Saturday, June 4, 2022

2022-06-10 / 13:00 ~ 14:00

by ()

Circadian rhythm is a robust internal 24 hours timekeeping mechanism maintained by the master circadian pacemaker Suprachiasmatic Nuclei (SCN). Numerous mathematical models have been proposed to capture SCN’s timekeeping mechanism and predict the circadian phase. There has been an increased demand for applying these models to the various unexplored data sets. One potential application is on data from commercially available wearable devices, which provide the noninvasive measurements of physiological proxies, such as activity and heart rate. Using these physiological proxies, we can estimate the circadian phase of the central and peripheral circadian pacemakers. Here, we propose a new framework for estimating the circadian phase using wearable data and the Level Set Kalman Filter on the nonlinear state-space model of the human circadian pacemaker. Analysis of over 200,000 days of wearable data from over 3,000 subjects using our framework successfully identified misalignment in central and peripheral pacemakers with a significantly smaller uncertainty than previous methods.

2022-06-10 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 대수기하학:

by ()

In this talk, we introduce a various methods of representations of graphs which are mathematical objects expressing a variety of non-Euclidean data such as Molecules, social networks, genes, transportation networks, citation networks of papers and so on. Graph representation as a Euclidean vector is inevitable in machine learning for classifications for graphs which is closely related to graph neural network in computer science. We would like to introduce a few literatures, Weisfeiler-lehman algortihm, random walks, graph convolution whci are commonly used techniques and explain the result of combining them with topological invarints of graphs

2022-06-10 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

by 조도상()

The introduction for the framework of geometric deep learning will be explained in the perspective of new methodology of A.I. and data analysis. Various applications can be discussed by utilizing geometry, algebra, topology.

2022-06-10 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 박사논문심사: 다중모집단에서 수집된 영과잉 시계열 가산자료 분석을 위한 계층적 모델링

by 심기성(KAIST)

심사위원장 : 정연승, 심사위원 : 김성호(명예교수), 박철우, 전현호, 김윤희(The University of Tokyo)

2022-06-07 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

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In this talk, I will describe the large deviation asymptotic of the sum of power-weighted edge lengths $\sum_{e \in E}|e|^\alpha$ in the Poisson $k$-nearest neighbor graph in $\mathbb R^d$. While the case $\alpha < d$ can be treated through classical methods from large deviations theory, an interesting dichotomy occurs if $\alpha > d$. Rare events in the lower tail can still be explained by subtle changes in the Poisson process throughout the sampling window. However, the most likely cause for rare events in the upper tail is a condensation phenomenon: the excess edge weight is caused by a negligible portion of Poisson points whose configuration can be described through a concrete geometric optimization problem. After presenting the general proof strategy, I will also elucidate on the prospects and limits of generalizing our approach to other spatial networks.

2022-06-07 / 16:00 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론:

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Abstract: We discuss a new application of (a part of) the Iwasawa main conjecture to the non-triviality of Kato's Kolyvagin systems and a structural refinement of Birch and Swinnerton-Dyer conjecture. In particular, the structure of Selmer groups is completely determined by certain modular symbols for a large class of elliptic curves. (Please contact Wansu Kim at wansu.math@kaist.ac.kr for Zoom meeting info or any inquiry.)

2022-06-08 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 서인석(서울대학교)

In this talk, we consider the Ising and Potts model defined on large lattices of dimension two or three at very low temperature regime. Under this regime, each monochromatic spin configuration is metastable in that exit from the energetic valley around that configuration is exponentially difficult. It is well-known that, under the presence of external magnetic fields, the metastable transition from a monochromatic configuration to another one is characterized solely by the appearance of a critical droplet. On the other hand, for the model without external field, the saddle structure is no longer characterized by a sharp droplet but has a huge and complex plateau structure. In this talk, we explain our recent research on the analysis of this energy landscape and its application to the demonstration of Eyring-Kramers formula for models on fixed two or three dimensional lattice (cf. https://arxiv.org/abs/2102.05565) or models on growing two-dimensional lattice (cf. https://arxiv.org/abs/2109.13583).

2022-06-10 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나: Stefan problem via optimal stopping time

by 김인원(캘리포니아 대학교 로스앤젤레스)

We consider an optimal transport problem where the cost depends on the stopping time of Brownian motion from a given distribution to another. When the target measure is fixed, it is often called the optimal Skorokhod embedding problem in the literature, a popular topic in math finance. Under a monotonicity assumption on the cost, the optimal stopping time is given by the hitting time to a space-time barrier set. When the target measure is optimized under an upper bound constraint, we will show that the optimal barrier set leads us to the Stefan problem, a free boundary problem for the heat equation describing phase transition between water and ice. This is joint work with Young-Heon Kim at UBC.

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