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DISCRETE CATS SEMINAR

Discrete CATS Seminar

Title:  Conditions for the toric homogenous Markov Chain models to have square-free quadratic Groebner basis

Abstract:  Discrete time Markov chains are often used in statistical models to fit the observed data from a random physical process. Sometimes, in order to simplify the model, it is convenient to consider time-homogeneous Markov chains, where the transition probabilities do not depend on the time.  While under the time-homogeneous Markov chain model it is assumed that the row sums of the transition probabilities are equal to one, under the the toric homogeneous Markov chain (THMC) model the parameters are free and the row sums of the transition probabilities are not restricted.

 

In this talk we consider a Markov basis and a Groebner basis for the toric ideal associate with the design matrix (configuration) defined by THMC model with the state space with $m$ states where $m \geq 2$ and we study when THMC with $m$ states have a square-free quadratic Groebner basis.  One such example is the embedded discrete Markov chain for the Kimura three parameter model. This is joint work with Abraham Martin del Campo and Akimichi Takemura.

Date:
-
Location:
745 Patterson Office Tower
Event Series:

Discrete CATS Seminar

Title:  An Algebraic Approach to Systems Biology.

Abstract:  This talk will present an algebraic perspective for modeling gene regulatory networks. Algebraic models can be represented by polynomials over finite fields. In this setting, several problems relevant to biology can be studied. For instance, the algebraic view has been successfully applied for the development of computational tools to determine the attractors of Boolean Networks, for network inference algorithms, and for the development of a theoretical framework for agent based models. In this talk, the algebraic perspective of discrete models will be applied for control problems. No background in mathematical biology will be assumed for this talk.

 

Date:
-
Location:
745 Patterson Office Tower
Event Series:

Discrete CATS Seminar

Title:  The combinatorial structure behind the free Lie algebra

Abstract:  We explore a beautiful interaction between algebra and combinatorics in the heart of the free Lie algebra on n generators: The multilinear component of the free Lie algebra Lie(n) is isomorphic as a representation of the symmetric group to the top cohomology of the poset of partitions of an n-set tensored with the sign representation. Then we can understand the algebraic object Lie(n) by applying poset theoretic techniques to the poset of partitions whose description is purely combinatorial. We will show how this relation generalizes further in order to study  free Lie algebras with multiple compatible brackets.

Date:
-
Location:
745 Patterson Office Tower
Event Series:
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