Global injectivity criteria inspired by properties of biochemical networks
Event details
| Date | 08.06.2010 |
| Hour | 10:15 |
| Speaker | Prof. Gheorghe Craciun, University of Wisconsin-Madison |
| Location | |
| Category | Conferences - Seminars |
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.
Prof. Craciun's homepage
Practical information
- General public
- Free