Friday, April 23, 2021

2021-04-27 / 16:30 ~ 17:30

by 안정호()

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First, the cliques in the partition can be arranged in a tree structure, and second, each clique is of arbitrary size. We mainly provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs and give a polynomial-time algorithm that given any graph, either finds an obstruction or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices are in FPT, parameterized by k, on well-partitioned chordal graphs, while on chordal graphs, these problems are only known to be in XP. From the other end, we introduce some problems that are polynomial-time solvable on split graphs but become NP-complete on well-partitioned chordal graphs. This is joint work with Lars Jaffke, O-joung Kwon, and Paloma T. Lima.

2021-04-23 / 16::0 ~ 17::0

학과 세미나/콜로퀴엄 - 대수기하학:

by 김영락()

Sheaf cohomology and direct images are fundamental objects in algebraic geometry. However, they are defined in an abstract way (as right derived functors), and thus they are often hard to compute in explicit examples. In this talk, we briefly review Bernstein-Gel'fand-Gel'fand (BGG) correspondence and resolutions over an exterior algebra. Then, we review Tate resolutions and how it can be used to understand a given coherent sheaf and its cohomology groups in terms of Beilinson monad. Finally, we discuss an algorithm to compute direct images using Eisenbud-Erman-Schreyer's generalization on products of projective spaces. A part of the talk is a joint work in progress with J. Barrott and F.-O. Schreyer.

2021-04-30 / 10:00 ~ 12:00

학과 세미나/콜로퀴엄 - SAARC 세미나:

by 김용대()

Deep generative models have received much attention recently since they can generate very realistic synthetic images. There are two regimes for the estimation of deep generaitve models. One is generative adversarial network (GAN) and the other is variational auto encoder (VAE), Even though GAN is known to generate more clean synthetic images, it suffers from numerical instability and mode collapsing problems. VAE is an useful alternative to GAN and an important advantage of VAE is that the representational learning (i.e. learning latent variables) is possible. In this talk, I explain my recent studies about VAE. The first topic is computation. Typically, the estimation of VAE is done by maximizing the ELBO – an upper bound of the marginal likelihood. However, it is known that ELBO is inferior to the maximum likelihood estimator. I propose an efficient EM algorithm for VAE which directly finds the maximizer of the likelihood (the maximum likelihood estimator, MLE). The second topic is theory. I explain how the MLE of VAE behaves asymptotically. I derive a convergence rate which depends on the noise level as well as the complexity of a deep architecture. A surprising observation is that the convergence rate of the MLE becomes slower when the noise level is too low. A new technique to modify the MLE when the noise level is small is proposed and is shown to outperform the original MLE by analyzing real data.

2021-04-26 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 계산수학 세미나: An Image inpainting via a constrained smoothing and dynamic mode decomposition

by 이영주(Texas State Univ.)

In this talk, we present an algebraic and graph theoretic (data-based) image inpainting algorithm. The algorithm is designed to reconstruct area or volume data from one and two dimensional slice data. More precisely, given one or two dimensional slice data, our algorithm begins with a simple algebraic pre-smoothing of the data, constructs low dimensional representation of pre-smoothed data via Dynamic Mode Decomposition, performs initial area or volume reconstruction via interpolation, and finishes with smoothing the outcome using a constraint bilateral smoothing. Numerical experiments including MRI of a three year old and a CT scan of a Covid-19 patient, are presented to demonstrate the superiority of the proposed techniques in comparisons with other commercial and published methods. Some further applications we are currently doing will also be presented. This work is jointly done with Gwanghyun Jo and Ivan Ojeda-Ruiz.

2021-04-30 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 수리생물학:

by ()

Oscillatory signals are ubiquitously observed in many different intracellular systems such as immune systems and DNA repair processes. While we know how oscillatory signals are created, we do not fully understand what a critical role they play to regulate signal pathway systems in cells. Recently by using a stochastic nucleosome system, we found that a special signal (NFkB signal) in an immune cell can enhance the variability of the immune response to inflammatory stimulations when the signal is oscillatory. Hence in this talk, we discuss the roles of oscillatory and non-oscillatory NFkB signals in an inflammatory system of immune cells as the main example for revealing the role of oscillatory signals. And then we will talk about how this finding can be generalized for other intra- or extra-cellular systems to study why cells use oscillations.

2021-04-23 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학: Introduction to infinity-categories V

by 조창연(QSMS Seoul National University)

This is part V of the lectures on the foundations of infinity-categories. After continued discussion about the role of model categories in the theory of infinity-categories, the simplicial and differential graded nerve constructions will be presented to provide a plethora of examples of infinity-categories. Finally, I'll talk about an analogy between the theories of ordinary categories and infinity-categories, which wraps up this series of talks.

Events for the 취소된 행사 포함