Scientific knowledge, written in the form of differential equations, plays a vital role in various deep learning fields. In this talk, I will present a graph neural network (GNN) design based on reaction-diffusion equations, which addresses the notorious oversmoothing problem of GNNs. Since the self-attention of Transformers can also be viewed as a special case of graph processing, I will present how we can enhance Transformers in a similar way. I will also introduce a spatiotemporal forecasting model based on neural controlled differential equations (NCDEs). NCDEs were designed to process irregular time series in a continuous manner and for spatiotemporal processing, it needs to be combined with a spatial processing module, i.e., GNN. I will show how this can be done.
This talk presents mathematical modeling, numerical analysis and simulation using finite element method in the field of electromagnetics at various scales, from analyzing quantum mechanical effects to calculating the scattering of electromagnetic wave in free space. First, we discuss and analyze the Schrodinger-Poisson system of quantum transport model to calculate electron states in three-dimensional heterostructures. Second, the electromagnetic vector wave scattering problem is solved to analyze the field characteristics in the presence of stealth platform. This talk also introduces several challenging issues in these applications and proposes their solutions through mathematical analysis.
by Dylan Thurston(University of Indiana, Bloomington)
The Julia set of a (hyperbolic) rational map
naturally comes embedded in the Riemann sphere, and thus has a
Hausdorff dimension. But the Hausdorff dimension varies if we tweak
the parameters slightly. Is there a "best" representative or more
invariant dimension? One answer comes from looking at
quasi-symmetries; the \emph{conformal dimension} of the Julia set is
the minimum Hausdorff dimension of any metri quasi-symmetric to the
original. We characterize the Ahlfors-regular conformal dimension of
Julia sets of rational maps using graphical energies arising from a
natural combinatorial description. (Ahlfors-regular is a dynamically
natural extra condition on the metric.)
This is joint work with Kevin Pilgrim.
“Transcriptome-wide analysis of cell cycle-dependent bursty gene expression from single-cell RNA-seq data using mechanistic model-based inference”, bioRxiv (2024) will be discussed in this Journal Club.
Bursty gene expression is quantified by two intuitive parameters: the burst frequency and the burst size. While these parameters are known to be cell-cycle dependent for some genes, a transcriptome-wide picture remains missing. Here we address this question by fitting a suite of mechanistic models of gene expression to mRNA count data for thousands of mouse genes, obtained by sequencing of single cells for which the cell-cycle position has been inferred using a deep-learning approach. This leads to the estimation of the burst frequency and size per allele in the G1 and G2/M cell-cycle phases, hence providing insight into the global patterns of transcriptional regulation. In particular, we identify an interesting balancing mechanism: on average, upon DNA replication, the burst frequency decreases by ≈ 50%, while the burst size increases by the same amount. We also show that for accurate estimation of the ratio of burst parameters in the G1 and G2/M phases, mechanistic models must explicitly account for gene copy number differences between cells but, surprisingly, additional corrections for extrinsic noise due to the coupling of transcription to cell age within the cell cycle or technical noise due to imperfect capture of RNA molecules in sequencing experiments are unnecessary.
If you want to participate in the seminar, you need to enter IBS builiding (https://www.ibs.re.kr/bimag/visiting/). Please contact if you first come IBS to get permission to enter IBS building.
2024-03-15 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 기타: Introduction to étale cohomology 1
by 이제학(KAIST)
This is an introductory reading seminar presented by a senior undergraduate student, Jaehak Lee, who is studying the subject.
In dimension 4, the works of Freedman and Donaldson led us to the striking discovery that the smooth category is drastically different from the topological category, compared to other dimensions. Since then, it has been extraordinarily successful in investigating the difference in various contexts. In contrast, our understanding of when smooth and topological categories would exhibit similarity in dimension 4 remained, at best, minimal. In this talk, we will introduce some recent progress on new “topological = smooth” results in dimension 4, focusing on embedded disks.
Motivated by the Cohen-Lenstra heuristics, Friedman and Washington studied the distribution of the cokernels of random matrices over the ring of p-adic integers. This has been generalized in many directions, as well as some applications to the distribution of random algebraic objects. In this talk, first we give an overview of random matrix theory over the ring of p-adic integers, together with their connections to conjectures in number theory. After that, we investigate the distribution of the cokernels of random p-adic matrices with given zero entries. The second part of this talk is based on work in progress with Gilyoung Cheong, Dong Yeap Kang and Myungjun Yu.
2024-03-22 / 14:00 ~ 16:00
학과 세미나/콜로퀴엄 - 기타: Introduction to complex algebraic geometry and Hodge theory #2
by 김재홍(KAIST)
This is part of an informal seminar series to be given by Mr. Jaehong Kim, who has been studying the book "Hodge theory and Complex Algebraic Geometry Vol 1 by Claire Voisin" for a few months. There will be 6-8 seminars during Spring 2024, and it will summarize about 70-80% of the book.
