Friday, April 12, 2024

2024-04-16 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Algorithmic aspects of linear delta-matroids

by Magnus Wahlström(Royal Holloway, University of London)

Delta-matroids are a generalization of matroids with connections to many parts of graph theory and combinatorics (such as matching theory and the structure of topological graph embeddings). Formally, a delta-matroid is a pair $D=(V,\mathcal F)$ where $\mathcal F$ is a collection of subsets of V known as "feasible sets." (They can be thought of as generalizing the set of bases of a matroid, while relaxing the condition that all bases must have the same cardinality.) Like with matroids, an important class of delta-matroids are linear delta-matroids, where the feasible sets are represented via a skew-symmetric matrix. Prominent examples of linear delta-matroids include linear matroids and matching delta-matroids (where the latter are represented via the famous Tutte matrix). However, the study of algorithms over delta-matroids seems to have been much less developed than over matroids. In this talk, we review recent results on representations of and algorithms over linear delta-matroids. We first focus on classical polynomial-time aspects. We present a new (equivalent) representation of linear delta-matroids that is more suitable for algorithmic purposes, and we show that so-called delta-sums and unions of linear delta-matroids are linear. As a result, we get faster (randomized) algorithms for Linear Delta-matroid Parity and Linear Delta-matroid Intersection, improving results from Geelen et al. (2004). We then move on to parameterized complexity aspects of linear delta-matroids. We find that many results regarding linear matroids which have had applications in FPT algorithms and kernelization directly generalize to linear delta-matroids of bounded rank. On the other hand, unlike with matroids, there is a significant difference between the "rank" and "cardinality" parameters - the structure of bounded-cardinality feasible sets in a delta-matroid of unbounded rank is significantly harder to deal with than feasible sets in a bounded-rank delta-matroid.

2024-04-12 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by 최준호(카이스트)

In the past decade, machine learning methods (MLMs) for solving partial differential equations (PDEs) have gained significant attention as a novel numerical approach. Indeed, a tremendous number of research projects have surged that apply MLMs to various applications, ranging from geophysics to biophysics. This surge in interest stems from the ability of MLMs to rapidly predict solutions for complex physical systems, even those involving multi-physics phenomena, uncertainty, and real-world data assimilation. This trend has led many to hopeful thinking MLMs as a potential game-changer in PDE solving. However, despite the hopeful thinking on MLMs, there are still significant challenges to overcome. These include limits compared to conventional numerical approaches, a lack of thorough analytical understanding of its accuracy, and the potentially long training times involved. In this talk, I will first assess the current state of MLMs for solving PDEs. Following this, we will explore what roles MLMs should play to become a conventional numerical scheme.

2024-04-12 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 3

by 이제학(KAIST)

This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.

2024-04-19 / 10:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by 정의민(IBS 의생명수학그룹)

"Phenotypic switching in gene regulatory networks", PNAS. (2014) will be discussed in this Journal Club. Noise in gene expression can lead to reversible phenotypic switching. Several experimental studies have shown that the abundance distributions of proteins in a population of isogenic cells may display multiple distinct maxima. Each of these maxima may be associated with a subpopulation of a particular phenotype, the quantification of which is important for understanding cellular decision-making. Here, we devise a methodology which allows us to quantify multimodal gene expression distributions and single-cell power spectra in gene regulatory networks. Extending the commonly used linear noise approximation, we rigorously show that, in the limit of slow promoter dynamics, these distributions can be systematically approximated as a mixture of Gaussian components in a wide class of networks. The resulting closed-form approximation provides a practical tool for studying complex nonlinear gene regulatory networks that have thus far been amenable only to stochastic simulation. We demonstrate the applicability of our approach in a number of genetic networks, uncovering previously unidentified dynamical characteristics associated with phenotypic switching. Specifically, we elucidate how the interplay of transcriptional and translational regulation can be exploited to control the multimodality of gene expression distributions in two-promoter networks. We demonstrate how phenotypic switching leads to birhythmical expression in a genetic oscillator, and to hysteresis in phenotypic induction, thus highlighting the ability of regulatory networks to retain memory. If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact if you first come IBS to get permission to enter IBS building.

2024-04-12 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

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