Colloquium March 17
Date: Friday March 17
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Melanie Fulton and Elena Dimitrova of Virginia Tech
Title: Finite Graphs and Quantum Automorphism Groups
Polynomial Models for Gene Regulatory Networks
Abstract
Elena's talk
Given a collection of polynomials
{g1,..., gt} and a
polynomial f over
Q[x1,..., xn], a deceptively easy
question such as whether f can be written in the form
h1g1 + ... + htgt for some polynomials hi, turns out to be difficult
to answer even for simple examples. This is the so-called ``ideal
membership problem" (Is f in the ideal
I = {h1g1 + ... + htgt | hi e Q[x1,...xn]}?) which is one of
the many problems brilliantly solved by introducing the Gröbner
basis of an ideal. Similar to changing the basis of a vector space,
a Gröbner basis G of I is a collection of polynomials
in I that
possesses wonderful properties such as uniqueness of remainder when a
polynomial f is divided by the elements of G in any order.
Many modeling methods use polynomial systems techniques that rely on
computing Gröbner bases. I will present the biological problem and
the modeling framework in which I encountered Gröbner bases in my
work: studying the gene regulatory network underlying the oxidative
stress response in yeast which we model using polynomial dynamical
systems. It will be demonstrated how Gröbner bases are used to
solve a model identification problem.
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