A Geometric Approach for Analyzing Parametric Biological Systems by Exploiting Block Triangular Structure

DOI10.1137/21M1436373zbMath1492.65143MaRDI QIDQ5090111

Wenyuan Wu, Changbo Chen

Publication date: 15 July 2022

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

real algebraic surfacebiological networkmultistationarityblock triangularparametric systemborder curve

Mathematics Subject Classification ID

Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Computational real algebraic geometry (14Q30)

Uses Software

• HOM4PS
• BioModels
• MetaFork

Cites Work

• Unnamed Item
• Unnamed Item
• A baby step-giant step roadmap algorithm for general algebraic sets
• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• The number of roots of a system of equations
• Efficient isolation of polynomial's real roots.
• Symbolic detection of steady states of autonomous differential biological systems by transformation into block triangular form
• Penalty function based critical point approach to compute real witness solution points of polynomial systems
• The influence of cytokinin-auxin cross-regulation on cell-fate determination in \textit{Arabidopsis thaliana} root development
• Robust certified numerical homotopy tracking
• Numerical roadmap of smooth bounded real algebraic surface
• Visualizing planar and space implicit real algebraic curves with singularities
• Identifying the parametric occurrence of multiple steady states for some biological networks
• Computing real witness points of positive dimensional polynomial systems
• Cell decomposition of almost smooth real algebraic surfaces
• Solving parametric polynomial systems
• Real solution isolation using interval arithmetic
• Real Root Isolation of Regular Chains
• A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications
• Finding points on real solution components and applications to differential polynomial systems
• Emergence of Scaling in Random Networks
• A Nearly Optimal Algorithm for Deciding Connectivity Queries in Smooth and Bounded Real Algebraic Sets
• A Survey of Methods for Deciding Whether a Reaction Network is Multistationary
• Algorithms to Study Large Metabolic Network Dynamics
• Introduction to Numerical Continuation Methods
• Community structure in social and biological networks
• A Polyhedral Method for Sparse Systems with Many Positive Solutions
• The Inheritance of Nondegenerate Multistationarity in Chemical Reaction Networks
• Multistability of Small Reaction Networks
• Which Small Reaction Networks Are Multistationary?
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Chordal Networks of Polynomial Ideals
• Depth-First Search and Linear Graph Algorithms
• The measure of the critical values of differentiable maps
• Symbolic Proof of Bistability in Reaction Networks
• Finding at least one point in each connected component of a real algebraic set defined by a single equation
• Revealing Bistability in Neurological Disorder Models By Solving Parametric Polynomial Systems Geometrically

This page was built for publication: A Geometric Approach for Analyzing Parametric Biological Systems by Exploiting Block Triangular Structure