Friday, May 21, 2021

2021-05-27 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 박사학위심사: 랜덤 행렬의 합과 곱의 스펙트럼

by 지홍창(KAIST)

심사위원장 이지운, 심사위원 강완모, 황강욱, 윤세영(AI 대학원), 강남규(고등과학원)

2021-05-27 / 13:00 ~ 14:00

학과 세미나/콜로퀴엄 - 박사학위심사: 확률적 블록 모형의 스펙트럼에 관한 연구

by 양우석(KAIST)

심사위원장 이지운, 심사위원 강완모, 황강욱, 윤세영(AI 대학원), 강남규(고등과학원)

2021-05-28 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

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One famous conjecture in quantum chaos and random matrix theory is the so-called phase transition conjecture of random band matrices. It predicts that the eigenvectors' localization-delocalization transition occurs at some critical bandwidth $W_c(d)$, which depends on the dimension $d$. The well-known Anderson model and Anderson conjecture have a similar phenomenon. It is widely believed that $W_c(d)$ matches $1/\lambda_c(d)$ in the Anderson conjecture, where $\lambda_c(d)$ is the critical coupling constant. Furthermore, this random matrix eigenvector phase transition coincides with the local eigenvalue statistics phase transition, which matches the Bohigas-Giannoni-Schmit conjecture in quantum chaos theory. We proved the eigenvector's delocalization property for most of the general $d>=8$ random band matrix as long as the size of this random matrix does not grow faster than its bandwidth polynomially. In other words, as long as bandwidth $W$ is larger than $L^\epislon$ for some $\epislon>0$, and matrix size $L$. It is joint work with H.T. Yau (Harvard) and F. Yang (Upenn).

2021-05-26 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 수리생물학: [BIMAG colloquium] Neural network aided approximation and parameter inference of stochastic models of gene expression

by Ramon Grima(University of Edinburgh)

Non-Markov models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markov models by the solutions of much simpler time-inhomogeneous Markov models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markov model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markov models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

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)

2021-05-26 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

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Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties. We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese, and consider various techniques to provide equations on the secants.In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

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.

2021-05-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄: Bayesian statistical methods of analyzing complex count data with applications to microbiome study

by 이주희(UC 산타크루즈)

The rapid development of high-throughput sequencing technology in recent years is providing unprecedented opportunities to profile microbial communities from a variety of environments, but analysis of such multivariate taxon count data remains challenging. I present two flexible Bayesian methods to analyze complex count data with application to microbiome study. The first project is to develop a Bayesian sparse multivariate regression method that model the relationship between microbe abundance and environmental factors. We extend conventional nonlocal priors, and construct asymmetric non-local priors for regression coefficients to efficiently identify relevant covariates and their effect directions. The developed Bayesian sparse regression model is applied to analyze an ocean microbiome dataset collected over time to study the association of harmful algal bloom conditions with microbial communities. For the second project, we develop a Bayesian nonparametric regression model for count data with excess zeros. The approach provides straightforward community-level insights into how characteristics of microbial communities such as taxa richness and diversity are related to covariates. The baseline counts of taxa in samples are carefully constructed to obtain improved estimates of differential abundance. We apply the model to a chronic wound microbiome dataset, comparing the microbial communities present in chronic wounds versus in healthy skin.

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