Tuesday, May 18, 2021

2021-05-20 / 12:30 ~ 13:30

학과 세미나/콜로퀴엄 - 대학원생 세미나: Independent Markov Decomposition: Towards modeling kinetics of biomolecular complexes

by Yun Min Song(KAIST)

We will discuss about “Independent Markov Decomposition: Towards modeling kinetics of biomolecular complexes”, Hempel et. al., bioRxiv, 2021 In order to advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) and Markov state models (MSMs) have enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increase exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called Independent Markov Decomposition (IMD) that leverages weak coupling between subsystems in order to compute a global kinetic model without requiring to sample all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

2021-05-18 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - Discrete Math:

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A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. A structural generalisation of vertex-flames and largeness to infinite digraphs was given by Joó and the analogue of Lovász’ result for countable digraphs was shown. In this talk, I present a strengthening of this result stating that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame. Joint work with Joshua Erde and Attila Joó.

2021-05-25 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사학위심사: 자기쌍대 천-사이먼스-슈뢰딩거 방정식의 폭발 역학에 대하여

by 김기현(KAIST)

심사위원장 권순식, 심사위원 김용정, 이지운, 허형진(중앙대 수학과), 오성진(University of California at Berkeley, 수학과)

2021-05-21 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by ()

We show that log-concavity is the weakest power concavity preserved by the Dirichlet heat flow in convex domains in ${\bf R}^N$, where $N\ge 2$. Jointly with what we already know, i.e. that log-concavity is the strongest power concavity preserved by the heat flow, we see that log-concavity is the only power concavity preserved by the Dirichlet heat flow. This is a joint work with Paolo Salani (Univ. of Florence) and Asuka Takatsu (Tokyo Metropolitan Univ.)

2021-05-21 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Motivic homotopy theory of logarithmic schemes II

by Doosung Park(University of Zürich, Switzerland)

The logarithmic analog of SH(k) is logSH(k). In logSH(k), topological cyclic homology is representable. Furthermore, the cyclotomic trace map from K to TC is representable too when k is a perfect field with resolution of singularities. In the second talk, I will explain the construction of logSH(k) and how we can achieve these results. This work is joint with Federico Binda and Paul Arne Østvær.

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