Thursday, October 20, 2022

2022-10-25 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar:

by 박종욱 변호사()

2022-10-26 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

by ()

We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how we are using models to inform the quantitative design of light interventions for mental health disorders and address contentious societal questions such as whether to move school start time for adolescents.

2022-10-21 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

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Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the “species”). If the counts of the species are low, then these systems are often modeled as continuous-time Markov chains on the d-dimensional integer lattice (with d being the number of species), with transition rates determined by stochastic mass-action kinetics. A natural (broad) mathematical question is: how do the qualitative properties of the dynamical system relate to the graph properties of the network? For example, it is of particular interest to know which graph properties imply that the stochastically modeled reaction network is positive recurrent, and therefore admits a stationary distribution. After a general introduction to the models of interest, I will discuss this problem, giving some of the known results. I will also discuss recent progress on the Chemical Recurrence Conjecture, which has been open for decades, which is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent.

2022-10-21 / 10:30 ~ 11:00

IBS-KAIST 세미나 - 수리생물학:

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TBA

2022-10-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves a [(1-1/e)OPT-ε] guarantee when the function is monotone and Hölder-smooth, meaning that it admits a Hölder-continuous gradient. For functions that are non-differentiable or non-smooth, we propose a variant of the mirror-prox algorithm that attains a [(1/2)OPT-ε] guarantee. We apply our algorithmic frameworks to robust submodular maximization and distributionally robust submodular maximization under Wasserstein ambiguity. In particular, the mirror-prox method applies to robust submodular maximization to obtain a single feasible solution whose value is at least [(1/2)OPT-ε]. For distributionally robust maximization under Wasserstein ambiguity, we deduce and work over a submodular-convex maximin reformulation whose objective function is Hölder-smooth, for which we may apply both the continuous greedy method and the mirror-prox method. This is joint work with Duksang Lee, a fifth-year Ph.D. student at KAIST Math, and Nam Ho-Nguyen from the University of Sydney.

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