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SUMMARY:A constrained approach to the simulation and analysis of stochasti
 c multiscale chemical kinetics - Simon Cotter (University of Manchester)
DTSTART:20160404T103000Z
DTEND:20160404T111500Z
UID:TALK65291@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Radek Erban (University of Oxford)\, Ioannis
  Kevrekidis (Princeton)\, Konstantinos Zygalakis (University of Southampto
 n)<br></span><span><br>In many applications in cell biology\, the inherent
  underlying stochasticity and discrete nature of individual reactions can 
 play a very important part in the dynamics. The Gillespie algorithm has be
 en around since the 1970s\, which allows us to simulate trajectories from 
 these systems\, by simulating in turn each reaction\, giving us a Markov j
 ump process. However\, in multiscale systems\, where there are some reacti
 ons which are occurring many times on a timescale for which others are unl
 ikely to happen at all\, this approach can be computationally intractable.
  Several approaches exist for the efficient approximation of the dynamics 
 of the &ldquo\;slow&rdquo\; reactions\, some of which rely on the &ldquo\;
 quasi-steady state assumption&rdquo\; (QSSA). In this talk\, we will prese
 nt the Constrained Multiscale Algorithm\, a method based on the equation f
 ree approach\, which was first used to construct diffusion approximations 
 of the slowly changing quantities in the system. We will compare this meth
 od with other methods which rely on the QSSA to compute the effective drif
 t and diffusion of the approximating SDE. We will then show how this metho
 d can be used\, back in the discrete setting\, to approximate an effective
  Markov jump generator for the slow variables in the system\, and quantify
  the errors in that approximation. If time permits\, we will show how thes
 e generators can then be used to sample approximate paths conditioned on t
 he values of their endpoints.</span>
LOCATION:Seminar Room 1\, Newton Institute
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