\n", + "\\item A data.frame: 10 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 1, 3, 1 & 2 & 1\\\\\n", + "\t 1, 3, 2, 1 & 3 & -1\\\\\n", + "\t 2, 3, 1, 2 & 3 & -1\\\\\n", + "\t 2, 3, 2 & 2 & 1\\\\\n", + "\t 1, 4, 2, 1 & 3 & 1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$loop\\_rep\\_index] 1\n", + "\\item[\\$jac\\_rep] \\begin{enumerate}\n", + "\\item A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & -1 & 1 & 0\\\\\n", + "\t -1 & -1 & 1 & 1\\\\\n", + "\t 1 & 1 & -1 & 0\\\\\n", + "\t -1 & 1 & 0 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$jac\\_rep\\_index] 1\n", + "\\end{description}\n" + ], + "text/markdown": [ + "$loop_rep\n", + ": 1. \n", + "A data.frame: 10 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "| 1, 3, 1 | 2 | 1 |\n", + "| 1, 3, 2, 1 | 3 | -1 |\n", + "| 2, 3, 1, 2 | 3 | -1 |\n", + "| 2, 3, 2 | 2 | 1 |\n", + "| 1, 4, 2, 1 | 3 | 1 |\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "$loop_rep_index\n", + ": 1\n", + "$jac_rep\n", + ": 1. \n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | -1 | 1 | 0 |\n", + "| -1 | -1 | 1 | 1 |\n", + "| 1 | 1 | -1 | 0 |\n", + "| -1 | 1 | 0 | -1 |\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "$jac_rep_index\n", + ": 1\n", + "\n", + "\n" + ], "text/plain": [ - "Plot with title \"Concentration vs Time (Unstimulated then Stimulated)\"" + "$loop_rep\n", + "$loop_rep[[1]]\n", + " loop length sign\n", + "1 1, 1 1 -1\n", + "2 2, 2 1 -1\n", + "3 3, 3 1 -1\n", + "4 4, 4 1 -1\n", + "5 1, 2, 1 2 1\n", + "6 1, 3, 1 2 1\n", + "7 1, 3, 2, 1 3 -1\n", + "8 2, 3, 1, 2 3 -1\n", + "9 2, 3, 2 2 1\n", + "10 1, 4, 2, 1 3 1\n", + "\n", + "\n", + "$loop_rep_index\n", + "[1] 1\n", + "\n", + "$jac_rep\n", + "$jac_rep[[1]]\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0\n", + "[2,] -1 -1 1 1\n", + "[3,] 1 1 -1 0\n", + "[4,] -1 1 0 -1\n", + "\n", + "\n", + "$jac_rep_index\n", + "[1] 1\n" ] }, - "metadata": { - "image/png": { - "height": 420, - "width": 420 - } - }, + "metadata": {}, "output_type": "display_data" } ], "source": [ - "matplot(\n", - " sol_full$time,\n", - " sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", - " type = \"l\", lwd = 2, log = \"y\",\n", - " xlab = \"Time\", ylab = \"Concentration\",\n", - " main = \"Concentration vs Time (Unstimulated then Stimulated)\"\n", - ")\n", - "legend(\"topleft\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")" + "res_tab" ] }, { "cell_type": "code", - "execution_count": 9, - "id": "0ab26b0c", + "execution_count": 21, + "id": "05e68bc3", "metadata": { "vscode": { "languageId": "r" @@ -355,154 +753,185 @@ }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "Unstimulated conditions:\n", - "Jacobian matrix:\n", - " [,1] [,2] [,3] [,4]\n", - "[1,] -6.3289739 -3.853766e-06 0.000227335 0.000000000\n", - "[2,] -5.5766599 -3.869107e-06 0.000227335 0.002138019\n", - "[3,] 6.3289739 3.853766e-06 -0.000227335 0.000000000\n", - "[4,] -0.7523141 1.534086e-08 0.000000000 -0.002138019\n", - "Signed Jacobian matrix:\n", - " [,1] [,2] [,3] [,4]\n", - "[1,] -1 -1 1 0\n", - "[2,] -1 -1 1 1\n", - "[3,] 1 1 -1 0\n", - "[4,] -1 1 0 -1\n" - ] + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1-1 1 0
-1-1 1 1
1 1-1 0
-1 1 0-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & -1 & 1 & 0\\\\\n", + "\t -1 & -1 & 1 & 1\\\\\n", + "\t 1 & 1 & -1 & 0\\\\\n", + "\t -1 & 1 & 0 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | -1 | 1 | 0 |\n", + "| -1 | -1 | 1 | 1 |\n", + "| 1 | 1 | -1 | 0 |\n", + "| -1 | 1 | 0 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0 \n", + "[2,] -1 -1 1 1 \n", + "[3,] 1 1 -1 0 \n", + "[4,] -1 1 0 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "# Numerical Jacobian + signed Jacobian\n", - "vf <- function(y, params) {\n", - " # deSolve model returns list(c(...)); unwrap\n", - " model_complex_formation_act_deact_cycle(t = 0, y = y, params = params)[[1]]\n", - "}\n", - "\n", - "# Evaluate Jacobian at the stabilized endpoint (same as Python: sol_act_deact.y[:, -1])\n", - "y_eval_un <- as.numeric(sol_act_deact[nrow(sol_act_deact), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", - "J_un <- numDeriv::jacobian(func = function(x) vf(x, params_act_deact_unstimulated), x = y_eval_un)\n", - "Jsign_un <- sign(J_un)\n", - "\n", - "# Evaluate Jacobian at end of sol_unstimulated (t=0-) for stimulated params (Python used sol_unstimulated.y[:, -1])\n", - "y_eval_st <- as.numeric(sol_unstimulated[nrow(sol_unstimulated), c(\"A\", \"B\", \"AB\", \"B_star\")])\n", - "J_st <- numDeriv::jacobian(func = function(x) vf(x, params_act_deact_stimulated), x = y_eval_st)\n", - "Jsign_st <- sign(J_st)\n", - "\n", - "cat(\"Unstimulated conditions:\\n\")\n", - "cat(\"Jacobian matrix:\\n\"); print(J_un)\n", - "cat(\"Signed Jacobian matrix:\\n\"); print(Jsign_un)" + "# The corresponding signed Jacobian matrix\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "b4802333", + "metadata": {}, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003]." ] }, { "cell_type": "code", - "execution_count": 11, - "id": "b7ddb306", + "execution_count": 52, + "id": "adbc93e2", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "
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A matrix: 4 × 4 of type dbl
-6.4374000-1.072900e-01 0.000227335 0.00000
-6.3181048-1.072903e-01 0.000227335 59.63689
6.4374000 1.072900e-01-0.000227335 0.00000
-0.1192952 2.969035e-07 0.000000000-59.63689
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -6.4374000 & -1.072900e-01 & 0.000227335 & 0.00000\\\\\n", + "\t -6.3181048 & -1.072903e-01 & 0.000227335 & 59.63689\\\\\n", + "\t 6.4374000 & 1.072900e-01 & -0.000227335 & 0.00000\\\\\n", + "\t -0.1192952 & 2.969035e-07 & 0.000000000 & -59.63689\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -6.4374000 | -1.072900e-01 | 0.000227335 | 0.00000 |\n", + "| -6.3181048 | -1.072903e-01 | 0.000227335 | 59.63689 |\n", + "| 6.4374000 | 1.072900e-01 | -0.000227335 | 0.00000 |\n", + "| -0.1192952 | 2.969035e-07 | 0.000000000 | -59.63689 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] \n", + "[1,] -6.4374000 -1.072900e-01 0.000227335 0.00000\n", + "[2,] -6.3181048 -1.072903e-01 0.000227335 59.63689\n", + "[3,] 6.4374000 1.072900e-01 -0.000227335 0.00000\n", + "[4,] -0.1192952 2.969035e-07 0.000000000 -59.63689" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "loop_summary_table <- function(loop_df) {\n", - " loop_df %>%\n", - " mutate(length = as.integer(length),\n", - " pos = sign > 0,\n", - " neg = sign < 0) %>%\n", - " group_by(length) %>%\n", - " summarise(\n", - " total = n(),\n", - " pos = sum(pos),\n", - " neg = sum(neg),\n", - " .groups = \"drop\"\n", - " ) %>%\n", - " arrange(length)\n", - "}" + "j_matrix <- numDeriv::jacobian(func_varusai15, initial_conditions_act_deact,method=\"complex\",\n", + " t=1,params=params_act_deact_stimulated)\n", + "j_matrix" ] }, { "cell_type": "code", - "execution_count": 23, - "id": "1a5a32c8", + "execution_count": 26, + "id": "d9a4b8c8", "metadata": { "vscode": { "languageId": "r" @@ -510,68 +939,132 @@ }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Unstimulated conditions:\n" - ] - }, + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 4 × 4 of type dbl
-1-1 1 0
-1-1 1 1
1 1-1 0
-1 1 0-1
\n" + ], + "text/latex": [ + "A matrix: 4 × 4 of type dbl\n", + "\\begin{tabular}{llll}\n", + "\t -1 & -1 & 1 & 0\\\\\n", + "\t -1 & -1 & 1 & 1\\\\\n", + "\t 1 & 1 & -1 & 0\\\\\n", + "\t -1 & 1 & 0 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 4 × 4 of type dbl\n", + "\n", + "| -1 | -1 | 1 | 0 |\n", + "| -1 | -1 | 1 | 1 |\n", + "| 1 | 1 | -1 | 0 |\n", + "| -1 | 1 | 0 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0 \n", + "[2,] -1 -1 1 1 \n", + "[3,] 1 1 -1 0 \n", + "[4,] -1 1 0 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "9fb5ce0e", + "metadata": {}, + "source": [ + "#### **2.1.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "cf1a9580", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "\u001b[90m# A tibble: 25 × 3\u001b[39m\n", - " loop length sign\n", - " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", - "\u001b[90m 1\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", - "\u001b[90m 2\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", - "\u001b[90m 3\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", - "\u001b[90m 4\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m\n", - "\u001b[90m 5\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m 6\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m 7\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m 8\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m 9\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m10\u001b[39m \u001b[90m\u001b[39m 2 1\n", - "\u001b[90m# ℹ 15 more rows\u001b[39m\n", - "\n", - "Loop summary for unstimulated conditions:\n", - "\u001b[90m# A tibble: 4 × 4\u001b[39m\n", - " length total pos neg\n", - " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", - "\u001b[90m1\u001b[39m 1 4 0 4\n", - "\u001b[90m2\u001b[39m 2 8 8 0\n", - "\u001b[90m3\u001b[39m 3 9 3 6\n", - "\u001b[90m4\u001b[39m 4 4 0 4\n" - ] + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" } ], "source": [ - "cat(\"\\nUnstimulated conditions:\\n\")\n", - "res_tab_complex_loop_rep <- find_loops_signed(Jsign_un, max_len = 4)\n", - "print(res_tab_complex_loop_rep)\n", + "matplot(\n", + " sol[,1], sol[,2:5],\n", + " type = \"l\",\n", + " lty = 1,\n", + " log = \"y\",\n", + " xlab = \"Time\",\n", + " ylab = \"Concentration\",\n", + "\n", + ")\n", "\n", - "cat(\"\\nLoop summary for unstimulated conditions:\\n\")\n", - "print(loop_summary_table(res_tab_complex_loop_rep))" + "legend(\n", + " \"topright\",\n", + " legend = c(\"A\", \"B\", \"AB\", \"B*\"),\n", + " col = 1:4,\n", + " lty = 1\n", + ")" ] }, { - "cell_type": "markdown", - "id": "c5046567", + "cell_type": "code", + "execution_count": 46, + "id": "1f18ff68", "metadata": { "vscode": { "languageId": "r" } }, + "outputs": [], "source": [ - "#### **2.7. Search time where signed Jacobian structure changes**" + "sol_for_plot <- as.data.frame(sol)\n", + "\n", + "# rename columns for clarity\n", + "colnames(sol_for_plot) <- c(\"time\", \"A\", \"B\", \"AB\", \"B*\")\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = A:`B*`, names_to = \"species\", values_to = \"value\")" ] }, { "cell_type": "code", - "execution_count": 14, - "id": "602f9742", + "execution_count": 47, + "id": "273651c0", "metadata": { "vscode": { "languageId": "r" @@ -579,79 +1072,116 @@ }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "At time 234.23 after the stimulus, the signed Jacobian structure changes.\n", - "Jacobian matrix at this time:\n", - " [,1] [,2] [,3] [,4]\n", - "[1,] -6.31881288 -3.859960e-06 0.000227335 0.000000000\n", - "[2,] 0.02316377 -4.167731e-06 0.000227335 0.002105474\n", - "[3,] 6.31881288 3.859960e-06 -0.000227335 0.000000000\n", - "[4,] -6.34197665 3.077716e-07 0.000000000 -0.002105474\n", - "Signed Jacobian matrix at this time:\n", - " [,1] [,2] [,3] [,4]\n", - "[1,] -1 -1 1 0\n", - "[2,] 1 -1 1 1\n", - "[3,] 1 1 -1 0\n", - "[4,] -1 1 0 -1\n", - "Loop summary at this time:\n", - "\u001b[90m# A tibble: 4 × 4\u001b[39m\n", - " length total pos neg\n", - " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m\n", - "\u001b[90m1\u001b[39m 1 4 0 4\n", - "\u001b[90m2\u001b[39m 2 8 6 2\n", - "\u001b[90m3\u001b[39m 3 9 6 3\n", - "\u001b[90m4\u001b[39m 4 4 0 4\n" - ] + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" } ], "source": [ - "Jsign_ref_un <- Jsign_un\n", - "Jsign_ref_st <- Jsign_st\n", - "\n", - "t_change <- NA_real_\n", - "J_change <- NULL\n", - "Jsign_change <- NULL\n", - "summary_change <- NULL\n", - "\n", - "# Use a modest stride to avoid heavy computation; set stride=1 for exact match (slower).\n", - "stride <- 1L\n", + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "colors <- c(\n", + " A = \"#EE7733\",\n", + " B = \"#0077BB\",\n", + " AB = \"#33BBEE\",\n", + " `B*` = \"#EE3377\"\n", + ")\n", "\n", - "for (idx in seq(1, nrow(sol_full), by = stride)) {\n", - " t_now <- sol_full$time[idx]\n", - " y_now <- as.numeric(sol_full[idx, c(\"A\", \"B\", \"AB\", \"B_star\")])\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(linewidth = 3) +\n", + " ## vertical dashed line\n", + " # geom_vline(\n", + " # xintercept = perturbation_point,\n", + " # linetype = \"dashed\",\n", + " # colour = \"black\",\n", + " # linewidth = 0.7\n", + " # ) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 5000, 1000),\n", + " minor_breaks = seq(0, 5000, 500),\n", + " limits = c(0, 5000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 5000), clip = \"on\") +\n", + " scale_y_log10(\n", + " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", + " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", + " ) + # log10 transformation\n", + " labs(\n", + " title = \"Dynamics of the 4-Variable Complex Formation Model\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", "\n", - " params_now <- if (t_now < 0) params_act_deact_unstimulated else params_act_deact_stimulated\n", - " J_now <- numDeriv::jacobian(func = function(x) vf(x, params_now), x = y_now)\n", - " Jsign_now <- sign(J_now)\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", "\n", - " Jsign_ref <- if (t_now < 0) Jsign_ref_un else Jsign_ref_st\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "markdown", + "id": "6f592bea", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **2.2. Stimulated Condition**\n", "\n", - " if (!isTRUE(all.equal(Jsign_now, Jsign_ref))) {\n", - " t_change <- t_now\n", - " J_change <- J_now\n", - " Jsign_change <- Jsign_now\n", - " summary_change <- loop_summary_table(find_loops_signed(Jsign_now, max_len = 4))\n", - " break\n", - " }\n", - "}\n", + "When introducing a stimulus at t=0 which increases kn3 from 1 to 20" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "id": "743969e4", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Now, draw temporal dynamics for unstimulated conditions from t=[-1000, 0], and then stimulated conditions from t=[0, 2000]\n", + "time_1 <- seq(-1000, 0, 0.1)\n", + "time_2 <- seq(0, 2000, 0.1)\n", + "sol_unstimulated <- deSolve::ode(y = as.numeric(s_star_end), times = time_1, func = func_list, \n", + " parms=params_act_deact_unstimulated)\n", + "sol_stimulated <- deSolve::ode(y = sol_unstimulated[nrow(sol_unstimulated),2:5], times = time_2, func = function(t,x,params){list(func_varusai15(t,x,params_act_deact_stimulated))}, \n", + " parms=params_act_deact_stimulated)\n", "\n", - "if (!is.na(t_change)) {\n", - " cat(sprintf(\"\\nAt time %.2f after the stimulus, the signed Jacobian structure changes.\\n\", t_change))\n", - " cat(\"Jacobian matrix at this time:\\n\"); print(J_change)\n", - " cat(\"Signed Jacobian matrix at this time:\\n\"); print(Jsign_change)\n", - " cat(\"Loop summary at this time:\\n\"); print(summary_change)\n", - "} else {\n", - " cat(\"\\nNo signed Jacobian structure change detected on the scanned grid.\\n\")\n", - "}\n" + "time_full <- c(time_1, time_2)\n", + "sol_full <- rbind(sol_unstimulated, sol_stimulated) " ] }, { "cell_type": "code", - "execution_count": 15, - "id": "cae9464f", + "execution_count": 72, + "id": "dccf2428", "metadata": { "vscode": { "languageId": "r" @@ -660,43 +1190,80 @@ "outputs": [ { "data": { - "image/png": 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yu+YRJHiGXjtAgCABAgQJEHAapOs5rnu+4+TDbZEJEjzjMEhl2DuLNN8RTpDgGYdBSkxwaTrtiiyY7wgnSPCMwyAFvb7vfP7GyAQJnnE61u7dC1kVwEbYIgECbo+RsqJ+xjES9sZl93fU67ULZ28xTpDgGbfnkZL6PFIQnzmPhH1hZAMgQJAAAfdBmu/4llQBuEaQAAGCBAgQJEDAbZCWXUOIIME7vxOkxdfqAn4Pu3aAAEECBAgSIECQAAGGCAECBAkQcB6kLK727eLCYhWAc66DFDVniUwwmySCBM84DlJqorIKUmpOtqoANuA4SIEpm247riKEXXEcpHq3jiBhdxwHKWy3SLkJbVUBbGCbY6QsMKmtKoANuO61i7mIPvZok/NIJr7YrAJwjpENgABBAgQIEiBAkAABggQIOL3R2OLrmxAkeMZhkFKChN1yuWuXB/OnYQVVANtweoyUz9+nT1EFsAm3nQ1p7zaylqoAtkCvHSDgW5D+/ZdHHrd7fMuzIP3bzhCPPG7x+J5nQQJ+E0ECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAg4DdL1HJtKnFxtVQFswmGQytA8RVaqADbiMEiJCS55/azIApPYqALYiMMgBSZ/PM9NYKMKYCMOg2TMuxeyKoCNsEUCBNweI2VF/YxjJOyNy+7vqNdrF5ZWqgC24fY8UlKfRwriM+eRsC+MbAAECBIgwBAhQIAhQoAAQ4QAAU7IAgIMEQIE2CIBlX/ah1b3auqvUxgiBG99/MQv/2v3j/8MJp3+6ySGCOG3fJuD7vlgyq//OpeRRRgihG0I0uG2wfMY2QDrpjLjRTq+QJAgNLmZmc7MzrgP0nzHt6QKuLFwM3MIBAlfmjucOS6ChM/edRRv2qjfsjZI58dI1MVvJ0j+mNpjw5SVQTo/zwwteuvCqQnShia2PvhoZZACk3711pkgmb7vW4XVhn1sGzfGNyuD9IePPLt2P2d07LNpW3y1MkixmR3qM/l2gvQ7lINkjm1lkIog+jDa5/XtBOkHDHoRtm7MHqzetfv6sIYg/QDSo+Y+SN9WAR22P9Yw1u442JGzyHmQsrjaeMWFxSowRneCdauDdKl+rhdflr45avYCTTCbJIIkxWbIvrVB6n71On+duofURGUVpNScxK3CK3bk3FkZpNQE2f0hWzrCITBl023HVYSs44jIpZVBCtsrA+UmXPZecyNIbhAip1RDhBZ2f4ftFulD8AjSGiRoA7It0ux16h7aY6RPu4IEaQU2RVtwfIx0i7mIvjUkaEOOe+2a80gfu8sJ0vfoWtjU+vNIS4Kxrgp8Row2xhChXSBFWyNIviNCP2FFkJpzQoz+3hbbot9AkAABh7t2ZshGFcfCtuiHOAxSSpCU6Kb7KaohQsGCkQ15sPRsE0H6hBj9GFGQikXHSPn8ffqmq8AUYvRjVgQpG+ypLRr9nfZuIytuFbClNVuksJ+jb6/KpW7VcbAx+kXur7T6bRUYIUi/iJENgIAqSNd4bUs+VgE2Rr9rbZASRjY4Q5f3D1sZpGeOMlmTbgRpEjH6Zavvj3S5RaYoIkOvnWXk6KcJeu3O961Rvvwnst9WgQY5+mmCIGXV9Ro4RsKhrQxSfN+1K0x4uxIkHNrKIGVVgOoLoMxegnhNFWCvzgNru7/P1auTWToa9S9VHB7dDB5gZAMgsPYYSbslmqoC8ACDVn8be3WeWH3t71LWlDdVHBtB8sTKIJVxJB3SMFHFodHP4IvVu3YMWrWHUar+IEg/jBj5g+7vH0aQ/EGQAAGX17X7WxWAB5xe1+5PVQAecHtdO4ut2huOj/zCde1+FEHyC0OEAAF67QABggQIrP5hX8jIBjmOj/yzMkhnhghZQJD8s/q6dqmsKW+qOB6GqnqIXrvfQ448tPpyXPywT40Nko9WBqkI+GGfGDnyEr9H+jXkyEsECRDghCwgQJAAgdVByuJqry4uRO2ZquJIOELy1NogRc3hkQmkSTpskOiy89XKIKUmKqsgpdyNQoIc+Wr1EKGyGd1Arx0OTTBEiCABgmt/VxnKuWYDDk1zjJSJR4ETJHhmba9d3I5rWHBTczMkbtUe0NXgL8l5JBNfFrwvJUgfECR/uRzZkAcLtlvrqvAaJ5E85nSIUL70ns1HDdLWLcCfrQ1SmVQX/Q6SZb/vS03+fRWHQZA8tvqHfe1ZJIYIrcaenc9WBikyp2pbVCYmVrVoXMVhkCOfqS5+wsiG1QiSzwRj7SrloiBdz81ppzj5cKGHQwYJPlsZpMTUFz+5Rgv648r+3SvmO8IJEjwj+T3SspENiQkuTaddkQXzwSNI8Mzq80iXam8tWjLSLuj1fedm9laZBAmecXhC1kz2Ukir8BhdDX5zGCS2SHMIkt8cBul+jJQ1p205RnpFkPzm8v5IUa/XLpwdU3TAIMFvTu+PdE3q80hBfOY8EvaF+yMBAtwfCRDY4v5In9N3uCDR1eC7Le6PRJBeECTfbXFbl+lpF1/QYY8Iku9+J0grW+U3guS7LW7rQpBeECTfEaRfQI68t370d7T0unZ/rmL/CJL3HP4eqbHoxmQECZ5Zfe3vILs/LL/297Ibkx0tSPDe6rtRND+NWHo3ioU3JiNI8IzjqwgtvDEZQYJnZFuk2R/qPd9rFt2YjCDBM46PkRbemOxgQaKvwX+Oe+0W3piMIMEzmqsILT+PtOzGZAQJnnE+smHRjckOFiT4b4shQj9RBaC0KkjFqT7SKUP1780JEjyzJkhF0NzMJVPfHokgwTdrghQ2N0eqr6G/bGDD11W86I7L/2nt6a/w2IogZeb8+FtspOO/37aq+9D9M/gI7uOv8NmKIJ16Fz4pFpxIMkPiVgFbWhGkLy6KX0sJEnZrRZCCby9wlwdLf7VEkOCZVbt22eNv2aKbMecL7us3qALwxIog5c9O7yJY1tmQ9u7sIm4VsKU13d+JCc5VMPJzsPyn5t9VAfhh1ciG570oZn/vuqYKwAvrxtoVSX0NobN2XANBgncYtAoIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIuAxSeTImytpCZkshSPCMwyCVganETSEECXviMEiJSe9pSoOoLoQgYU8cBilo3lgEYUGQsDMOg9Rlp4wigoSdcRik0JTds4ggYV8cBik1p/ZZYSKChF1x2f2dPNKTGYKEXXF6QjaPu2fFiSBhTxjZAAgQJEDAaZCu57gZ3JBcbVUBbMLlEKHQPEVWqgA24nSIUHDJ62dFFpjERhXARpwOEcofz3MT2KgC2MgGQ4ReX8iqADbCFgkQcHuMlBX1M46RsDcuu7+jXq9dWM5NSZDgGbfnkZL6PFIQnzmPhH1hZAMgQJAAgS2CNN/1LakCcIsgAQK/EyTTt7YKwK3fCZK0CsAtggQIECRAgO5vQMB5kLK42iDFhcUqAOdcBylq+uRMMJskggTPOA5SaqKyCtLzYpHyKoANOA5SYMqmr4Ef9mFXHAep3q0jSNgdx0EK2y1SbkJbVQAb2OYYKQuqm47ZqQLYgOteu5jr2mGPNjmPZOKLzSoA5xjZAAgQJECAIAECBAkQIEiAgNNrfy/+NTlBgmccBiklSNgtl7t2eTB/GlZQBbANp8dI+fyl8xVVAJtw29mQ9u7sYqkKYAv02gECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBDYIUhqYMLVbBeCYyyDlsQnS29lUIjtVANtwGKS8TlBiTuWtiM3sNokgwTMOg3Qyye2WmKB6XprQRhXARhwGydRvNHHvhboKYCPOg3Rp9umaDZO6CmAjTnft7kdHjbLezdNXAWzEYZDK4LE/Z+Y3SAQJvnF6Hinp4hPMbo8IErzDyAZAgCABAk6DdD3H9UnZOLnaqgLYhMvOhtA8MUQIu+IwSIkJLnn9rMgCur+xKw6DFJj88TznhCx2xfnIhqkXsiqAjbBFAgTcHiNlRf2MYyTsjcvu76jXaxeWc1MSJHjG7XmkpD6PFMRnziNhXxjZAAgQJEBgiyDNd31LqgDcIkiAwO8EyfStrQJw63eCJK0CcIsgAQIECRCg+xsQcB6kLK42SHFhsQrAOddBipo+ORPMJokgwTOOg5SaqKyClJqTrSqADTgOUmDKpq+BH/ZhVxwHqd6tI0jYHcdBCtstUs5tXbAr2xwjZQE3GsOuuO61i7muHfZok/NIJr7YrAJwjpENgABBAgQIEiBAkAABggQIOL329+JfkxMkeMZhkFKChN1yuWuXB/OnYQVVANtweoyUz186X1EFsAm3nQ1p784ulqoAtkCvHSBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAwLcgGWBDf/jIKt8iq2Lr5YiD+/4j+4dPuQ67dvAMQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSIAAQQIECBI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"text/markdown": [ + "10001" + ], + "text/plain": [ + "[1] 10001" + ] }, + "metadata": {}, "output_type": "display_data" } ], "source": [ - "if (!is.na(t_change)) {\n", - " matplot(\n", - " sol_full$time,\n", - " sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")],\n", - " type = \"l\", lwd = 2, log = \"y\",\n", - " xlab = \"Time\", ylab = \"Concentration\",\n", - " main = \"Concentration vs Time (before/after Jacobian sign change)\"\n", - " )\n", - " usr <- par(\"usr\")\n", - " rect(xleft = min(sol_full$time), ybottom = usr[3], xright = t_change, ytop = usr[4],\n", - " border = NA, col = rgb(0, 0, 1, alpha = 0.1))\n", - " rect(xleft = t_change, ybottom = usr[3], xright = max(sol_full$time), ytop = usr[4],\n", - " border = NA, col = rgb(1, 0, 0, alpha = 0.1))\n", - " matlines(sol_full$time, sol_full[, c(\"A\", \"B\", \"AB\", \"B_star\")], lwd = 2)\n", - " legend(\"topleft\", legend = c(\"A\", \"B\", \"AB\", \"B*\"), lty = 1, lwd = 2, bty = \"n\")\n", - "}" + "nrow(sol_unstimulated)" ] }, { "cell_type": "code", - "execution_count": 16, - "id": "7f0b9cdd", + "execution_count": 123, + "id": "b0e64f58", "metadata": { "vscode": { "languageId": "r" @@ -705,60 +1272,206 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "Plot with title \"Dynamics of B\"" + "plot without title" ] }, "metadata": { "image/png": { - "height": 420, - "width": 420 + "height": 360, + "width": 480 } }, "output_type": "display_data" } ], "source": [ - "plot(sol_full$time, sol_full$B, type = \"l\", lwd = 2,\n", - " xlim = c(-999, 2000),\n", - " xlab = \"Time\", ylab = \"Concentration\",\n", - " main = \"Dynamics of B\")\n", - "axis(1, at = c(0, 2000))" + "# Plotting\n", + "sol_for_plot_2 <- as.data.frame(sol_full)\n", + "# rename columns for clarity\n", + "colnames(sol_for_plot_2) <- c(\"time\", \"A\", \"B\", \"AB\", \"B*\")\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot_2 %>%\n", + " pivot_longer(cols = A:`B*`, names_to = \"species\", values_to = \"value\")\n", + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "colors <- c(\n", + " A = \"#EE7733\",\n", + " B = \"#0077BB\",\n", + " AB = \"#33BBEE\",\n", + " `B*` = \"#EE3377\"\n", + ")\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(linewidth = 3) +\n", + " ## vertical dashed line\n", + " geom_vline(\n", + " xintercept = 0,\n", + " linetype = \"dashed\",\n", + " colour = \"black\",\n", + " linewidth = 0.7\n", + " ) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(-1000, 2000, 500),\n", + " minor_breaks = seq(-1000, 2000, 250),\n", + " limits = c(-1000, 2000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(-1000, 2000), clip = \"on\"\n", + " ) +\n", + " scale_y_log10(\n", + " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", + " labels = scales::trans_format(\"log10\", scales::math_format(10^.x))\n", + " ) + # log10 transformation\n", + " labs(\n", + " title = \"Model 3: Varusai 4 Variables\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + " \n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1" ] }, { "cell_type": "code", - "execution_count": null, - "id": "24150e8f", + "execution_count": 107, + "id": "d1ea7751", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "ce89ef50", - "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1] \"Jacobian matrix changed at index 12332 and time 233\"\n", + "[1] \"Unstimulated Jacobian:\"\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0\n", + "[2,] -1 -1 1 1\n", + "[3,] 1 1 -1 0\n", + "[4,] -1 1 0 -1\n", + "[1] \"Stimulated Jacobian:\"\n", + " [,1] [,2] [,3] [,4]\n", + "[1,] -1 -1 1 0\n", + "[2,] 1 -1 1 1\n", + "[3,] 1 1 -1 0\n", + "[4,] -1 1 0 -1\n" + ] + } + ], "source": [ - "## 3. Additional features" + "# Search for changes in loops upon stimulation over time_full\n", + "res_tab_0 <- find_loops_vset(func_varusai15,vset=list(initial_conditions_act_deact),t=1,params=params_act_deact_unstimulated,max_num_loops=10)\n", + "j_0 <- res_tab_0$jac_rep[[1]]\n", + "\n", + "for (idx in 1:(nrow(sol_full))) {\n", + " # compute loopsl\n", + " res_tab <- find_loops_vset(func_varusai15,vset=list(sol_full[idx,2:5]),t=idx,params=params_act_deact_stimulated,max_num_loops=10)\n", + " j_1 <- res_tab$jac_rep[[1]]\n", + " if (!identical(j_0, j_1)) {\n", + " print(paste(\"Jacobian matrix changed at index\", idx, \"and time\", time_full[idx], sep=\" \"))\n", + " print(\"Unstimulated Jacobian:\")\n", + " print(j_0)\n", + " print(\"Stimulated Jacobian:\")\n", + " print(j_1)\n", + " break\n", + " }\n", + "}" ] }, { - "cell_type": "markdown", - "id": "3a0acda4", - "metadata": {}, + "cell_type": "code", + "execution_count": 115, + "id": "243d080c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1] \"Loop summary unstimulated conditions:\"\n" + ] + }, + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 4
len_1len_2len_3len_4
<dbl><dbl><dbl><dbl>
all4431
pos0410
neg4021
\n" + ], + "text/latex": [ + "A data.frame: 3 × 4\n", + "\\begin{tabular}{r|llll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\tall & 4 & 4 & 3 & 1\\\\\n", + "\tpos & 0 & 4 & 1 & 0\\\\\n", + "\tneg & 4 & 0 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 4\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> |\n", + "|---|---|---|---|---|\n", + "| all | 4 | 4 | 3 | 1 |\n", + "| pos | 0 | 4 | 1 | 0 |\n", + "| neg | 4 | 0 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4\n", + "all 4 4 3 1 \n", + "pos 0 4 1 0 \n", + "neg 4 0 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "### 3.1. Add subject ID to make the loop result more comprehensible" + "res_tab_0 <- find_loops_vset(func_varusai15,vset=list(initial_conditions_act_deact),t=1,params=params_act_deact_unstimulated)\n", + "print(\"Loop summary unstimulated conditions:\")\n", + "loop_summary(res_tab_0$loop_rep[[1]])" ] }, { "cell_type": "code", - "execution_count": 17, - "id": "5d78b4f6", + "execution_count": 116, + "id": "75fdb42d", "metadata": { "vscode": { "languageId": "r" @@ -769,47 +1482,251 @@ "name": "stdout", "output_type": "stream", "text": [ - "\u001b[90m# A tibble: 25 × 4\u001b[39m\n", - " loop length sign loop_subject\n", - " \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \u001b[3m\u001b[90m\u001b[39m\u001b[23m \n", - "\u001b[90m 1\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", - "\u001b[90m 2\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", - "\u001b[90m 3\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", - "\u001b[90m 4\u001b[39m \u001b[90m\u001b[39m 1 -\u001b[31m1\u001b[39m \u001b[90m\u001b[39m \n", - "\u001b[90m 5\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m 6\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m 7\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m 8\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m 9\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m10\u001b[39m \u001b[90m\u001b[39m 2 1 \u001b[90m\u001b[39m \n", - "\u001b[90m# ℹ 15 more rows\u001b[39m\n" + "[1] \"Loop summary stimulated conditions:\"\n" ] + }, + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 4
len_1len_2len_3len_4
<dbl><dbl><dbl><dbl>
all4431
pos0320
neg4111
