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SUMMARY:Global injectivity criteria inspired by properties of biochemical 
 networks
DTSTART:20100608T101500
DTSTAMP:20260603T234754Z
UID:bdcbb3343fabd467d3ea4c8247c1d8282d823b0da6646ff24b22db8b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Gheorghe Craciun\, University of Wisconsin-Madison\nThe 
 property of global injectivity is often essential for\nthe identifiability
  of parameters in mathematical models\, and for\nshowing uniqueness of equ
 ilibria for high-dimensional nonlinear\ndynamical systems. On the other ha
 nd\, there are no comprehensive\ncomputational tools for checking the glob
 al injectivity of general\nnonlinear function\, especially if they depend 
 on several variables\nand contain several unknown parameters.\nIn particul
 ar\, mathematical models of biochemical reaction networks\ngive rise to dy
 namical systems that are usually high dimensional\,\nnonlinear\, and have 
 many unknown parameters. Nevertheless\, we show\nthat it is often possible
  to use reaction network properties to\nconclude global injectivity of the
  associated vector field.\nMoreover\, some of these criteria for global in
 jectivity hold for very\nwide classes of nonlinear functions\, even if the
 se function are not\nrelated to any biochemical network. We also explain h
 ow these\ncriteria are related to other problems\, such as the Jacobian\nc
 onjecture in algebraic geometry and the Bezier self-intersection\nproblem 
 in computer graphics.\nProf. Craciun's homepage
LOCATION:BC 01 https://plan.epfl.ch/?room==BC%2001
STATUS:CONFIRMED
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