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Global injectivity criteria inspired by properties of biochemical networks

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Abstract:
The property of global injectivity is often essential for the identifiability of parameters in mathematical models, and for showing uniqueness of equilibria for high-dimensional nonlinear dynamical systems. On the other hand, there are no comprehensive computational tools for checking the global injectivity of general nonlinear function, especially if they depend on several variables and contain several unknown parameters. In particular, mathematical models of biochemical reaction networks give rise to dynamical systems that are usually high dimensional, nonlinear, and have many unknown parameters. Nevertheless, we show that it is often possible to use reaction network properties to conclude global injectivity of the associated vector field. Moreover, some of these criteria for global injectivity hold for very wide classes of nonlinear functions, even if these function are not related to any biochemical network. We also explain how these criteria are related to other problems, such as the Jacobian conjecture in algebraic geometry and the Bezier self-intersection problem in computer graphics.

http://www.math.wisc.edu/~craciun/
Type of Seminar:
Public Seminar
Speaker:
Ass. Prof. Gheorghe Craciun
Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison
Date/Time:
Jun 11, 2010   16:15
Location:

ML H 41.1, Sonneggstrasse 3
Contact Person:

Prof. J. Lygeros
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Biographical Sketch:
Gheorghe Craciun has obtained a Diploma in Mathematics from Bucharest University (1993), an MS degree in Computer Science (1998) and a PhD in Mathematics (2002) from Ohio State University, and was a postdoctoral researcher at the Mathematical Biosciences Institute in Columbus, Ohio (2002-2005). Currently, he is an Assistant Professor in the Department of Mathematics and the Department of Biomolecular Chemistry at University of Wisconsin- Madison. He is interested in mathematical and computational approaches in biology and medicine, and especially the analysis of mathematical models of biological interaction networks.