Thursday, May 1, 2025

2025-05-01 / 11:50 ~ 12:40

대학원생 세미나 - 대학원생 세미나: Introduction to Mathematical Modeling for Heterogeneous Diffusion

by 박준성(카이스트 수리과학과)

In undergraduate PDE course, one may have learned that the (classical) diffusion equation can be expressed as $u_t=D \Delta u$, where $D$ is a constant diffusivity. This is true for homogeneous environment. However, for (spatially) heterogeneous environment, $D$ is no longer a constant, and diffusion phenomena in those environments such as fractionation, or Soret effect, cannot be explained with the classical diffusion equation. In this talk, I will first discuss how to model and derive some of the diffusion equations in heterogeneous environment by using basic random walk theory. We will see that the heterogeneity of components, such as speed, walk length, sojourn time, etc, can explain the diffusion phenomena. Then, I will give some specific examples how such models can be applied in science, based on my recent works.

2025-05-02 / 14:00 ~ 15:30

학과 세미나/콜로퀴엄 - 기타: Introduction to Homotopical Algebra through Model Categories I

by Naing Zaw Lu(KAIST)

(This is part of the reading seminar given by the undergrad student Mr. Naing Zaw Lu for his Individual Study project.) This is an introductory talk on homotopy theory in model categories. Over the course of three lectures, we will familiarize ourselves with model categories, see how powerful cofibrant/fibrant objects can be, and build up the tools necessary to define the (Quillen) homotopy category of a model category.

2025-05-08 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 문하은(서울대학교 통계학과)

De novo mutations provide a powerful source of information for identifying risk genes associated with phenotypes under selection, such as autism spectrum disorder (ASD), obsessive-compulsive disorder (OCD), congenital heart disease, and schizophrenia (SCZ). However, identifying de novo variants is costly, as it requires trio-based sequencing to obtain parental genotypes. To address this limitation, we propose a method to infer inheritance class using only offspring genetic data. In our new integrated model, we evaluate variation in case and control samples, attempt to distinguish de novo mutations from inherited variation, and incorporate this information into a gene-based association framework. We validate our method through ASD gene identification, demonstrating that it provides a robust and powerful approach for identifying risk genes.

Events for the 취소된 행사 포함