Friday, May 14, 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.

2021-05-14 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 홍영훈(중앙대)

For the mass-critical/supercritical pseudo-relativistic nonlinear Schrödinger equation, Bellazzini, Georgiev and Visciglia constructed a class of stationary solutions as local energy minimizers under an additional kinetic energy constraint, and they showed the orbital stability of the energy minimizer manifold. In this talk, by proving its local uniqueness, we show the orbital stability of the solitary wave, not that of the energy minimizer set. The key new aspect is reformulation of the variational problem in the non-relativistic regime, which is, we think, more natural because the proof heavily relies on the sub-critical nature of the limiting model. By this approach, the meaning of the additional constraint is clarified, a more suitable Gagliardo-Nirenberg inequality is introduced, and the non-relativistic limit is proved. Finally, using the non-relativistic limit, we obtain the local uniqueness and the non-degeneracy of the minimizer. This talk is based on joint work with Sangdon Jin.

2021-05-14 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 현동훈(서울대학교 수리과학부)

다중관점기하학(multiple view geometry)에서는 카메라 관점의 변화에 따라 피사체의 영상이 어떻게 변화하는 지를 분석하고, 여러 관점에서 얻은 2차원 영상으로부터 3차원 모델을 재구성하는 기법을 연구한다. 본 강연에서는 다중관점기하학의 기본적인 개념과 테크닉을 설명하고, 이를 의료영상, 자율주행, 스마트헬스케어 등 다양한 산업분야에 적용하는 것에 대하여 소개한다.

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

학과 세미나/콜로퀴엄 - SAARC 세미나:

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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.

2021-05-14 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Infinitesimal regulators

by Sinan Ünver(Koc University, Istanbul, Turkey)

We will describe a construction of infinitesimal invariants of thickened one dimensional cycles in three dimensional space, which are the simplest cycles that are not in the Milnor range. This is an analog of a construction of J. Park in the context of additive Chow groups. The construction allows us to prove the infinitesimal version of the strong reciprocity conjecture for thickenings of all orders. Classical analogs of our invariants are based on the dilogarithm function and our invariant could be seen as their infinitesimal version. Despite this analogy, the infinitesimal version cannot be obtained from their classical counterparts through a limiting process.

Events for the 취소된 행사 포함