Journal: Bulletin of Mathematical Biology
Article Title: Waves in a Stochastic Cell Motility Model
doi: 10.1007/s11538-023-01164-1
Figure Lengend Snippet: In ( a ), we show a simulation similar to those in Fig. , but with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =0.045$$\end{document} σ = 0.045 and a homogeneous initial condition with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u^*,4v^*)$$\end{document} ( u ∗ , 4 v ∗ ) plus a small perturbation. The red boxes are the result of the pattern finding algorithm regionprops in MATLAB; it identifies all the regions of excitations which we would also find by eye, see “Appendix A” for details. In ( b ), we used this algorithm to find the length, width and maximum of these pulses (left axis), as well as the total number of activation events (right axis). For each value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} σ , the number of events is averaged over 100 simulations, and the length, width and maximum are averaged over all events in the 100 simulations. We plot the average together with the standard deviation (Color figure online)
Article Snippet: In ( a ), we only show the simulation of wave integrated up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=20$$\end{document} T = 20 because the solution remains in the background state; afterwards, the other three figures are shown up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=100$$\end{document} T = 100 (Color figure online) In order to quantify this notion of optimality in the noise intensity, we must first quantify the size and shape of the patterns in Fig. b and c. Using MATLAB’s regionprops algorithm, we can automatically detect the patches with a high value for the activator u (see “Appendix A” for details), giving us the possibility to compute the number of activation events and determine the width and duration of each event, see Fig. a.
Techniques: Activation Assay, Standard Deviation
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![In ( a ), we show a simulation similar to those in Fig. , but with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =0.045$$\end{document} σ = 0.045 and a homogeneous initial condition with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u^*,4v^*)$$\end{document} ( u ∗ , 4 v ∗ ) plus a small perturbation. The red boxes are the result of the pattern finding algorithm <t>regionprops</t> in MATLAB; it identifies all the regions of excitations which we would also find by eye, see “Appendix A” for details. In ( b ), we used this algorithm to find the length, width and maximum of these pulses (left axis), as well as the total number of activation events (right axis). For each value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} σ , the number of events is averaged over 100 simulations, and the length, width and maximum are averaged over all events in the 100 simulations. We plot the average together with the standard deviation (Color figure online)](https://pub-med-central-images-cdn.bioz.com/pub_med_central_ids_ending_with_6800/pmc10276800/pmc10276800__11538_2023_1164_Fig8_HTML.jpg)