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Sign patterns and determinant expansions for chemical reaction networks

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Dr. Igor Klep

Department of Mathematics

University of California, San Diego

## Abstract

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A signed matrix is actually a class of matrices consisting of all matrices
whose (i,j)-th entry has the same sign. There is a classical theory associating
a graph to such a class and analyzing the sign of determinants of matrices in
the class. We extend this to give more refined determinant results. It has been
recently observed that substantial numbers of chemical reaction networks
(these play a prominent role in systems biology) have dynamics dx/dt = f(x)
with the Jacobian of f(x) having a sign pattern or something similar.
Our results will be applied to this.
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Joint work with Bill Helton, Raul Gomez.
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