\n" + ], + "text/latex": [ + "A data.frame: 3 × 4\n", + "\\begin{tabular}{r|llll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4\\\\\n", + " & & & & \\\\\n", + "\\hline\n", + "\tall & 4 & 4 & 3 & 1\\\\\n", + "\tpos & 0 & 3 & 2 & 0\\\\\n", + "\tneg & 4 & 1 & 1 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 4\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> |\n", + "|---|---|---|---|---|\n", + "| all | 4 | 4 | 3 | 1 |\n", + "| pos | 0 | 3 | 2 | 0 |\n", + "| neg | 4 | 1 | 1 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4\n", + "all 4 4 3 1 \n", + "pos 0 3 2 0 \n", + "neg 4 1 1 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res_tab <- find_loops_vset(func_varusai15,vset=list(sol_full[idx,2:5]),t=idx,params=params_act_deact_stimulated)\n", + "print(\"Loop summary stimulated conditions:\")\n", + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 139, + "id": "d703b6e6", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" } ], "source": [ - "id_to_subject <- c(\"A\", \"B\", \"AB\", \"B*\")\n", - "names(id_to_subject) <- as.character(0:3)\n", + "# Plot again including the color area in the background to indicate unstimulated and stimulated loop structures changes (at idx, t)\n", + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "colors <- c(\n", + " A = \"#EE7733\",\n", + " B = \"#0077BB\",\n", + " AB = \"#33BBEE\",\n", + " `B*` = \"#EE3377\"\n", + ")\n", "\n", - "df_loops <- res_tab_complex_loop_rep %>%\n", - " mutate(\n", - " loop_subject = map(loop, ~ unname(id_to_subject[as.character(.x)]))\n", - " ) %>%\n", - " arrange(length, loop)\n", + "t_change <- time_full[idx]\n", + "yr <- range(sol_long$value, na.rm = TRUE)\n", "\n", - "print(df_loops)" + "plot2 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " # Add background colored areas \n", + " annotate(\"rect\",\n", + " xmin = -1000, xmax = t_change,\n", + " ymin = 10**-4, ymax = yr[2]+1000,\n", + " alpha = 0.2, fill = \"lightblue\") +\n", + " annotate(\"rect\",\n", + " xmin = t_change, xmax = 2000,\n", + " ymin = 10**-4, ymax = yr[2]+1000,\n", + " alpha = 0.2, fill = \"lightgreen\") +\n", + " ## vertical dashed line\n", + " geom_vline(\n", + " xintercept = 0,\n", + " linetype = \"dashed\",\n", + " colour = \"black\",\n", + " linewidth = 0.7\n", + " ) +\n", + " ## Another vertical line at the time of loop structure change\n", + " geom_vline(\n", + " xintercept = t_change,\n", + " linetype = \"dotted\",\n", + " colour = \"blue\",\n", + " linewidth = 0.7\n", + " ) +\n", + " ## Trajectory lines\n", + " geom_line(linewidth = 3) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(-1000, 2000, 500),\n", + " minor_breaks = seq(-1000, 2000, 250),\n", + " limits = c(-1000, 2000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(-1000, 2000), clip = \"on\", ylim = c(10**-4, yr[2]+1000)\n", + " ) +\n", + " scale_y_log10(\n", + " breaks = scales::trans_breaks(\"log10\", function(x) 10^x),\n", + " labels = scales::trans_format(\"log10\", scales::math_format(10^.x)),\n", + " limits = c(10**-4, yr[2]+1000),\n", + " expand = c(0, 0)\n", + " ) + # log10 transformation\n", + " labs(\n", + " title = \"Model 3: Varusai 4 Variables\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + " \n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "plot2\n", + "# ggsave(\"POSm4_plot_stimulated_loops.png\", plot2, width = 10, height = 8, units = \"in\", dpi = 300)" ] }, { "cell_type": "code", - "execution_count": null, - "id": "24878ee0", + "execution_count": 149, + "id": "1a104392", "metadata": { "vscode": { "languageId": "r" } }, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "# Zoom in around the perturbation point to see the dynamics more clearly (of only B)\n", + "options(repr.plot.width = 8, repr.plot.height = 6)\n", + "\n", + "plot3 <- ggplot(sol_long %>% filter(species == \"B\"), aes(x = time, y = value, colour = species)) +\n", + " ## vertical dashed line\n", + " geom_vline(\n", + " xintercept = 0,\n", + " linetype = \"dashed\",\n", + " colour = \"black\",\n", + " linewidth = 0.7\n", + " ) +\n", + " ## Another vertical line at the time of loop structure change\n", + " geom_vline(\n", + " xintercept = t_change,\n", + " linetype = \"dotted\",\n", + " colour = \"blue\",\n", + " linewidth = 0.7\n", + " ) +\n", + " ## Trajectory lines\n", + " geom_line(linewidth = 3) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(-1000, 2000, 500),\n", + " minor_breaks = seq(-1000, 2000, 250),\n", + " limits = c(-1000, 2000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(-1000, 2000), clip = \"on\"\n", + " ) +\n", + " scale_y_continuous(\n", + " minor_breaks = seq(-293, 295, 0.2),\n", + " breaks = seq(-293, 295, 1),\n", + " # limits = c(10**-2, yr[2]+1000),\n", + " # expand = c(0, 0)\n", + " ) + \n", + " labs(\n", + " title = \"Dynamics of B\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + " \n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "plot3\n", + "# ggsave(\"POSm4_plot_stimulated_loops_zoomed.png\", plot" + ] } ], "metadata": { diff --git a/examples/model_5_MAPK_reduced_R.ipynb b/examples/model_5_MAPK_reduced_R.ipynb new file mode 100644 index 0000000..f825bff --- /dev/null +++ b/examples/model_5_MAPK_reduced_R.ipynb @@ -0,0 +1,5735 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5c5107a0", + "metadata": {}, + "source": [ + "## **0. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "0aa853b2", + "metadata": {}, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad430870", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f2d7c70f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "# Download and install\n", + "install.packages(\"LoopDetectR\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1c741284", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "1d32152b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + } + ], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")\n", + "library(deSolve)\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3eb6dbbb", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "colors <- c('#EE7733', '#0077BB', '#33BBEE', '#EE3377', '#CC3311', '#009988', '#BBBBBB')" + ] + }, + { + "cell_type": "markdown", + "id": "de63ff1e", + "metadata": {}, + "source": [ + "## **1. Model definition**" + ] + }, + { + "cell_type": "markdown", + "id": "39347b82", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **Example 5: Reduced MAPK Model (with and without explicit feedback)**" + ] + }, + { + "cell_type": "markdown", + "id": "21903465", + "metadata": {}, + "source": [ + "The model for the mitogen-activated phosphorylation kinase (MAPK) cascade proposed in [7] captures the first, second and third level of a phosphorylation cascade which occurs for example in epidermal growth factor (EGF) signaling. The kinase on the first level can be reversibly phosphorylated once, the kinases on levels two andthree can be reversibly phosphorylated twice. The phosphorylated kinase of the first level acts positively on the phosphorylations on the second level, the double phosphorylated kinase of the second level acts positively on the phosphorylations on the third level. The model contains an explicit negative feedback regulation: The double phosphorylated kinase of the third level acts negatively on the phosphorylation on the first level. All phosphorylations are governed by Michaelis-Menten kinetics. The model contains eight variables, ten rate coefficients, eleven inhibition or activation constants, and one Hill coefficient." + ] + }, + { + "cell_type": "markdown", + "id": "8f5f1511", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{aligned}\n", + "\\frac{dS_1}{dt} &=\n", + "- k_1 \\, \\frac{S_1}{kn_2 + S_1} \\, \\frac{kn_1^{n_1}}{kn_1^{n_1} + S_8^{n_1}}\n", + "+ k_2 \\, \\frac{S_2}{S_2 + kn_3}, \\\\[8pt]\n", + "\n", + "\\frac{dS_2}{dt} &=\n", + "\\phantom{-}\\, k_1 \\, \\frac{S_1}{kn_2 + S_1} \\, \\frac{kn_1^{n_1}}{kn_1^{n_1} + S_8^{n_1}}\n", + "- k_2 \\, \\frac{S_2}{S_2 + kn_3}, \\\\[10pt]\n", + "\n", + "\\frac{dS_3}{dt} &=\n", + "\\phantom{-}\\, k_6 \\, \\frac{S_4}{kn_7 + S_4}\n", + "- k_3 \\, \\frac{S_2 \\, S_3}{kn_4 + S_3}, \\\\[10pt]\n", + "\n", + "\\frac{dS_4}{dt} &=\n", + "\\phantom{-}\\, k_3 \\, \\frac{S_2 \\, S_3}{kn_4 + S_3}\n", + "- k_6 \\, \\frac{S_4}{kn_7 + S_4}\n", + "+ k_5 \\, \\frac{S_5}{kn_6 + S_5}\n", + "- k_4 \\, \\frac{S_2 \\, S_4}{kn_5 + S_4}, \\\\[10pt]\n", + "\n", + "\\frac{dS_5}{dt} &=\n", + "\\phantom{-}\\, k_4 \\, \\frac{S_2 \\, S_4}{kn_5 + S_4}\n", + "- k_5 \\, \\frac{S_5}{kn_6 + S_5}, \\\\[10pt]\n", + "\n", + "\\frac{dS_6}{dt} &=\n", + "\\phantom{-}\\, k_{10} \\, \\frac{S_7}{kn_{11} + S_7}\n", + "- k_7 \\, \\frac{S_5 \\, S_6}{kn_8 + S_6}, \\\\[10pt]\n", + "\n", + "\\frac{dS_7}{dt} &=\n", + "\\phantom{-}\\, k_7 \\, \\frac{S_5 \\, S_6}{kn_8 + S_6}\n", + "- k_{10} \\, \\frac{S_7}{kn_{11} + S_7}\n", + "- k_8 \\, \\frac{S_5 \\, S_7}{kn_9 + S_7}\n", + "+ k_9 \\, \\frac{S_8}{kn_{10} + S_8}, \\\\[10pt]\n", + "\n", + "\\frac{dS_8}{dt} &=\n", + "\\phantom{-}\\, k_8 \\, \\frac{S_5 \\, S_7}{kn_9 + S_7}\n", + "- k_9 \\, \\frac{S_8}{kn_{10} + S_8}.\n", + "\\end{aligned}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "d486b5d6", + "metadata": {}, + "source": [ + "In the table below, the notation we used is given together with the notation used in the original publication [7], and we provide the initial conditions and reference parameter set published together with the model." + ] + }, + { + "cell_type": "markdown", + "id": "9340d377", + "metadata": {}, + "source": [ + "**Initial conditions**\n", + "\n", + "| Var | Name (short) | Name (long) | Initial value |\n", + "|------:|-------------|-------------|---------------|\n", + "| S₁ | MKKK | MAPKKK | 100 nM |\n", + "| S₂ | MKKK-P | MAPKKK* | 0 |\n", + "| S₃ | MKK | MAPKK | 300 nM |\n", + "| S₄ | MKK-P | MAPKK* | 0 |\n", + "| S₅ | MKK-PP | MAPKK** | 0 |\n", + "| S₆ | MAPK | MAPK | 300 nM |\n", + "| S₇ | MAPK-P | MAPK* | 0 |\n", + "| S₈ | MAPK-PP | MAPK** | 0 |\n" + ] + }, + { + "cell_type": "markdown", + "id": "201db642", + "metadata": {}, + "source": [ + "**Parameters**\n", + "| Parameter | Symbol | Value | Units |\n", + "|----------:|--------|-------|-------|\n", + "| k₁ | V₁ | 2.5 | nM·s⁻¹ |\n", + "| k₂ | V₂ | 0.25 | nM·s⁻¹ |\n", + "| k₃ | k₃ | 0.025 | s⁻¹ |\n", + "| k₄ | k₄ | 0.025 | s⁻¹ |\n", + "| k₅ | V₅ | 0.75 | nM·s⁻¹ |\n", + "| k₆ | V₆ | 0.75 | nM·s⁻¹ |\n", + "| k₇ | k₇ | 0.025 | s⁻¹ |\n", + "| k₈ | k₈ | 0.025 | s⁻¹ |\n", + "| k₉ | V₉ | 0.5 | nM·s⁻¹ |\n", + "| k₁₀ | V₁₀ | 0.5 | nM·s⁻¹ |\n" + ] + }, + { + "cell_type": "markdown", + "id": "9fb78a52", + "metadata": {}, + "source": [ + "The MAPK cascade model without explicit feedback regulation is exactly the same as the one described above, but for the corresponding regulation term omitted from the ODE system. Therefore, only the first two equations of the ODE model are altered to:" + ] + }, + { + "cell_type": "markdown", + "id": "cb1f8ad9", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{aligned}\n", + "\\frac{dS_1}{dt} &=\n", + "- k_1 \\, \\frac{S_1}{kn_2 + S_1}\n", + "+ k_2 \\, \\frac{S_2}{S_2 + kn_3}, \\\\[8pt]\n", + "\n", + "\\frac{dS_2}{dt} &=\n", + "\\phantom{-}\\, k_1 \\, \\frac{S_1}{kn_2 + S_1}\n", + "- k_2 \\, \\frac{S_2}{S_2 + kn_3}.\n", + "\\end{aligned}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "f038b36a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **1.1. Reduced MAPK Model with aexplicit feedback**" + ] + }, + { + "cell_type": "code", + "execution_count": 117, + "id": "9edacb63", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "model_mapk_simple_w_feedback <- function(t, y, klin, kn, n1) {\n", + " # Unpack state\n", + " S1 <- y[1]; S2 <- y[2]; S3 <- y[3]; S4 <- y[4]\n", + " S5 <- y[5]; S6 <- y[6]; S7 <- y[7]; S8 <- y[8]\n", + "\n", + " # Kinetic parameters\n", + " k1 <- klin[1]; k2 <- klin[2]; k3 <- klin[3]; k4 <- klin[4]; k5 <- klin[5]\n", + " k6 <- klin[6]; k7 <- klin[7]; k8 <- klin[8]; k9 <- klin[9]; k10 <- klin[10]\n", + "\n", + " # Saturation constants\n", + " kn1 <- kn[1]; kn2 <- kn[2]; kn3 <- kn[3]; kn4 <- kn[4]; kn5 <- kn[5]\n", + " kn6 <- kn[6]; kn7 <- kn[7]; kn8 <- kn[8]; kn9 <- kn[9]; kn10 <- kn[10]\n", + " kn11 <- kn[11]\n", + "\n", + " # dS1/dt\n", + " term_inhibit <- (kn1^n1) / (kn1^n1 + S8^n1)\n", + " dS1 <- -k1 * (S1/(kn2 + S1)) * term_inhibit +\n", + " k2 * (S2/(S2 + kn3))\n", + "\n", + " # dS2/dt\n", + " dS2 <- k1 * (S1/(kn2 + S1)) * term_inhibit -\n", + " k2 * (S2/(S2 + kn3))\n", + "\n", + " # dS3/dt\n", + " dS3 <- k6 * (S4/(kn7 + S4)) -\n", + " k3 * (S2*S3/(kn4 + S3))\n", + "\n", + " # dS4/dt\n", + " dS4 <- k3 * (S2*S3/(kn4 + S3)) -\n", + " k6 * (S4/(kn7 + S4)) +\n", + " k5 * (S5/(kn6 + S5)) -\n", + " k4 * (S2*S4/(kn5 + S4))\n", + "\n", + " # dS5/dt\n", + " dS5 <- k4 * (S2*S4/(kn5 + S4)) -\n", + " k5 * (S5/(kn6 + S5))\n", + "\n", + " # dS6/dt\n", + " dS6 <- k10 * (S7/(kn11 + S7)) -\n", + " k7 * (S5*S6/(kn8 + S6))\n", + "\n", + " # dS7/dt\n", + " dS7 <- k7 * (S5*S6/(kn8 + S6)) -\n", + " k10 * (S7/(kn11 + S7)) -\n", + " k8 * (S5*S7/(kn9 + S7)) +\n", + " k9 * (S8/(kn10 + S8))\n", + "\n", + " # dS8/dt\n", + " dS8 <- k8 * (S5*S7/(kn9 + S7)) -\n", + " k9 * (S8/(kn10 + S8))\n", + " \n", + " dx <- rep(0,8)\n", + " dx[1] <- dS1\n", + " dx[2] <- dS2\n", + " dx[3] <- dS3\n", + " dx[4] <- dS4\n", + " dx[5] <- dS5\n", + " dx[6] <- dS6\n", + " dx[7] <- dS7\n", + " dx[8] <- dS8\n", + " \n", + " return(dx)\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "51df3daa", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **1.2. Reduced MAPK Model without explicit feedback**" + ] + }, + { + "cell_type": "code", + "execution_count": 116, + "id": "64a3f6ca", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "model_mapk_simple_wo_feedback <- function(t, y, klin, kn, n1) {\n", + " # Unpack state\n", + " S1 <- y[1]; S2 <- y[2]; S3 <- y[3]; S4 <- y[4]\n", + " S5 <- y[5]; S6 <- y[6]; S7 <- y[7]; S8 <- y[8]\n", + "\n", + " # Kinetic parameters\n", + " k1 <- klin[1]; k2 <- klin[2]; k3 <- klin[3]; k4 <- klin[4]; k5 <- klin[5]\n", + " k6 <- klin[6]; k7 <- klin[7]; k8 <- klin[8]; k9 <- klin[9]; k10 <- klin[10]\n", + "\n", + " # Saturation constants\n", + " kn1 <- kn[1]; kn2 <- kn[2]; kn3 <- kn[3]; kn4 <- kn[4]; kn5 <- kn[5]\n", + " kn6 <- kn[6]; kn7 <- kn[7]; kn8 <- kn[8]; kn9 <- kn[9]; kn10 <- kn[10]\n", + " kn11 <- kn[11]\n", + "\n", + " # dS1/dt\n", + " dS1 <- -k1 * (S1/(kn2 + S1)) +\n", + " k2 * (S2/(S2 + kn3))\n", + "\n", + " # dS2/dt\n", + " dS2 <- k1 * (S1/(kn2 + S1)) -\n", + " k2 * (S2/(S2 + kn3))\n", + "\n", + " # dS3/dt\n", + " dS3 <- k6 * (S4/(kn7 + S4)) -\n", + " k3 * (S2*S3/(kn4 + S3))\n", + "\n", + " # dS4/dt\n", + " dS4 <- k3 * (S2*S3/(kn4 + S3)) -\n", + " k6 * (S4/(kn7 + S4)) +\n", + " k5 * (S5/(kn6 + S5)) -\n", + " k4 * (S2*S4/(kn5 + S4))\n", + "\n", + " # dS5/dt\n", + " dS5 <- k4 * (S2*S4/(kn5 + S4)) -\n", + " k5 * (S5/(kn6 + S5))\n", + "\n", + " # dS6/dt\n", + " dS6 <- k10 * (S7/(kn11 + S7)) -\n", + " k7 * (S5*S6/(kn8 + S6))\n", + "\n", + " # dS7/dt\n", + " dS7 <- k7 * (S5*S6/(kn8 + S6)) -\n", + " k10 * (S7/(kn11 + S7)) -\n", + " k8 * (S5*S7/(kn9 + S7)) +\n", + " k9 * (S8/(kn10 + S8))\n", + "\n", + " # dS8/dt\n", + " dS8 <- k8 * (S5*S7/(kn9 + S7)) -\n", + " k9 * (S8/(kn10 + S8))\n", + " \n", + " dx <- rep(0,8)\n", + " dx[1] <- dS1\n", + " dx[2] <- dS2\n", + " dx[3] <- dS3\n", + " dx[4] <- dS4\n", + " dx[5] <- dS5\n", + " dx[6] <- dS6\n", + " dx[7] <- dS7\n", + " dx[8] <- dS8\n", + " \n", + " return(dx)\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "44e7e155", + "metadata": {}, + "source": [ + "## **2. Result reproduction**" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "4e5b9062", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Parameters from supplementary material\n", + "klin <- c(\n", + " 2.5, # k1\n", + " 0.25, # k2\n", + " 0.025, # k3\n", + " 0.025, # k4\n", + " 0.75, # k5\n", + " 0.75, # k6\n", + " 0.025, # k7\n", + " 0.025, # k8\n", + " 0.5, # k9\n", + " 0.5 # k10\n", + ")\n", + "\n", + "kn <- c(\n", + " 9, # kn1 = KI\n", + " 10, # kn2 = K1\n", + " 8, # kn3 = K2\n", + " 15, # kn4\n", + " 15, # kn5\n", + " 15, # kn6\n", + " 15, # kn7\n", + " 15, # kn8\n", + " 15, # kn9\n", + " 15, # kn10\n", + " 15 # kn11\n", + ")\n", + "\n", + "n1 <- 1\n", + "\n", + "# Initial conditions\n", + "initial_conditions <- c(\n", + " S1 = 100, # S1: MKKK, MAPKKK\n", + " S2 = 0, # S2: MKKK-P, MKKK*\n", + " S3 = 300, # S3: MKK, MAPKK\n", + " S4 = 0, # S4: MKK-P, MAPKK*,\n", + " S5 = 0, # S5: MKK-PP, MAPKK**\n", + " S6 = 300, # S6: MAPK, MAPK\n", + " S7 = 0, # S7: MAPK-P, MAPK*\n", + " S8 = 0 # S8: MAPK-PP, MAPK** \n", + ")\n", + "\n", + "all_labels <- c('MAPKKK (S1)', 'MAPKKK* (S2)', 'MAPKK (S3)', 'MAPKK* (S4)', \n", + " 'MAPKK** (S5)', 'MAPK (S6)', 'MAPK* (S7)', 'MAPK** (S8)')\n" + ] + }, + { + "cell_type": "markdown", + "id": "b927c538", + "metadata": {}, + "source": [ + "### **2.1. Reduced MAPK Model with explicit feedback**" + ] + }, + { + "cell_type": "markdown", + "id": "b9c9522a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **2.1.1. Loop structure (at first)**" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "6c2540e5", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 7 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
4, 41-1
5, 51-1
7, 71-1
8, 81-1
1, 2, 12 1
\n" + ], + "text/latex": [ + "A data.frame: 7 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 5, 5 & 1 & -1\\\\\n", + "\t 7, 7 & 1 & -1\\\\\n", + "\t 8, 8 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 7 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 5, 5 | 1 | -1 |\n", + "| 7, 7 | 1 | -1 |\n", + "| 8, 8 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 4, 4 1 -1 \n", + "4 5, 5 1 -1 \n", + "5 7, 7 1 -1 \n", + "6 8, 8 1 -1 \n", + "7 1, 2, 1 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute loops\n", + "res_tab <- find_loops_vset(model_mapk_simple_w_feedback,vset=list(initial_conditions),t=1,klin=klin,kn=kn,n1=n1,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]] \n", + "# To access a specific loop representation: e.g., the sixth loop, add [6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "3d056cc3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 2
len_1len_2
<dbl><dbl>
all61
pos01
neg60
\n" + ], + "text/latex": [ + "A data.frame: 3 × 2\n", + "\\begin{tabular}{r|ll}\n", + " & len\\_1 & len\\_2\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\tall & 6 & 1\\\\\n", + "\tpos & 0 & 1\\\\\n", + "\tneg & 6 & 0\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 2\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> |\n", + "|---|---|---|\n", + "| all | 6 | 1 |\n", + "| pos | 0 | 1 |\n", + "| neg | 6 | 0 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2\n", + "all 6 1 \n", + "pos 0 1 \n", + "neg 6 0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e9a5ecf2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 2 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
71, 2, 12 1
\n" + ], + "text/latex": [ + "A data.frame: 2 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t7 & 1, 2, 1 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 2 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 7 | 1, 2, 1 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "7 1, 2, 1 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2 \n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "9f0fc026", + "metadata": {}, + "source": [ + "#### **2.1.2. Calculating the Jacobian matrix**\n", + "\n", + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "05e68bc3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-1 10 0 00 0 1
1-10 0 00 0-1
0-10 1 00 0 0
0 10-1 10 0 0
0 00 0-10 0 0
0 00 0-10 1 0
0 00 0 10-1 1
0 00 0 00 0-1
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\t 0 & -1 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "| 0 | -1 | 0 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 0 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 1 \n", + "[2,] 1 -1 0 0 0 0 0 -1 \n", + "[3,] 0 -1 0 1 0 0 0 0 \n", + "[4,] 0 1 0 -1 1 0 0 0 \n", + "[5,] 0 0 0 0 -1 0 0 0 \n", + "[6,] 0 0 0 0 -1 0 1 0 \n", + "[7,] 0 0 0 0 1 0 -1 1 \n", + "[8,] 0 0 0 0 0 0 0 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix (at initialization point)\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "b4802333", + "metadata": {}, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003]." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "adbc93e2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
S1
95.6517023027939
S2
4.34829769720574
S3
208.414606568695
S4
74.5151466422457
S5
17.0702467890569
S6
6.84331427771254
S7
15.1917577910863
S8
277.9649279312
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[S1] 95.6517023027939\n", + "\\item[S2] 4.34829769720574\n", + "\\item[S3] 208.414606568695\n", + "\\item[S4] 74.5151466422457\n", + "\\item[S5] 17.0702467890569\n", + "\\item[S6] 6.84331427771254\n", + "\\item[S7] 15.1917577910863\n", + "\\item[S8] 277.9649279312\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "S1\n", + ": 95.6517023027939S2\n", + ": 4.34829769720574S3\n", + ": 208.414606568695S4\n", + ": 74.5151466422457S5\n", + ": 17.0702467890569S6\n", + ": 6.84331427771254S7\n", + ": 15.1917577910863S8\n", + ": 277.9649279312\n", + "\n" + ], + "text/plain": [ + " S1 S2 S3 S4 S5 S6 S7 \n", + " 95.651702 4.348298 208.414607 74.515147 17.070247 6.843314 15.191758 \n", + " S8 \n", + "277.964928 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The function func_POSm4 returns a vector, but deSolve needs the vector within\n", + "# a list as output. Therefore, we define a function that simply puts the output \n", + "# of func_POSm4 into a list:\n", + "func_list <- function(t,x,klin,kn,n1){list(model_mapk_simple_w_feedback(t,x,klin,kn,n1))}\n", + "sol <- deSolve::ode(y = initial_conditions, times = seq(0,3650,1), func = func_list, \n", + " parms=klin, kn=kn, n1=n1)\n", + "\n", + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star_end <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star_end" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "1d134ecb", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-7.024262e-05 0.013116435 0.000000e+00 0.0000000000 0.000000000 0.00000000 0.000000000 2.473666e-04
7.024262e-05-0.013116435 0.000000e+00 0.0000000000 0.000000000 0.00000000 0.000000000-2.473666e-04
0.000000e+00-0.023321506-3.266837e-05 0.0014039753 0.000000000 0.00000000 0.000000000 0.000000e+00
0.000000e+00 0.002510742 3.266837e-05-0.0016074721 0.010938252 0.00000000 0.000000000 0.000000e+00
0.000000e+00 0.020810765 0.000000e+00 0.0002034968-0.010938252 0.00000000 0.000000000 0.000000e+00
0.000000e+00 0.000000000 0.000000e+00 0.0000000000-0.007832276-0.01341634 0.008227814 0.000000e+00
0.000000e+00 0.000000000 0.000000e+00 0.0000000000-0.004747116 0.01341634-0.015250355 8.738361e-05
0.000000e+00 0.000000000 0.000000e+00 0.0000000000 0.012579392 0.00000000 0.007022541-8.738361e-05
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -7.024262e-05 & 0.013116435 & 0.000000e+00 & 0.0000000000 & 0.000000000 & 0.00000000 & 0.000000000 & 2.473666e-04\\\\\n", + "\t 7.024262e-05 & -0.013116435 & 0.000000e+00 & 0.0000000000 & 0.000000000 & 0.00000000 & 0.000000000 & -2.473666e-04\\\\\n", + "\t 0.000000e+00 & -0.023321506 & -3.266837e-05 & 0.0014039753 & 0.000000000 & 0.00000000 & 0.000000000 & 0.000000e+00\\\\\n", + "\t 0.000000e+00 & 0.002510742 & 3.266837e-05 & -0.0016074721 & 0.010938252 & 0.00000000 & 0.000000000 & 0.000000e+00\\\\\n", + "\t 0.000000e+00 & 0.020810765 & 0.000000e+00 & 0.0002034968 & -0.010938252 & 0.00000000 & 0.000000000 & 0.000000e+00\\\\\n", + "\t 0.000000e+00 & 0.000000000 & 0.000000e+00 & 0.0000000000 & -0.007832276 & -0.01341634 & 0.008227814 & 0.000000e+00\\\\\n", + "\t 0.000000e+00 & 0.000000000 & 0.000000e+00 & 0.0000000000 & -0.004747116 & 0.01341634 & -0.015250355 & 8.738361e-05\\\\\n", + "\t 0.000000e+00 & 0.000000000 & 0.000000e+00 & 0.0000000000 & 0.012579392 & 0.00000000 & 0.007022541 & -8.738361e-05\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -7.024262e-05 | 0.013116435 | 0.000000e+00 | 0.0000000000 | 0.000000000 | 0.00000000 | 0.000000000 | 2.473666e-04 |\n", + "| 7.024262e-05 | -0.013116435 | 0.000000e+00 | 0.0000000000 | 0.000000000 | 0.00000000 | 0.000000000 | -2.473666e-04 |\n", + "| 0.000000e+00 | -0.023321506 | -3.266837e-05 | 0.0014039753 | 0.000000000 | 0.00000000 | 0.000000000 | 0.000000e+00 |\n", + "| 0.000000e+00 | 0.002510742 | 3.266837e-05 | -0.0016074721 | 0.010938252 | 0.00000000 | 0.000000000 | 0.000000e+00 |\n", + "| 0.000000e+00 | 0.020810765 | 0.000000e+00 | 0.0002034968 | -0.010938252 | 0.00000000 | 0.000000000 | 0.000000e+00 |\n", + "| 0.000000e+00 | 0.000000000 | 0.000000e+00 | 0.0000000000 | -0.007832276 | -0.01341634 | 0.008227814 | 0.000000e+00 |\n", + "| 0.000000e+00 | 0.000000000 | 0.000000e+00 | 0.0000000000 | -0.004747116 | 0.01341634 | -0.015250355 | 8.738361e-05 |\n", + "| 0.000000e+00 | 0.000000000 | 0.000000e+00 | 0.0000000000 | 0.012579392 | 0.00000000 | 0.007022541 | -8.738361e-05 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] \n", + "[1,] -7.024262e-05 0.013116435 0.000000e+00 0.0000000000 0.000000000\n", + "[2,] 7.024262e-05 -0.013116435 0.000000e+00 0.0000000000 0.000000000\n", + "[3,] 0.000000e+00 -0.023321506 -3.266837e-05 0.0014039753 0.000000000\n", + "[4,] 0.000000e+00 0.002510742 3.266837e-05 -0.0016074721 0.010938252\n", + "[5,] 0.000000e+00 0.020810765 0.000000e+00 0.0002034968 -0.010938252\n", + "[6,] 0.000000e+00 0.000000000 0.000000e+00 0.0000000000 -0.007832276\n", + "[7,] 0.000000e+00 0.000000000 0.000000e+00 0.0000000000 -0.004747116\n", + "[8,] 0.000000e+00 0.000000000 0.000000e+00 0.0000000000 0.012579392\n", + " [,6] [,7] [,8] \n", + "[1,] 0.00000000 0.000000000 2.473666e-04\n", + "[2,] 0.00000000 0.000000000 -2.473666e-04\n", + "[3,] 0.00000000 0.000000000 0.000000e+00\n", + "[4,] 0.00000000 0.000000000 0.000000e+00\n", + "[5,] 0.00000000 0.000000000 0.000000e+00\n", + "[6,] -0.01341634 0.008227814 0.000000e+00\n", + "[7,] 0.01341634 -0.015250355 8.738361e-05\n", + "[8,] 0.00000000 0.007022541 -8.738361e-05" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "j_matrix <- numDeriv::jacobian(model_mapk_simple_w_feedback, s_star_end,method=\"complex\",\n", + " t=3650,klin=klin, kn=kn, n1=n1)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "d9a4b8c8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-1 1 0 0 0 0 0 1
1-1 0 0 0 0 0-1
0-1-1 1 0 0 0 0
0 1 1-1 1 0 0 0
0 1 0 1-1 0 0 0
0 0 0 0-1-1 1 0
0 0 0 0-1 1-1 1
0 0 0 0 1 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "| 0 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | 1 | 1 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 1 \n", + "[2,] 1 -1 0 0 0 0 0 -1 \n", + "[3,] 0 -1 -1 1 0 0 0 0 \n", + "[4,] 0 1 1 -1 1 0 0 0 \n", + "[5,] 0 1 0 1 -1 0 0 0 \n", + "[6,] 0 0 0 0 -1 -1 1 0 \n", + "[7,] 0 0 0 0 -1 1 -1 1 \n", + "[8,] 0 0 0 0 1 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "9fb5ce0e", + "metadata": {}, + "source": [ + "#### **2.1.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "b6906e49", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol <- deSolve::ode(y = s_star_end, times = seq(0,5000,1), func = func_list, \n", + " parms=klin, kn=kn, n1=n1)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "a9e0a20b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "296.620110566778" + ], + "text/latex": [ + "296.620110566778" + ], + "text/markdown": [ + "296.620110566778" + ], + "text/plain": [ + "[1] 296.6201" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "max(sol[,9])" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "6e020cf1", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 5001
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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol[,1], sol[,2:dim(sol)[2]],\n", + " type = \"l\",\n", + " lty = 1,\n", + " xlab = \"Time\",\n", + " ylab = \"Concentration\",\n", + ")\n", + "\n", + "legend(\n", + " \"topright\",\n", + " legend = all_labels,\n", + " col = 1:8,\n", + " lty = 1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "id": "9a37d5b5", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "investigate_label <- c('MAPKK** (S5)', 'MAPK (S6)', 'MAPK* (S7)')\n", + "investigate_index <- c(6, 7, 8)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "id": "1f18ff68", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_for_plot <- as.data.frame(sol[, c(1, investigate_index)])\n", + "\n", + "# rename columns for clarity (use time + investigate_label)\n", + "colnames(sol_for_plot) <- c(\"time\", investigate_label)\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = `MAPKK** (S5)`:`MAPK* (S7)`, names_to = \"species\", values_to = \"value\")" + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "id": "273651c0", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 840 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "options(repr.plot.width = 14, repr.plot.height = 6)\n", + "colors <- c(\n", + " `MAPKK** (S5)` = \"#EE7733\",\n", + " `MAPK (S6)` = \"#0077BB\",\n", + " `MAPK* (S7)` = \"#33BBEE\"\n", + ")\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(linewidth = 2) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 5000, 1000),\n", + " minor_breaks = seq(0, 5000, 500),\n", + " limits = c(0, 5000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 5000), clip = \"on\") +\n", + " labs(\n", + " title = \"Dynamics of the Reduced MAPK Model with Explicit Feedback\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + "\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "code", + "execution_count": 101, + "id": "a506b026", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_list <- lapply(1:nrow(sol), function(i) as.numeric(sol[i, 2:9]))\n", + "res_tab_all <- find_loops_vset(model_mapk_simple_w_feedback,vset=sol_list,t=1,klin=klin,kn=kn,n1=n1)" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "id": "ec8b3250", + "metadata": { + "vscode": { + "languageId": "r" + } + }, 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  259. 1
  260. 1
  261. 1
  262. 1
  263. 1
  264. 1
  265. 1
  266. 1
  267. 1
  268. 1
  269. 1
  270. 1
  271. 1
  272. 1
  273. 1
  274. 1
  275. 1
  276. 1
  277. 1
  278. 1
  279. 1
  280. 1
  281. 1
  282. 1
  283. 1
  284. 1
  285. 1
  286. 1
  287. 1
  288. 1
  289. 1
  290. 1
  291. 1
  292. 1
  293. 1
  294. 1
  295. 1
  296. 1
  297. 1
  298. 1
  299. 1
  300. 1
  301. 1
  302. 1
  303. 1
  304. 1
  305. 1
  306. 1
  307. 1
  308. 1
  309. 1
  310. 1
  311. 1
  312. 1
  313. 1
  314. 1
  315. 1
  316. 1
  317. 1
  318. 1
  319. 1
  320. 1
  321. 1
  322. 1
  323. 1
  324. 1
  325. 1
  326. 1
  327. 1
  328. 1
  329. 1
  330. 1
  331. 1
  332. 1
  333. 1
  334. 1
  335. 1
  336. 1
  337. 1
  338. 1
  339. 1
  340. 1
  341. 1
  342. 1
  343. 1
  344. 1
  345. 1
  346. 1
  347. 1
  348. 1
  349. 1
  350. 1
  351. 1
  352. 1
  353. 1
  354. 1
  355. 1
  356. 1
  357. 1
  358. 1
  359. 1
  360. 1
  361. 1
  362. 1
  363. 1
  364. 1
  365. 1
  366. 1
  367. 1
  368. 1
  369. 1
  370. 1
  371. 1
  372. 1
  373. 1
  374. 1
  375. 1
  376. 1
  377. 1
  378. 1
  379. 1
  380. 1
  381. 1
  382. 1
  383. 1
  384. 1
  385. 1
  386. 1
  387. 1
  388. 1
  389. 1
  390. 1
  391. 1
  392. 1
  393. 1
  394. 1
  395. 1
  396. 1
  397. 1
  398. 1
  399. 1
  400. 1
  401. 1
\n", + "
\n", + "\t
$jac_rep
\n", + "\t\t
    \n", + "\t
  1. \n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
    A matrix: 8 × 8 of type dbl
    -1 1 0 0 0 0 0 1
    1-1 0 0 0 0 0-1
    0-1-1 1 0 0 0 0
    0 1 1-1 1 0 0 0
    0 1 0 1-1 0 0 0
    0 0 0 0-1-1 1 0
    0 0 0 0-1 1-1 1
    0 0 0 0 1 0 1-1
    \n", + "
    2. \n", + "\t
  2. \n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
    A matrix: 8 × 8 of type dbl
    -1 1 0 0 0 0 0 1
    1-1 0 0 0 0 0-1
    0-1-1 1 0 0 0 0
    0 1 1-1 1 0 0 0
    0 1 0 1-1 0 0 0
    0 0 0 0-1-1 1 0
