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In many applications in cell biology\, th e inherent underlying stochasticity and discrete n ature of individual reactions can play a very impo rtant part in the dynamics. The Gillespie algorith m has been around since the 1970s\, which allows u s to simulate trajectories from these systems\, by simulating in turn each reaction\, giving us a Ma rkov jump process. However\, in multiscale systems \, where there are some reactions which are occurr ing many times on a timescale for which others are unlikely to happen at all\, this approach can be computationally intractable. Several approaches ex ist for the efficient approximation of the dynamic s of the &ldquo\;slow&rdquo\; reactions\, some of which rely on the &ldquo\;quasi-steady state assum ption&rdquo\; (QSSA). In this talk\, we will prese nt the Constrained Multiscale Algorithm\, a method based on the equation free approach\, which was f irst used to construct diffusion approximations of the slowly changing quantities in the system. We will compare this method with other methods which rely on the QSSA to compute the effective drift an d diffusion of the approximating SDE. We will then show how this method can be used\, back in the di screte setting\, to approximate an effective Marko v jump generator for the slow variables in the sys tem\, and quantify the errors in that approximatio n. If time permits\, we will show how these genera tors can then be used to sample approximate paths conditioned on the values of their endpoints. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR