Monomials and Basin Cylinders for Network Dynamics

Authors

Daniel Austin, Oregon Health & Science University
Ian H. Dinwoodie, Portland State UniversityFollow

Sponsor

Supported by NIH R01AG024059, P30 AG024978, and P30 AG008017.

Published In

SIAM Journal of Mathematical Analysis

Document Type

Article

Publication Date

1-8-2015

Subjects

Biomathematics, Biology -- Mathematical models, Biological systems -- Mathematical models

Abstract

We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks.

Description

Copyright 2015 Society for Industrial and Applied Mathematics. This is the publishers PDF archived here with author and publisher permission.

DOI

10.1137/140975929

Persistent Identifier

http://archives.pdx.edu/ds/psu/16591

Citation Details

Austin, D., & Dinwoodie, I. H. (2015). Monomials and Basin Cylinders for Network Dynamics. SIAM Journal on Applied Dynamical Systems, 14(1), 25-42.