Xiaoxian Tang

Applying Algebraic Methods in Mathematical Biology

Date: 2/1/2019
Time: 4:00PM-5:00PM
Place: 315 Armstrong Hall

Abstract: Many challenging problems in mathematical biology, for instance, in biochemical reaction networks and phylogenetics, involve solving non-linear polynomial systems. Therefore, methods and algorithms in computational algebraic geometry are natural and powerful tools to deal with these problems. However, the existing tools in computer algebra systems have exponential complexities, which might not be applicable for huge systems from biology. One typical example is the multistationarity problem: whether a given biochemical reaction network has two or more positive steady states? In this talk, we develop a simple critical function method to determine multistationarity for a large class of networks arising from biology and to identify the parameter values for which the given network exhibits multistationarity. Particularly, networks having "binomial steady states" are widely seen in biochemistry. For these networks, we prove our method is much less expensive than standard real quantifier elimination methods in computational algebraic geometry.

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