Thursday, April 28, 2022

2022-05-04 / 15:00 ~ 16:30

학과 세미나/콜로퀴엄 - 박사논문심사: 희소 랜덤 그래프의 스펙트럼과 관련 문제들

by 이재훈(KAIST)

심사위원장 : 폴정, 심사위원 : 이지운, 남경식, 강남규(겸직교수), 서인석(서울대학교)

2022-05-04 / 16:00 ~ 17:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

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We investigate in depth the behaviour of Monge-Ampère volumes of quasi-psh functions on a given compact hermitian manifold. We prove that the property for these Monge-Ampère volumes to stay bounded away from zero or infinity is a bimeromorphic invariant. We show in particular that a conjecture of Demailly-Paun holds true if and only if such Monge-Ampère volumes stay bounded away from infinity. This is a joint work with Vincent Guedj.

2022-05-02 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: The complexity of the matroid-homomorphism problems

by 허철원(성균관대)

In this talk, we introduce homomorphisms between binary matroids that generalize graph homomorphisms. For a binary matroid $N$, we prove a complexity dichotomy for the problem $\rm{Hom}_\mathbb{M}(N)$ of deciding if a binary matroid $M$ admits a homomorphism to $N$. The problem is polynomial-time solvable if $N$ has a loop or has no circuits of odd length, and is otherwise $\rm{NP}$-complete. We also get dichotomies for the list, extension, and retraction versions of the problem. This is joint work with Hyobin Kim and Mark Siggers at Kyungpook National University.

2022-04-29 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나:

by 안정연(KAIST, 산업및시스템공학과)

Asymptoticswith consideration of ultra-high dimensional data must consider an increasing number of variables, i.e., dimensions, rather than growing the number of observations. High-dimensional asymptotic studies have revealed some unexpected characteristics of data with an exceedingly large number of variables, such as gene expressions. In the context of binary classification, i.e., supervised learning with dichotomous labels, data piling refers to the phenomenon that training data vectors from each class project to a single point for classification. This interesting phenomenon has been a key to understanding many distinctive properties of high-dimensional discrimination. In this talk, high-dimensional asymptoticsof data piling is investigated under equal covariance assumption, which reveals its close connection to the well-known ridged linear classifier. In particular, we show that a negatively ridged discriminant vector can asymptotically achieve data piling of independent test data, essentially yielding a perfect classification. Double data pilingis generalized to heterogeneous covariance models and we propose a data-splitting approach to estimate the direction for the second data piling of test data.

2022-04-29 / 10:00 ~ 11:00

SAARC 세미나 - SAARC 세미나: Double data piling for perfect high-dimensional classification

by 안정연(한국과학기술원)

TBA

2022-04-28 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit solution of the three-dimensional incompressible Euler equations. The flow is axi-symmetric with no swirl, the vortex core is simply a ball sliding on the axis of symmetry with a constant speed, and the vorticity in the core is proportional to the distance from the symmetry axis. We use the variational setting introduced by A. Friedman and B. Turkington (Trans. Amer. Math. Soc., 1981). As a consequence, the stability up to a translation is obtained by using a concentrated compactness method. As an application, we prove linear in time filamentation near Hill’s vortex: there exists an arbitrary small outward perturbation growing linearly for all times. These results rigorously confirm numerical simulations by Pozrikidis in 1986. The second part is joint work with In-Jee Jeong(SNU).

2022-04-28 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

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Outputs from health biological systems display complex fluctuations that are not random but display robust and often self-similar (fractal) temporal correlations at different time scales— scaling behaviors. The scaling behaviors in the fluctuations of biological outputs such as neural activities, cardiac dynamics, motor activity are believed to be originated from feedbacks within the complex biological networks, reflecting the system adaptability to internal and external inputs. Supporting this concept, our studies have demonstrated a mechanistic link between the scaling regulation of physiological fluctuations and the circadian control system— a result of evolutionary adaptation to daily environmental light-dark cycles on the earth. In this talk, I will discuss certain evidence for this ‘scaling-circadian’ link and its related implications. Moreover, I will review some recent studies, in which we examined how the scaling patterns of human motor activity fluctuations change with aging and in Alzheimer’s disease. Our results showed that (1) alterations in scaling activity patterns occur before the clinical manifestation of Alzheimer’s disease (i.e., cognitive impairment) and predict cognitive decline and the risk for Alzheimer’s dementia; and (2) the progression of Alzheimer’s disease accelerates the aging effect on the scaling activity patterns. Our work provides strong evidence that altered scaling activity patterns may also be a risk factor for neurodegeneration, playing a role in the development and progression of Alzheimer’s disease.

Events for the 취소된 행사 포함