Friday, November 11, 2022

2022-11-18 / 11:00 ~ 12:00

by 강상우()

The development and analysis of efficient methods and techniques for solving an inverse scattering problem are of great interest due to their potential in various applications, such as nondestructive testing, biomedical imaging, radar imaging, and structural imaging, among others. Sampling-type imaging methods allow us to non-iteratively retrieve the support of (possibly multiconnected) targets with low computational cost, assuming no a priori information about the targets. A sampling method tests a region of interest with its associated indicator function; the indicator function blows up if a test location is in support of inhomogeneities. Even though the sampling methods show promising results in ideal (multistatic, full-aperture, sufficiently many receivers) measurement configuration, one can frequently encounter limited measurement cases in practical applications. This presentation introduces the sampling-type imaging methods in two-dimensional limited-aperture, monostatic, and bistatic measurement cases. We identify the asymptotic structure of imaging methods to explore the applicability and intrinsic properties.

2022-11-15 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 대수기하학: Coregularity of Fano varieties

by Joaquín Moraga(UCLA)

In this talk, we will introduce the absolute coregularity of Fano varieties. The coregularity measures the singularities of the anti-pluricanonical sections. Philosophically, most Fano varieties have coregularity 0. In the talk, we will explain some theorems that support this philosophy. We will show that a Fano variety of coregularity 0 admits a non-trivial section in |-2K_X|, independently of the dimension of X. This is joint work with Fernando Figueroa, Stefano Filipazzo, and Junyao Peng. * ZOOM information will not be provided. Please send an email to Jinhyung Park if you are interested in.

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

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by ()

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this talk, we will present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. To demonstrate the applicability and reliability of our framework, we will also present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions.

2022-11-18 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

TBA

2022-11-11 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - PDE 세미나:

by 최영필(연세대)

In this talk, we discuss the Cauchy problem for the Vlasov-Riesz system, which is a Vlasov equation featuring interaction potentials generalizing various previously studied cases, including the Coulomb and Manev potentials. For the first time, we extend the local theory of classical solutions to interaction potentials which are more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known singularity formation result for attractive Vlasov-Poisson. Our local well-posedness and singularity formation results extend to cases with linear diffusion and damping in velocity.

2022-11-15 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Excluding single-crossing matching minors in bipartite graphs

by Sebastian Wiederrecht(IBS 이산수학그룹)

By a seminal result of Valiant, computing the permanent of (0, 1)-matrices is, in general, #P-hard. In 1913 Pólya asked for which (0, 1)-matrices A it is possible to change some signs such that the permanent of A equals the determinant of the resulting matrix. In 1975, Little showed these matrices to be exactly the biadjacency matrices of bipartite graphs excluding $K_{3,3}$ as a matching minor. This was turned into a polynomial time algorithm by McCuaig, Robertson, Seymour, and Thomas in 1999. However, the relation between the exclusion of some matching minor in a bipartite graph and the tractability of the permanent extends beyond K3,3. Recently it was shown that the exclusion of any planar bipartite graph as a matching minor yields a class of bipartite graphs on which the permanent of the corresponding (0, 1)-matrices can be computed efficiently. In this paper we unify the two results above into a single, more general result in the style of the celebrated structure theorem for single-crossing minor-free graphs. We identify a class of bipartite graphs strictly generalising planar bipartite graphs and $K_{3,3}$ which includes infinitely many non-Pfaffian graphs. The exclusion of any member of this class as a matching minor yields a structure that allows for the efficient evaluation of the permanent. Moreover, we show that the evaluation of the permanent remains #P-hard on bipartite graphs which exclude $K_{5,5}$ as a matching minor. This establishes a first computational lower bound for the problem of counting perfect matchings on matching minor closed classes. As another application of our structure theorem, we obtain a strict generalisation of the algorithm for the k-vertex disjoint directed paths problem on digraphs of bounded directed treewidth. This is joint work with Archontia Giannopoulou and Dimitrios Thilikos.

2022-11-15 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar:

by 최영상 상무(삼성전자 종합기술원)

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

SAARC 세미나 - SAARC 세미나:

by 윤철희(KAIST 김재철 AI 대학원)

Stochastic finite-sum optimization problems are ubiquitous in many areas such as machine learning, and stochastic optimization algorithms to solve these finite-sum problems are actively studied in the literature. However, there is a major gap between practice and theory: practical algorithms shuffle and iterate through component indices, while most theoretical analyses of these algorithms assume uniformly sampling the indices. In this talk, we talk about recent research efforts to close this theory-practice gap. We will discuss recent developments in the theoretical convergence analysis of shuffling-based optimization methods. We will first consider minimization algorithms, mainly focusing on stochastic gradient descent (SGD) with shuffling; we will then briefly talk about some new progress on minimax optimization methods.

2022-11-17 / 11:50 ~ 12:30

대학원생 세미나 - 대학원생 세미나: Hyperbolicity in Groups

by 김준석(KAIST)

Geometric group theory concerns about how to see geometric properties in finitely generated groups. Defining Cayley graph of a finitely generated group with respect to finite generating set gives a perspective to describe geometric properties of finitely generated groups. Once we get a geometric perspective, we can classify finitely generated groups via quasi-isometry, since two Cayley graphs are quasi-isometric. In this talk, we will explain some basic notions appeared in geometric group theory (for example, quasi-isometry, hyperbolic groups, Švarc–Milnor lemma) and some theorems related to (relative) hyperbolicity of groups.

Events for the 취소된 행사 포함