    0 0 0 0 1 1-1 1
    0 0 0 0 1 0 1-1
    \n", + "
    3. \n", + "
\n", + "
\n", + "\t
$jac_rep_index
\n", + "\t\t
\n", + "
  1. 1
  2. 1
  3. 1
  4. 1
  5. 1
  6. 1
  7. 1
  8. 1
  9. 1
  10. 1
  11. 1
  12. 1
  13. 1
  14. 1
  15. 1
  16. 1
  17. 1
  18. 1
  19. 1
  20. 1
  21. 1
  22. 1
  23. 1
  24. 1
  25. 1
  26. 1
  27. 1
  28. 1
  29. 1
  30. 1
  31. 1
  32. 1
  33. 1
  34. 1
  35. 1
  36. 1
  37. 1
  38. 1
  39. 1
  40. 1
  41. 1
  42. 1
  43. 1
  44. 1
  45. 1
  46. 1
  47. 1
  48. 1
  49. 1
  50. 1
  51. 1
  52. 1
  53. 1
  54. 1
  55. 1
  56. 1
  57. 1
  58. 1
  59. 1
  60. 1
  61. 1
  62. 1
  63. 1
  64. 1
  65. 1
  66. 1
  67. 1
  68. 1
  69. 1
  70. 1
  71. 1
  72. 1
  73. 1
  74. 1
  75. 1
  76. 1
  77. 1
  78. 1
  79. 1
  80. 1
  81. 1
  82. 1
  83. 1
  84. 1
  85. 1
  86. 1
  87. 1
  88. 1
  89. 1
  90. 1
  91. 1
  92. 1
  93. 1
  94. 1
  95. 1
  96. 1
  97. 1
  98. 1
  99. 1
  100. 1
  101. 1
  102. 1
  103. 1
  104. 1
  105. 1
  106. 1
  107. 1
  108. 1
  109. 1
  110. 2
  111. 2
  112. 2
  113. 2
  114. 2
  115. 2
  116. 2
  117. 2
  118. 2
  119. 2
  120. 2
  121. 2
  122. 2
  123. 2
  124. 2
  125. 2
  126. 2
  127. 2
  128. 2
  129. 2
  130. 2
  131. 2
  132. 2
  133. 2
  134. 2
  135. 2
  136. 2
  137. 2
  138. 2
  139. 2
  140. 2
  141. 2
  142. 2
  143. 2
  144. 2
  145. 2
  146. 2
  147. 2
  148. 2
  149. 2
  150. 2
  151. 2
  152. 2
  153. 2
  154. 2
  155. 2
  156. 2
  157. 2
  158. 2
  159. 2
  160. 2
  161. 2
  162. 2
  163. 2
  164. 2
  165. 2
  166. 2
  167. 2
  168. 2
  169. 2
  170. 2
  171. 2
  172. 2
  173. 2
  174. 2
  175. 2
  176. 2
  177. 2
  178. 2
  179. 2
  180. 2
  181. 2
  182. 2
  183. 2
  184. 2
  185. 2
  186. 2
  187. 2
  188. 2
  189. 2
  190. 2
  191. 2
  192. 2
  193. 2
  194. 2
  195. 2
  196. 2
  197. 2
  198. 2
  199. 2
  200. 2
  201. ⋯
  202. 1
  203. 1
  204. 1
  205. 1
  206. 1
  207. 1
  208. 1
  209. 1
  210. 1
  211. 1
  212. 1
  213. 1
  214. 1
  215. 1
  216. 1
  217. 1
  218. 1
  219. 1
  220. 1
  221. 1
  222. 1
  223. 1
  224. 1
  225. 1
  226. 1
  227. 1
  228. 1
  229. 1
  230. 1
  231. 1
  232. 1
  233. 1
  234. 1
  235. 1
  236. 1
  237. 1
  238. 1
  239. 1
  240. 1
  241. 1
  242. 1
  243. 1
  244. 1
  245. 1
  246. 1
  247. 1
  248. 1
  249. 1
  250. 1
  251. 1
  252. 1
  253. 1
  254. 1
  255. 1
  256. 1
  257. 1
  258. 1
  259. 1
  260. 1
  261. 1
  262. 1
  263. 1
  264. 1
  265. 1
  266. 1
  267. 1
  268. 1
  269. 1
  270. 1
  271. 1
  272. 1
  273. 1
  274. 1
  275. 1
  276. 1
  277. 1
  278. 1
  279. 1
  280. 1
  281. 1
  282. 1
  283. 1
  284. 1
  285. 1
  286. 1
  287. 1
  288. 1
  289. 1
  290. 1
  291. 1
  292. 1
  293. 1
  294. 1
  295. 1
  296. 1
  297. 1
  298. 1
  299. 1
  300. 1
  301. 1
  302. 1
  303. 1
  304. 1
  305. 1
  306. 1
  307. 1
  308. 1
  309. 1
  310. 1
  311. 1
  312. 1
  313. 1
  314. 1
  315. 1
  316. 1
  317. 1
  318. 1
  319. 1
  320. 1
  321. 1
  322. 1
  323. 1
  324. 1
  325. 1
  326. 1
  327. 1
  328. 1
  329. 1
  330. 1
  331. 1
  332. 1
  333. 1
  334. 1
  335. 1
  336. 1
  337. 1
  338. 1
  339. 1
  340. 1
  341. 1
  342. 1
  343. 1
  344. 1
  345. 1
  346. 1
  347. 1
  348. 1
  349. 1
  350. 1
  351. 1
  352. 1
  353. 1
  354. 1
  355. 1
  356. 1
  357. 1
  358. 1
  359. 1
  360. 1
  361. 1
  362. 1
  363. 1
  364. 1
  365. 1
  366. 1
  367. 1
  368. 1
  369. 1
  370. 1
  371. 1
  372. 1
  373. 1
  374. 1
  375. 1
  376. 1
  377. 1
  378. 1
  379. 1
  380. 1
  381. 1
  382. 1
  383. 1
  384. 1
  385. 1
  386. 1
  387. 1
  388. 1
  389. 1
  390. 1
  391. 1
  392. 1
  393. 1
  394. 1
  395. 1
  396. 1
  397. 1
  398. 1
  399. 1
  400. 1
  401. 1
\n", + "
\n", + "
\n" + ], + "text/latex": [ + "\\begin{description}\n", + "\\item[\\$loop\\_rep] \\begin{enumerate}\n", + "\\item A data.frame: 31 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 5, 5 & 1 & -1\\\\\n", + "\t 6, 6 & 1 & -1\\\\\n", + "\t 7, 7 & 1 & -1\\\\\n", + "\t 8, 8 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 3, 4, 3 & 2 & 1\\\\\n", + "\t 4, 5, 4 & 2 & 1\\\\\n", + "\t 6, 7, 6 & 2 & 1\\\\\n", + "\t 5, 8, 1,.... & 6 & -1\\\\\n", + "\t 5, 8, 1,.... & 5 & 1\\\\\n", + "\t 5, 8, 1,.... & 4 & 1\\\\\n", + "\t 5, 8, 2,.... & 5 & 1\\\\\n", + "\t 5, 8, 2,.... & 4 & -1\\\\\n", + "\t 5, 8, 2, 5 & 3 & -1\\\\\n", + "\t 7, 8, 1,.... & 8 & 1\\\\\n", + "\t 7, 8, 1,.... & 7 & 1\\\\\n", + "\t 7, 8, 1,.... & 7 & -1\\\\\n", + "\t 7, 8, 1,.... & 6 & -1\\\\\n", + "\t 7, 8, 1,.... & 6 & -1\\\\\n", + "\t 7, 8, 1,.... & 5 & -1\\\\\n", + "\t 7, 8, 2,.... & 7 & -1\\\\\n", + "\t 7, 8, 2,.... & 6 & -1\\\\\n", + "\t 7, 8, 2,.... & 6 & 1\\\\\n", + "\t 7, 8, 2,.... & 5 & 1\\\\\n", + "\t 7, 8, 2,.... & 5 & 1\\\\\n", + "\t 7, 8, 2,.... & 4 & 1\\\\\n", + "\t 7, 8, 7 & 2 & 1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A data.frame: 31 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 3, 3 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 5, 5 & 1 & -1\\\\\n", + "\t 6, 6 & 1 & -1\\\\\n", + "\t 7, 7 & 1 & -1\\\\\n", + "\t 8, 8 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\t 3, 4, 3 & 2 & 1\\\\\n", + "\t 4, 5, 4 & 2 & 1\\\\\n", + "\t 6, 7, 6 & 2 & 1\\\\\n", + "\t 5, 8, 1,.... & 6 & -1\\\\\n", + "\t 5, 8, 1,.... & 5 & 1\\\\\n", + "\t 5, 8, 1,.... & 4 & 1\\\\\n", + "\t 5, 8, 2,.... & 5 & 1\\\\\n", + "\t 5, 8, 2,.... & 4 & -1\\\\\n", + "\t 5, 8, 2, 5 & 3 & -1\\\\\n", + "\t 7, 8, 1,.... & 8 & 1\\\\\n", + "\t 7, 8, 1,.... & 7 & -1\\\\\n", + "\t 7, 8, 1,.... & 7 & -1\\\\\n", + "\t 7, 8, 1,.... & 6 & 1\\\\\n", + "\t 7, 8, 1,.... & 6 & -1\\\\\n", + "\t 7, 8, 1,.... & 5 & 1\\\\\n", + "\t 7, 8, 2,.... & 7 & -1\\\\\n", + "\t 7, 8, 2,.... & 6 & 1\\\\\n", + "\t 7, 8, 2,.... & 6 & 1\\\\\n", + "\t 7, 8, 2,.... & 5 & -1\\\\\n", + "\t 7, 8, 2,.... & 5 & 1\\\\\n", + "\t 7, 8, 2,.... & 4 & -1\\\\\n", + "\t 7, 8, 7 & 2 & 1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$loop\\_rep\\_index] \\begin{enumerate*}\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item ⋯\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\end{enumerate*}\n", + "\n", + "\\item[\\$jac\\_rep] \\begin{enumerate}\n", + "\\item A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 1 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$jac\\_rep\\_index] \\begin{enumerate*}\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item ⋯\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 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1 |\n", + "| 6, 7, 6 | 2 | 1 |\n", + "| 5, 8, 1,.... | 6 | -1 |\n", + "| 5, 8, 1,.... | 5 | 1 |\n", + "| 5, 8, 1,.... | 4 | 1 |\n", + "| 5, 8, 2,.... | 5 | 1 |\n", + "| 5, 8, 2,.... | 4 | -1 |\n", + "| 5, 8, 2, 5 | 3 | -1 |\n", + "| 7, 8, 1,.... | 8 | 1 |\n", + "| 7, 8, 1,.... | 7 | 1 |\n", + "| 7, 8, 1,.... | 7 | -1 |\n", + "| 7, 8, 1,.... | 6 | -1 |\n", + "| 7, 8, 1,.... | 6 | -1 |\n", + "| 7, 8, 1,.... | 5 | -1 |\n", + "| 7, 8, 2,.... | 7 | -1 |\n", + "| 7, 8, 2,.... | 6 | -1 |\n", + "| 7, 8, 2,.... | 6 | 1 |\n", + "| 7, 8, 2,.... | 5 | 1 |\n", + "| 7, 8, 2,.... | 5 | 1 |\n", + "| 7, 8, 2,.... | 4 | 1 |\n", + "| 7, 8, 7 | 2 | 1 |\n", + "\n", + "\n", + "2. \n", + "A data.frame: 31 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 3, 3 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 5, 5 | 1 | -1 |\n", + "| 6, 6 | 1 | -1 |\n", + "| 7, 7 | 1 | -1 |\n", + "| 8, 8 | 1 | -1 |\n", + "| 1, 2, 1 | 2 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+ "311. 1\n", + "312. 1\n", + "313. 1\n", + "314. 1\n", + "315. 1\n", + "316. 1\n", + "317. 1\n", + "318. 1\n", + "319. 1\n", + "320. 1\n", + "321. 1\n", + "322. 1\n", + "323. 1\n", + "324. 1\n", + "325. 1\n", + "326. 1\n", + "327. 1\n", + "328. 1\n", + "329. 1\n", + "330. 1\n", + "331. 1\n", + "332. 1\n", + "333. 1\n", + "334. 1\n", + "335. 1\n", + "336. 1\n", + "337. 1\n", + "338. 1\n", + "339. 1\n", + "340. 1\n", + "341. 1\n", + "342. 1\n", + "343. 1\n", + "344. 1\n", + "345. 1\n", + "346. 1\n", + "347. 1\n", + "348. 1\n", + "349. 1\n", + "350. 1\n", + "351. 1\n", + "352. 1\n", + "353. 1\n", + "354. 1\n", + "355. 1\n", + "356. 1\n", + "357. 1\n", + "358. 1\n", + "359. 1\n", + "360. 1\n", + "361. 1\n", + "362. 1\n", + "363. 1\n", + "364. 1\n", + "365. 1\n", + "366. 1\n", + "367. 1\n", + "368. 1\n", + "369. 1\n", + "370. 1\n", + "371. 1\n", + "372. 1\n", + "373. 1\n", + "374. 1\n", + "375. 1\n", + "376. 1\n", + "377. 1\n", + "378. 1\n", + "379. 1\n", + "380. 1\n", + "381. 1\n", + "382. 1\n", + "383. 1\n", + "384. 1\n", + "385. 1\n", + "386. 1\n", + "387. 1\n", + "388. 1\n", + "389. 1\n", + "390. 1\n", + "391. 1\n", + "392. 1\n", + "393. 1\n", + "394. 1\n", + "395. 1\n", + "396. 1\n", + "397. 1\n", + "398. 1\n", + "399. 1\n", + "400. 1\n", + "401. 1\n", + "\n", + "\n", + "\n", + "$jac_rep\n", + ": 1. \n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "| 0 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | 1 | 1 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |\n", + "\n", + "\n", + "2. \n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "| 0 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | 1 | 1 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | 1 | 1 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "$jac_rep_index\n", + ": 1. 1\n", + "2. 1\n", + "3. 1\n", + "4. 1\n", + "5. 1\n", + "6. 1\n", + "7. 1\n", + "8. 1\n", + "9. 1\n", + "10. 1\n", + "11. 1\n", + "12. 1\n", + "13. 1\n", + "14. 1\n", + "15. 1\n", + "16. 1\n", + "17. 1\n", + "18. 1\n", + "19. 1\n", + "20. 1\n", + "21. 1\n", + "22. 1\n", + "23. 1\n", + "24. 1\n", + "25. 1\n", + "26. 1\n", + "27. 1\n", + "28. 1\n", + "29. 1\n", + "30. 1\n", + "31. 1\n", + "32. 1\n", + "33. 1\n", + "34. 1\n", + "35. 1\n", + "36. 1\n", + "37. 1\n", + "38. 1\n", + "39. 1\n", + "40. 1\n", + "41. 1\n", + "42. 1\n", + "43. 1\n", + "44. 1\n", + "45. 1\n", + "46. 1\n", + "47. 1\n", + "48. 1\n", + "49. 1\n", + "50. 1\n", + "51. 1\n", + "52. 1\n", + "53. 1\n", + "54. 1\n", + "55. 1\n", + "56. 1\n", + "57. 1\n", + "58. 1\n", + "59. 1\n", + "60. 1\n", + "61. 1\n", + "62. 1\n", + "63. 1\n", + "64. 1\n", + "65. 1\n", + "66. 1\n", + "67. 1\n", + "68. 1\n", + "69. 1\n", + "70. 1\n", + "71. 1\n", + "72. 1\n", + "73. 1\n", + "74. 1\n", + "75. 1\n", + "76. 1\n", + "77. 1\n", + "78. 1\n", + "79. 1\n", + "80. 1\n", + "81. 1\n", + "82. 1\n", + "83. 1\n", + "84. 1\n", + "85. 1\n", + "86. 1\n", + "87. 1\n", + "88. 1\n", + "89. 1\n", + "90. 1\n", + "91. 1\n", + "92. 1\n", + "93. 1\n", + "94. 1\n", + "95. 1\n", + "96. 1\n", + "97. 1\n", + "98. 1\n", + "99. 1\n", + "100. 1\n", + "101. 1\n", + "102. 1\n", + "103. 1\n", + "104. 1\n", + "105. 1\n", + "106. 1\n", + "107. 1\n", + "108. 1\n", + "109. 1\n", + "110. 2\n", + "111. 2\n", + "112. 2\n", + "113. 2\n", + "114. 2\n", + "115. 2\n", + "116. 2\n", + "117. 2\n", + "118. 2\n", + "119. 2\n", + "120. 2\n", + "121. 2\n", + "122. 2\n", + "123. 2\n", + "124. 2\n", + "125. 2\n", + "126. 2\n", + "127. 2\n", + "128. 2\n", + "129. 2\n", + "130. 2\n", + "131. 2\n", + "132. 2\n", + "133. 2\n", + "134. 2\n", + "135. 2\n", + "136. 2\n", + "137. 2\n", + "138. 2\n", + "139. 2\n", + "140. 2\n", + "141. 2\n", + "142. 2\n", + "143. 2\n", + "144. 2\n", + "145. 2\n", + "146. 2\n", + "147. 2\n", + "148. 2\n", + "149. 2\n", + "150. 2\n", + "151. 2\n", + "152. 2\n", + "153. 2\n", + "154. 2\n", + "155. 2\n", + "156. 2\n", + "157. 2\n", + "158. 2\n", + "159. 2\n", + "160. 2\n", + "161. 2\n", + "162. 2\n", + "163. 2\n", + "164. 2\n", + "165. 2\n", + "166. 2\n", + "167. 2\n", + "168. 2\n", + "169. 2\n", + "170. 2\n", + "171. 2\n", + "172. 2\n", + "173. 2\n", + "174. 2\n", + "175. 2\n", + "176. 2\n", + "177. 2\n", + "178. 2\n", + "179. 2\n", + "180. 2\n", + "181. 2\n", + "182. 2\n", + "183. 2\n", + "184. 2\n", + "185. 2\n", + "186. 2\n", + "187. 2\n", + "188. 2\n", + "189. 2\n", + "190. 2\n", + "191. 2\n", + "192. 2\n", + "193. 2\n", + "194. 2\n", + "195. 2\n", + "196. 2\n", + "197. 2\n", + "198. 2\n", + "199. 2\n", + "200. 2\n", + "201. ⋯\n", + "202. 1\n", + "203. 1\n", + "204. 1\n", + "205. 1\n", + "206. 1\n", + "207. 1\n", + "208. 1\n", + "209. 1\n", + "210. 1\n", + "211. 1\n", + "212. 1\n", + "213. 1\n", + "214. 1\n", + "215. 1\n", + "216. 1\n", + "217. 1\n", + "218. 1\n", + "219. 1\n", + "220. 1\n", + "221. 1\n", + "222. 1\n", + "223. 1\n", + "224. 1\n", + "225. 1\n", + "226. 1\n", + "227. 1\n", + "228. 1\n", + "229. 1\n", + "230. 1\n", + "231. 1\n", + "232. 1\n", + "233. 1\n", + "234. 1\n", + "235. 1\n", + "236. 1\n", + "237. 1\n", + "238. 1\n", + "239. 1\n", + "240. 1\n", + "241. 1\n", + "242. 1\n", + "243. 1\n", + "244. 1\n", + "245. 1\n", + "246. 1\n", + "247. 1\n", + "248. 1\n", + "249. 1\n", + "250. 1\n", + "251. 1\n", + "252. 1\n", + "253. 1\n", + "254. 1\n", + "255. 1\n", + "256. 1\n", + "257. 1\n", + "258. 1\n", + "259. 1\n", + "260. 1\n", + "261. 1\n", + "262. 1\n", + "263. 1\n", + "264. 1\n", + "265. 1\n", + "266. 1\n", + "267. 1\n", + "268. 1\n", + "269. 1\n", + "270. 1\n", + "271. 1\n", + "272. 1\n", + "273. 1\n", + "274. 1\n", + "275. 1\n", + "276. 1\n", + "277. 1\n", + "278. 1\n", + "279. 1\n", + "280. 1\n", + "281. 1\n", + "282. 1\n", + "283. 1\n", + "284. 1\n", + "285. 1\n", + "286. 1\n", + "287. 1\n", + "288. 1\n", + "289. 1\n", + "290. 1\n", + "291. 1\n", + "292. 1\n", + "293. 1\n", + "294. 1\n", + "295. 1\n", + "296. 1\n", + "297. 1\n", + "298. 1\n", + "299. 1\n", + "300. 1\n", + "301. 1\n", + "302. 1\n", + "303. 1\n", + "304. 1\n", + "305. 1\n", + "306. 1\n", + "307. 1\n", + "308. 1\n", + "309. 1\n", + "310. 1\n", + "311. 1\n", + "312. 1\n", + "313. 1\n", + "314. 1\n", + "315. 1\n", + "316. 1\n", + "317. 1\n", + "318. 1\n", + "319. 1\n", + "320. 1\n", + "321. 1\n", + "322. 1\n", + "323. 1\n", + "324. 1\n", + "325. 1\n", + "326. 1\n", + "327. 1\n", + "328. 1\n", + "329. 1\n", + "330. 1\n", + "331. 1\n", + "332. 1\n", + "333. 1\n", + "334. 1\n", + "335. 1\n", + "336. 1\n", + "337. 1\n", + "338. 1\n", + "339. 1\n", + "340. 1\n", + "341. 1\n", + "342. 1\n", + "343. 1\n", + "344. 1\n", + "345. 1\n", + "346. 1\n", + "347. 1\n", + "348. 1\n", + "349. 1\n", + "350. 1\n", + "351. 1\n", + "352. 1\n", + "353. 1\n", + "354. 1\n", + "355. 1\n", + "356. 1\n", + "357. 1\n", + "358. 1\n", + "359. 1\n", + "360. 1\n", + "361. 1\n", + "362. 1\n", + "363. 1\n", + "364. 1\n", + "365. 1\n", + "366. 1\n", + "367. 1\n", + "368. 1\n", + "369. 1\n", + "370. 1\n", + "371. 1\n", + "372. 1\n", + "373. 1\n", + "374. 1\n", + "375. 1\n", + "376. 1\n", + "377. 1\n", + "378. 1\n", + "379. 1\n", + "380. 1\n", + "381. 1\n", + "382. 1\n", + "383. 1\n", + "384. 1\n", + "385. 1\n", + "386. 1\n", + "387. 1\n", + "388. 1\n", + "389. 1\n", + "390. 1\n", + "391. 1\n", + "392. 1\n", + "393. 1\n", + "394. 1\n", + "395. 1\n", + "396. 1\n", + "397. 1\n", + "398. 1\n", + "399. 1\n", + "400. 1\n", + "401. 1\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "$loop_rep\n", + "$loop_rep[[1]]\n", + " loop length sign\n", + "1 1, 1 1 -1\n", + "2 2, 2 1 -1\n", + "3 3, 3 1 -1\n", + "4 4, 4 1 -1\n", + "5 5, 5 1 -1\n", + "6 6, 6 1 -1\n", + "7 7, 7 1 -1\n", + "8 8, 8 1 -1\n", + "9 1, 2, 1 2 1\n", + "10 3, 4, 3 2 1\n", + "11 4, 5, 4 2 1\n", + "12 6, 7, 6 2 1\n", + "13 5, 8, 1,.... 6 -1\n", + "14 5, 8, 1,.... 5 1\n", + "15 5, 8, 1,.... 4 1\n", + "16 5, 8, 2,.... 5 1\n", + "17 5, 8, 2,.... 4 -1\n", + "18 5, 8, 2, 5 3 -1\n", + "19 7, 8, 1,.... 8 1\n", + "20 7, 8, 1,.... 7 1\n", + "21 7, 8, 1,.... 7 -1\n", + "22 7, 8, 1,.... 6 -1\n", + "23 7, 8, 1,.... 6 -1\n", + "24 7, 8, 1,.... 5 -1\n", + "25 7, 8, 2,.... 7 -1\n", + "26 7, 8, 2,.... 6 -1\n", + "27 7, 8, 2,.... 6 1\n", + "28 7, 8, 2,.... 5 1\n", + "29 7, 8, 2,.... 5 1\n", + "30 7, 8, 2,.... 4 1\n", + "31 7, 8, 7 2 1\n", + "\n", + "$loop_rep[[2]]\n", + " loop length sign\n", + "1 1, 1 1 -1\n", + "2 2, 2 1 -1\n", + "3 3, 3 1 -1\n", + "4 4, 4 1 -1\n", + "5 5, 5 1 -1\n", + "6 6, 6 1 -1\n", + "7 7, 7 1 -1\n", + "8 8, 8 1 -1\n", + "9 1, 2, 1 2 1\n", + "10 3, 4, 3 2 1\n", + "11 4, 5, 4 2 1\n", + "12 6, 7, 6 2 1\n", + "13 5, 8, 1,.... 6 -1\n", + "14 5, 8, 1,.... 5 1\n", + "15 5, 8, 1,.... 4 1\n", + "16 5, 8, 2,.... 5 1\n", + "17 5, 8, 2,.... 4 -1\n", + "18 5, 8, 2, 5 3 -1\n", + "19 7, 8, 1,.... 8 1\n", + "20 7, 8, 1,.... 7 -1\n", + "21 7, 8, 1,.... 7 -1\n", + "22 7, 8, 1,.... 6 1\n", + "23 7, 8, 1,.... 6 -1\n", + "24 7, 8, 1,.... 5 1\n", + "25 7, 8, 2,.... 7 -1\n", + "26 7, 8, 2,.... 6 1\n", + "27 7, 8, 2,.... 6 1\n", + "28 7, 8, 2,.... 5 -1\n", + "29 7, 8, 2,.... 5 1\n", + "30 7, 8, 2,.... 4 -1\n", + "31 7, 8, 7 2 1\n", + "\n", + "\n", + "$loop_rep_index\n", + " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\n", + " [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [482] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [556] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [667] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [704] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [741] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [815] 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1407] 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1444] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1481] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1555] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1592] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1666] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1777] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1814] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1851] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1888] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1962] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2110] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2332] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2406] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2480] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2554] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2591] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2628] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2702] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2739] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2776] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2850] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2887] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2924] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2998] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3035] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3072] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3109] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3146] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3183] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3220] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3257] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3294] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3368] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3405] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3442] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3479] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3516] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3590] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3627] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3664] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3738] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3775] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3812] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3886] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3923] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3960] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3997] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4071] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4108] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4145] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4182] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4219] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4256] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4626] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4663] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4700] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4774] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4811] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4848] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4922] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4959] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4996] 1 1 1 1 1 1\n", + "\n", + "$jac_rep\n", + "$jac_rep[[1]]\n", + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 1\n", + "[2,] 1 -1 0 0 0 0 0 -1\n", + "[3,] 0 -1 -1 1 0 0 0 0\n", + "[4,] 0 1 1 -1 1 0 0 0\n", + "[5,] 0 1 0 1 -1 0 0 0\n", + "[6,] 0 0 0 0 -1 -1 1 0\n", + "[7,] 0 0 0 0 -1 1 -1 1\n", + "[8,] 0 0 0 0 1 0 1 -1\n", + "\n", + "$jac_rep[[2]]\n", + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 1\n", + "[2,] 1 -1 0 0 0 0 0 -1\n", + "[3,] 0 -1 -1 1 0 0 0 0\n", + "[4,] 0 1 1 -1 1 0 0 0\n", + "[5,] 0 1 0 1 -1 0 0 0\n", + "[6,] 0 0 0 0 -1 -1 1 0\n", + "[7,] 0 0 0 0 1 1 -1 1\n", + "[8,] 0 0 0 0 1 0 1 -1\n", + "\n", + "\n", + "$jac_rep_index\n", + " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\n", + " [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [482] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [556] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [667] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [704] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [741] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [815] 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1666] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1777] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1814] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1851] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1888] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1962] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2110] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2332] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2406] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2480] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2554] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2591] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2628] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2702] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2739] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2776] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2850] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2887] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2924] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2998] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3035] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3072] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3109] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3146] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3183] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3220] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3257] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3294] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3368] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[3405] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3442] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3479] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3516] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3590] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3627] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3664] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3738] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3775] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3812] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3886] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3923] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3960] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[3997] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4071] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4108] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4145] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4182] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4219] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4256] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4626] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4663] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[4700] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4774] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4811] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4848] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4922] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4959] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[4996] 1 1 1 1 1 1" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res_tab_all$loop_rep_index" + ] + }, + { + "cell_type": "code", + "execution_count": 111, + "id": "a1881f7e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Draw background in the plot corresponding to the time points where\n", + "# certain loop structures are present\n", + "\n", + "# 1-to-1 time vector (must match loop_rep_index length)\n", + "time_vec <- sort(unique(sol_long$time))\n", + "\n", + "stopifnot(length(res_tab_all$loop_rep_index) == length(time_vec))\n", + "\n", + "# Run-length encode to get contiguous segments of the same loop structure\n", + "r <- rle(res_tab_all$loop_rep_index)\n", + "\n", + "end_idx <- cumsum(r$lengths)\n", + "start_idx <- c(1, head(end_idx + 1, -1))\n", + "\n", + "bands <- tibble(\n", + " loop_type = factor(r$values),\n", + " t_start = time_vec[start_idx],\n", + " t_end = time_vec[end_idx]\n", + ")\n", + "transition_times <- bands$t_end[-nrow(bands)]" + ] + }, + { + "cell_type": "code", + "execution_count": 112, + "id": "8725b19d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 840 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plot2 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " # background bands (behind lines)\n", + " geom_rect(\n", + " data = bands,\n", + " aes(xmin = t_start, xmax = t_end, ymin = -Inf, ymax = Inf, fill = loop_type),\n", + " inherit.aes = FALSE,\n", + " alpha = 0.1\n", + " ) +\n", + " geom_vline(\n", + " xintercept = transition_times,\n", + " colour = \"grey40\",\n", + " linewidth = 0.7,\n", + " alpha = 0.35\n", + " ) +\n", + " geom_line(linewidth = 2) +\n", + " scale_colour_manual(values = colors) +\n", + " scale_fill_brewer(palette = \"Set2\", name = \"Loop structure\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 5000, 1000),\n", + " minor_breaks = seq(0, 5000, 500),\n", + " limits = c(0, 5000),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 5000), clip = \"on\") +\n", + " labs(\n", + " title = \"Dynamics of the Reduced MAPK Model with Explicit Feedback\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " panel.grid = element_blank(),\n", + " panel.border = element_rect(colour = \"black\", fill = NA, linewidth = 1.1)\n", + " )\n", + "\n", + "plot2\n" + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "id": "3bc28d1d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 8
len_1len_2len_3len_4len_5len_6len_7len_8
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
all85135531
pos05024111
neg80111420
\n" + ], + "text/latex": [ + "A data.frame: 3 × 8\n", + "\\begin{tabular}{r|llllllll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4 & len\\_5 & len\\_6 & len\\_7 & len\\_8\\\\\n", + " & & & & & & & & \\\\\n", + "\\hline\n", + "\tall & 8 & 5 & 1 & 3 & 5 & 5 & 3 & 1\\\\\n", + "\tpos & 0 & 5 & 0 & 2 & 4 & 1 & 1 & 1\\\\\n", + "\tneg & 8 & 0 & 1 & 1 & 1 & 4 & 2 & 0\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 8\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> | len_5 <dbl> | len_6 <dbl> | len_7 <dbl> | len_8 <dbl> |\n", + "|---|---|---|---|---|---|---|---|---|\n", + "| all | 8 | 5 | 1 | 3 | 5 | 5 | 3 | 1 |\n", + "| pos | 0 | 5 | 0 | 2 | 4 | 1 | 1 | 1 |\n", + "| neg | 8 | 0 | 1 | 1 | 1 | 4 | 2 | 0 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4 len_5 len_6 len_7 len_8\n", + "all 8 5 1 3 5 5 3 1 \n", + "pos 0 5 0 2 4 1 1 1 \n", + "neg 8 0 1 1 1 4 2 0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab_all$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "id": "0a868f1a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 8
len_1len_2len_3len_4len_5len_6len_7len_8
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
all85135531
pos05014301
neg80121230
\n" + ], + "text/latex": [ + "A data.frame: 3 × 8\n", + "\\begin{tabular}{r|llllllll}\n", + " & len\\_1 & len\\_2 & len\\_3 & len\\_4 & len\\_5 & len\\_6 & len\\_7 & len\\_8\\\\\n", + " & & & & & & & & \\\\\n", + "\\hline\n", + "\tall & 8 & 5 & 1 & 3 & 5 & 5 & 3 & 1\\\\\n", + "\tpos & 0 & 5 & 0 & 1 & 4 & 3 & 0 & 1\\\\\n", + "\tneg & 8 & 0 & 1 & 2 & 1 & 2 & 3 & 0\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 8\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> | len_3 <dbl> | len_4 <dbl> | len_5 <dbl> | len_6 <dbl> | len_7 <dbl> | len_8 <dbl> |\n", + "|---|---|---|---|---|---|---|---|---|\n", + "| all | 8 | 5 | 1 | 3 | 5 | 5 | 3 | 1 |\n", + "| pos | 0 | 5 | 0 | 1 | 4 | 3 | 0 | 1 |\n", + "| neg | 8 | 0 | 1 | 2 | 1 | 2 | 3 | 0 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2 len_3 len_4 len_5 len_6 len_7 len_8\n", + "all 8 5 1 3 5 5 3 1 \n", + "pos 0 5 0 1 4 3 0 1 \n", + "neg 8 0 1 2 1 2 3 0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab_all$loop_rep[[2]])" + ] + }, + { + "cell_type": "markdown", + "id": "6f592bea", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "### **2.2. Reduced MAPK Model without explicit feedback**" + ] + }, + { + "cell_type": "markdown", + "id": "f59d6720", + "metadata": {}, + "source": [ + "#### **2.1.1. Loop structure (at first)**" + ] + }, + { + "cell_type": "code", + "execution_count": 118, + "id": "f152e382", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 7 × 3
looplengthsign
<I<list>><dbl><dbl>
1, 11-1
2, 21-1
4, 41-1
5, 51-1
7, 71-1
8, 81-1
1, 2, 12 1
\n" + ], + "text/latex": [ + "A data.frame: 7 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 4, 4 & 1 & -1\\\\\n", + "\t 5, 5 & 1 & -1\\\\\n", + "\t 7, 7 & 1 & -1\\\\\n", + "\t 8, 8 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 7 × 3\n", + "\n", + "| loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|\n", + "| 1, 1 | 1 | -1 |\n", + "| 2, 2 | 1 | -1 |\n", + "| 4, 4 | 1 | -1 |\n", + "| 5, 5 | 1 | -1 |\n", + "| 7, 7 | 1 | -1 |\n", + "| 8, 8 | 1 | -1 |\n", + "| 1, 2, 1 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "1 1, 1 1 -1 \n", + "2 2, 2 1 -1 \n", + "3 4, 4 1 -1 \n", + "4 5, 5 1 -1 \n", + "5 7, 7 1 -1 \n", + "6 8, 8 1 -1 \n", + "7 1, 2, 1 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# compute loops\n", + "res_tab <- find_loops_vset(model_mapk_simple_wo_feedback,vset=list(initial_conditions),t=1,klin=klin,kn=kn,n1=n1,max_num_loops=10)\n", + "# The loop list is reported\n", + "res_tab$loop_rep[[1]] \n", + "# To access a specific loop representation: e.g., the sixth loop, add [6,]" + ] + }, + { + "cell_type": "code", + "execution_count": 119, + "id": "8f02f293", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 2
len_1len_2
<dbl><dbl>
all61
pos01
neg60
\n" + ], + "text/latex": [ + "A data.frame: 3 × 2\n", + "\\begin{tabular}{r|ll}\n", + " & len\\_1 & len\\_2\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\tall & 6 & 1\\\\\n", + "\tpos & 0 & 1\\\\\n", + "\tneg & 6 & 0\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 2\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> |\n", + "|---|---|---|\n", + "| all | 6 | 1 |\n", + "| pos | 0 | 1 |\n", + "| neg | 6 | 0 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2\n", + "all 6 1 \n", + "pos 0 1 \n", + "neg 6 0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "id": "b5415ec2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 2 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
71, 2, 12 1
\n" + ], + "text/latex": [ + "A data.frame: 2 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t7 & 1, 2, 1 & 2 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 2 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 7 | 1, 2, 1 | 2 | 1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "7 1, 2, 1 2 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2 \n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "f5fbad0b", + "metadata": {}, + "source": [ + "#### **2.1.2. Calculating the Jacobian matrix**\n", + "\n", + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" + ] + }, + { + "cell_type": "code", + "execution_count": 121, + "id": "b058ca06", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-1 10 0 00 0 0
1-10 0 00 0 0
0-10 1 00 0 0
0 10-1 10 0 0
0 00 0-10 0 0
0 00 0-10 1 0
0 00 0 10-1 1
0 00 0 00 0-1
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & -1 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 |\n", + "| 0 | -1 | 0 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 0 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 0 \n", + "[2,] 1 -1 0 0 0 0 0 0 \n", + "[3,] 0 -1 0 1 0 0 0 0 \n", + "[4,] 0 1 0 -1 1 0 0 0 \n", + "[5,] 0 0 0 0 -1 0 0 0 \n", + "[6,] 0 0 0 0 -1 0 1 0 \n", + "[7,] 0 0 0 0 1 0 -1 1 \n", + "[8,] 0 0 0 0 0 0 0 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix (at initialization point)\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "34b4f161", + "metadata": {}, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003]." + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "id": "299e548b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
S1
1.01955086432784
S2
98.9804491356722
S3
1.43623788843733
S4
6.07643921148842
S5
292.487322900074
S6
0.0670824395339598
S7
1.04469160783373
S8
298.888225952632
\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[S1] 1.01955086432784\n", + "\\item[S2] 98.9804491356722\n", + "\\item[S3] 1.43623788843733\n", + "\\item[S4] 6.07643921148842\n", + "\\item[S5] 292.487322900074\n", + "\\item[S6] 0.0670824395339598\n", + "\\item[S7] 1.04469160783373\n", + "\\item[S8] 298.888225952632\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "S1\n", + ": 1.01955086432784S2\n", + ": 98.9804491356722S3\n", + ": 1.43623788843733S4\n", + ": 6.07643921148842S5\n", + ": 292.487322900074S6\n", + ": 0.0670824395339598S7\n", + ": 1.04469160783373S8\n", + ": 298.888225952632\n", + "\n" + ], + "text/plain": [ + " S1 S2 S3 S4 S5 S6 \n", + " 1.01955086 98.98044914 1.43623789 6.07643921 292.48732290 0.06708244 \n", + " S7 S8 \n", + " 1.04469161 298.88822595 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The function func_POSm4 returns a vector, but deSolve needs the vector within\n", + "# a list as output. Therefore, we define a function that simply puts the output \n", + "# of func_POSm4 into a list:\n", + "func_list <- function(t,x,klin,kn,n1){list(model_mapk_simple_wo_feedback(t,x,klin,kn,n1))}\n", + "sol <- deSolve::ode(y = initial_conditions, times = seq(0,500,1), func = func_list, \n", + " parms=klin, kn=kn, n1=n1)\n", + "\n", + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star_end <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star_end" + ] + }, + { + "cell_type": "code", + "execution_count": 124, + "id": "99caeba0", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-0.006018131 0.0001747516 0.0000000 0.00000000 0.0000000000 0.0000000 0.00000000 2.196046e-05
0.006018131-0.0001747516 0.0000000 0.00000000 0.0000000000 0.0000000 0.00000000-2.196046e-05
0.000000000-0.0021845600-0.1373966 0.02532550 0.0000000000 0.0000000 0.00000000 0.000000e+00
0.000000000-0.0050230608 0.1373966-0.10888315 0.0001189866 0.0000000 0.00000000 0.000000e+00
0.000000000 0.0072076207 0.0000000 0.08355765-0.0001189866 0.0000000 0.00000000 0.000000e+00
0.000000000 0.0000000000 0.0000000 0.00000000-0.0001113063-0.4831478 0.02913389 0.000000e+00
0.000000000 0.0000000000 0.0000000 0.00000000-0.0015164776 0.4831478-0.45519861 7.612218e-05
0.000000000 0.0000000000 0.0000000 0.00000000 0.0016277839 0.0000000 0.42606471-7.612218e-05
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -0.006018131 & 0.0001747516 & 0.0000000 & 0.00000000 & 0.0000000000 & 0.0000000 & 0.00000000 & 2.196046e-05\\\\\n", + "\t 0.006018131 & -0.0001747516 & 0.0000000 & 0.00000000 & 0.0000000000 & 0.0000000 & 0.00000000 & -2.196046e-05\\\\\n", + "\t 0.000000000 & -0.0021845600 & -0.1373966 & 0.02532550 & 0.0000000000 & 0.0000000 & 0.00000000 & 0.000000e+00\\\\\n", + "\t 0.000000000 & -0.0050230608 & 0.1373966 & -0.10888315 & 0.0001189866 & 0.0000000 & 0.00000000 & 0.000000e+00\\\\\n", + "\t 0.000000000 & 0.0072076207 & 0.0000000 & 0.08355765 & -0.0001189866 & 0.0000000 & 0.00000000 & 0.000000e+00\\\\\n", + "\t 0.000000000 & 0.0000000000 & 0.0000000 & 0.00000000 & -0.0001113063 & -0.4831478 & 0.02913389 & 0.000000e+00\\\\\n", + "\t 0.000000000 & 0.0000000000 & 0.0000000 & 0.00000000 & -0.0015164776 & 0.4831478 & -0.45519861 & 7.612218e-05\\\\\n", + "\t 0.000000000 & 0.0000000000 & 0.0000000 & 0.00000000 & 0.0016277839 & 0.0000000 & 0.42606471 & -7.612218e-05\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -0.006018131 | 0.0001747516 | 0.0000000 | 0.00000000 | 0.0000000000 | 0.0000000 | 0.00000000 | 2.196046e-05 |\n", + "| 0.006018131 | -0.0001747516 | 0.0000000 | 0.00000000 | 0.0000000000 | 0.0000000 | 0.00000000 | -2.196046e-05 |\n", + "| 0.000000000 | -0.0021845600 | -0.1373966 | 0.02532550 | 0.0000000000 | 0.0000000 | 0.00000000 | 0.000000e+00 |\n", + "| 0.000000000 | -0.0050230608 | 0.1373966 | -0.10888315 | 0.0001189866 | 0.0000000 | 0.00000000 | 0.000000e+00 |\n", + "| 0.000000000 | 0.0072076207 | 0.0000000 | 0.08355765 | -0.0001189866 | 0.0000000 | 0.00000000 | 0.000000e+00 |\n", + "| 0.000000000 | 0.0000000000 | 0.0000000 | 0.00000000 | -0.0001113063 | -0.4831478 | 0.02913389 | 0.000000e+00 |\n", + "| 0.000000000 | 0.0000000000 | 0.0000000 | 0.00000000 | -0.0015164776 | 0.4831478 | -0.45519861 | 7.612218e-05 |\n", + "| 0.000000000 | 0.0000000000 | 0.0000000 | 0.00000000 | 0.0016277839 | 0.0000000 | 0.42606471 | -7.612218e-05 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] [,6] \n", + "[1,] -0.006018131 0.0001747516 0.0000000 0.00000000 0.0000000000 0.0000000\n", + "[2,] 0.006018131 -0.0001747516 0.0000000 0.00000000 0.0000000000 0.0000000\n", + "[3,] 0.000000000 -0.0021845600 -0.1373966 0.02532550 0.0000000000 0.0000000\n", + "[4,] 0.000000000 -0.0050230608 0.1373966 -0.10888315 0.0001189866 0.0000000\n", + "[5,] 0.000000000 0.0072076207 0.0000000 0.08355765 -0.0001189866 0.0000000\n", + "[6,] 0.000000000 0.0000000000 0.0000000 0.00000000 -0.0001113063 -0.4831478\n", + "[7,] 0.000000000 0.0000000000 0.0000000 0.00000000 -0.0015164776 0.4831478\n", + "[8,] 0.000000000 0.0000000000 0.0000000 0.00000000 0.0016277839 0.0000000\n", + " [,7] [,8] \n", + "[1,] 0.00000000 2.196046e-05\n", + "[2,] 0.00000000 -2.196046e-05\n", + "[3,] 0.00000000 0.000000e+00\n", + "[4,] 0.00000000 0.000000e+00\n", + "[5,] 0.00000000 0.000000e+00\n", + "[6,] 0.02913389 0.000000e+00\n", + "[7,] -0.45519861 7.612218e-05\n", + "[8,] 0.42606471 -7.612218e-05" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "j_matrix <- numDeriv::jacobian(model_mapk_simple_w_feedback, s_star_end,method=\"complex\",\n", + " t=3650,klin=klin, kn=kn, n1=n1)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "id": "d1b442c8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 8 × 8 of type dbl
-1 1 0 0 0 0 0 1
1-1 0 0 0 0 0-1
0-1-1 1 0 0 0 0
0-1 1-1 1 0 0 0
0 1 0 1-1 0 0 0
0 0 0 0-1-1 1 0
0 0 0 0-1 1-1 1
0 0 0 0 1 0 1-1
\n" + ], + "text/latex": [ + "A matrix: 8 × 8 of type dbl\n", + "\\begin{tabular}{llllllll}\n", + "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", + "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", + "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", + "\t 0 & -1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", + "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", + "\t 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\\\\n", + "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 8 × 8 of type dbl\n", + "\n", + "| -1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |\n", + "| 1 | -1 | 0 | 0 | 0 | 0 | 0 | -1 |\n", + "| 0 | -1 | -1 | 1 | 0 | 0 | 0 | 0 |\n", + "| 0 | -1 | 1 | -1 | 1 | 0 | 0 | 0 |\n", + "| 0 | 1 | 0 | 1 | -1 | 0 | 0 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | -1 | 1 | 0 |\n", + "| 0 | 0 | 0 | 0 | -1 | 1 | -1 | 1 |\n", + "| 0 | 0 | 0 | 0 | 1 | 0 | 1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", + "[1,] -1 1 0 0 0 0 0 1 \n", + "[2,] 1 -1 0 0 0 0 0 -1 \n", + "[3,] 0 -1 -1 1 0 0 0 0 \n", + "[4,] 0 -1 1 -1 1 0 0 0 \n", + "[5,] 0 1 0 1 -1 0 0 0 \n", + "[6,] 0 0 0 0 -1 -1 1 0 \n", + "[7,] 0 0 0 0 -1 1 -1 1 \n", + "[8,] 0 0 0 0 1 0 1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "b007c715", + "metadata": {}, + "source": [ + "#### **2.1.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "id": "1d8fa1ab", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 840 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol[,1], sol[,2:dim(sol)[2]],\n", + " type = \"l\",\n", + " lty = 1,\n", + " xlab = \"Time\",\n", + " ylab = \"Concentration\",\n", + ")\n", + "\n", + "legend(\n", + " \"topright\",\n", + " legend = all_labels,\n", + " col = 1:8,\n", + " lty = 1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "id": "5cc9b71e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "investigate_label <- c('MAPKK** (S5)', 'MAPK** (S8)')\n", + "investigate_index <- c(6, 9)" + ] + }, + { + "cell_type": "code", + "execution_count": 129, + "id": "cf8c7b52", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_for_plot <- as.data.frame(sol[, c(1, investigate_index)])\n", + "\n", + "# rename columns for clarity (use time + investigate_label)\n", + "colnames(sol_for_plot) <- c(\"time\", investigate_label)\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = `MAPKK** (S5)`:`MAPK** (S8)`, names_to = \"species\", values_to = \"value\")" + ] + }, + { + "cell_type": "code", + "execution_count": 134, + "id": "e0fc16f0", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 300, + "width": 480 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "options(repr.plot.width = 8, repr.plot.height = 5)\n", + "colors <- c(\n", + " `MAPKK** (S5)` = \"#EE7733\",\n", + " `MAPK** (S8)` = \"#0077BB\"\n", + ")\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(linewidth = 2) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 500, 100),\n", + " minor_breaks = seq(0, 500, 50),\n", + " limits = c(0, 500),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 500), clip = \"on\") +\n", + " labs(\n", + " title = \"Dynamics of Model without Explicit Feedback\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + "\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "code", + "execution_count": 137, + "id": "7334152c", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 2
len_1len_2
<dbl><dbl>
all85
pos05
neg80
\n" + ], + "text/latex": [ + "A data.frame: 3 × 2\n", + "\\begin{tabular}{r|ll}\n", + " & len\\_1 & len\\_2\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\tall & 8 & 5\\\\\n", + "\tpos & 0 & 5\\\\\n", + "\tneg & 8 & 0\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 2\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> |\n", + "|---|---|---|\n", + "| all | 8 | 5 |\n", + "| pos | 0 | 5 |\n", + "| neg | 8 | 0 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2\n", + "all 8 5 \n", + "pos 0 5 \n", + "neg 8 0 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res_tab <- find_loops_vset(model_mapk_simple_wo_feedback,vset=list(sol[dim(sol)[1],2:9]),t=1,klin=klin,kn=kn,n1=n1)\n", + "loop_summary(res_tab$loop_rep[[1]])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/model_6_calcium_oscillations_R.ipynb b/examples/model_6_calcium_oscillations_R.ipynb new file mode 100644 index 0000000..8567232 --- /dev/null +++ b/examples/model_6_calcium_oscillations_R.ipynb @@ -0,0 +1,3491 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5c5107a0", + "metadata": {}, + "source": [ + "## **0. Initialization**" + ] + }, + { + "cell_type": "markdown", + "id": "0aa853b2", + "metadata": {}, + "source": [ + "### **Installation**\n", + "LoopDetectR is on CRAN and can be installed within R by" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ad430870", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Before running the R code cells in jupyter notebook,\n", + "# initialize the R kernel by this line of code:\n", + "# IRkernel::installspec()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f2d7c70f", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'LoopDetectR' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "# Download and install\n", + "install.packages(\"LoopDetectR\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1c741284", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'deSolve' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Installing package into 'C:/Users/Admin/AppData/Local/R/win-library/4.5'\n", + "(as 'lib' is unspecified)\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "package 'numDeriv' successfully unpacked and MD5 sums checked\n", + "\n", + "The downloaded binary packages are in\n", + "\tC:\\Users\\Admin\\AppData\\Local\\Temp\\Rtmpk1kCL5\\downloaded_packages\n" + ] + } + ], + "source": [ + "install.packages(\"deSolve\") # if not already installed\n", + "install.packages(\"numDeriv\") # if not already installed" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1d32152b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n", + "\u001b[32m✔\u001b[39m \u001b[34mdplyr \u001b[39m 1.1.4 \u001b[32m✔\u001b[39m \u001b[34mreadr \u001b[39m 2.1.6\n", + "\u001b[32m✔\u001b[39m \u001b[34mforcats \u001b[39m 1.0.1 \u001b[32m✔\u001b[39m \u001b[34mstringr \u001b[39m 1.6.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mggplot2 \u001b[39m 4.0.1 \u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.3.0\n", + "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.4 \u001b[32m✔\u001b[39m \u001b[34mtidyr \u001b[39m 1.3.1\n", + "\u001b[32m✔\u001b[39m \u001b[34mpurrr \u001b[39m 1.2.0 \n", + "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n", + "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m masks \u001b[34mstats\u001b[39m::lag()\n", + "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m\u001b[39m\u001b[23m) to force all conflicts to become errors\n" + ] + } + ], + "source": [ + "# Load package\n", + "library(\"LoopDetectR\")\n", + "library(deSolve)\n", + "library(tidyverse)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3eb6dbbb", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "colors <- c('#EE7733', '#0077BB', '#33BBEE', '#EE3377', '#CC3311', '#009988', '#BBBBBB')" + ] + }, + { + "cell_type": "markdown", + "id": "de63ff1e", + "metadata": {}, + "source": [ + "## **1. Model definition**" + ] + }, + { + "cell_type": "markdown", + "id": "8ebe4f73", + "metadata": {}, + "source": [ + "#### **Example 6: Calcium oscillations model**" + ] + }, + { + "cell_type": "markdown", + "id": "ed0a97ed", + "metadata": {}, + "source": [ + "The reactions (flows) constituting the model are given by\n", + "$$\n", + "\\begin{aligned}\n", + "\\nu_1 &= k_1,\\\\[6pt]\n", + "\\nu_2 &= k_2,\\\\[6pt]\n", + "\\nu_3 &= k_3 \\cdot \\frac{S_1^{n_1}}{kn_1^{\\,n_1} + S_1^{n_1}},\\\\[10pt]\n", + "\\nu_4 &= k_4 \\cdot \n", + " \\frac{S_2^{n_2}}{kn_2^{\\,n_2} + S_2^{n_2}} \\cdot\n", + " \\frac{S_1^{n_3}}{kn_3^{\\,n_3} + S_1^{n_3}},\\\\[10pt]\n", + "\\nu_5 &= k_5 \\cdot S_2,\\\\[6pt]\n", + "\\nu_6 &= k_6 \\cdot S_1.\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "The model is composed from these six reactions by\n", + "$$\n", + "\\begin{aligned}\n", + "\\frac{dS_1}{dt} &= \\nu_1 + \\nu_2 - \\nu_3 + \\nu_4 + \\nu_5 - \\nu_6,\\\\[6pt]\n", + "\\frac{dS_2}{dt} &= \\nu_3 - \\nu_4 - \\nu_5.\n", + "\\end{aligned}\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "0a5aff3a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "model_calcium_oscillation <- function(t, y, klin, kn, n0) {\n", + " # Unpack state variables\n", + " S1 <- y[1]\n", + " S2 <- y[2]\n", + "\n", + " # Kinetic parameters\n", + " k1 <- klin[1]; k2 <- klin[2]; k3 <- klin[3]\n", + " k4 <- klin[4]; k5 <- klin[5]; k6 <- klin[6]\n", + "\n", + " # Saturation constants\n", + " kn1 <- kn[1]; kn2 <- kn[2]; kn3 <- kn[3]\n", + "\n", + " # Hill exponents\n", + " n1 <- n0[1]; n2 <- n0[2]; n3 <- n0[3]\n", + "\n", + " # Reaction rates\n", + " v1 <- k1\n", + " v2 <- k2\n", + " v3 <- k3 * (S1^n1) / (kn1^n1 + S1^n1)\n", + " v4 <- k4 *\n", + " (S2^n2) / (kn2^n2 + S2^n2) *\n", + " (S1^n3) / (kn3^n3 + S1^n3)\n", + " v5 <- k5 * S2\n", + " v6 <- k6 * S1\n", + "\n", + " # ODEs\n", + " dS1 <- v1 + v2 - v3 + v4 + v5 - v6\n", + " dS2 <- v3 - v4 - v5\n", + "\n", + " dx = rep(0, 2)\n", + " dx[1] = dS1\n", + " dx[2] = dS2\n", + " return(dx)\n", + "}" + ] + }, + { + "cell_type": "markdown", + "id": "44e7e155", + "metadata": {}, + "source": [ + "## **2. Result reproduction**" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4e5b9062", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Parameters from supplementary material\n", + "initial_conditions_calcium <- c(0.3920, 1.6456)\n", + "klin_calcium <- c(1, 7.3 * 0.4, 65, 500, 1, 10) # Fix k2 to 40% of original value as the new params from Prof. Baum\n", + "kn_calcium <- c(1, 2, 0.9)\n", + "n_calcium <- c(2, 2, 4)\n", + "time_points <- seq(0, 3, length.out = 301)\n", + "\n", + "# Additional variables \n", + "all_labels <- c(\"S1\", \"S2\")" + ] + }, + { + "cell_type": "markdown", + "id": "b927c538", + "metadata": {}, + "source": [ + "### **2.1. Reduced MAPK Model with explicit feedback**" + ] + }, + { + "cell_type": "markdown", + "id": "b9c9522a", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "source": [ + "#### **2.1.1. Loop structure (at first)**" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "6c2540e5", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 3 × 3
looplengthsign
<I<list>><dbl><dbl>
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A data.frame: 3 × 2
len_1len_2
<dbl><dbl>
all21
pos10
neg11
\n" + ], + "text/latex": [ + "A data.frame: 3 × 2\n", + "\\begin{tabular}{r|ll}\n", + " & len\\_1 & len\\_2\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\tall & 2 & 1\\\\\n", + "\tpos & 1 & 0\\\\\n", + "\tneg & 1 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 2\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> |\n", + "|---|---|---|\n", + "| all | 2 | 1 |\n", + "| pos | 1 | 0 |\n", + "| neg | 1 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2\n", + "all 2 1 \n", + "pos 1 0 \n", + "neg 1 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab$loop_rep[[1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "e9a5ecf2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A data.frame: 2 × 3
looplengthsign
<I<list>><dbl><dbl>
2 2, 21-1
31, 2, 12-1
\n" + ], + "text/latex": [ + "A data.frame: 2 × 3\n", + "\\begin{tabular}{r|lll}\n", + " & loop & length & sign\\\\\n", + " & > & & \\\\\n", + "\\hline\n", + "\t2 & 2, 2 & 1 & -1\\\\\n", + "\t3 & 1, 2, 1 & 2 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 2 × 3\n", + "\n", + "| | loop <I<list>> | length <dbl> | sign <dbl> |\n", + "|---|---|---|---|\n", + "| 2 | 2, 2 | 1 | -1 |\n", + "| 3 | 1, 2, 1 | 2 | -1 |\n", + "\n" + ], + "text/plain": [ + " loop length sign\n", + "2 2, 2 1 -1 \n", + "3 1, 2, 1 2 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Index of node of interest\n", + "noi <- 2 \n", + "# Return all loops from loop_list containing node 2\n", + "loop_list <- res_tab$loop_rep[[1]]\n", + "loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),]" + ] + }, + { + "cell_type": "markdown", + "id": "9f0fc026", + "metadata": {}, + "source": [ + "#### **2.1.2. Calculating the Jacobian matrix**\n", + "\n", + "Sign jacobian matrix can be access via `res_tab` variable that we have calculated above, or derived from a jacobian matrix at a specific state" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "05e68bc3", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 2 × 2 of type dbl
1 1
-1-1
\n" + ], + "text/latex": [ + "A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t 1 & 1\\\\\n", + "\t -1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 2 × 2 of type dbl\n", + "\n", + "| 1 | 1 |\n", + "| -1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2]\n", + "[1,] 1 1 \n", + "[2,] -1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# The corresponding signed Jacobian matrix (at initialization point)\n", + "res_tab$jac_rep[[1]]" + ] + }, + { + "cell_type": "markdown", + "id": "b4802333", + "metadata": {}, + "source": [ + "The function jacobian from the numDeriv package can be used to determine numerically the Jacobian matrix of an ODE system at a certain set of values for the variables, `s_star`. The approach is that of finite differences (with real step) or complex step approach, the latter of which is supposed to deliver more exact results [Martins et al., 2003]." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "adbc93e2", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n" + ], + "text/latex": [ + "\\begin{description*}\n", + "\\item[1] 0.310611331644207\n", + "\\item[2] 1.87644941000528\n", + "\\end{description*}\n" + ], + "text/markdown": [ + "1\n", + ": 0.3106113316442072\n", + ": 1.87644941000528\n", + "\n" + ], + "text/plain": [ + " 1 2 \n", + "0.3106113 1.8764494 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "func_list <- function(t,x,klin,kn,n0){list(model_calcium_oscillation(t,x,klin,kn,n0))}\n", + "sol <- deSolve::ode(y = initial_conditions_calcium, times = time_points, func = func_list, \n", + " parms=klin_calcium, kn=kn_calcium, n0=n_calcium)\n", + " \n", + "# Set the last point of the numeric solution as point of interest, omit the \n", + "# first column (it contains the time)\n", + "s_star_end <- sol[dim(sol)[1],2:dim(sol)[2]]\n", + "s_star_end" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "1d134ecb", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 2 × 2 of type dbl
-2.007491 2.856177
-7.992509-2.856177
\n" + ], + "text/latex": [ + "A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t -2.007491 & 2.856177\\\\\n", + "\t -7.992509 & -2.856177\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 2 × 2 of type dbl\n", + "\n", + "| -2.007491 | 2.856177 |\n", + "| -7.992509 | -2.856177 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2] \n", + "[1,] -2.007491 2.856177\n", + "[2,] -7.992509 -2.856177" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "j_matrix <- numDeriv::jacobian(model_calcium_oscillation, s_star_end,method=\"complex\",\n", + " t=3650,klin=klin_calcium, kn=kn_calcium, n0=n_calcium)\n", + "j_matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "d9a4b8c8", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
A matrix: 2 × 2 of type dbl
-1 1
-1-1
