Monday, June 6, 2022

2022-06-13 / 16:00 ~ 17:00

by ()

The connection between deep neural networks and ordinary differential equations (ODEs) is an active field of research in machine learning. In this talk, we view the hidden states of a neural network as a continuous object governed by a dynamical system. The underlying vector field is written using a dictionary representation motivated by the equation discovery method. Within this framework, we develop models for two particular machine learning tasks: time-series classification and dimension reduction. We train the parameters in the models by minimizing a loss, which is defined using the solution to the governing ODE. To attain a regular vector field, we introduce a regularization term measuring the mean total kinetic energy of the flow, which is motivated by optimal transportation theory. We solve the optimization problem using a gradient-based method where the gradients are computed via the adjoint method from optimal control theory. Through various experiments on synthetic and real-world datasets, we demonstrate the performance of the proposed models. We also interpret the learned models by visualizing the phase plots of the underlying vector field and solution trajectories.

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

IBS-KAIST 세미나 - 수리생물학:

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)

2022-06-13 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Twin-width and forbidden subdivisions

by Amadeus Reinald(ENS de Lyon / IBS 이산수학그룹)

Twin-width is a recently introduced graph parameter based on vertex contraction sequences. On classes of bounded twin-width, problems expressible in FO logic can be solved in FPT time when provided with a sequence witnessing the bound. Classes of bounded twin-width are very diverse, notably including bounded rank-width, $\Omega ( \log (n) )$-subdivisions of graphs of size $n$, and proper minor closed classes. In this talk, we look at developing a structural understanding of twin-width in terms of induced subdivisions. Structural characterizations of graph parameters have mostly looked at graph minors, for instance, bounded tree-width graphs are exactly those forbidding a large wall minor. An analogue in terms of induced subgraphs could be that, for sparse graphs, large treewidth implies the existence of an induced subdivision of a large wall. However, Sintiari and Trotignon have ruled out such a characterization by showing the existence of graphs with arbitrarily large girth avoiding any induced subdivision of a theta ($K_{2,3}$). Abrishami, Chudnovsky, Hajebi and Spirkl have recently shown that such (theta, triangle)-free classes have nevertheless logarithmic treewidth. After an introduction to twin-width and its ties to vertex orderings, we show that theta-free graphs of girth at least 5 have bounded twin-width. Joint work with Édouard Bonnet, Eun Jung Kim, Stéphan Thomassé and Rémi Watrigant.

2022-06-13 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 대수기하학: Construction of monotone Lagrangian tori in flag varieties via toric degenerations

by 조윤형(성균관대)

A monotone symplectic manifold is a symplectic analogue of a smooth Fano variety and it provides an important classes of objects, called monotone Lagrangian tori, in view of mirror symmetry. In this talk, I will explain a way of producing monotone Lagrangian tori in a given smooth Fano variety using toric degeneration. Using this technique, we prove that there exist infinitely many monotone Lagrangian tori not Hamiltonian isotopic to each other in a full flag variety. This is based on joint work with Myungho Kim, Yoosik Kim, Jaehoon Kwon, and Euiyong Park at Center for Quantum Structures in Modules and Spaces (QSMS).

2022-06-13 / 15:15 ~ 16:15

학과 세미나/콜로퀴엄 - 대수기하학: Reconstruction problem for toric log del Pezzo surfaces using semicascades

by 황동선(IBS-CCG)

Given a space, one can study its singularities. The converse direction is called reconstruction problem: How to reconstruct spaces from given singularity information? In this talk, by introducing a notion called a semicascade we derive a bound of Picard number for toric log del Pezzo surfaces in terms of the singular points generalizing some results of Dais and Suyama, which solves the reconstruction problem with the help of computer. We also discuss Kähler-Einstein toric log del Pezzo surfaces as an application of semicascades.

2022-06-13 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학: Vector bundles on surfaces and singular degeneration

by 조용화(IBS-CCG)

For the last decade, there have been a number of studies reporting that certain surface singularities give rise to vector bundle on their smoothing. The first result is by Hacking, who studies this correspondence for Wahl singularities. I am going to introduce a generalization of Hacking's result to singularities of class T, which is a natural extension of Wahl singularities. Also, if time permits, I will introduce a recent result of Tevelev-Urzua which generalizes this to arbitrary cyclic quotient surface singularities.

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

SAARC 세미나 - SAARC 세미나:

by ()

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:

by ()

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).

2022-06-13 / 14:30 ~ 16:00

학과 세미나/콜로퀴엄 - 박사논문심사: 심층신경망을 이용한 사람 치아 영상에서의 개별 치아 분할

by 김성은(KAIST)

심사위원장 : 이창옥, 심사위원 : 임미경, 김동환, 예종철(겸임교수), 김윤호(UNIST 자연과학부)

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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