Back to Departmental Colloquium: Spring 2015
Departmental Colloquium
Date: Thursday, Feb 5, 2015
Time: 4:00PM
Location: LCB 219
Alan Veliz-Cuba
University of Houston and Rice University
Title |
From structure to dynamics and from dynamics to structure: a systems mathematics approach |
Abstract |
Understanding the interplay between network structure and dynamical properties is a key problem in systems theory. Although much progress has been made to understand systems, there is still no framework that focuses on the system itself instead of the representation of its components. In this talk, I will present frameworks to study the problem of predicting dynamical properties from network structure and the problem of inferring network structure from dynamical properties. These approaches focus on the way the components of the system interact instead of their representation; thus, this “systems mathematics” approach is a formalization of the systems biology paradigm. To infer dynamical properties of an ODE from its structure, we use the topological features of the wiring diagram to first infer dynamical properties of a “Boolean representation” of the original system. Then, based on the relationship between ODE and Boolean systems, we can use the predicted “Boolean dynamics” to infer dynamical features of the original ODE. To infer network structure from time series data, we first encode the data as an algebraic object. Then, using algebraic tools we can find the decomposition of this algebraic object, which gives precisely the best networks that are consistent with the time series data. Furthermore, given enough data, the method guarantees perfect recovery of the network structure. These approaches use tools from dynamical systems, algebraic geometry, and graph theory. February 10: SPECIAL COLLOQUIUM Room and Day: JWB 335, Tuesday |
Representation Theory
Algebraic Geometry
Commutative Algebra