\n" + ], + "text/latex": [ + "A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t -1 & 1\\\\\n", + "\t -1 & -1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A matrix: 2 × 2 of type dbl\n", + "\n", + "| -1 | 1 |\n", + "| -1 | -1 |\n", + "\n" + ], + "text/plain": [ + " [,1] [,2]\n", + "[1,] -1 1 \n", + "[2,] -1 -1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "signed_jacobian <- sign(j_matrix)\n", + "signed_jacobian" + ] + }, + { + "cell_type": "markdown", + "id": "9fb5ce0e", + "metadata": {}, + "source": [ + "#### **2.1.3. Temporal dynamics**" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "b6906e49", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol <- deSolve::ode(y = initial_conditions_calcium, times = seq(0,2.64,0.01), func = func_list, \n", + " parms=klin_calcium, kn=kn_calcium, n0=n_calcium)\n", + "\n", + "s_star_end <- sol[dim(sol)[1],2:dim(sol)[2]]" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "20cd5293", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol <- deSolve::ode(y = s_star_end, times = seq(0,3,0.001), func = func_list, \n", + " parms=klin_calcium, kn=kn_calcium, n0=n_calcium)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "cf1a9580", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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bFoFIxSDS7W2D02DpEKmYCasR/kUEIt3cFJGsmbIaxlOxB5FubloGIhWDSDc3jQ4iRWL8aqRoNe107uEQqRhEurVleBApEqNXI/6hBkS6tSEi2TN+NcynYg8i3diwFEQqRlykQ7D6dBnCtUg3VaSXp+Gb+oEKS0Rh7GpkeGaHSDe2K2aiSC/DgEgPt0uA9F4igUiL4bV+gLoSYRi5GrRaf+KLZPtAdLVEGMaK5DAVexDp6mblTBRpNezqB6grEQZEurZZCuKLtF0s/6sfoapEGMatRo5ndoh0fbNyJj+142DDo61S8B1OO51nOEQqBpGubJWD+CI5oSNSkmd2iHRlI0TyYdxquEzFHkS6slENk0X6t/x4Wrf6Vz9MeYkgINLlRklIINLy+xXSsn6c0hJRGLMa2VqNdH/bNBXpdVi8ffzzZnyGQ2SR6lbDZyr2INLlNlVMFOlp2Bz+3QxP9QOVlQgDIl1sk4X4Iv0e9Z7P4e+aydFqMXj/jlWzdL0ekRb1A5WVCAMiXWyThTEiVZbgNVIxDVajHz8iVaTLEy6BSLM6alffatK9Rrhjpr+PtJrN+0jKraadLoNILiBSc6rTSYdDJEcQ6XQDr5k4UB+upUifR7xndfa3cqtpp2sQDpGKef8NXrqB10w8qO21TAdSgovkiIRIqVqtXiS3mTjQYB+ISMVUi+Q2Ew8Q6fj29SWsThFazODMBkQ6urnfTBzII9KW10iXt3ebiQeIdHz7+hITRHobjpnB2d91q5Gr1RDp+OYjSkx5RHo69sj0qlyI1BxEOrr5iBJWr5FsQaTm1KWTDtdDJCcQqTmI9HfrniL9txpRvK5Eb6RbTTtdg3BTRVpzZsONWzvOxAPpdPFF+vPobUz1khJhkG61unTS4bqItBj+7ZfDdrscOGp3emPPmXggna4uXA+RPp/RvXw8Gm1s/0Q2tkgl08vWaoj0d+NRJQxEevu8XsOcXiPNXqS84fzSTRRp9fHUbjs87f9DpLMbe87EA0T6vfGoEhNFevsU6HABlOdR5QtKhKFmNdK1GiL93nZciamHv18+v3sehvW48iUloiAu0s8XiDQKzmwoBpHOb5qG+CKtbB+JrpUIAyKd3zQN8UWa5Umrj6eXr9WOpiyYrsHSTRTpadiNLFxcIgyIdHHTLMQXabdamp7ScKVEGBDp/JZ5KH/i2kmkWV6OC5HSgUiBKBcpdauRbhQc/i4Gkc5vmYfidKPDIVIxfyK5rUZH/FutJ+FFmuV17SR7DZHObliJkUizuq6dZK8h0untapkg0myva+e3Gh1BpNPb1TLlEWmu17UTF0k7XUSR9nM9RUi71e6nSxkuvkhOhBSpwWp0BJFOb1cLIpWDSPuk4UqXbkK4qSK9PM3mzIYGq9ERRNr3FOllRqcIIdLZ7RIRXqTF5xWE7Iku0t0JZm81wXDxRZrTUbtButekwzVIN1Gk1Yz+sK9QJFotIOFF2i7m84d9iLQXTzclHH+PVAwi7cXTIVITECltuPgiOYFIzTme9u10ScMhUiQQKW24DCK9rT6f1a22E+bwqEQQykQSaDXtdE7hpoq0/Hp5NCxMTUKk5kiL1GDpJor0Oix3nyK9zuDTKBApbbj4Ii2G3dfZDRy1+yZrryFSV5EOT+tmKJJer0mHiy/S0/cj0mYG12xApLThipZuWjib10hvxmeB5xUpa6shUl+R9qvv8xqKPtT8v5evm6/WD07QQ6TmIFJfkQ7vIw2rfwXb7Y6vOnRfPERqDiJ1Fqmc9bD4tzl8tf14Knj3o/4QqTnS4bREWgyb3683w91LHCNSc6TDJRBpt/40YrEu+Pu+kyPk9w+XpxUpbaudzlwtXXyRtovvd5EKThGawyNS2lbTTtcg3ESRlsPz52PRbj2sHm738Rrp7Us33ddIaVtNO118kX6foZWc2bA8vlb43eeCiNQc6XTxRVp8X/xkV3SK0H/rw/tIi9WL6vtIaVutJJ1IOJ90E0VaD4eLn/y3vP9UbUqJMDRYjY4g0sQSEzdZ1pzZMK5EFBCpzUwcSCDS/t/ns7Wl8fVWs4qUt9UQqbdIY+smfx8JkTLRYOniiHTyQZoWJayZkUhq6YRF6l6iHulWK0gnHa67SDP6fCRESkt8keb0+UiIlJb4Is3p85GkRRoen7WaN1yLvYTVKUK2JBUpc6sh0sQS0zaZ6+cj7a/OMXOrIdLEEtM2qfl8pGEoPsKNSK2Zk0guSzf5qV35wYZXRIrLY5EShxMTab9ZlJ6Rh0itQaSpJZps8s2m9BxxRGoNIk0t0WSTH16P/trcqYQfiJSWDCL9W5Ze1250iSA8XI3UrbaXTucfjr9HKgaR0hJfpNdh8fbxz/yu/S3Xaog0scS0TZ6+X/TM7tMo5FoNkSaWmLZJ1VWExpUIw7xFyhwugUh/j0h3L/g4pUQYECkt8UWa8WskrV6blUge6ThqV8yj1cjdaog0scTUTf4Vfz7S6BJBeNRruVtt1iIZhGt7ZkOgEvUgUloQKRKzFil1uPAibZ8Phxh2T9Z/b45IrZEOF12k7eLrw1zeij4eaVSJSEj32nm483Spw7VYuikiPX19ONLhGvqmJzYgUnMQaXKJ0Zu8DS+/P1sNpsftEKk1sxbJItwEkZ6PLnyytX0jKaNIWq2mnS6WSBUfrjy2RCgQKS0P0nUWaTFzkRxWox+INLnE6E2eh7ffn70VfBjziBKhmLNIucMFF2nzd9B7u5jhwQapXpMOF1yk/XpYvHz+FcXmZTGLk1aVe006XHSRjj6L4tlgKldLBEK61y7CnabLHS68SPvt+nANoRfb8xoQqT1zFskkHCetFtNgNfqBSJNLtNgkYIl6ECktiBQJREoLIkXifq+ptZqSSMNFAETqyIxFSh/OPx0iFSPea9LhECkQd3steashkkGNBpsELFEPImXlvkg24RCplBar0Q9Eml6jwSYBS1QzN5GE0iFSJGYsUv5wiBQHdZHupJMOh0iNQaS0IFIkECktiBQJ6VbTTtciHCKVcmU1/uaZvdVmJ5L50iFSKYiUFkSKBCKlBZEiMV+RFMMhUjcQKS2IFAlESgsiRWJ2Iv2mkw6HSK2RbjXtdC3CIVIp0q2mnQ6RIiHdatrproX7SYdIrZFuNe10iBSJFqvRjzsiaYZDpF4gUloQKRKfc7rRa/lbDZEMajTYJGCJahApLXdEMguHSKXMTySZdC2WDpFKmatIGuEQKQyIlBZEigQipQWRIoFIaUGkSNxeDYFWm6FIN346pYb/JgFLVINIaUGkSLRYjX4gkkEN/00ClqhGWiTpcIgUCulekw6HSKGQ7jXpcIgUCuleuxHj6iunfNxcOsNwiFRKi9Xoxo3DCkLpECkKiJQWRIrEPEVSCIdIoUCktCBSJG69HpdpNUSaWsN/k4AlqkGktLRYOkQqBZHSgkiRmKVIEuEQKRSIlJYW6RCpFERKCyJF4sZqSLeadjpE6gIipaXF0iFSKXMU6T3iQtSDSJFApLS0SIdIpSBSWq6ne0ekLtxYjZBzreYrxGU6iXBNlg6RSkGktCBSJGYokkg4RArF1dV4jznXahDJpIb7JgFLVINIaWmxdIhUCiKlBZEiMT+R3vdK6RApCNdWQ6vVVNN9Z7hMh0g9uNZrKq02Q5GswyFSKbMT6f3vF7lBpEg0WY1uzE6kd+t0iFTI1dU4/k1qbqaTDodIHZidSNLhEKkb11pNute0wyFSL36mdLQc76e/yczsRDr5jWER500ClqjlUqR3aZHeT3+TmSb7QEQq5IpIZ7/JzMxEcgiHSIXMQqS/dO/nv0kMIkVCutW00/1GeD/7F5E6cL4a70qtdiHS+8VvEtNk6RCpkIvVuPKrvPyK9H78z/FvEnN76RCpPX+rcViH92u/ystpunfNvcT3qvksHSIVcrQa7yedFnK2tdxOJx0OkdpzNKX308WIONtaTtLd+k1WmiwdIhVyZ0oBZ1vL7QjS4RCpPYiUFkSKxFxFEkiHSJGQbjXtdIgUCelW006HSJGYa6tpp0Ok5iBSWhApEtK9Jh0OkUIh3WvS4dqkQ6RCpHtNOhwihUK616TDIVIopHtNOhwihUK616TDIVIopHvtbgDpdIjUGkRKCyJFApHSgkiBmG+raadDpMbMt9VIN72Ib+m+JSq5P6N4860DkXyL+JbuW6ISRMoLIgUCkdLSZukQqQxESgsiRWLGImVPh0iRkG417XSIFAnpVtNOh0iRkG417XSIFAnpVtNOh0iReDCjeBOuApGcq7iW7luiEkRKS5ulQ6QypEWSDodIoZDuNelwiBQK6V6TDodIoZDuNelwiBQK6V57NHvpdIjUFERKCyJFApHSgkiRQKS0IFIkECktiBQJ6V4jnH8Zv8qdS1RCr2Xl4eRt0iFSEY1WoxOI1KCMV+HeJepApLQgUiQQKS2yIr0+DcPqzbWEPfMWKXU6PZGGw4bL4cDapYQb0q2mnU5UpPWw3u332/Xw6lHCDelW004nKtJi2H1+vRuePEq4Id1q2ulERRqGo2/MS7gh3Wra6R7P3SRda5Gef0RaeJRwo9Fq9EE6nKRIq5fXt+Hfx5e79f2jDeEWTrrXpMNJivTF4cvFzqOEG9K9Jh1OUKT9ZvP6ulodDjms73oUb+Gke006nKJIoUrUId1rBVOXTodI7UCktCBSIObeaonTtQrXS6Rc7yNJt5p2uvmJNBxjUcIQ6VbTTqcuUvcSVZTMJ9qcy5m7SCbpEKkERPKfhROIFAlpkaTDaYr038vq8Apotf7Pq4QP0r0mHU5RpN3T0dGEpUsJL6R7TTqcokjrYfFvc/hq+7bIddKqdK8VTVw6XTKRFsPm9+tNqj+joNW00yUT6eTdoVRvyNJqadM1C8cjUgHSraadTlGkj9dIb9vDV9leI5VNJ9iki0GkZCL9XInrwFOmP+yTFkk6XLt0bd9HWh/eR1qsXnK9jyTda9LhREWKVKIG6V6TDodIoZDuNelwiBSJwtnEmnQx0unahUOkx0i3mnY6RIqEdKtpp0OkSNBqFbeLRbt0iPQY6V6TDodI/iUqkO416XCI5F+inOLJhJp1KdIiNVw6RHoIItXdMBCI5F+iHOlW006HSP4lyqHVKm8ZB0TyL1EMrVZ7yzggkn+JYirmEmnahUiL1DIcIj1CWiTpcE3TIdIjpHtNOhwiRVq0mqkEmnYhiFR/U7MBEMnitjGQFqnp0iHSA6RFqpqwdDpEcqbqo5riTLsQaZHaLh0i3Ue61bTTtQ2HSPepm0mceRchHQ6R2pQoo3IiYeZdhrRIlZ+fOjUdIt0FkcbeujuNlw6R7lH7qdBR5l2GdDhEalSiiNp5RJl3EdWfHZ8rnfPtDbZHJLPbd6V6spnSNd9LINIdpFtNO139XCemQ6Q7NF+NlmiHQ6RWJQqIed8Y0b7VWtJ+6WI2S4glG9FqMSZehHY4RGpW4jFjJhFi4iWMmmiWdGM8QiQvaLXLrayn4USPcIh0awq0mtFWzemydIh0YwbardZ0s8aMXLqJ6RDp+gTGzqD7zEvo02qN6LR0iGQ7ge4zL0B8L9F8w7Fb64s0utO6z7wE8XQdthy59QxE6rJpIyZ4FD9dv3CIdFl8UvXovTYpHeEstxYXaZpH0XtNei/Rc+kQ6bx0+/cT2iEdrm86RDqrPLV05F6bHE47HSLZ1Z1eOHCrSafrHQ6Rjssa1A3bahbhSGe5rapIg8liRO018XDd0yHST0mbtQjaa+LhAqRDpO+KZiUD9ppZp0VMFyQcIh3qGRYM12qGnRYyneFYbbeVE8lyLfbRes1Uo2jhAi3d7EUybrR9rF4zTycdDpHGFzJfi0i9Jp0uWLhZi+SxFuZPN8biEy6KSE5L13RTEZGcGm0fo9fc0kmHa/vXTAoiDX5rEaDXXMP1Thd06eYokutS7HuLJJ0ubrjZieS9FIca3gVuV/ZP11GkBuFGF5iXSC0s2nc857ZFOulwTS+dknWxGi3Fvtepgq2qSqdDpAcDNmy0ffNekw+XIN0cRGq7EoeKDUvJp2tX7VCx3XapROrQZ/t2x4i7hGv4dnmipVMWqc9KfJVuUEI9XK50qiJ1XIlDed/R+4bTTodIf0OEK5UAAAZBSURBVFt37rPDHNwGVg6XOJ2YSBEW4oDbAXzZdHHCjZqFkEhhVuKA8UyGUOnM/8opUriR3deojm+JWAtxwPBKAhHT2Y0UMNyY+aQXKWKbHbCYU9xw2unabBNGpLAL8YXBEZPA4bTTRd3EvETwhTgw/oPxEoTTTjdifulEGjIsxBdjliNNuBHptMONKFK/iVmJLAvxRc1kE3XZN9LpqiebTKRkFDVPosfYU4rmnDVcrUqI5MvdJkqr0Dcl4UTTXd56RIH6TQKWaMaVZhrSN9kP10LIhKs6LxiRGjCc03tCllyEk053+4Yjxp4wrzglACxBJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADgooEkIwRXW4vTsTakqUkQ2W9/xApbynJUFnvP0TKW0oyVNb7D5HylpIMlfX+Q6S8pSRDZb3/EClvKclQWe8/RMpbSjJU1vsPkfKWkgyV9f5DpLylJENlvf8QKW8pyVBZ7z9EyltKMlTW+w+R8paSDJX1/uPUbAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxoLtJ6MSzWu3s/cCs1+gLpJbyejuuX6qySY6jXp2ZLdV7KLdXueRieN8c/MQrVWqTl4Q56uvMDt1IbT5E2p+P6pTqr5BhqfRh48ddjfqHOS/mlWhzGPTLJKlRjkf4bFpv9ZjH8d/MHfqU2w8q8yO/Yi5NV90t1Xskv1GZ43n0+/D3//MAv1EUpt1Trzxrro9HNQjUWaT28ffz/3/By8wd+pV4divwOvTxpb79U55X8Qq2+yvxV8wt1Ucot1WLYnRSyC9VYpNWw3Z/scC5+4FfqdXg1L/LNsN6ftLdfqvNKjqG+C/5W8wt1Uco51bD4/dIsVGORhvN9z8UP/Eqthrfnj9eV5oU+2Jwl8Et1Xskx1IHdsPz50i/URSnfVOsjTc1CzUqkA8ubW1iUu1HbrZJvqM/Hhrezum4iHZXyTPVvGI4MRaQxpf597PbWTs8aOonkG2q/Xfw953EW6bSUX6rX1eLoFREi1Zf6YudzULqXSF94hdotjh4UfEU6KfX9I6dU++c/Q7OKtDif98UP/Ep949QIJ8P6pboxqlOo5XEnu4Y6LfWN14Pf7u9og1moLkfttudH7bZuR+0uR24hkl+q80p3fjaZ7dNye/StZ6izUt+4vRw7PxRpEKqxSC+HF5Rvfy/3Ln7gV+rrPQSn7j5ddL9U55UcQ72dvdh3DHVeyi3Vz8C/D39moWZ0ZsP6897arf+ODZnS6syGs0p+obbnB838Ql2Uckt1OLNht/p7jZT1zIb9099xza+GeHI70Hleavd1npXTuxM/7e2d6qySX6jn4e+EN+dQF6X8Ui28+q+1SLvDybZfpYezH7Qo9eT1lvmpSH6prlVyCTVciOQW6nopn6X6G9g2VGuRACRBJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxAJAADEAnAAEQCMACRAAxApAwMR/h91jdMgEXJACKFh0VJAwJFhsVJAyJFhsVJw/GnmX/89zIsXvb79TB8fST369Ow8PrEdngMIqXhVKSXz9dLb8vP/3+atDq8flp2neCsQaQ0nIq03O1fv/+/2O/fPr/aLYe3vlOcMYiUhlOR/jt8tf3+fjXsPr7aDauO85s3iJSGs9dI++P//x0chz5wz6cBkSLDPZ+G+yL1mxd8wgKk4Z5IKw4zdAaR0nBPpH/DYrPfv3KwoRuIlIZ7Iu0PbygNi2232c0dRErDXZE+z2wYnvGoG4gEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAG/A9g8TzuJ60nUwAAAABJRU5ErkJggg==", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 420, + "width": 420 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "matplot(\n", + " sol[,1], sol[,2:dim(sol)[2]],\n", + " type = \"l\",\n", + " lty = 1,\n", + " xlab = \"Time\",\n", + " ylab = \"Concentration\",\n", + ")\n", + "\n", + "legend(\n", + " \"topright\",\n", + " legend = all_labels,\n", + " col = 1:8,\n", + " lty = 1\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "76f56970", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 'time'
  2. 'S1'
  3. 'S2'
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 'time'\n", + "\\item 'S1'\n", + "\\item 'S2'\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 'time'\n", + "2. 'S1'\n", + "3. 'S2'\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] \"time\" \"S1\" \"S2\" " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "c(\"time\", all_labels)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "01a98770", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "
  1. 'S1'
  2. 'S2'
\n" + ], + "text/latex": [ + "\\begin{enumerate*}\n", + "\\item 'S1'\n", + "\\item 'S2'\n", + "\\end{enumerate*}\n" + ], + "text/markdown": [ + "1. 'S1'\n", + "2. 'S2'\n", + "\n", + "\n" + ], + "text/plain": [ + "[1] \"S1\" \"S2\"" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "all_of(all_labels)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "1f18ff68", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_for_plot <- as.data.frame(sol)\n", + "\n", + "# rename columns for clarity (use time + investigate_label)\n", + "colnames(sol_for_plot) <- c(\"time\", all_labels)\n", + "\n", + "# reshape to long format\n", + "sol_long <- sol_for_plot %>%\n", + " pivot_longer(cols = all_of(all_labels), names_to = \"species\", values_to = \"value\")" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "273651c0", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 840 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "options(repr.plot.width = 14, repr.plot.height = 6)\n", + "colors <- c(\n", + " `S1` = \"#EE7733\",\n", + " `S2` = \"#0077BB\"\n", + ")\n", + "\n", + "plot1 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " geom_line(linewidth = 2) +\n", + " scale_colour_manual(values = colors) + # scale_colour_brewer(palette = \"Dark2\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 3, 0.5),\n", + " minor_breaks = seq(0, 3, 0.1),\n", + " limits = c(0, 3),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 3), clip = \"on\") +\n", + " labs(\n", + " title = \"Dynamics of the Reduced MAPK Model with Explicit Feedback\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " # panel.grid.minor = element_blank(),\n", + " panel.grid = element_blank(),\n", + "\n", + " ## black outer box\n", + " panel.border = element_rect(\n", + " colour = \"black\",\n", + " fill = NA,\n", + " linewidth = 1.1\n", + " )\n", + " )\n", + "\n", + "plot1\n", + "# ggsave(\"POSm4_plot.png\", plot1, width = 10, height = 8, units = \"in\", dpi = 300)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "a506b026", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "sol_list <- lapply(1:nrow(sol), function(i) as.numeric(sol[i, 2:3]))\n", + "res_tab_all <- find_loops_vset(model_calcium_oscillation,vset=sol_list,t=1,klin=klin_calcium,kn=kn_calcium,n0=n_calcium)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "ec8b3250", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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  246. 1
  247. 1
  248. 1
  249. 1
  250. 1
  251. 1
  252. 1
  253. 1
  254. 1
  255. 1
  256. 1
  257. 1
  258. 1
  259. 1
  260. 1
  261. 1
  262. 1
  263. 1
  264. 1
  265. 1
  266. 1
  267. 1
  268. 1
  269. 1
  270. 1
  271. 1
  272. 1
  273. 1
  274. 1
  275. 1
  276. 1
  277. 1
  278. 1
  279. 1
  280. 1
  281. 1
  282. 1
  283. 1
  284. 1
  285. 1
  286. 1
  287. 1
  288. 1
  289. 1
  290. 1
  291. 1
  292. 1
  293. 1
  294. 1
  295. 1
  296. 1
  297. 1
  298. 1
  299. 1
  300. 1
  301. 1
  302. 1
  303. 1
  304. 1
  305. 1
  306. 1
  307. 1
  308. 1
  309. 1
  310. 1
  311. 1
  312. 1
  313. 1
  314. 1
  315. 1
  316. 1
  317. 1
  318. 1
  319. 1
  320. 1
  321. 1
  322. 1
  323. 1
  324. 1
  325. 1
  326. 1
  327. 1
  328. 1
  329. 1
  330. 1
  331. 1
  332. 1
  333. 1
  334. 1
  335. 1
  336. 1
  337. 1
  338. 1
  339. 1
  340. 1
  341. 1
  342. 1
  343. 1
  344. 1
  345. 1
  346. 1
  347. 1
  348. 1
  349. 1
  350. 1
  351. 1
  352. 1
  353. 1
  354. 1
  355. 1
  356. 1
  357. 1
  358. 1
  359. 1
  360. 1
  361. 1
  362. 1
  363. 1
  364. 1
  365. 1
  366. 1
  367. 1
  368. 1
  369. 1
  370. 1
  371. 1
  372. 1
  373. 1
  374. 1
  375. 1
  376. 1
  377. 1
  378. 1
  379. 1
  380. 1
  381. 1
  382. 1
  383. 1
  384. 1
  385. 1
  386. 1
  387. 1
  388. 1
  389. 1
  390. 1
  391. 1
  392. 1
  393. 1
  394. 1
  395. 1
  396. 1
  397. 1
  398. 1
  399. 1
  400. 1
  401. 1
\n", + "
\n", + "\t
$jac_rep
\n", + "\t\t
    \n", + "\t
  1. \n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
    A matrix: 2 × 2 of type dbl
    -1 1
    1-1
    \n", + "
    2. \n", + "\t
  2. \n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
    A matrix: 2 × 2 of type dbl
    -1 1
    -1-1
    \n", + "
    3. \n", + "\t
  3. \n", + "\n", + "\n", + "\t\n", + "\t\n", + "\n", + "
    A matrix: 2 × 2 of type dbl
    1 1
    -1-1
    \n", + "
    4. \n", + "
\n", + "
\n", + "\t
$jac_rep_index
\n", + "\t\t
\n", + "
  1. 1
  2. 1
  3. 1
  4. 1
  5. 1
  6. 1
  7. 1
  8. 1
  9. 1
  10. 1
  11. 1
  12. 1
  13. 1
  14. 1
  15. 1
  16. 1
  17. 1
  18. 1
  19. 1
  20. 1
  21. 1
  22. 1
  23. 1
  24. 1
  25. 1
  26. 1
  27. 1
  28. 1
  29. 1
  30. 1
  31. 1
  32. 1
  33. 1
  34. 1
  35. 1
  36. 1
  37. 1
  38. 1
  39. 1
  40. 1
  41. 1
  42. 1
  43. 1
  44. 1
  45. 1
  46. 1
  47. 1
  48. 1
  49. 1
  50. 1
  51. 1
  52. 1
  53. 1
  54. 1
  55. 1
  56. 1
  57. 1
  58. 1
  59. 1
  60. 1
  61. 1
  62. 1
  63. 1
  64. 1
  65. 1
  66. 1
  67. 1
  68. 1
  69. 1
  70. 1
  71. 1
  72. 1
  73. 1
  74. 1
  75. 1
  76. 1
  77. 1
  78. 1
  79. 1
  80. 1
  81. 1
  82. 1
  83. 1
  84. 1
  85. 1
  86. 1
  87. 1
  88. 1
  89. 1
  90. 1
  91. 1
  92. 1
  93. 1
  94. 1
  95. 1
  96. 1
  97. 1
  98. 1
  99. 1
  100. 1
  101. 1
  102. 1
  103. 1
  104. 1
  105. 1
  106. 1
  107. 1
  108. 1
  109. 1
  110. 1
  111. 1
  112. 1
  113. 1
  114. 1
  115. 1
  116. 1
  117. 1
  118. 1
  119. 1
  120. 1
  121. 1
  122. 1
  123. 1
  124. 1
  125. 1
  126. 1
  127. 1
  128. 1
  129. 1
  130. 1
  131. 1
  132. 1
  133. 1
  134. 1
  135. 1
  136. 1
  137. 1
  138. 1
  139. 1
  140. 1
  141. 1
  142. 1
  143. 1
  144. 1
  145. 1
  146. 1
  147. 1
  148. 1
  149. 1
  150. 1
  151. 1
  152. 1
  153. 1
  154. 1
  155. 1
  156. 1
  157. 1
  158. 1
  159. 1
  160. 1
  161. 1
  162. 1
  163. 1
  164. 1
  165. 1
  166. 1
  167. 1
  168. 1
  169. 1
  170. 1
  171. 1
  172. 1
  173. 1
  174. 1
  175. 1
  176. 1
  177. 1
  178. 1
  179. 1
  180. 1
  181. 1
  182. 1
  183. 1
  184. 1
  185. 1
  186. 1
  187. 1
  188. 1
  189. 1
  190. 1
  191. 1
  192. 1
  193. 1
  194. 1
  195. 1
  196. 1
  197. 1
  198. 1
  199. 1
  200. 1
  201. ⋯
  202. 3
  203. 2
  204. 2
  205. 2
  206. 2
  207. 2
  208. 2
  209. 2
  210. 2
  211. 2
  212. 2
  213. 2
  214. 2
  215. 1
  216. 1
  217. 1
  218. 1
  219. 1
  220. 1
  221. 1
  222. 1
  223. 1
  224. 1
  225. 1
  226. 1
  227. 1
  228. 1
  229. 1
  230. 1
  231. 1
  232. 1
  233. 1
  234. 1
  235. 1
  236. 1
  237. 1
  238. 1
  239. 1
  240. 1
  241. 1
  242. 1
  243. 1
  244. 1
  245. 1
  246. 1
  247. 1
  248. 1
  249. 1
  250. 1
  251. 1
  252. 1
  253. 1
  254. 1
  255. 1
  256. 1
  257. 1
  258. 1
  259. 1
  260. 1
  261. 1
  262. 1
  263. 1
  264. 1
  265. 1
  266. 1
  267. 1
  268. 1
  269. 1
  270. 1
  271. 1
  272. 1
  273. 1
  274. 1
  275. 1
  276. 1
  277. 1
  278. 1
  279. 1
  280. 1
  281. 1
  282. 1
  283. 1
  284. 1
  285. 1
  286. 1
  287. 1
  288. 1
  289. 1
  290. 1
  291. 1
  292. 1
  293. 1
  294. 1
  295. 1
  296. 1
  297. 1
  298. 1
  299. 1
  300. 1
  301. 1
  302. 1
  303. 1
  304. 1
  305. 1
  306. 1
  307. 1
  308. 1
  309. 1
  310. 1
  311. 1
  312. 1
  313. 1
  314. 1
  315. 1
  316. 1
  317. 1
  318. 1
  319. 1
  320. 1
  321. 1
  322. 1
  323. 1
  324. 1
  325. 1
  326. 1
  327. 1
  328. 1
  329. 1
  330. 1
  331. 1
  332. 1
  333. 1
  334. 1
  335. 1
  336. 1
  337. 1
  338. 1
  339. 1
  340. 1
  341. 1
  342. 1
  343. 1
  344. 1
  345. 1
  346. 1
  347. 1
  348. 1
  349. 1
  350. 1
  351. 1
  352. 1
  353. 1
  354. 1
  355. 1
  356. 1
  357. 1
  358. 1
  359. 1
  360. 1
  361. 1
  362. 1
  363. 1
  364. 1
  365. 1
  366. 1
  367. 1
  368. 1
  369. 1
  370. 1
  371. 1
  372. 1
  373. 1
  374. 1
  375. 1
  376. 1
  377. 1
  378. 1
  379. 1
  380. 1
  381. 1
  382. 1
  383. 1
  384. 1
  385. 1
  386. 1
  387. 1
  388. 1
  389. 1
  390. 1
  391. 1
  392. 1
  393. 1
  394. 1
  395. 1
  396. 1
  397. 1
  398. 1
  399. 1
  400. 1
  401. 1
\n", + "
\n", + "
\n" + ], + "text/latex": [ + "\\begin{description}\n", + "\\item[\\$loop\\_rep] \\begin{enumerate}\n", + "\\item A data.frame: 3 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & 1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A data.frame: 3 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & -1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A data.frame: 3 × 3\n", + "\\begin{tabular}{lll}\n", + " loop & length & sign\\\\\n", + " > & & \\\\\n", + "\\hline\n", + "\t 1, 1 & 1 & 1\\\\\n", + "\t 2, 2 & 1 & -1\\\\\n", + "\t 1, 2, 1 & 2 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$loop\\_rep\\_index] \\begin{enumerate*}\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item ⋯\n", + "\\item 3\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 2\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\end{enumerate*}\n", + "\n", + "\\item[\\$jac\\_rep] \\begin{enumerate}\n", + "\\item A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t -1 & 1\\\\\n", + "\t 1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t -1 & 1\\\\\n", + "\t -1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\item A matrix: 2 × 2 of type dbl\n", + "\\begin{tabular}{ll}\n", + "\t 1 & 1\\\\\n", + "\t -1 & -1\\\\\n", + "\\end{tabular}\n", + "\n", + "\\end{enumerate}\n", + "\n", + "\\item[\\$jac\\_rep\\_index] \\begin{enumerate*}\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + "\\item 1\n", + 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-1\n", + "\n", + "\n", + "$loop_rep_index\n", + " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\n", + " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [371] 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [408] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [445] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [482] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [519] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [556] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [630] 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [667] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [704] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1\n", + " [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2\n", + "[1296] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1333] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1370] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1407] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1444] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1481] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1518] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1555] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1592] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1629] 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1666] 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1703] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1740] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1814] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1851] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1888] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1962] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1999] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2036] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2073] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2110] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2\n", + "[2332] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2369] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2406] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2443] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2480] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2517] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2554] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2591] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2628] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2665] 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2702] 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2739] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2776] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2\n", + "[2813] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2850] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2887] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2924] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2961] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2998] 1 1 1 1\n", + "\n", + "$jac_rep\n", + "$jac_rep[[1]]\n", + " [,1] [,2]\n", + "[1,] -1 1\n", + "[2,] 1 -1\n", + "\n", + "$jac_rep[[2]]\n", + " [,1] [,2]\n", + "[1,] -1 1\n", + "[2,] -1 -1\n", + "\n", + "$jac_rep[[3]]\n", + " [,1] [,2]\n", + "[1,] 1 1\n", + "[2,] -1 -1\n", + "\n", + "\n", + "$jac_rep_index\n", + " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\n", + " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [371] 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [408] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [445] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [482] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [519] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [556] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + " [630] 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [667] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + " [704] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1\n", + " [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2\n", + "[1296] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1333] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1370] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1407] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1444] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1481] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1518] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1555] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1592] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1629] 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1666] 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1703] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[1740] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[1777] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1814] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1851] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1888] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1925] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1962] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[1999] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2036] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2073] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2110] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2\n", + "[2332] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2369] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2406] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2443] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2480] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2517] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2554] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2591] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2628] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2665] 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", + "[2702] 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2739] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3\n", + "[2776] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2\n", + "[2813] 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2850] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2887] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2924] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2961] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", + "[2998] 1 1 1 1\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "res_tab_all" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "a1881f7e", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [], + "source": [ + "# Draw background in the plot corresponding to the time points where\n", + "# certain loop structures are present\n", + "\n", + "# 1-to-1 time vector (must match loop_rep_index length)\n", + "time_vec <- sort(unique(sol_long$time))\n", + "\n", + "stopifnot(length(res_tab_all$loop_rep_index) == length(time_vec))\n", + "\n", + "# Run-length encode to get contiguous segments of the same loop structure\n", + "r <- rle(res_tab_all$loop_rep_index)\n", + "\n", + "end_idx <- cumsum(r$lengths)\n", + "start_idx <- c(1, head(end_idx + 1, -1))\n", + "\n", + "bands <- tibble(\n", + " loop_type = factor(r$values),\n", + " t_start = time_vec[start_idx],\n", + " t_end = time_vec[end_idx]\n", + ")\n", + "transition_times <- bands$t_end[-nrow(bands)]" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "8725b19d", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "plot without title" + ] + }, + "metadata": { + "image/png": { + "height": 360, + "width": 840 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "plot2 <- ggplot(sol_long, aes(x = time, y = value, colour = species)) +\n", + " # background bands (behind lines)\n", + " geom_rect(\n", + " data = bands,\n", + " aes(xmin = t_start, xmax = t_end, ymin = -Inf, ymax = Inf, fill = loop_type),\n", + " inherit.aes = FALSE,\n", + " alpha = 0.1\n", + " ) +\n", + " geom_vline(\n", + " xintercept = transition_times,\n", + " colour = \"grey40\",\n", + " linewidth = 0.7,\n", + " alpha = 0.35\n", + " ) +\n", + " geom_line(linewidth = 2) +\n", + " scale_colour_manual(values = colors) +\n", + " scale_fill_brewer(palette = \"Set2\", name = \"Loop structure\") +\n", + " scale_x_continuous(\n", + " breaks = seq(0, 3, 0.5),\n", + " minor_breaks = seq(0, 3, 0.1),\n", + " limits = c(0, 3),\n", + " expand = c(0, 0)\n", + " ) +\n", + " coord_cartesian(xlim = c(0, 3), clip = \"on\") +\n", + " labs(\n", + " title = \"Dynamics of Calcium Oscillation Model\",\n", + " x = \"Time (a.u.)\",\n", + " y = \"Concentration (a.u.)\",\n", + " colour = \"Species\"\n", + " ) +\n", + " theme_minimal(base_size = 16) +\n", + " theme(\n", + " plot.title = element_text(face = \"bold\", hjust = 0.5),\n", + " panel.grid = element_blank(),\n", + " panel.border = element_rect(colour = \"black\", fill = NA, linewidth = 1.1)\n", + " )\n", + "\n", + "plot2\n" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "2f90ae6b", + "metadata": { + "vscode": { + "languageId": "r" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1] \"Loop structure 1:\"\n" + ] + }, + { + "data": { + "text/html": [ + "
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    A matrix: 2 × 2 of type dbl
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A data.frame: 3 × 2
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A data.frame: 3 × 2
len_1len_2
<dbl><dbl>
all21
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\n" + ], + "text/latex": [ + "A data.frame: 3 × 2\n", + "\\begin{tabular}{r|ll}\n", + " & len\\_1 & len\\_2\\\\\n", + " & & \\\\\n", + "\\hline\n", + "\tall & 2 & 1\\\\\n", + "\tpos & 1 & 0\\\\\n", + "\tneg & 1 & 1\\\\\n", + "\\end{tabular}\n" + ], + "text/markdown": [ + "\n", + "A data.frame: 3 × 2\n", + "\n", + "| | len_1 <dbl> | len_2 <dbl> |\n", + "|---|---|---|\n", + "| all | 2 | 1 |\n", + "| pos | 1 | 0 |\n", + "| neg | 1 | 1 |\n", + "\n" + ], + "text/plain": [ + " len_1 len_2\n", + "all 2 1 \n", + "pos 1 0 \n", + "neg 1 1 " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "loop_summary(res_tab_all$loop_rep[[3]])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "R", + "language": "R", + "name": "ir" + }, + "language_info": { + "codemirror_mode": "r", + "file_extension": ".r", + "mimetype": "text/x-r-source", + "name": "R", + "pygments_lexer": "r", + "version": "4.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From e67381cb17097757060d392774a2cf79d0eb7c0f Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Fri, 6 Feb 2026 15:49:50 +0100 Subject: [PATCH 09/12] Remove test cells --- .../model_3_complex_formation_extend_R.ipynb | 86 +- examples/model_5_MAPK_reduced_R.ipynb | 3349 ----------------- 2 files changed, 2 insertions(+), 3433 deletions(-) diff --git a/examples/model_3_complex_formation_extend_R.ipynb b/examples/model_3_complex_formation_extend_R.ipynb index e5f61fe..00b7299 100644 --- a/examples/model_3_complex_formation_extend_R.ipynb +++ b/examples/model_3_complex_formation_extend_R.ipynb @@ -320,7 +320,7 @@ }, { "cell_type": "code", - "execution_count": 113, + "execution_count": 7, "id": "6c2540e5", "metadata": { "vscode": { @@ -415,7 +415,7 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 8, "id": "3d056cc3", "metadata": { "vscode": { @@ -1178,88 +1178,6 @@ "sol_full <- rbind(sol_unstimulated, sol_stimulated) " ] }, - { - "cell_type": "code", - "execution_count": 72, - "id": "dccf2428", - "metadata": { - "vscode": { - "languageId": "r" - } - }, - "outputs": [ - { - "data": { - "text/html": [ - "
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    A data.frame: 31 × 3
    looplengthsign
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    2, 21-1
    3, 31-1
    4, 41-1
    5, 51-1
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    2, 21-1
    3, 31-1
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    5, 51-1
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  2. 1
  3. 1
  4. 1
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  63. 1
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  66. 1
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  91. 1
  92. 1
  93. 1
  94. 1
  95. 1
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  100. 1
  101. 1
  102. 1
  103. 1
  104. 1
  105. 1
  106. 1
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  110. 2
  111. 2
  112. 2
  113. 2
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  115. 2
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  118. 2
  119. 2
  120. 2
  121. 2
  122. 2
  123. 2
  124. 2
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  130. 2
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  133. 2
  134. 2
  135. 2
  136. 2
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  138. 2
  139. 2
  140. 2
  141. 2
  142. 2
  143. 2
  144. 2
  145. 2
  146. 2
  147. 2
  148. 2
  149. 2
  150. 2
  151. 2
  152. 2
  153. 2
  154. 2
  155. 2
  156. 2
  157. 2
  158. 2
  159. 2
  160. 2
  161. 2
  162. 2
  163. 2
  164. 2
  165. 2
  166. 2
  167. 2
  168. 2
  169. 2
  170. 2
  171. 2
  172. 2
  173. 2
  174. 2
  175. 2
  176. 2
  177. 2
  178. 2
  179. 2
  180. 2
  181. 2
  182. 2
  183. 2
  184. 2
  185. 2
  186. 2
  187. 2
  188. 2
  189. 2
  190. 2
  191. 2
  192. 2
  193. 2
  194. 2
  195. 2
  196. 2
  197. 2
  198. 2
  199. 2
  200. 2
  201. ⋯
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  203. 1
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  235. 1
