Monday, November 6, 2023

2023-11-07 / 13:30 ~ 14:30

SAARC 세미나 - SAARC 세미나:

by 지홍창()

The spectrum of a general non-Hermitian (non-normal) matrix is unstable; a tiny perturbation of the matrix may result in a huge difference in its eigenvalues. This instability is often quantified as eigenvalue condition numbers in numerical linear algebra or as eigenvector overlap in random matrix theory. In this talk, we show that adding a smoothly random noise matrix regularizes this instability, by proving a nearly optimal upper bound of eigenvalue condition numbers. If time permits, we will also discuss the effect of the noise matrix on a macroscopic scale in terms of the Brown measure of free circular Brownian motion. This talk is based on joint works with László Erdős.

2023-11-13 / 17:00 ~ 18:00

학과 세미나/콜로퀴엄 - 박사논문심사: 타원 곡선의 모델-베유 군과 아벨리안 다양체의 자기동형 군

by 김한솔()

2023-11-10 / 11:00 ~ 12:00

학과 세미나/콜로퀴엄 - 응용 및 계산수학 세미나:

by ()

In this talk, I will introduce the use of deep neural networks (DNNs) to solve high-dimensional evolution equations. Unlike some existing methods (e.g., least squares method/physics-informed neural networks) that simultaneously deal with time and space variables, we propose a deep adaptive basis approximation structure. On the one hand, orthogonal polynomials are employed to form the temporal basis to achieve high accuracy in time. On the other hand, DNNs are employed to create the adaptive spatial basis for high dimensions in space. Numerical examples, including high-dimensional linear parabolic and hyperbolic equations and a nonlinear Allen–Cahn equation, are presented to demonstrate that the performance of the proposed DABG method is better than that of existing DNNs. zoom link: https://kaist.zoom.us/j/3844475577 zoom ID: 384 447 5577

2023-11-10 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally efficient likelihood-based workflow that addresses all three steps in a unified way. Recently developed methods for constructing profile-wise prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters, and then combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. We apply our methods to a range of synthetic data and real-world ecological data describing re-growth of coral reefs on the Great Barrier Reef after some external disturbance, such as a tropical cyclone or coral bleaching event.

2023-11-07 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Some Variants of the Erdős-Sós Conjecture

by Bruce A. Reed(Academia Sinica)

Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The celebrated 50-year-old Erdős-Sós conjecture states that for every k, if G has average degree exceeding k-2 then it contains every tree T with k vertices as a subgraph. This is tight as the clique with k-1 vertices contains no tree with k vertices as a subgraph. We present some variants of this conjecture. We first consider replacing bounds on the average degree by bounds on the minimum and maximum degrees. We then consider replacing subgraph by minor in the statement.

2023-11-09 / 14:30 ~ 15:45

학과 세미나/콜로퀴엄 - 기타:

by ()

(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

2023-11-09 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 하승열()

In this talk, we address a question whether a mean-field approach for a large particle system is always a good approximation for a large particle system or not. For definiteness, we consider an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row (or columm)-summable network topology, we show that a homogeneous ensemble exhibits complete synchronization, and the infinite Kuramoto model can cast as a gradient flow, whereas we obtain a weak synchronization estimate, namely practical synchronization for a heterogeneous ensemble. Unlike with the finite Kuramoto model, phase diameter can be constant for some class of network topologies which is a novel feature of the infinite model. We also consider a second class of network topology (so-called a sender network) in which coupling strengths are proportional to a constant that depends only on sender's index number. For this network topology, we have a better control on emergent dynamics. For a homogeneous ensemble, there are only two possible asymptotic states, complete phase synchrony or bi-cluster configuration in any positive coupling strengths. In contrast, for a heterogeneous ensemble, complete synchronization occurs exponentially fast for a class of initial configuration confined in a quarter arc. This is a joint work with Euntaek Lee (SNU) and Woojoo Shim (Kyungpook National University).

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