**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**

**Slide 4**

**Slide 5**

**Motivation: Gene regulatory
networks**

**Slide 7**

**Slide 8**

**Slide 9**

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

**Network inference using
finite dynamical systems models**

**"Important model
information obtained from"**

**Slide 13**

**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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