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  238. 1
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  240. 1
  241. 1
  242. 1
  243. 1
  244. 1
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  250. 1
  251. 1
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  256. 1
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  262. 1
  263. 1
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  266. 1
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  270. 1
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  272. 1
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  294. 1
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  297. 1
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    A matrix: 8 × 8 of type dbl
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    A matrix: 8 × 8 of type dbl
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  1. 1
  2. 1
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  5. 1
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  17. 1
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  33. 1
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  53. 1
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  56. 1
  57. 1
  58. 1
  59. 1
  60. 1
  61. 1
  62. 1
  63. 1
  64. 1
  65. 1
  66. 1
  67. 1
  68. 1
  69. 1
  70. 1
  71. 1
  72. 1
  73. 1
  74. 1
  75. 1
  76. 1
  77. 1
  78. 1
  79. 1
  80. 1
  81. 1
  82. 1
  83. 1
  84. 1
  85. 1
  86. 1
  87. 1
  88. 1
  89. 1
  90. 1
  91. 1
  92. 1
  93. 1
  94. 1
  95. 1
  96. 1
  97. 1
  98. 1
  99. 1
  100. 1
  101. 1
  102. 1
  103. 1
  104. 1
  105. 1
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  109. 1
  110. 2
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  201. ⋯
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\n", - "
\n", - "
\n" - ], - "text/latex": [ - "\\begin{description}\n", - "\\item[\\$loop\\_rep] \\begin{enumerate}\n", - "\\item A data.frame: 31 × 3\n", - "\\begin{tabular}{lll}\n", - " loop & length & sign\\\\\n", - " > & & \\\\\n", - "\\hline\n", - "\t 1, 1 & 1 & -1\\\\\n", - "\t 2, 2 & 1 & -1\\\\\n", - "\t 3, 3 & 1 & -1\\\\\n", - "\t 4, 4 & 1 & -1\\\\\n", - "\t 5, 5 & 1 & -1\\\\\n", - "\t 6, 6 & 1 & -1\\\\\n", - "\t 7, 7 & 1 & -1\\\\\n", - "\t 8, 8 & 1 & -1\\\\\n", - "\t 1, 2, 1 & 2 & 1\\\\\n", - "\t 3, 4, 3 & 2 & 1\\\\\n", - "\t 4, 5, 4 & 2 & 1\\\\\n", - "\t 6, 7, 6 & 2 & 1\\\\\n", - "\t 5, 8, 1,.... & 6 & -1\\\\\n", - "\t 5, 8, 1,.... & 5 & 1\\\\\n", - "\t 5, 8, 1,.... & 4 & 1\\\\\n", - "\t 5, 8, 2,.... & 5 & 1\\\\\n", - "\t 5, 8, 2,.... & 4 & -1\\\\\n", - "\t 5, 8, 2, 5 & 3 & -1\\\\\n", - "\t 7, 8, 1,.... & 8 & 1\\\\\n", - "\t 7, 8, 1,.... & 7 & 1\\\\\n", - "\t 7, 8, 1,.... & 7 & -1\\\\\n", - "\t 7, 8, 1,.... & 6 & -1\\\\\n", - "\t 7, 8, 1,.... & 6 & -1\\\\\n", - "\t 7, 8, 1,.... & 5 & -1\\\\\n", - "\t 7, 8, 2,.... & 7 & -1\\\\\n", - "\t 7, 8, 2,.... & 6 & -1\\\\\n", - "\t 7, 8, 2,.... & 6 & 1\\\\\n", - "\t 7, 8, 2,.... & 5 & 1\\\\\n", - "\t 7, 8, 2,.... & 5 & 1\\\\\n", - "\t 7, 8, 2,.... & 4 & 1\\\\\n", - "\t 7, 8, 7 & 2 & 1\\\\\n", - "\\end{tabular}\n", - "\n", - "\\item A data.frame: 31 × 3\n", - "\\begin{tabular}{lll}\n", - " loop & length & sign\\\\\n", - " > & & \\\\\n", - "\\hline\n", - "\t 1, 1 & 1 & -1\\\\\n", - "\t 2, 2 & 1 & -1\\\\\n", - "\t 3, 3 & 1 & -1\\\\\n", - "\t 4, 4 & 1 & -1\\\\\n", - "\t 5, 5 & 1 & -1\\\\\n", - "\t 6, 6 & 1 & -1\\\\\n", - "\t 7, 7 & 1 & -1\\\\\n", - "\t 8, 8 & 1 & -1\\\\\n", - "\t 1, 2, 1 & 2 & 1\\\\\n", - "\t 3, 4, 3 & 2 & 1\\\\\n", - "\t 4, 5, 4 & 2 & 1\\\\\n", - "\t 6, 7, 6 & 2 & 1\\\\\n", - "\t 5, 8, 1,.... & 6 & -1\\\\\n", - "\t 5, 8, 1,.... & 5 & 1\\\\\n", - "\t 5, 8, 1,.... & 4 & 1\\\\\n", - "\t 5, 8, 2,.... & 5 & 1\\\\\n", - "\t 5, 8, 2,.... & 4 & -1\\\\\n", - "\t 5, 8, 2, 5 & 3 & -1\\\\\n", - "\t 7, 8, 1,.... & 8 & 1\\\\\n", - "\t 7, 8, 1,.... & 7 & -1\\\\\n", - "\t 7, 8, 1,.... & 7 & -1\\\\\n", - "\t 7, 8, 1,.... & 6 & 1\\\\\n", - "\t 7, 8, 1,.... & 6 & -1\\\\\n", - "\t 7, 8, 1,.... & 5 & 1\\\\\n", - "\t 7, 8, 2,.... & 7 & -1\\\\\n", - "\t 7, 8, 2,.... & 6 & 1\\\\\n", - "\t 7, 8, 2,.... & 6 & 1\\\\\n", - "\t 7, 8, 2,.... & 5 & -1\\\\\n", - "\t 7, 8, 2,.... & 5 & 1\\\\\n", - "\t 7, 8, 2,.... & 4 & -1\\\\\n", - "\t 7, 8, 7 & 2 & 1\\\\\n", - "\\end{tabular}\n", - "\n", - "\\end{enumerate}\n", - "\n", - "\\item[\\$loop\\_rep\\_index] \\begin{enumerate*}\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item 2\n", - "\\item ⋯\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\end{enumerate*}\n", - "\n", - "\\item[\\$jac\\_rep] \\begin{enumerate}\n", - "\\item A matrix: 8 × 8 of type dbl\n", - "\\begin{tabular}{llllllll}\n", - "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", - "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", - "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", - "\t 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", - "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", - "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", - "\t 0 & 0 & 0 & 0 & -1 & 1 & -1 & 1\\\\\n", - "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", - "\\end{tabular}\n", - "\n", - "\\item A matrix: 8 × 8 of type dbl\n", - "\\begin{tabular}{llllllll}\n", - "\t -1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n", - "\t 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1\\\\\n", - "\t 0 & -1 & -1 & 1 & 0 & 0 & 0 & 0\\\\\n", - "\t 0 & 1 & 1 & -1 & 1 & 0 & 0 & 0\\\\\n", - "\t 0 & 1 & 0 & 1 & -1 & 0 & 0 & 0\\\\\n", - "\t 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0\\\\\n", - "\t 0 & 0 & 0 & 0 & 1 & 1 & -1 & 1\\\\\n", - "\t 0 & 0 & 0 & 0 & 1 & 0 & 1 & -1\\\\\n", - "\\end{tabular}\n", - "\n", - "\\end{enumerate}\n", - "\n", - "\\item[\\$jac\\_rep\\_index] \\begin{enumerate*}\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - "\\item 1\n", - 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"85. 1\n", - "86. 1\n", - "87. 1\n", - "88. 1\n", - "89. 1\n", - "90. 1\n", - "91. 1\n", - "92. 1\n", - "93. 1\n", - "94. 1\n", - "95. 1\n", - "96. 1\n", - "97. 1\n", - "98. 1\n", - "99. 1\n", - "100. 1\n", - "101. 1\n", - "102. 1\n", - "103. 1\n", - "104. 1\n", - "105. 1\n", - "106. 1\n", - "107. 1\n", - "108. 1\n", - "109. 1\n", - "110. 2\n", - "111. 2\n", - "112. 2\n", - "113. 2\n", - "114. 2\n", - "115. 2\n", - "116. 2\n", - "117. 2\n", - "118. 2\n", - "119. 2\n", - "120. 2\n", - "121. 2\n", - "122. 2\n", - "123. 2\n", - "124. 2\n", - "125. 2\n", - "126. 2\n", - "127. 2\n", - "128. 2\n", - "129. 2\n", - "130. 2\n", - "131. 2\n", - "132. 2\n", - "133. 2\n", - "134. 2\n", - "135. 2\n", - "136. 2\n", - "137. 2\n", - "138. 2\n", - "139. 2\n", - "140. 2\n", - "141. 2\n", - "142. 2\n", - "143. 2\n", - "144. 2\n", - "145. 2\n", - "146. 2\n", - "147. 2\n", - "148. 2\n", - "149. 2\n", - "150. 2\n", - "151. 2\n", - "152. 2\n", - "153. 2\n", - "154. 2\n", - "155. 2\n", - "156. 2\n", - "157. 2\n", - "158. 2\n", - "159. 2\n", - "160. 2\n", - "161. 2\n", - "162. 2\n", - "163. 2\n", - "164. 2\n", - "165. 2\n", - "166. 2\n", - "167. 2\n", - "168. 2\n", - "169. 2\n", - "170. 2\n", - "171. 2\n", - "172. 2\n", - "173. 2\n", - "174. 2\n", - "175. 2\n", - "176. 2\n", - "177. 2\n", - "178. 2\n", - "179. 2\n", - "180. 2\n", - "181. 2\n", - "182. 2\n", - "183. 2\n", - "184. 2\n", - "185. 2\n", - "186. 2\n", - "187. 2\n", - "188. 2\n", - "189. 2\n", - "190. 2\n", - "191. 2\n", - "192. 2\n", - "193. 2\n", - "194. 2\n", - "195. 2\n", - "196. 2\n", - "197. 2\n", - "198. 2\n", - "199. 2\n", - "200. 2\n", - "201. ⋯\n", - "202. 1\n", - "203. 1\n", - "204. 1\n", - "205. 1\n", - "206. 1\n", - "207. 1\n", - "208. 1\n", - "209. 1\n", - "210. 1\n", - "211. 1\n", - "212. 1\n", - "213. 1\n", - "214. 1\n", - "215. 1\n", - "216. 1\n", - "217. 1\n", - "218. 1\n", - "219. 1\n", - "220. 1\n", - "221. 1\n", - "222. 1\n", - "223. 1\n", - "224. 1\n", - "225. 1\n", - "226. 1\n", - "227. 1\n", - "228. 1\n", - "229. 1\n", - "230. 1\n", - "231. 1\n", - "232. 1\n", - "233. 1\n", - "234. 1\n", - "235. 1\n", - "236. 1\n", - "237. 1\n", - "238. 1\n", - "239. 1\n", - "240. 1\n", - "241. 1\n", - "242. 1\n", - "243. 1\n", - "244. 1\n", - "245. 1\n", - "246. 1\n", - "247. 1\n", - "248. 1\n", - "249. 1\n", - "250. 1\n", - "251. 1\n", - "252. 1\n", - "253. 1\n", - "254. 1\n", - "255. 1\n", - "256. 1\n", - "257. 1\n", - "258. 1\n", - "259. 1\n", - "260. 1\n", - "261. 1\n", - "262. 1\n", - "263. 1\n", - "264. 1\n", - "265. 1\n", - "266. 1\n", - "267. 1\n", - "268. 1\n", - "269. 1\n", - "270. 1\n", - "271. 1\n", - "272. 1\n", - "273. 1\n", - "274. 1\n", - "275. 1\n", - "276. 1\n", - "277. 1\n", - "278. 1\n", - "279. 1\n", - "280. 1\n", - "281. 1\n", - "282. 1\n", - "283. 1\n", - "284. 1\n", - "285. 1\n", - "286. 1\n", - "287. 1\n", - "288. 1\n", - "289. 1\n", - "290. 1\n", - "291. 1\n", - "292. 1\n", - "293. 1\n", - "294. 1\n", - "295. 1\n", - "296. 1\n", - "297. 1\n", - "298. 1\n", - "299. 1\n", - "300. 1\n", - "301. 1\n", - "302. 1\n", - "303. 1\n", - "304. 1\n", - "305. 1\n", - "306. 1\n", - "307. 1\n", - "308. 1\n", - "309. 1\n", - "310. 1\n", - "311. 1\n", - "312. 1\n", - "313. 1\n", - "314. 1\n", - "315. 1\n", - "316. 1\n", - "317. 1\n", - "318. 1\n", - "319. 1\n", - "320. 1\n", - "321. 1\n", - "322. 1\n", - "323. 1\n", - "324. 1\n", - "325. 1\n", - "326. 1\n", - "327. 1\n", - "328. 1\n", - "329. 1\n", - "330. 1\n", - "331. 1\n", - "332. 1\n", - "333. 1\n", - "334. 1\n", - "335. 1\n", - "336. 1\n", - "337. 1\n", - "338. 1\n", - "339. 1\n", - "340. 1\n", - "341. 1\n", - "342. 1\n", - "343. 1\n", - "344. 1\n", - "345. 1\n", - "346. 1\n", - "347. 1\n", - "348. 1\n", - "349. 1\n", - "350. 1\n", - "351. 1\n", - "352. 1\n", - "353. 1\n", - "354. 1\n", - "355. 1\n", - "356. 1\n", - "357. 1\n", - "358. 1\n", - "359. 1\n", - "360. 1\n", - "361. 1\n", - "362. 1\n", - "363. 1\n", - "364. 1\n", - "365. 1\n", - "366. 1\n", - "367. 1\n", - "368. 1\n", - "369. 1\n", - "370. 1\n", - "371. 1\n", - "372. 1\n", - "373. 1\n", - "374. 1\n", - "375. 1\n", - "376. 1\n", - "377. 1\n", - "378. 1\n", - "379. 1\n", - "380. 1\n", - "381. 1\n", - "382. 1\n", - "383. 1\n", - "384. 1\n", - "385. 1\n", - "386. 1\n", - "387. 1\n", - "388. 1\n", - "389. 1\n", - "390. 1\n", - "391. 1\n", - "392. 1\n", - "393. 1\n", - "394. 1\n", - "395. 1\n", - "396. 1\n", - "397. 1\n", - "398. 1\n", - "399. 1\n", - "400. 1\n", - "401. 1\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ], - "text/plain": [ - "$loop_rep\n", - "$loop_rep[[1]]\n", - " loop length sign\n", - "1 1, 1 1 -1\n", - "2 2, 2 1 -1\n", - "3 3, 3 1 -1\n", - "4 4, 4 1 -1\n", - "5 5, 5 1 -1\n", - "6 6, 6 1 -1\n", - "7 7, 7 1 -1\n", - "8 8, 8 1 -1\n", - "9 1, 2, 1 2 1\n", - "10 3, 4, 3 2 1\n", - "11 4, 5, 4 2 1\n", - "12 6, 7, 6 2 1\n", - "13 5, 8, 1,.... 6 -1\n", - "14 5, 8, 1,.... 5 1\n", - "15 5, 8, 1,.... 4 1\n", - "16 5, 8, 2,.... 5 1\n", - "17 5, 8, 2,.... 4 -1\n", - "18 5, 8, 2, 5 3 -1\n", - "19 7, 8, 1,.... 8 1\n", - "20 7, 8, 1,.... 7 1\n", - "21 7, 8, 1,.... 7 -1\n", - "22 7, 8, 1,.... 6 -1\n", - "23 7, 8, 1,.... 6 -1\n", - "24 7, 8, 1,.... 5 -1\n", - "25 7, 8, 2,.... 7 -1\n", - "26 7, 8, 2,.... 6 -1\n", - "27 7, 8, 2,.... 6 1\n", - "28 7, 8, 2,.... 5 1\n", - "29 7, 8, 2,.... 5 1\n", - "30 7, 8, 2,.... 4 1\n", - "31 7, 8, 7 2 1\n", - "\n", - "$loop_rep[[2]]\n", - " loop length sign\n", - "1 1, 1 1 -1\n", - "2 2, 2 1 -1\n", - "3 3, 3 1 -1\n", - "4 4, 4 1 -1\n", - "5 5, 5 1 -1\n", - "6 6, 6 1 -1\n", - "7 7, 7 1 -1\n", - "8 8, 8 1 -1\n", - "9 1, 2, 1 2 1\n", - "10 3, 4, 3 2 1\n", - "11 4, 5, 4 2 1\n", - "12 6, 7, 6 2 1\n", - "13 5, 8, 1,.... 6 -1\n", - "14 5, 8, 1,.... 5 1\n", - "15 5, 8, 1,.... 4 1\n", - "16 5, 8, 2,.... 5 1\n", - "17 5, 8, 2,.... 4 -1\n", - "18 5, 8, 2, 5 3 -1\n", - "19 7, 8, 1,.... 8 1\n", - "20 7, 8, 1,.... 7 -1\n", - "21 7, 8, 1,.... 7 -1\n", - "22 7, 8, 1,.... 6 1\n", - "23 7, 8, 1,.... 6 -1\n", - "24 7, 8, 1,.... 5 1\n", - "25 7, 8, 2,.... 7 -1\n", - "26 7, 8, 2,.... 6 1\n", - "27 7, 8, 2,.... 6 1\n", - "28 7, 8, 2,.... 5 -1\n", - "29 7, 8, 2,.... 5 1\n", - "30 7, 8, 2,.... 4 -1\n", - "31 7, 8, 7 2 1\n", - "\n", - "\n", - "$loop_rep_index\n", - " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\n", - " [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [482] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [556] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [667] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [704] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [741] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [815] 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1407] 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1444] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1481] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1555] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1592] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1666] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1777] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1814] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1851] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1888] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1962] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2110] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2332] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2406] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2480] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2554] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2591] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2628] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2702] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2739] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2776] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2850] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2887] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2924] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2998] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3035] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3072] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3109] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3146] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3183] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3220] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3257] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3294] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3368] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3405] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3442] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3479] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3516] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3590] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3627] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3664] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3738] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3775] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3812] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3886] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3923] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3960] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3997] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4071] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4108] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4145] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4182] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4219] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4256] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4626] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4663] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4700] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4774] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4811] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4848] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4922] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4959] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4996] 1 1 1 1 1 1\n", - "\n", - "$jac_rep\n", - "$jac_rep[[1]]\n", - " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", - "[1,] -1 1 0 0 0 0 0 1\n", - "[2,] 1 -1 0 0 0 0 0 -1\n", - "[3,] 0 -1 -1 1 0 0 0 0\n", - "[4,] 0 1 1 -1 1 0 0 0\n", - "[5,] 0 1 0 1 -1 0 0 0\n", - "[6,] 0 0 0 0 -1 -1 1 0\n", - "[7,] 0 0 0 0 -1 1 -1 1\n", - "[8,] 0 0 0 0 1 0 1 -1\n", - "\n", - "$jac_rep[[2]]\n", - " [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]\n", - "[1,] -1 1 0 0 0 0 0 1\n", - "[2,] 1 -1 0 0 0 0 0 -1\n", - "[3,] 0 -1 -1 1 0 0 0 0\n", - "[4,] 0 1 1 -1 1 0 0 0\n", - "[5,] 0 1 0 1 -1 0 0 0\n", - "[6,] 0 0 0 0 -1 -1 1 0\n", - "[7,] 0 0 0 0 1 1 -1 1\n", - "[8,] 0 0 0 0 1 0 1 -1\n", - "\n", - "\n", - "$jac_rep_index\n", - " [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\n", - " [112] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [149] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [186] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [445] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [482] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [556] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [593] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [630] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [667] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [704] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [741] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [778] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - " [815] 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - " [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1000] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1037] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1074] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1111] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1148] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1185] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1222] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1259] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1296] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1333] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1407] 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1444] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1481] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1555] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1592] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1666] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1777] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1814] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1851] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1888] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1962] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2110] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2332] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2406] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2480] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2554] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2591] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2628] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2702] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2739] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2776] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2850] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2887] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2924] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2998] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3035] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - 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"[1370] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[1407] 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1444] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1481] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1555] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1592] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1629] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1666] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1777] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1814] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1851] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1888] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1925] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1962] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2110] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2147] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2184] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2221] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2258] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2295] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2332] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2369] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2406] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2443] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2480] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2517] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2554] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2591] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2628] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2665] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[2702] 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2739] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2776] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2850] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2887] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2924] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2961] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[2998] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3035] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3072] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3109] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3146] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3183] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3220] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3257] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3294] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3368] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[3405] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3442] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3479] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3516] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3553] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3590] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3627] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3664] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3701] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3738] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3775] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3812] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3849] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3886] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3923] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3960] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[3997] 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4071] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4108] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4145] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4182] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4219] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4256] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4626] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4663] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n", - "[4700] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4737] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4774] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4811] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4848] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4885] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4922] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4959] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n", - "[4996] 1 1 1 1 1 1" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "res_tab_all$loop_rep_index" - ] - }, { "cell_type": "code", "execution_count": 111, From c898155b9f3469f1e766c86791bc5fd4ad67d0d6 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Tue, 24 Feb 2026 12:14:59 +0100 Subject: [PATCH 10/12] Fix minor stuffs and some typos --- examples/model_6_calcium_oscillations_R.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/examples/model_6_calcium_oscillations_R.ipynb b/examples/model_6_calcium_oscillations_R.ipynb index 8567232..aad6932 100644 --- a/examples/model_6_calcium_oscillations_R.ipynb +++ b/examples/model_6_calcium_oscillations_R.ipynb @@ -296,7 +296,7 @@ "id": "b927c538", "metadata": {}, "source": [ - "### **2.1. Reduced MAPK Model with explicit feedback**" + "### **2.1. Reduced Calcium Oscillations Model**" ] }, { @@ -924,7 +924,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": null, "id": "273651c0", "metadata": { "vscode": { @@ -966,7 +966,7 @@ " ) +\n", " coord_cartesian(xlim = c(0, 3), clip = \"on\") +\n", " labs(\n", - " title = \"Dynamics of the Reduced MAPK Model with Explicit Feedback\",\n", + " title = \"Dynamics of the Calcium Oscillation Model\",\n", " x = \"Time (a.u.)\",\n", " y = \"Concentration (a.u.)