Journal: BMC Bioinformatics
Article Title: Polynomial superlevel set representation of the multistationarity region of chemical reaction networks
doi: 10.1186/s12859-022-04921-6
Figure Lengend Snippet: PSS representation of different degrees of the mulistationarity region of the network of Example 3.4 inside the hyperrectangle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B=[(0.0005,0),(0.001,2)]$$\end{document} B = [ ( 0.0005 , 0 ) , ( 0.001 , 2 ) ] using the information we got from the sampling representation of the multistationairy region. The orange colored points are the points with three steady states and their union is considered as approximation of K . The yellow colored area is the difference of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(p)-K$$\end{document} U ( p ) - K . One expects to see that this difference is getting smaller as the degree increases. However, the Matlab code that we wrote using YALMIP and SeDuMi does not behave as expected. a – c gives the PSS representation of the original problem of degrees 2, 6 and 10 respectively. d – f gives the PSS representation of those degrees for the problem after after rescaling the parameters for better numerical behavior via YALMIP and SeDuMi
Article Snippet: These sub-rectangles are colored orange in Fig. . We use the YALMIP and SeDuMi packages of Matlab to solve the SOS optimization discussed before this example.
Techniques: Sampling
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![PSS representation of different degrees of the mulistationarity region of the network of Example 3.4 inside the hyperrectangle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B=[(0.0005,0),(0.001,2)]$$\end{document} B = [ ( 0.0005 , 0 ) , ( 0.001 , 2 ) ] using the information we got from the sampling representation of the multistationairy region. The orange colored points are the points with three steady states and their union is considered as approximation of K . The yellow colored area is the difference of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(p)-K$$\end{document} U ( p ) - K . One expects to see that this difference is getting smaller as the degree increases. However, the Matlab code that we wrote <t>using</t> <t>YALMIP</t> and <t>SeDuMi</t> does not behave as expected. a – c gives the PSS representation of the original problem of degrees 2, 6 and 10 respectively. d – f gives the PSS representation of those degrees for the problem after after rescaling the parameters for better numerical behavior via YALMIP and SeDuMi](https://pub-med-central-images-cdn.bioz.com/pub_med_central_ids_ending_with_3955/pmc09513955/pmc09513955__12859_2022_4921_Fig7_HTML.jpg)