Polynomial dynamical systems over finite fields, with applications to modeling and simulation of biological networks.

IMA Workshop on
Applications of Algebraic Geometry in
Biology, Dynamics, and Statistics
March 6, 2007

Polynomial dynamical systems

Example

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Motivation: Gene regulatory networks

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Motivation (2): a mathematical formalism for agent-based simulation

Network inference using finite dynamical systems models

"Important model information obtained from"

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The model space

Wiring diagrams

The “minimal sets” algorithm

The algorithm

The algorithm

The algorithm

Scoring method

Model selection

“Biological theory”

Nested canalyzing functions

Slide 24

A non-canalyzing Boolean network

A nested canalyzing Boolean network

Polynomial form of nested canalyzing Boolean functions

The vector space of Boolean polynomial functions

The variety of nested canalyzing functions

Input and output values as functions of the coefficients

The algebraic geometry

Dynamics from structure

Questions

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