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public 44:51

Gary Zhou : Elliptic Curves Over Dedekind Domains

  -   Presentations ( 246 Views )

public 02:33:52

Thomas Witelski : Math 551 Review session

  -   Presentations ( 223 Views )

public 01:34:51

Thomas Witelski : Grant Writing Workshop

  -   Presentations ( 204 Views )

public 59:53

Jason Ferguson : PRUV Research

  -   Presentations ( 183 Views )

public 05:53

Matthias Heymann : Computing maximum likelihood paths of rare transition events, and applications to synthetic biology

  -   Presentations ( 177 Views )

Dynamical systems with small noise (e.g. SDEs) allow for rare transitions from one stable state into another that would not be possible without the presence of noise. Large deviation theory provides the means to analyze both the frequency of these transitions and the maximum likelihood transition path. The key object for the determination of both is the quasipotential, V(x,y) = inf S_T(phi), where S_T(phi) is the action functional associated to the system, and where the infimum is taken over all T>0 and all paths phi:[0,T]->R^n leading from x to y. The numerical evaluation of V(x,y) however is made difficult by the fact that in most cases of interest no minimizer exists.

In my work I prove an alternative geometric formulation of V(x,y) that resolves this issue by introducing an action on the space of curves ( i.e. this action is independent of the parametrization of phi). In this formulation, a minimizer exists, and we use it to build a flexible algorithm (the geometric minimum action method, gMAM) for finding the maximum likelihood transition curve.

In one application I show how the gMAM can be useful in the newly emerging field of synthetic biology: We propose a method to identify the sources of instabilities in (genetic) networks.

This work was done in collaboration with my adviser Eric Vanden-Eijnden and is the core of my PhD thesis at NYU.

public 13:15

Yee Lok Wong : Models of Instant Runoff Voting

  -   Presentations ( 170 Views )

public 01:34:52

Ingrid Daubechies : Wavelets and their Applications

  -   Presentations ( 147 Views )