Wednesday, December 29, 2021

2022-01-05 / 16:00 ~ 17:30

IBS-KAIST 세미나 - 수리생물학: Structure-based analysis of chemical reaction networks 1/2

by Yuji Hirono(APCTP)

Abstract: Inside living cells, chemical reactions form a large web of networks. Understanding the behavior of those complex reaction networks is an important and challenging problem. In many situations, it is hard to identify the details of the reactions, such as the reaction kinetics and parameter values. It would be good if we can clarify what we can say about the behavior of reaction systems, when we know the structure of reaction networks but reaction kinetics is unknown. In these talks, I plan to introduce two approaches in this spirit. Firstly, we will discuss the sensitivity analysis of reaction systems based on the structural information of reaction networks [1]. I will give an introduction to the method of identifying subnetworks inside which the effects of the perturbation of reaction parameters are confined. Secondly, I will introduce the reduction method that we developed recently [2]. In those two methods, an integer determined by the topology of a subnetwork, which we call an influence index, plays a crucial role. References [1] T. Okada, A. Mochizuki, “Law of Localization in Chemical Reaction Networks,” Phys. Rev. Lett. 117, 048101 (2016); T. Okada, A. Mochizuki, “Sensitivity and network topology in chemical reaction systems,” Phys. Rev. E 96, 022322 (2017). [2] Y. Hirono, T. Okada, H. Miyazaki, Y. Hidaka, “Structural reduction of chemical reaction networks based on topology”, Phys. Rev. Research 3, 043123 (2021).

2022-01-04 / 11:10 ~ 12:00

IBS-KAIST 세미나 - 수리생물학: Stem cell dynamics in the intestine and stomach

by 구본경(Institute of Molecular Biotechnology of the Austri)

In adult tissues, stem cells undergo clonal competition because they proliferate while the stem cell niche provides limited space. This clonal competition allows the selection of healthy stem cells over time as unfit stem cells tend to lose from the competition. It could also be a mechanism to select a supercompetitor with tumorigenic mutations, which may lead to tumorigenesis. I am going to explain general concepts of clonal competition and how a simple model can explain the behaviour of adult stem cells. I will also show how geometric constraints affect the overall dynamics of stem cell competition.

2021-12-30 / 14:00 ~ 15:00

학과 세미나/콜로퀴엄 - 대수기하학:

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In this talk, we prove a generalization of the del Pezzo-Bertini classification of varieties of minimal degree to higher secant varieties of minimal degree. It states that higher secant varieties of minimal degree are mostly divided into two classes: scroll type and Veronese type. Its proof is based on methods of gluing some 1-generic matrices. We also present some simple examples to explain our result. This is a joint work with Prof. Sijong Kwak.

2022-01-04 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Transversals and colorings of simplicial spheres

by 이승훈(Binghamton University)

Motivated from the surrounding property of a point set in $\mathbb{R}^d$ introduced by Holmsen, Pach and Tverberg, we consider the transversal number and chromatic number of a simplicial sphere. As an attempt to give a lower bound for the maximum transversal ratio of simplicial $d$-spheres, we provide two infinite constructions. The first construction gives infinitely many $(d+1)$-dimensional simplicial polytopes with the transversal ratio exactly $\frac{2}{d+2}$ for every $d\geq 2$. In the case of $d=2$, this meets the previously well-known upper bound $1/2$ tightly. The second gives infinitely many simplicial 3-spheres with the transversal ratio greater than $1/2$. This was unexpected from what was previously known about the surrounding property. Moreover, we show that, for $d\geq 3$, the facet hypergraph $\mathcal{F}(\mathbf{P})$ of a $(d+1)$-dimensional simplicial polytope $\mathbf{P}$ has the chromatic number $\chi(\mathcal{F}(\mathbf{P})) \in O(n^{\frac{\lceil d/2\rceil-1}{d}})$, where $n$ is the number of vertices of $\mathbf{P}$. This slightly improves the upper bound previously obtained by Heise, Panagiotou, Pikhurko, and Taraz. This is a joint work with Joseph Briggs and Michael Gene Dobbins.

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