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Abstract:
Elucidating the topology and dynamics of biological networks from high
throughput data is a central goal of the emerging field of systems biology.
Mathematical modeling plays an essential role as it is used to construct and
analyze models that capture the dynamics and provide insights at the system
level. Recently polynomial dynamical systems over finite fields have been
introduced as a new framework for modeling and analyzing biological networks
as multi-states finite dynamical systems, generalizing Boolean networks and
logical models. Within this algebraic framework, using tools from
computational algebra and algebraic geometry, the whole model space is
presented and different algebraic methods have been proposed for identifying
a particular model from the model space. Furthermore, methods for analyzing
the dynamics of classes of polynomial systems have been developed. In this
talk I will present this new approach and some of the main results.
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