Tuesday, January 18, 2022

2022-01-25 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Reduced bandwidth: a qualitative strengthening of twin-width in minor-closed classes (and beyond)

by 권오정(인천대 / IBS 이산수학그룹)

In a reduction sequence of a graph, vertices are successively identified until the graph has one vertex. At each step, when identifying $u$ and $v$, each edge incident to exactly one of $u$ and $v$ is coloured red. Bonnet, Kim, Thomassé, and Watrigant [FOCS 2020] defined the twin-width of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has maximum degree at most $k$. For any graph parameter $f$, we define the reduced-$f$ of a graph $G$ to be the minimum integer $k$ such that there is a reduction sequence of $G$ in which every red graph has $f$ at most $k$. Our focus is on graph classes with bounded reduced-bandwidth, which implies and is stronger than bounded twin-width (reduced-maximum-degree). We show that every proper minor-closed class has bounded reduced-bandwidth, which is qualitatively stronger than a result of Bonnet et al. for bounded twin-width. In many instances, we also make quantitative improvements. For example, all previous upper bounds on the twin-width of planar graphs were at least $2^{1000}$. We show that planar graphs have reduced-bandwidth at most $466$ and twin-width at most $583$; moreover, the witnessing reduction sequence can be constructed in polynomial time. We show that $d$-powers of graphs in a proper minor-closed class have bounded reduced-bandwidth (irrespective of the degree of the vertices). This is joint work with Édouard bonnet and David Wood.

2022-01-18 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학: 다중 오믹스 분야의 현황 및 유전자-환경 상호 모델링의 필요성

by 서민석(고려대학교)

본 발표에서는 다양한 기초 생명-의학 분야에서 생성되고 있는 오믹스 자료의 연구 개발 현황에 대해서 다룰 예정이다. 보다 큰 규모로, 보다 빠르게, 보다 정확하게, 보다 정밀하게 라는 궁극적인 목표하에 이뤄지고 있는 오믹스 자료의 진화에 발맞춰, 이를 분석하는 수리통계적 모형 역시 진화하고 있다. 그 중, 이번 발표에서는 미국의 초 대형 정밀의료 프로젝트인 TopMed에서 진행하고 있는 COPD에 관한 다중 오믹스 자료의 통합 분석 방법 및 결과에 대해서 자세히 다룰 예정이다. 아울러 정밀의료라는 목표를 달성하기 위해 반드시 모형에서 고려해야 하는 “환경 특이적 효과”에 대해 강연할 예정이다.

2022-01-21 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 금융수학 세미나: Changing the financial paradigm in the post-pandemic era (2)

by 김경수(성균관대학교)

This seminar has two purposes. One is to understand the nature of finance and the current international monetary order that contributed to the root cause of the global financial crisis. They are the financial system risk caused by maturity transformation, which is the core of the financial activity, the procyclicality of finance in which credit expands in an asset market boom and shrinks in a recession, and safe assets, etc. Another is to understand the ripple effect of the 21st century digital technology revolution. Just as cryptocurrencies cause conflicts with states monopolizing creating money, currencies based on digital platforms are causing conflicts with existing finance by shifting the core function of finance from intermediation to payment and settlement. Moreover, the democratization of finance thanks to the development of digital technology is another conflicting factor against the existing elite-centered finance, where the financial elite evaluates risks and receives rewards. Along with asset inflation, the pandemic has significantly increased debt on the one hand and accelerated the digitalization of finance on the other. The challenge in the post-pandemic era is to normalize increased debt and liquidity to a sustainable level while minimizing economic costs, and to come up with an alternative solution to the dilemma of the dollar-centered international monetary order. The first day of the seminar will focus on the attributes of finance, and the second day will discuss the challenges facing finance in the post-pandemic era and the digitalization of finance.

2022-01-20 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 금융수학 세미나: Changing the financial paradigm in the post-pandemic era (1)

by 김경수(성균관대학교)

2022-01-18 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: A rainbow Turán problem for color-critical graphs

by 서재현(KAIST)

For given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensures a 'colorful' copy of $H$, i.e. a copy of $H$ containing at most one edge from each $G_i$? Keevash, Saks, Sudakov, and Verstraëte defined $\operatorname{ex}_k(n,H)$ to be the maximum total number of edges of the graphs $G_1,\dots, G_k$ on a common vertex set of size $n$ having no colorful copy of $H$. They completely determined $\operatorname{ex}_k(n,K_r)$ for large $n$ by showing that, depending on the value of $k$, one of the two natural constructions is always the extremal construction. Moreover, they conjectured the same holds for every color-critical graphs and proved it for $3$-color-critical graphs. We prove their conjecture for $4$-color-critical graphs and for almost all $r$-color-critical graphs when $r > 4$. Moreover, we show that for every non-color-critical non-bipartite graphs, none of the two natural constructions is extremal for certain values of $k$. This is a joint work with Debsoumya Chakraborti, Jaehoon Kim, Hyunwoo Lee, and Hong Liu.

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