Friday, April 21, 2023

2023-04-25 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: On perfect subdivision tilings

by 이현우(KAIST)

For a given graph $H$, we say that a graph $G$ has a perfect $H$-subdivision tiling if $G$ contains a collection of vertex-disjoint subdivisions of $H$ covering all vertices of $G.$ Let $\delta_{sub}(n, H)$ be the smallest integer $k$ such that any $n$-vertex graph $G$ with minimum degree at least $k$ has a perfect $H$-subdivision tiling. For every graph $H$, we asymptotically determined the value of $\delta_{sub}(n, H)$. More precisely, for every graph $H$ with at least one edge, there is a constant $1 < \xi^*(H)\leq 2$ such that $\delta_{sub}(n, H) = \left(1 - \frac{1}{\xi^*(H)} + o(1) \right)n$ if $H$ has a bipartite subdivision with two parts having different parities. Otherwise, the threshold depends on the parity of $n$.

2023-04-25 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - Mathematics & Beyond Seminar: The story of the human in the picture

by 박상흠(순천향대학병원)

[1] 인간의 질병 발생과 예방을 근본적으로 파악하려면 '인간에 대한 이해'가 필요합니다. 인간의 몸은 물질이며, 물질은 특성상 물리적 및 화학적 반복자극에 반드시 손상됩니다. 부모님께 몸을 받아 수십 년간 살다 보면 인간 내부의 태생적-구조적 요인과 외부의 환경적 요인에 의하여 부지불식중 가해지는 내부 및 외부 자극에 반복적으로 노출될 수밖에 없습니다. 이에 그와 같이 질병으로 진행될 수 밖에 없는 인간의 특성을 명화(그림)을 통하여 소개할 예정입니다. [2] 인간의 또 다른 이해로 과학적 혹은 수학적 평가로 가시화(객관화)하기 어려운 부문에 대한 내용을 역시 명화를 통하여 논의할 예정입니다.

2023-04-28 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

The well-known two-process model of sleep regulation makes accurate predictions of sleep timing and duration, as well as neurobehavioral performance, for a variety of acute sleep deprivation and nap sleep scenarios, but it fails to predict the effects of chronic sleep restriction on neurobehavioral performance. The two-process model belongs to a broader class of coupled, non-homogeneous, first-order, ordinary differential equations (ODEs), which can capture the effects of chronic sleep restriction. These equations exhibit a bifurcation, which appears to be an essential feature of performance impairment due to sleep loss. The equations implicate a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations, such as the adenosinergic neuromodulator/receptor system, as a key mechanism for the regulation of neurobehavioral functioning under conditions of sleep loss. The equations account for dynamic interaction with circadian rhythmicity, and also provide a new approach to dynamically tracking the magnitude of sleep inertia upon awakening from restricted sleep. This presentation will describe the development of the ODE system and its experimental calibration and validation, and will discuss some novel predictions.

2023-04-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by ()

In many different areas of mathematics (such as number theory, discrete geometry, and combinatorics), one is often presented with a large "unstructured" object, and asked to find a smaller "structured" object inside it. One of the earliest and most influential examples of this phenomenon was the theorem of Ramsey, proved in 1930, which states that if n = n(k) is large enough, then in any red-blue colouring of the edges of the complete graph on n vertices, there exists a monochromatic clique on k vertices. In this talk I will discuss some of the questions, ideas, and new techniques that were inspired by this theorem, and present some recent progress on one of the central problems in the area: bounding the so-called "diagonal" Ramsey numbers. Based on joint work with Marcelo Campos, Simon Griffiths and Julian Sahasrabudhe.

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