\",\n", " colour = \"Species\"\n", From 6ef410d968982b76f30e6d675c76b2447d74f919 Mon Sep 17 00:00:00 2001 From: Anh HM Vo Date: Sun, 23 Aug 2026 21:39:10 +0200 Subject: [PATCH 11/12] Update git ignore --- .gitignore | 1 + .../00_pkg_src/LoopDetectR/DESCRIPTION | 25 + .../00_pkg_src/LoopDetectR/NAMESPACE | 9 + .../00_pkg_src/LoopDetectR/NEWS.md | 7 + .../00_pkg_src/LoopDetectR/R/data.R | 78 +++ .../LoopDetectR/R/further_functions.R | 194 ++++++ .../LoopDetectR/R/loop_detection_functions.R | 475 +++++++++++++ .../LoopDetectR/data/func_POSm4.rda | Bin 0 -> 32827 bytes .../00_pkg_src/LoopDetectR/data/func_li08.rda | Bin 0 -> 34283 bytes .../LoopDetectR/data/li08_solution.rda | Bin 0 -> 85103 bytes .../LoopDetectR/man/compare_loop_list.Rd | 53 ++ .../00_pkg_src/LoopDetectR/man/find_edge.Rd | 35 + .../00_pkg_src/LoopDetectR/man/find_loops.Rd | 57 ++ .../LoopDetectR/man/find_loops_noscc.Rd | 73 ++ .../LoopDetectR/man/find_loops_vset.Rd | 92 +++ .../00_pkg_src/LoopDetectR/man/func_POSm4.Rd | 25 + .../00_pkg_src/LoopDetectR/man/func_li08.Rd | 33 + .../LoopDetectR/man/li08_solution.Rd | 34 + .../LoopDetectR/man/loop_summary.Rd | 39 ++ .../LoopDetectR/man/sort_loop_index.Rd | 29 + .../vignettes/looplist_func_POSm4.RData | Bin 0 -> 225 bytes .../vignettes/looplist_func_POSm4.txt | 7 + .../vignettes/workflow_LoopDetectR.Rmd | 384 +++++++++++ LoopDetectR.Rcheck/00install.out | 16 + LoopDetectR.Rcheck/LoopDetectR-Ex.R | 223 ++++++ LoopDetectR.Rcheck/LoopDetectR-Ex.Rout | 253 +++++++ LoopDetectR.Rcheck/LoopDetectR-Ex.pdf | Bin 0 -> 3611 bytes LoopDetectR.Rcheck/LoopDetectR-Ex.timings | 8 + LoopDetectR.Rcheck/LoopDetectR-manual.pdf | Bin 0 -> 169868 bytes LoopDetectR.Rcheck/LoopDetectR/DESCRIPTION | 26 + LoopDetectR.Rcheck/LoopDetectR/INDEX | 13 + LoopDetectR.Rcheck/LoopDetectR/NAMESPACE | 9 + LoopDetectR.Rcheck/LoopDetectR/NEWS.md | 7 + LoopDetectR.Rcheck/LoopDetectR/R/LoopDetectR | 27 + .../LoopDetectR/R/LoopDetectR.rdb | Bin 0 -> 18463 bytes .../LoopDetectR/R/LoopDetectR.rdx | Bin 0 -> 363 bytes LoopDetectR.Rcheck/LoopDetectR/data/Rdata.rdb | Bin 0 -> 158279 bytes LoopDetectR.Rcheck/LoopDetectR/data/Rdata.rds | Bin 0 -> 116 bytes LoopDetectR.Rcheck/LoopDetectR/data/Rdata.rdx | Bin 0 -> 299 bytes LoopDetectR.Rcheck/LoopDetectR/help/AnIndex | 10 + .../LoopDetectR/help/LoopDetectR.rdb | Bin 0 -> 26171 bytes .../LoopDetectR/help/LoopDetectR.rdx | Bin 0 -> 394 bytes .../LoopDetectR/help/aliases.rds | Bin 0 -> 185 bytes LoopDetectR.Rcheck/LoopDetectR/help/paths.rds | Bin 0 -> 269 bytes .../LoopDetectR/html/00Index.html | 47 ++ LoopDetectR.Rcheck/LoopDetectR/html/R.css | 130 ++++ old/workflow_LoopDetectR.html | 640 ++++++++++++++++++ 47 files changed, 3059 insertions(+) create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/DESCRIPTION create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NAMESPACE create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NEWS.md create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/data.R create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/further_functions.R create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/loop_detection_functions.R create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/data/func_POSm4.rda create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/data/func_li08.rda create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/data/li08_solution.rda create mode 100644 LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/man/compare_loop_list.Rd create 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100644 LoopDetectR.Rcheck/LoopDetectR/data/Rdata.rdx create mode 100644 LoopDetectR.Rcheck/LoopDetectR/help/AnIndex create mode 100644 LoopDetectR.Rcheck/LoopDetectR/help/LoopDetectR.rdb create mode 100644 LoopDetectR.Rcheck/LoopDetectR/help/LoopDetectR.rdx create mode 100644 LoopDetectR.Rcheck/LoopDetectR/help/aliases.rds create mode 100644 LoopDetectR.Rcheck/LoopDetectR/help/paths.rds create mode 100644 LoopDetectR.Rcheck/LoopDetectR/html/00Index.html create mode 100644 LoopDetectR.Rcheck/LoopDetectR/html/R.css create mode 100644 old/workflow_LoopDetectR.html diff --git a/.gitignore b/.gitignore index 710c7fc..b07e4d4 100644 --- a/.gitignore +++ b/.gitignore @@ -8,6 +8,7 @@ source/ /.Rhistory /.Rproj.user/* LoopDetectR.Rproj +/LoopDetectR.Rcheck # Compiled source # diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/DESCRIPTION b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/DESCRIPTION new file mode 100644 index 0000000..708b378 --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/DESCRIPTION @@ -0,0 +1,25 @@ +Package: LoopDetectR +Type: Package +Title: Comprehensive Feedback Loop Detection in ODE Models +Version: 0.1.3 +Authors@R: c(person("Katharina", "Baum", email = "katharina.baum@hpi.de", + role = c("aut", "cre"), comment = c(ORCID = "0000-0001-7256-0566")), + person("Sandra", "Krüger", role = c("ctb"))) +Description: Detect feedback loops (cycles, circuits) between species (nodes) in ordinary differential equation (ODE) models. Feedback loops are paths from a node to itself without visiting any other node twice, and they have important regulatory functions. Loops are reported with their order of participating nodes and their length, and whether the loop is a positive or a negative feedback loop. An upper limit of the number of feedback loops limits runtime (which scales with feedback loop count). Model parametrizations and values of the modelled variables are accounted for. Computation uses the characteristics of the Jacobian matrix as described e.g. in Thomas and Kaufman (2002) . Input can be the Jacobian matrix of the ODE model or the ODE function definition; in the latter case, the Jacobian matrix is determined using 'numDeriv'. Graph-based algorithms from 'igraph' are employed for path detection. +Imports: igraph, numDeriv +Suggests: deSolve, knitr, markdown, remotes, rmarkdown, utils +License: GPL-3 +Encoding: UTF-8 +LazyData: true +Depends: R (>= 4.0.0) +RoxygenNote: 7.3.3 +VignetteBuilder: knitr +URL: https://github.com/DILiS-lab/LoopDetectR, + https://cran.r-project.org/package=LoopDetectR +BugReports: https://github.com/DILiS-lab/LoopDetectR/issues +NeedsCompilation: no +Packaged: 2026-06-19 23:55:45 UTC; Admin +Author: Katharina Baum [aut, cre] (ORCID: + ), + Sandra Krüger [ctb] +Maintainer: Katharina Baum diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NAMESPACE b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NAMESPACE new file mode 100644 index 0000000..3d5d647 --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NAMESPACE @@ -0,0 +1,9 @@ +# Generated by roxygen2: do not edit by hand + +export(compare_loop_list) +export(find_edge) +export(find_loops) +export(find_loops_noscc) +export(find_loops_vset) +export(loop_summary) +export(sort_loop_index) diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NEWS.md b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NEWS.md new file mode 100644 index 0000000..20c8f71 --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/NEWS.md @@ -0,0 +1,7 @@ +# LoopDetectR 0.1.3 + +* Updated installation instructions from GitLab to GitHub. +* Added GitHub repository and issue tracker links to DESCRIPTION. +* Cleaned repository metadata and normalized text-file formatting. +* Removed local development history files from the repository. +* Added GitHub Actions checks for package validation. \ No newline at end of file diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/data.R b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/data.R new file mode 100644 index 0000000..aeb62d6 --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/data.R @@ -0,0 +1,78 @@ + +#' Solution for the cell cycle model related to func_li08 +#' +#' The file contains the solution over time (3 oscillatory cycles) for the +#' ordinary differential equation model as given in func_li08. In addition, +#' events as constructed in the +#' original publication [Li et al., 2008] are considered. +#' +#' @format A dataframe with 634 rows and 19 columns +#' \describe{ +#' \item{time}{time variable} +#' \item{y1}{first variable value} +#' \item{y2}{second variable value, } +#' \item{etc.}{etc. } +#' \item{y18}{18th variable value} +#' } +#' +#' @source The Caulobacter cell cycle model was proposed in +#' Li S, Brazhnik P, Sobral B, Tyson JJ. A Quantitative Study of the +#' Division Cycle of Caulobacter crescentus Stalked Cells. Plos Comput Biol. +#' 2008;4(1):e9. The solutions were generated with MATLAB using the +#' functions accompanying the above reference on +#' \doi{10.1371/journal.pcbi.0040009}. +#' +"li08_solution" + + + +#' Example ODE function: chain model with positive regulation. +#' +#' The file contains the function definition an ordinary differential equation +#' model of a chain model of 4 variables with positive feedback. +#' +#' @format R file with definition of function func_POSm4 that takes as +#' input arguments time t (dimension 1), variable values x (dimension 4), and +#' kinetic parameter values klin (dimension 8) and knonlin (dimension 2). +#' +#' @source +#' The chain model was used in +#' Baum K, Politi AZ, Kofahl B, Steuer R, Wolf J. Feedback, Mass +#' Conservation and Reaction Kinetics Impact the Robustness of Cellular +#' Oscillations. PLoS Comput Biol. 2016;12(12):e1005298. +#' +"func_POSm4" + + + +#' Example ODE function: bacterial cell cycle. +#' +#' The file contains the function definition an ordinary differential equation +#' model of Caulobacter crescentus cell cycle as proposed by Li et al., 2008. +#' It has 18 variables. +#' +#' @format R file with definition of function func_li08 that takes as +#' input arguments time t (dimension 1), and variable values y (dimension 18). +#' the kinetic parameters are defined within the function. +#' +#' @source The Caulobacter cell cycle model was proposed in +#' Li S, Brazhnik P, Sobral B, Tyson JJ. A Quantitative Study of the +#' Division Cycle of Caulobacter crescentus Stalked Cells. Plos Comput Biol. +#' 2008;4(1):e9. The function corresponds to the MATLAB function modelwtin(t,y) +#' as given on \doi{10.1371/journal.pcbi.0040009}. +#' +#' @details +#' The Caulobacter cell cycle model function will only give the solution as +#' shown in the publication [Li et al., 2008] if the change in variables at +#' defined events are taken into account. Please refer to the original +#' reference for details. +#' +"func_li08" + + + + + + + + diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/further_functions.R b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/further_functions.R new file mode 100644 index 0000000..22d78e6 --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/further_functions.R @@ -0,0 +1,194 @@ + +sort_loop_index <- function(loop_list){ + #' Sort loop indices + #' + #' Changes the loop representation such that every loop starts with the + #' smallest node index. Returns a loop list of the same dimensions, only + #' column \code{loop} will be altered. + #' + #' @param loop_list Dataframe with a column \code{loop} that contains the lists + #' of loops, e.g. obtained from \code{find_loops()}. + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the feedback loops of the system + #' loop_list <- find_loops(jac_matrix,10) + #' #sort the loop indices to start with the smallest + #' sorted_loop_list <- sort_loop_index(loop_list) + #' + #' @seealso \code{\link{compare_loop_list}} + #' + #' @export + + sorted_loop_list <- loop_list + sorted_loops <- lapply(sorted_loop_list$loop,function(x){ + ind_min <- which.min(x) + if (ind_min>1){ + return(x[c(ind_min:length(x),(2:ind_min))]) + } else { + return(x) + } + }) + sorted_loop_list$loop <- sorted_loops + return(sorted_loop_list) +} + + + +find_edge <- function(loop_list,source_node,target_node){ + #' Detecting loops with a certain edge + #' + #' @description Finds those loops in a loop list that contain a regulation + #' from a certain variable (source node) to a certain variable (target node). + #' + #' @param loop_list Dataframe with a column \code{loop} that contains the lists + #' of loops, e.g. obtained from \code{\link{find_loops}}. + #' @param source_node Index of the variable that is the source of the + #' queried interaction, i.e. that regulates the target node. + #' @param target_node Index of the variable that is the target of the + #' queried interaction, i.e. that is regulated by the source node. + #' + #' @return A vector that gives the indices in the loop list of those loops + #' that contain the indicated edge. + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the feedback loops of the system + #' loop_list <- find_loops(jac_matrix,10) + #' #find the loops containing the regulation from variable 3 to variable 4 + #' inds_3_to_4 <- find_edge(loop_list,3,4) + #' + #' @export + + vec_is_edge <- vapply(loop_list$loop,function(x){ + source_ind <- which(x==source_node) #find index of source node + if (length(source_ind)==0){ #if the source node was not found + return(FALSE) + } else { + if (target_node==x[source_ind[1]+1]){ #check whether the subsequent + #node of the source node is the target node + return(TRUE) + } else { + return(FALSE) + } + }},logical(1)) + + return(which(vec_is_edge)) +} + + + +loop_summary <- function(loop_list,column_val='length'){ + #' Summary of a loop list + #' + #' Summarizes the loops in a loop list by their length and sign, returns an + #' overview table of the numbers of all, negative and positive loops divided + #' by their lengths. + #' + #' @details Lengths are abbreviated by \code{len_1}, \code{len_2}, + #' \code{len_3} etc., signs are + #' abbreviated by \code{pos} for positive, \code{neg} for negative loops. The table + #' contains entries for each loop length from 1 to the maximal loop length + #' encountered in the table, and zeros are filled in if no loops of a + #' certain length exist in the table. + #' + #' @param loop_list List of loops as dataframe with columns \code{length}, + #' \code{sign}. + #' @param column_val String indicating the orientation of the summary table. + #' By default, rows of the results table are the sign of the loops, columns + #' are loop lengths. If \code{column_val} is set to \code{"sign"}, columns + #' and rows are exchanged. + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the feedback loops of the system + #' loop_list <- find_loops(jac_matrix,10) + #' #loop summary table + #' loop_sum_tab <- loop_summary(loop_list) + #' + #' @export + + res_mat <- table(loop_list$length) + loop_tab <- data.frame( + matrix(0,ncol=as.numeric(names(res_mat))[length(names(res_mat))],nrow=3), + row.names=c('all','pos','neg')) + loop_tab[1,as.numeric(row.names(res_mat))] <- res_mat + res_mat_temp <- table(loop_list$length[loop_list$sign==1]) + loop_tab[2,as.numeric(row.names(res_mat_temp))] <- res_mat_temp + res_mat_temp <- table(loop_list$length[loop_list$sign==-1]) + loop_tab[3,as.numeric(row.names(res_mat_temp))] <- res_mat_temp + colnames(loop_tab) <- paste0('len_',1:length(loop_tab)) + + if (column_val == 'sign') { + loop_tab <- t(loop_tab[2:3,]) + } + + return(loop_tab) +} + + + +compare_loop_list <- function(loop_list_a, loop_list_b){ + #' Compare two loop lists + #' + #' Compared two loop lists and returns the indices of those loops that are + #' identical in both lists, that switch only the sign or that do not occur + #' in both lists + #' + #' @details Indices of loops are given with respect to the order of the + #' loops in the first supplied loop list as well as for the second loop + #' list. The loops are sorted to represent their loops starting from the + #' smallest variable index (using the function \code{\link{sort_loop_index}}). + #' + #' @param loop_list_a,loop_list_b Loop lists with columns \code{loop} and + #' \code{sign}, for example generated from \code{\link{find_loops}}. + #' + #' @return A list with 5 (possible empty) vectors as entries. + #' \itemize{ + #' \item \code{ind_a_id} - indices of the loops in the first loop list that occur + #' identically in the second loop list + #' \item \code{ind_a_switch} - indices of the loops in the first loop list that occur + #' in the second loop list with a different sign + #' \item \code{ind_a_notin} - indices of the loops in the first loop list that do not + #' occur in the second loop list + #' \item \code{ind_b_id} - indices of loops in the second loop list corresponding to + #' the loops reported in \code{ind_a_id} + #' \item \code{ind_b_switch} - indices of loops in the second loop list corresponding + #' to loops reported in \code{ind_a_switch}. + #' } + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the feedback loops of the system + #' loop_list <- find_loops(jac_matrix,10) + #' #a slightly different Jacobian matrix of the system with 4 variables + #' jac_matrix_alt <- rbind(c(-1,0,0,1),c(1,-1,0,-1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the feedback loops of the system + #' loop_list_alt <- find_loops(jac_matrix_alt,10) + #' #compare the loop lists + #' comp_loop_list <- compare_loop_list(loop_list,loop_list_alt) + #' #loops that switch sign + #' comp_loop_list[['ind_a_switch']] + #' + #' @export + + sorted_loop_list_a <- sort_loop_index(loop_list_a) + sorted_loop_list_b <- sort_loop_index(loop_list_b) + + inds_a_in_b <- match(sorted_loop_list_a$loop,sorted_loop_list_b$loop) + ind_a_notin <- which(is.na(inds_a_in_b)) + ind_a_in <- which(!is.na(inds_a_in_b)) + #check whether signs are the same in the matching loops + logvec_a_id <- sorted_loop_list_a$sign[ind_a_in] == sorted_loop_list_b$sign[inds_a_in_b[ind_a_in]] + + return(list('ind_a_id' = ind_a_in[logvec_a_id], + 'ind_a_switch' = ind_a_in[!logvec_a_id], + 'ind_a_notin' = ind_a_notin, + 'ind_b_id' = inds_a_in_b[ind_a_in[logvec_a_id]], + 'ind_b_switch' = inds_a_in_b[ind_a_in[!logvec_a_id]])) + +} diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/loop_detection_functions.R b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/loop_detection_functions.R new file mode 100644 index 0000000..b4fad7d --- /dev/null +++ b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/R/loop_detection_functions.R @@ -0,0 +1,475 @@ + +find_loops_noscc <- function(jacobian, max_num_loops=100000){ + #' @title Loop detection in a matrix + #' + #' @description Given the Jacobian matrix of an ODE system or the adjacency + #' matrix of a graph, this function determines all loops in the system up + #' to the maximal number supplied. No + #' decomposition into strongly connected components is performed. + #' + #' @details The input matrix delivers the directed interactions in the ODE + #' system; if entry \code{(i,j)} is non-zero it means that variable (or + #' node) \code{i} is regulated by variable (node) \code{j}. Johnson's + #' algorithm for path detections + #' from the igraph package (function: + #' \code{\link[igraph]{all_simple_paths}}) is used. + #' No decomposition into strongly connected components is employed which + #' could be beneficial for smaller systems (compared to + #' \code{\link{find_loops}}). + #' The queried graph is increased stepwise leading to the output of loops + #' in a certain order determined by the order of occurrence in the Jacobian + #' matrix: + #' \itemize{ + #' \item first the self-loops, + #' \item then feedback loops incorporating only the first and second species of + #' the Jacobian, + #' \item then feedback loops incorporating the third and at most also the first + #' and second species of the jacobian, etc.} + #' If the maximal number of loops, max_num_loops, is reached, no warning is + #' issued. It is very probable that not all feedback loops of the system + #' have been found. + #' Up to which species this function searched before stopping due to + #' reaching the maximal allowed loop number can be inferred from the last + #' exported feedback loop. + #' Running the function multiple times with re-ordered jacobian as input + #' can enable detection of alternative feedback loops while limiting the + #' runtime and output size of single runs. + #' If columns of the Jacobian are named, + #' the identification is given by the attribute \code{node_ids}, + #' \code{attr(result,"node_ids")}. + #' + #' @param jacobian Square Jacobian matrix of an ODE system or the adjacency + #' matrix of a graph; captures interactions such that entry \code{(i,j)} is + #' negative (positive) if variable \code{j} regulates variable \code{i} + #' negatively (positively). + #' + #' @param max_num_loops Positive numeric value indicating the maximal number + #' of loops that are reported. Default: \eqn{10^5}. + #' + #' @return A data.frame with three columns: \code{loop}, \code{length}, \code{sign} + #' containing up to \code{max_num_loops} loops of the systems defined + #' by matrix \code{jacobian}. Each entry in the loop column is a list of + #' identifiers that correspond to the indices of the variable in the + #' Jacobian matrix and denote + #' in which order the variables form the loop. + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the first 5 feedback loops of the system + #' loop_list <- find_loops_noscc(jac_matrix,5) + #' + #' @seealso \code{\link{find_loops}}, \code{\link{find_loops_vset}} + #' + #' @export + #' + + #initialize variables + all_loops <- vector('list',max_num_loops) #list to store all loops + loop_signs <- numeric(max_num_loops) #vector to store if the loops are positive or negative + loop_length <- numeric(max_num_loops) #vector to store the length of all loops + loopcount <- 0 + + #determine the sign of the entries only once, this is important to avoid overflow for large entries + sig_jacobian <- sign(jacobian) + + #determine self-loops + for (i in which(diag(sig_jacobian)!=0)){ #iterate over all nonzero entries of the diagonal, these are self-loops + loopcount <- loopcount+1 + loop_signs[loopcount] <- sig_jacobian[i,i] #sign of the self-loop + loop_length[loopcount] <- 1 + all_loops[loopcount] <- list(c(i,i)) + } + + #only include these nodes into the examination for which we have at least one outgoing and one ingoing edge + #this makes computation a lot faster for sparse matrices. Might increase runtime for smaller matrices. + node_inds <- which(sapply(1:dim(sig_jacobian)[1],function(x){any(sig_jacobian[x,][-x]!=0) & any(sig_jacobian[,x][-x]!=0)})) + node_count <- 1 + + #determine loops with length > 1 + for (i in node_inds[-1]){ #initialize a loop from the first row/column of the jacobian matrix to the last + node_count <- node_count + 1 #keeps track of the node count + if (loopcount < max_num_loops){ + sign_tmp_jacobian <- sig_jacobian[node_inds[1:node_count],node_inds[1:node_count]] #store the current sub-jacobian in a temporary matrix + if (i==node_inds[2]) { # for the first graph with more than one node + #build the directed graph from the current jacobian matrix, assign the id in the jacobian to the nodes + jac_graph <- igraph::graph_from_adjacency_matrix(t(abs(sign_tmp_jacobian)),mode="directed",diag=FALSE, add.colnames = NA) + #find the nodes which affect the most recently added node (not the node itself) + secondlastnodes <- which(sign_tmp_jacobian[node_count,1:(node_count-1)] != 0) + } else {# if it is not the first node + #just add the one node (this will be the node with index node_count) + jac_graph <- igraph::add_vertices(jac_graph,nv=1) + #species acting on node i, omit self-edges: + spec_act_on_i <- which(sign_tmp_jacobian[node_count,1:(node_count-1)] != 0) + #odes which affect the most recently added node are used further + secondlastnodes <- spec_act_on_i + #add the edges to the graph + if (length(spec_act_on_i)>0){ + jac_graph <- igraph::add_edges(jac_graph, c(rbind(spec_act_on_i, node_count))) + } + #species on which node i acts: + spec_i_acts_on <- which(sign_tmp_jacobian[1:(node_count-1),node_count]!=0) + #add the edges to the graph + if (length(spec_i_acts_on)>0){ + jac_graph <- igraph::add_edges(jac_graph, c(rbind(node_count, spec_i_acts_on))) + } + + } + + #search all simple paths from the current node to the nodes affecting node i + if (length(secondlastnodes)!=0){ #only iterate over the nodes if the list is not empty + #loop over all nodes which have an edge to node i + for (k in secondlastnodes) { + #ensure that the limit of numbers of loops is not yet exceeded + if (loopcount < max_num_loops){ + #find and store all paths from the current node i to node k + tmp_path <- igraph::all_simple_paths(jac_graph,from=node_count,to=k) + if (length(tmp_path)!=0) { # if there are simple paths found + #iterate over all paths in the list + for (j in 1:length(tmp_path)){ + #ensure that the limit of numbers of loops is not yet exceeded + if (loopcount < max_num_loops){ + #store the current loop in the variable + #(e.g. k = 1, tmp_path[[j]] = 4 3 2 1 --> loop = 1 4 3 2 1) + loop <- c(k, igraph::as_ids(tmp_path[[j]])) + #count how many loops have been found + loopcount <- loopcount+1 + #store the loop in the list of all paths (and reformulate to original node ids) + all_loops[loopcount] <- list(node_inds[loop]) + #store the loop length (it is loop length-1, because the edges should be counted and not the nodes in the loop) + loop_length[loopcount] <- length(loop)-1 + #edge indices of the loop path + edge_vec <- cbind(loop[-1],loop[-length(loop)]) + #check the product of all weights along the path to determine the sign of the loop + loop_signs[loopcount] <- sign(prod(sign_tmp_jacobian[edge_vec])) + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + } + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + } + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + + #save results + result <- data.frame(loop=I(all_loops[1:loopcount]), length=loop_length[1:loopcount],sign=loop_signs[1:loopcount]) #store the results in a dataframe + #add node identifiers if column names are provided in the Jacobian + if (!is.null(colnames(jacobian))){ + name_vec <- (1:dim(jacobian)[2]) + names(name_vec) <- colnames(jacobian) + attr(result,'node_ids') <- name_vec + } + return(result) #return the data frame +} + + + +find_loops <- function(jacobian, max_num_loops=100000){ + #' @title Loop detection in a matrix + #' + #' @description Given the Jacobian matrix of an ODE system or the adjacency + #' matrix of a graph, this function determines all loops in the system up + #' to the maximal number supplied. + #' + #' @details The input matrix delivers the directed interactions in the ODE + #' system; if entry \code{(i,j)} is non-zero it means that variable (or node) \code{i} is + #' regulated by variable (node) \code{j}. Johnson's algorithm for path detection + #' as well as Tarjan's algorithm for detecting strongly connected + #' components are used as implemented in the igraph package (functions: + #' \code{\link[igraph]{all_simple_paths}}, \code{\link[igraph]{components}}) . + #' If the maximal number of loops, max_num_loops, is reached, no warning is + #' issued. It is very probable that not all feedback loops of the system + #' have been found. + #' Running the function multiple times with re-ordered jacobian as input + #' can enable detection of alternative feedback loops while limiting the + #' runtime and output size of single runs. + #' If columns of the Jacobian are named, + #' the identification is given by the attribute \code{node_ids}, + #' \code{attr(result,"node_ids")}. + #' + #' + #' @param jacobian Square Jacobian matrix of an ODE system or the adjacency + #' matrix of a graph; captures interactions such that entry \code{(i,j)} is + #' negative (positive) if variable \code{j} regulates variable \code{i} negatively + #' (positively). + #' + #' @param max_num_loops Positive numeric value indicating the maximal number + #' of loops that are reported. Default: \eqn{10^5}. + #' + #' @return A data.frame with three columns: \code{loop}, \code{length}, \code{sign} + #' containing up to \code{max_num_loops} loops of the systems defined + #' by matrix \code{jacobian}. Each entry in the loop column is a list of + #' identifiers that correspond to the indices of the variable in the + #' Jacobian matrix and denote + #' in which order the variables form the loop. + #' + #' @examples + #' #sample Jacobian matrix of a system with 4 variables + #' jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) + #' #find the first 5 feedback loops of the system + #' loop_list <- find_loops(jac_matrix,5) + #' + #' @seealso \code{\link{find_loops_noscc}}, \code{\link{find_loops_vset}} + #' + #' @export + + + #initialize variables + all_loops <- vector('list',max_num_loops)#list to store all loops + loop_signs <- numeric(max_num_loops) #vector to store if the loops are positive or negative + loop_length <- numeric(max_num_loops) #vector to store the length of all loops + #number of detected loops + loopcount <- 0 + + #determine the sign of the entries only once, this is important to avoid overflow for large entries + sig_jacobian <- sign(jacobian) + + #determine self-loops + for (i in which(diag(jacobian)!=0)){ #iterate over all nonzero entries of the diagonal, these are self-loops + loopcount <- loopcount+1 + loop_signs[loopcount] <- sig_jacobian[i,i] #sign of the self-loop + loop_length[loopcount] <- 1 + all_loops[loopcount] <- list(c(i,i)) + } + + #only include these nodes into the examination for which we have at least one outgoing and one ingoing edge + #this makes computation a lot faster for sparse matrices. Might increase runtime for smaller matrices. + glob_node_inds <- which(sapply(1:dim(sig_jacobian)[1],function(x){any(sig_jacobian[x,][-x]!=0) & any(sig_jacobian[,x][-x]!=0)})) + + #determine strongly connected components in the associated graph + jac_graph <- igraph::graph_from_adjacency_matrix(t(abs(sig_jacobian[glob_node_inds,glob_node_inds])),mode="directed",diag=FALSE, add.colnames = NA) + str_comp <- igraph::components(jac_graph, mode="strong") + + #for all clusters of size>1 + for (clus_id in which(str_comp$csize>1)) { + #determine node_inds + node_inds <- glob_node_inds[str_comp$membership==clus_id] + # + node_count <- 1 + #determine loops with length > 1 + for (i in node_inds[-1]){ #initialize a loop from the first row/column of the jacobian matrix to the last + node_count <- node_count + 1 #keeps track of the node count + if (loopcount < max_num_loops){ + sign_tmp_jacobian <- sig_jacobian[node_inds[1:node_count],node_inds[1:node_count]] #store the current sub-jacobian in a temporary matrix + if (i==node_inds[2]) { # for the first graph with more than one node + #build the directed graph from the current jacobian matrix, assign the id in the jacobian to the nodes + jac_graph <- igraph::graph_from_adjacency_matrix(t(abs(sign_tmp_jacobian)),mode="directed",diag=FALSE, add.colnames = NA) + #find the nodes which affect the most recently added node (not the node itself) + secondlastnodes <- which(sign_tmp_jacobian[node_count,1:(node_count-1)] != 0) + } else {# if it is not the first node + #just add the one node + jac_graph <- igraph::add_vertices(jac_graph,nv=1) + #species acting on node i, omit self-edges: + spec_act_on_i <- which(sign_tmp_jacobian[node_count,1:(node_count-1)]!=0) + #the nodes which affect the most recently added node are used further + secondlastnodes <- spec_act_on_i + #add the edges to the graph + if (length(spec_act_on_i)>0){ + jac_graph <- igraph::add_edges(jac_graph, c(rbind(spec_act_on_i, node_count))) + } + #species on which node i acts: + spec_i_acts_on <- which(sign_tmp_jacobian[1:(node_count-1),node_count]!=0) + #add the edges to the graph + if (length(spec_i_acts_on)>0){ + jac_graph <- igraph::add_edges(jac_graph, c(rbind(node_count, spec_i_acts_on))) + } + + } + + #search all simple paths from the current node to the nodes affecting the ith node + if (length(secondlastnodes)!=0){ #only iterate over the nodes if the list is not empty + #loop over all nodes which have an edge to node i + for (k in secondlastnodes) { + #ensure that the limit of numbers of loops is not yet exceeded + if (loopcount < max_num_loops){ + #find and store all paths from the current node node_count to node k + tmp_path <- igraph::all_simple_paths(jac_graph,from=node_count,to=k) + if (length(tmp_path)!