Friday, April 4, 2025

2025-04-07 / 16:00 ~ 17:30

편미분방정식 통합연구실 세미나 - 편미분방정식: Behaviors of a solution of the logistic diffusive model and its equilibrium

by 이유빈()

Abstract:The logistic diffusive model provides the population distribution of a species according to time under a fixed open domain in R^n, a dispersal rate, and a given resource distribution. In this talk, we discuss the solution of the model and its equilibrium. First, we show the existence, uniqueness, and regularity results of the solution and the equilibrium. Then, we investigate two contrasting behaviors of the equilibrium with respect to the dispersal rate by applying two methods for each case: sub-super solution method and asymptotic expansion. Finally, we introduce an optimizing problem of a total population of the equilibrium with respect to resource distribution and prove a significant property of an optimal control called bang-bang. References: [1] Cantrell, R.S., Cosner, C. Spatial ecology via reaction-diffusion equation. Wiley series in mathematical and computational biology, John Wiley & Sons Ltd (2003) [2] I. Mazari, G. Nadin, Y. Privat, Optimization of the total population size for logistic diffusive equations: Bang-bang property and fragmentation rate, Communications in Partial Differential Equation 47 (4) (Dec 2021) 797-828

2025-04-11 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학: [Journal Club] Entrainment and multi-stability of the p53 oscillator in human cells

by 정의민(IBS 의생명수학그룹)

In this talk, we discuss the paper, “Entrainment and multi-stability of the p53 oscillator in human cells” by Alba Jiménez et al., Cell Systems, 2024.

2025-04-04 / 14:00 ~ 16:00

IBS-KAIST 세미나 - 수리생물학: [Journal Club] Accurate predictions on small data with a tabular foundation model

by 임동주(KAIST)

In this talk, we discuss the paper “Accurate predictions on small data with a tabular foundation model” by Noah Hollmann et al., Nature (2025).

2025-04-09 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 미분기하 세미나:

by 서검교(숙명여자대학교)

Serrin’s overdetermined problem is a famous result in mathematics that deals with the uniqueness and symmetry of solutions to certain boundary value problems. It is called "overdetermined" because it has more boundary conditions than usually required to determine a solution, which leads to strong restrictions on the shape of the domain. In this talk, we discuss overdetermined boundary value problems in a Riemannian manifold and discuss a Serrin-type symmetry result to the solution to an overdetermined Steklov eigenvalue problem on a domain in a Riemannian manifold with nonnegative Ricci curvature and it will be discussed about an overdetermined problems with a nonconstant Neumann boundary condition in a warped product manifold.

2025-04-08 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나:

by 김승혁(한양대학교 수학과)

We present recent developments on the quantitative stability of the Sobolev inequalities, as well as the stability of critical points of their Euler–Lagrange equations. In particular, we introduce our recent joint work with H. Chen (Hanyang University) and J. Wei (The Chinese University of Hong Kong) on the stability of the Yamabe problem, the fractional Lane–Emden equation for all possible orders, and the Brezis-Nirenberg problem.

2025-04-04 / 11:00 ~ 12:00

IBS-KAIST 세미나 - IBS-KAIST 세미나:

by ()

The advent of single-cell transcriptomics has brought a greatly improved understanding of the heterogeneity of gene expression across cell types, with important applications in developmental biology and cancer research. Single-cell RNA sequencing datasets, which are based on tags called universal molecular identifiers, typically include a large number of zeroes. For such datasets, genes with even moderate expression may be poorly represented in sequencing count matrices. Standard pipelines often retain only a small subset of genes for further analysis, but we address the problem of estimating relative expression across the entire transcriptome by adopting a multivariate lognormal Poisson count model. We propose empirical Bayes estimation procedures to estimate latent cell-cell correlations, and to recover meaningful estimates for genes with low expression. For small groups of cells, an important sampling procedure uses the full cell-cell correlation structure and is computationally feasible. For larger datasets, we propose a gene-level shrinkage procedure that has favorable performance for datasets with approximately compound symmetric cell-cell correlation. A fast procedure that incorporates matrix approximations is also promising, and extensible to very large datasets. We apply our approaches to simulated and real datasets, and demonstrate favorable performance in comparisons to competing normalization approaches. We further illustrate the applications of our approach in downstream analyses, including cell-type clustering and identification.

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