=0) { # if there are simple paths found + #iterate over all paths in the list + for (j in 1:length(tmp_path)){ + #ensure that the limit of numbers of loops is not yet exceeded + if (loopcount < max_num_loops){ + #store the current loop in the variable + #(e.g. k = 1, tmp_path[[j]] = 4 3 2 1 --> loop = 1 4 3 2 1) + loop <- c(k, igraph::as_ids(tmp_path[[j]])) + #count how many loops have been found + loopcount <- loopcount+1 + #store the loop in the list of all paths (and reformulate to original node ids) + all_loops[loopcount] <- list(node_inds[loop]) + #store the loop length (it is loop length-1, because the edges should be counted and not the nodes in the loop) + loop_length[loopcount] <- length(loop)-1 + #edge indices of the loop path + edge_vec <- cbind(loop[-1],loop[-length(loop)]) + #check the product of all weights along the path to determine the sign of the loop + loop_signs[loopcount] <- sign(prod(sign_tmp_jacobian[edge_vec])) + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + } + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + } + } else { #stop execution if we reach the upper limit to the number of nodes + break + } + } + } + #save results + result <- data.frame(loop=I(all_loops[1:loopcount]), length=loop_length[1:loopcount],sign=loop_signs[1:loopcount]) #store the results in a dataframe + #add node identifiers if column names are provided in the Jacobian + if (!is.null(colnames(jacobian))){ + name_vec <- (1:dim(jacobian)[2]) + names(name_vec) <- colnames(jacobian) + attr(result,'node_ids') <- name_vec + } + return(result) #return the data frame +} + + + +find_loops_vset <- function(fun, vset, ..., max_num_loops=100000, compute_full_list=TRUE){ + #' @title Loop detection for an ODE model at multiple sets of variables + #' + #' @description Determines loop lists for an ODE system given by a function + #' and at multiple sets of variables. Loop lists are reported if signs of + #' Jacobian matrix have changed. + #' + #' @param fun Function defining the ODE system, returns the vector \eqn{dx/dt}. + #' May depend on further parameters in \code{...}. + #' @param vset List of variable values at which the loops are determined. + #' @param ... Further parameters except variable values to the function \code{fun}, + #' none called \code{x}. + #' @param max_num_loops Positive numeric value indicating the maximal number + #' of loops that are reported in a loop list. Default: \eqn{10^5}. + #' @param compute_full_list Logical value indicating whether for each + #' Jacobian matrix with any different sign the loop list is computed (\code{TRUE}, + #' default), or whether further checks are performed to ensure that loops + #' may be altered. + #' + #' @details + #' The supplied function can take more arguments, but only the variables + #' are allowed to be named \code{x} (they can also be named differently). + #' The Jacobian matrices are computed for each of the variable + #' values defined in vset using the \code{\link[numDeriv]{jacobian}} function + #' from the \code{NumDeriv} package with option \code{method = 'complex'}, i.e. using a + #' complex-step approach. + #' If \code{compute_full_list = TRUE} (default), loop lists are not re-computed + #' for Jacobians that clearly do not allow for altered loop lists. This is + #' the case if no new regulation appear and only signs of regulations are + #' altered that are not member of any loop. Loop lists can still be + #' identical for different Jacobians, e.g. if two sign switches occur that + #' are both affecting the same loops. + #' + #' @return A list with four entries: + #' \itemize{ + #' \item \code{loop_rep} List of loop lists. + #' \item \code{loop_rep_index} Vector of integer numbers returning the index of the + #' loop list in loop_rep belonging to each entry in \code{vset}. + #' \item \code{jac_rep} List of signed Jacobian matrices. + #' \item \code{jac_rep_index} Vector of integer numbers returning the index of the + #' Jacobian matrix in jac_rep belonging to each entry in \code{vset}. + #' } + #' + #' @details + #' If there is only one class of Jacobian matrix (i.e. the signs of the + #' Jacobian matrix are the same for all entries in \code{vset}), \code{loop_rep} and + #' \code{jac_rep} will have only one entry each. The number of entries for + #' \code{loop_rep_index} and \code{jac_rep_index} corresponds to the length of \code{vset}. + #' Only if \code{compute_full_list} is set to \code{FALSE}, \code{loop_rep} can contain + #' fewer elements than \code{jac_rep}, otherwise both have the same number of + #' elements. + #' + #' @examples + #' #default call to determine loops from an ODE model given by a function + #' #read in example functions + #' data("func_POSm4") + #' #the loaded function func_POSm4 takes arguments t, x, klin, knonlin + #' res_tab <- find_loops_vset(func_POSm4,vset=list(c(1,1,1,1)),t=1, + #' klin=c(1,2,0.5,1,2,0.1,3,2,3),knonlin=c(1,2)) + #' #computed loop list: + #' res_tab$loop_rep[[1]] #or res_tab[[1]][[1]] + #' + #' #determine loops from an ODE model over the course of a solution + #' #read in the example function defining the bacterial cell cycle + #' data("func_li08") + #' #kinetic parameter values are defined within the function + #' #read in a set of variable values (the solution of func_li08 with events) + #' data("li08_solution") + #' #transform the solution (columns: variables) to the correct list format + #' #and remove the time (first column) + #' li08_sol_list <- as.list(as.data.frame(t(li08_solution[,-1]))) + #' res_tab <- find_loops_vset(func_li08,vset=li08_sol_list,t=1, + #' compute_full_list=FALSE) + #' + #' @export + + #compute all jacobians + jacob_list <- lapply(vset,function(y){ + sign(numDeriv::jacobian(fun,x=y,method="complex",...))}) + #find different signed Jacobians + jac_rep <- unique(jacob_list) + + #identify the indices back + jac_rep_index <- match(jacob_list,jac_rep) + + if (compute_full_list) { #if we compute loops for all Jacobians + loop_rep <- lapply(jac_rep,function(y){ + find_loops(y,max_num_loops) + }) + loop_rep_index <- jac_rep_index + } else { #if we search for different patterns before + #loop list for the first Jacobian + loop_rep <- list(find_loops(jac_rep[[1]],max_num_loops)) + loop_rep_index <- rep(0,length(jac_rep_index)) + loop_rep_index[jac_rep_index==1] <- 1 + #we go through every Jacobian separately + if (length(jac_rep)>1) { #if we have more than one Jacobian + for (i in 2:length(jac_rep)) { #check each Jacobian (if there are more + #than 1) + J_temp <- jac_rep[[i]] + #determine if there is a switch from zero to nonzero + switch_to_nonzero <- vapply(jac_rep[1:i-1],function(x) + {any(abs(J_temp[x==0])>0)},logical(1)) + existing_loop_changed <- rep(FALSE,i-1) + for (j in which(switch_to_nonzero==0)) { #for the Jacobians in which + #no additional regulation came up: determine if the sign + #switches of an edge that is contained in a loop + #target-source node pairs of altered Jacobian entries + tn_sn_ind <- which(!((J_temp-jac_rep[[j]])==0),arr.ind=T) + #find loops that contain any of the edges + for (k in 1:length(tn_sn_ind)) { + if (length(find_edge(loop_rep[[loop_rep_index[jac_rep_index==j][1]]],#bug fixed on Oct 12, 2020, was loop_rep[[j]] + tn_sn_ind[k,2],tn_sn_ind[k,1]))>0){ + #in case we found an edge that is affected + existing_loop_changed[j] <- TRUE + break + } + } + } + #if there is a relevant difference for all existing Jacobians + if (all(switch_to_nonzero|existing_loop_changed)) { + loop_rep[[length(loop_rep)+1]] <- + find_loops(J_temp,max_num_loops) + loop_rep_index[jac_rep_index==i] <- max(loop_rep_index)+1 + } else { #if there is one Jacobian for which no interaction came up + # AND no edge of a loop changed - assign index of the first + # similar Jacobian (in principle, there only should be one) + loop_rep_index[jac_rep_index==i] <- + loop_rep_index[jac_rep_index==which(!(switch_to_nonzero|existing_loop_changed))[1]][1] + + } + } + } + } + return(list('loop_rep'=loop_rep,'loop_rep_index'=loop_rep_index, + 'jac_rep'=jac_rep,'jac_rep_index'=jac_rep_index)) +} diff --git a/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/data/func_POSm4.rda b/LoopDetectR.Rcheck/00_pkg_src/LoopDetectR/data/func_POSm4.rda new file mode 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Call the following +commands in an R session. + +```{r install_fromgit, message=FALSE, results='hide', eval=FALSE} +# Install the package including the vignette and the manual +remotes::install_github( + "DILiS-lab/LoopDetectR", + build_manual = TRUE, + build_vignettes = TRUE +) + +``` + +After installation, load the package. +```{r load_package} +# Load package +library("LoopDetectR") +``` + +## In brief and quick start + +The package LoopDetectR enables determining all feedback loops of +an ordinary differential equation (ODE) system at user-defined values of +the model parameters and of the modelled variables. + +The following call reports (up to 10) feedback loops for an ODE system +determined by a function, here the example function `func_POSm4`, at variable +values `s_star` (here, these are all equal to 1). Additional arguments to the +example function are supplied. + +```{r quick_example} + +# Load example ODE system with function func_POSm4, 4 variables +data("func_POSm4") +# Example variable values +s_star <- rep(1,4) +# Further arguments of func_POSm4, in addition: time t as argument +klin <- rep(1,8) +knonlin <- c(2.5,3) + +# compute loops +res_tab <- find_loops_vset(func_POSm4,vset=list(s_star),t=1,klin=klin, + knonlin=knonlin,max_num_loops=10) +# The loop list is reported +res_tab$loop_rep[[1]] +# This is the sixth loop of the list. It is a positive feedback loop (sign in +# the loop list equals +1) of length 3 in that variable 3 regulates variable 4, +# variable 4 regulates variable 2, and variable 2 regulates variable 3. +res_tab$loop_rep[[1]][6,] +# The corresponding signed Jacobian matrix +res_tab$jac_rep[[1]] +``` + +## Introduction + +Ordinary differential equation (ODE) models are used frequently to +mathematically represent biological systems. Feedback loops are important +regulatory features of biological systems and can give rise to different +dynamic behavior such as multistability for positive feedback loops or +oscillations for negative feedback loops. + +The feedback loops in an ODE system can be detected with the help of its +Jacobian matrix, the matrix of partial derivatives of the variables. +It captures all interactions between the variables and gives rise to the +interaction graph of the ODE model. In this graph, each modelled variable +is a node and non-zero entries in the Jacobian matrix are (weighted) +edges of the graph. Interactions can be positive or negative, according +to the sign of the Jacobian matrix entry. + +Directed path detection in this graph is used to determine all feedback +loops (in graphs also called cycles or circuits) of the system. They are +marked by a set of directed interactions forming a chain in which only +the first and the last node (variable) is the same. Thereby, self-loops +(loops of length one) can also occur. + +LoopDetectR allows for detection of all loops of the graph and also reports +the sign of each loop, i.e. whether it is a positive feedback loop +(the number of negative interactions is even) or a negative feedback loop +(the number of negative interactions is uneven). +The output is a table that captures the order of the variables forming +the loop, their length and the sign of each loop. + +Jacobian determination in LoopDetectR relies on the package `numDeriv`, and path +finding in graphs uses algorithms supplied in the package `igraph`. + +## Solving the ODE model to generate variable values of interest + +Solving an ODE model can be performed with the package `deSolve`. +Note: You can skip this step if you already have a point of interest in state +space, or if you want to use dummy values for the variables such as +`s_star <- 1:4`. + +```{r solving_ODE} +# Load example ODE system with function func_POSm4, +# Positive feedback chain model from [Baum et al., 2016], 4 variables +data(func_POSm4) +# The function func_POSm4 returns a vector, but deSolve needs the vector within +# a list as output. Therefore, we define a function that simply puts the output +# of func_POSm4 into a list: +func_POSm4_list <- function(t,x,klin,knonlin){list(func_POSm4(t,x,klin,knonlin))} +# Kinetic parameters of the model, supplied as arguments to func_POSm4 +klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1) +knonlin <- c(0.3,2) +# Solve the system using deSolve +sol <- deSolve::ode(y = rep(1,4), times = seq(0,15,0.1), func = func_POSm4_list, + parms=klin, knonlin=knonlin) +# The solution of the 4-variable system is oscillatory, showing only the first +# variable here +plot(sol[,1],sol[,2],type='l',xlab='time',ylab ='variable 1') +# Set the last point of the numeric solution as point of interest, omit the +# first column (it contains the time) +s_star <- sol[dim(sol)[1],2:dim(sol)[2]] +``` + +State variable values of interest could be steady state values, +values at a specific point in time (e.g. after a stimulus) or even a set +of values (see section *Determining loops over a set of variable values*). + + +## Calculating the Jacobian matrix + +The function `jacobian` from the `numDeriv` package can be used to determine +numerically the Jacobian matrix of an ODE system at a certain set of values +for the variables, `s_star`. +The approach is that of finite differences (with real step) or +complex step approach, the latter of which is supposed to deliver more exact +results [Martins et al., 2003]. + +The input function, in the example `func_POSm4` (positive feedback chain model +from [Baum et al., 2016]) defines the time derivatives of the modelled variables +as a vector: $f_i(s)=dS_i/dt$. Note that only those input arguments to the +function that encode the modelled variables (and hence in whose direction the +partial derivatives are taken) are allowed to be called `x`. + +```{r compute_jacobian} +klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1) +knonlin <- c(0.3,2) +j_matrix <- numDeriv::jacobian(func_POSm4,s_star,method="complex", + t=1,klin=klin,knonlin=knonlin,) +j_matrix +signed_jacobian <- sign(j_matrix) +``` + +The (i,j)th entry of the Jacobian matrix denotes the partial derivative +of variable $S_i$ with respect to variable $S_j$, +$J_{ij}=\delta S_i/\delta S_j$, which is positive if $S_j$ has a direct positive +effect on $S_i$, negative if $S_j$ has a direct negative effect on $S_i$ and zero +if $S_j$ does not have a direct effect on $S_i$. For example, the entry in row 2, +column 4, $J_{24}$, of the `signed_jacobian` matrix above is positive, meaning that +in the underlying ODE model, variable 4 positively regulates variable 2. + +## Computing all feedback loops and useful functions for loop search + +The Jacobian matrix is used to compute feedback loops in the generated +interaction graph. The default function for this is `find_loops`, in that +strongly +connected components are determined to reduce runtime. For smaller +systems, the function `find_loops_noscc` skips this step and thus can be +faster. The optional second input argument, `max_num_loops`, sets an upper +limit to the number of detected and reported loops and thus can prevent overly +long runtime (but also potentially not all loops are returned). + +```{r find_loops} +# Determine the loop_list from Jacobian matrix j_matrix +loop_list <- find_loops(j_matrix) +loop_list +# The signed Jacobian matrix can be supplied instead, delivering the same results +loop_list <- find_loops(signed_jacobian) +loop_list +``` + +The output loop list is an R data.frame with one row for each detected loop. +The column +`loop` contains the order of the variables that form the loop (as vector in a +list); `length` contains the loop length (i.e. the number of variables involved); +`sign` denotes whether the loop is negative, `-1`, or positive, `1`. +The data.frame can be queried as usual for single loops or loops of a certain +length or sign. + +```{r retrieve_loops} +# Retrieve fifth loop +loop_list[5,1] +# In order to obtain the vector of the order of variables of a loop, you have to +# call the list element +loop_list[5,1][[1]] +# Retrieve all loops of length 4 +loop_list[loop_list$length==4,] +``` + +The LoopDetectR function `loop_summary` provides a convenient report on total +number of loops, subdivided by their lengths (`len_i`) and signs (`all`, `pos`, +`neg`). + +```{r loop_summary} +loop_summary(loop_list) +``` + +One can filter the loop list for loops containing specific variables, for +example the one with index 2: + +```{r loops_with_specific_node} +# Index of node of interest +noi <- 2 +# Return all loops from loop_list containing node 2 +loop_list[vapply(loop_list$loop,function(x){noi %in% x},logical(1)),] +``` + +The LoopDetectR function `find_edge` can be used to search a loop list for loops +containing specific edges defined by the indices of the ingoing and outgoing +nodes. This example returns the indices of all loops with a regulation of node +3 by node 2. These are only two here. + +```{r find_edge} +# Obtain the indices of the loops with edge '2 regulates 3' in loop_list +loop_edge_ind <- find_edge(loop_list,source_node=2,target_node=3); +loops_with_edge_2_to_3 <- loop_list[loop_edge_ind,] +loops_with_edge_2_to_3 +``` + +Loop lists can be saved and loaded as R objects using the usual save (or +saveRDS) and load (loadRDS) R functions. Saving the loop list into table files +is possible, but the vectors containing the loops are saved as string +`"c(x,y,z)"` and need special handling when loading back into R or into other +programming language frameworks. + +```{r save_files} +# This writes a file 'looplist_func_POSm4.RData' +save(loop_list,file=file.path(tempdir(),'looplist_func_POSm4.RData')) +# This loads the object 'loop_list' into the workspace +load(file.path(tempdir(),'looplist_func_POSm4.RData')) + +# This saves the loop list into a table with separation by tab +write.table(loop_list,file=file.path(tempdir(),'looplist_func_POSm4.txt'), + sep='\t',quote=F,row.names=F) +# This reads the loop list back into the R session, as object ll +ll <- read.table(file.path(tempdir(),'looplist_func_POSm4.txt'), + header=T,sep='\t') +ll +# This transforms the "c(x,y,z)"-entries into the format used by LoopDetectR +ll$loop <- lapply(ll$loop,function(x){eval(parse(text=x))}) +ll +``` + +## Computing feedback loops over multiple sets of variable values of interest + +In this example of a model of the bacterial cell cycle [Li et al., 2008], +it is demonstrated how feedback loops can be determined over multiple sets of +variable values. Here, it is focused on the solution of the ODE +systems along the time axis (provided as data in the package, +*li08_solution.RData*). + +```{r li_example} +# Load in the example ODE model function func_li08, the kinetic parameters are +# defined within the function, and the function returns a vector of the time +# derivatives (in the same order as the modelled variables in the arguments) +data("func_li08") +# Load sets of variable values (solution to the ODE over time) +data("li08_solution") #loads the data.frame li08_solution, columns: variables +# Cast the solution into the correct list format and remove time (first column) +li08_sol_list <- as.list(as.data.frame(t(li08_solution[,-1]))) +# Compute all different loop lists along the solution +res_tab <- find_loops_vset(func_li08,vset=li08_sol_list,t=1, + compute_full_list=FALSE) +``` + +The solutions of the example ODE model give rise to seven different loop lists +that are saved as elements of the list `res_tab$loop_rep`. +Here, two examples of resulting loop lists are given (without +self-loops). + +```{r example_loop_lists_li} +loop_list_2 <- res_tab$loop_rep[[2]][res_tab$loop_rep[[2]]$length>1,] +loop_list_2 +loop_list_7 <- res_tab$loop_rep[[7]][res_tab$loop_rep[[7]]$length>1,] +loop_list_7 +``` + +The entry `res_tab$loop_rep_index` is a vector of the same length as the +number of different states at which the loops were determined +(`length(li08_sol_list)`), and returns which entry of `res_tab$loop_rep` belongs +to each input state. + +```{r example_li_index} +# Determine the loop list belonging to the 10th up to 20th input state. +# It is loop_list_2 for all of these input states. +res_tab$loop_rep_index[10:20] +``` + +Similarly, `res_tab$jac_rep` and `res_tab$jac_rep_index` capture the different +Jacobian matrices and for each input state which Jacobian belongs to it. + +Results of this analysis could be plotted along the solution and analyzed +further to discover reasons of changing loops. Please note that in order +to obtain the sample solution in *li08_solution.RData* also event functions +are required; the solution cannot be retrieved from integrating +`func_li08` alone. Please refer to the model's publication [Li et al., +2008] for details. + + +## Comparing two loop lists + +LoopDetectR provides a function for comparing the loops of two systems, +`compare_loop_list`. For a meaningful comparison, the loop indices in +the compared systems should point to the same variables. This could be the case +when regulations change within one system between different sets of variables of +interest (along a dynamic trajectory, at different steady states of the system), +or when comparing different systems in which one or more regulations are altered +(as in the below example the positive feedback chain model vs. the negative +feedback chain model, [Baum et al., 2016]). + +```{r compare_loops} +# Load the ODE function of the positive feedback chain model +data(func_POSm4) +# Set kinetic parameters +klin <- c(165,0.044,0.27,550,5000,78,4.4,5.1) +knonlin <- c(0.3,2) +# Compute the Jacobian matrix of the system at the state [1,1,1,1] +j_matrix <- numDeriv::jacobian(func_POSm4,rep(1,4),method="complex", + t=1, klin=klin, knonlin=knonlin) +# Compute all loops for this Jacobian +loop_list_pos <- find_loops(j_matrix) + +# Function with negative regulation. The altered regulation affects +# two entries of the Jacobian matrix. Parameter values and the set of +# variable values remain identical. +j_matrix_neg <- sign(j_matrix) +j_matrix_neg[1:2,4] <- -sign(j_matrix[1:2,4]) +# Compute the loop list for this Jacobian with altered regulation +loop_list_neg <- find_loops(j_matrix_neg); + +# Compute comparison +comp_inds <- compare_loop_list(loop_list_pos,loop_list_neg) +# Only the four self-loops remain identical in both systems (the indices +# with respect to the first input list, loop_list_pos, are saved in ind_a_id). +loop_list_pos[comp_inds$ind_a_id,] +# ind_b_id saves the indices of the corresponding loops in the negatively +# regulated system, loop_list_neg. +loop_list_neg[comp_inds$ind_b_id,] +# Two loops are the same in both systems but they have switched their signs. +# Their indices in the first list are saved in ind_a_switch +loop_list_pos[comp_inds$ind_a_switch,] +# Their indices in the second list are saved in ind_b_switch +loop_list_neg[comp_inds$ind_b_switch,] +# All loops in the positively regulated system do also occur in the negatively +# regulated system, i.e. ind_a_notin is empty. +comp_inds$ind_a_notin +``` + +## References + +Baum K, Politi AZ, Kofahl B, Steuer R, Wolf J. Feedback, Mass +Conservation and Reaction Kinetics Impact the Robustness of Cellular +Oscillations. PLoS Comput Biol. 2016;12(12):e1005298. + +Li S, Brazhnik P, Sobral B, Tyson JJ. A Quantitative Study of the +Division Cycle of Caulobacter crescentus Stalked Cells. Plos Comput Biol. +2008;4(1):e9. + +Martins JRRA, Sturdza P, Alonso JJ. The complex-step derivative +approximation. ACM Trans Math Softw. 2003;29(3):245–62. diff --git a/LoopDetectR.Rcheck/00install.out b/LoopDetectR.Rcheck/00install.out new file mode 100644 index 0000000..9acd6bb --- /dev/null +++ b/LoopDetectR.Rcheck/00install.out @@ -0,0 +1,16 @@ +* installing *source* package 'LoopDetectR' ... +** this is package 'LoopDetectR' version '0.1.3' +** using staged installation +** R +** data +*** moving datasets to lazyload DB +** inst +** byte-compile and prepare package for lazy loading +** help +*** installing help indices +** building package indices +** installing vignettes +** testing if installed package can be loaded from temporary location +** testing if installed package can be loaded from final location +** testing if installed package keeps a record of temporary installation path +* DONE (LoopDetectR) diff --git a/LoopDetectR.Rcheck/LoopDetectR-Ex.R b/LoopDetectR.Rcheck/LoopDetectR-Ex.R new file mode 100644 index 0000000..be5c279 --- /dev/null +++ b/LoopDetectR.Rcheck/LoopDetectR-Ex.R @@ -0,0 +1,223 @@ +pkgname <- "LoopDetectR" +source(file.path(R.home("share"), "R", "examples-header.R")) +options(warn = 1) +options(pager = "console") +base::assign(".ExTimings", "LoopDetectR-Ex.timings", pos = 'CheckExEnv') +base::cat("name\tuser\tsystem\telapsed\n", file=base::get(".ExTimings", pos = 'CheckExEnv')) +base::assign(".format_ptime", +function(x) { + if(!is.na(x[4L])) x[1L] <- x[1L] + x[4L] + if(!is.na(x[5L])) x[2L] <- x[2L] + x[5L] + options(OutDec = '.') + format(x[1L:3L], digits = 7L) +}, +pos = 'CheckExEnv') + +### * +library('LoopDetectR') + +base::assign(".oldSearch", base::search(), pos = 'CheckExEnv') +base::assign(".old_wd", base::getwd(), pos = 'CheckExEnv') +cleanEx() +nameEx("compare_loop_list") +### * compare_loop_list + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: compare_loop_list +### Title: Compare two loop lists +### Aliases: compare_loop_list + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the feedback loops of the system +loop_list <- find_loops(jac_matrix,10) +#a slightly different Jacobian matrix of the system with 4 variables +jac_matrix_alt <- rbind(c(-1,0,0,1),c(1,-1,0,-1),c(0,1,-1,0),c(0,0,1,-1)) +#find the feedback loops of the system +loop_list_alt <- find_loops(jac_matrix_alt,10) +#compare the loop lists +comp_loop_list <- compare_loop_list(loop_list,loop_list_alt) +#loops that switch sign +comp_loop_list[['ind_a_switch']] + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("compare_loop_list", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("find_edge") +### * find_edge + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: find_edge +### Title: Detecting loops with a certain edge +### Aliases: find_edge + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the feedback loops of the system +loop_list <- find_loops(jac_matrix,10) +#find the loops containing the regulation from variable 3 to variable 4 +inds_3_to_4 <- find_edge(loop_list,3,4) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("find_edge", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("find_loops") +### * find_loops + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: find_loops +### Title: Loop detection in a matrix +### Aliases: find_loops + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the first 5 feedback loops of the system +loop_list <- find_loops(jac_matrix,5) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("find_loops", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("find_loops_noscc") +### * find_loops_noscc + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: find_loops_noscc +### Title: Loop detection in a matrix +### Aliases: find_loops_noscc + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the first 5 feedback loops of the system +loop_list <- find_loops_noscc(jac_matrix,5) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("find_loops_noscc", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("find_loops_vset") +### * find_loops_vset + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: find_loops_vset +### Title: Loop detection for an ODE model at multiple sets of variables +### Aliases: find_loops_vset + +### ** Examples + +#default call to determine loops from an ODE model given by a function +#read in example functions +data("func_POSm4") +#the loaded function func_POSm4 takes arguments t, x, klin, knonlin +res_tab <- find_loops_vset(func_POSm4,vset=list(c(1,1,1,1)),t=1, +klin=c(1,2,0.5,1,2,0.1,3,2,3),knonlin=c(1,2)) +#computed loop list: +res_tab$loop_rep[[1]] #or res_tab[[1]][[1]] + +#determine loops from an ODE model over the course of a solution +#read in the example function defining the bacterial cell cycle +data("func_li08") +#kinetic parameter values are defined within the function +#read in a set of variable values (the solution of func_li08 with events) +data("li08_solution") +#transform the solution (columns: variables) to the correct list format +#and remove the time (first column) +li08_sol_list <- as.list(as.data.frame(t(li08_solution[,-1]))) +res_tab <- find_loops_vset(func_li08,vset=li08_sol_list,t=1, +compute_full_list=FALSE) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("find_loops_vset", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("loop_summary") +### * loop_summary + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: loop_summary +### Title: Summary of a loop list +### Aliases: loop_summary + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the feedback loops of the system +loop_list <- find_loops(jac_matrix,10) +#loop summary table +loop_sum_tab <- loop_summary(loop_list) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("loop_summary", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +cleanEx() +nameEx("sort_loop_index") +### * sort_loop_index + +flush(stderr()); flush(stdout()) + +base::assign(".ptime", proc.time(), pos = "CheckExEnv") +### Name: sort_loop_index +### Title: Sort loop indices +### Aliases: sort_loop_index + +### ** Examples + +#sample Jacobian matrix of a system with 4 variables +jac_matrix <- rbind(c(-1,0,0,-1),c(1,-1,0,1),c(0,1,-1,0),c(0,0,1,-1)) +#find the feedback loops of the system +loop_list <- find_loops(jac_matrix,10) +#sort the loop indices to start with the smallest +sorted_loop_list <- sort_loop_index(loop_list) + + + + +base::assign(".dptime", (proc.time() - get(".ptime", pos = "CheckExEnv")), pos = "CheckExEnv") +base::cat("sort_loop_index", base::get(".format_ptime", pos = 'CheckExEnv')(get(".dptime", pos = "CheckExEnv")), "\n", file=base::get(".ExTimings", pos = 'CheckExEnv'), append=TRUE, sep="\t") +### *