Tuesday, January 16, 2024

2024-01-17 / 11:00 ~ 12:00

by 김준일(숭실대학교)

Reconstruction of gene regulatory networks (GRNs) is a powerful approach to capture a prioritized gene set controlling cellular processes. In our previous study, we developed TENET a GRN reconstructor from single cell RNA sequencing (scRNAseq). TENET has a superior capability to identify key regulators compared with other algorithms. However, accurate inference of gene regulation is still challenging. Here, we suggest an integrative strategy called TENET+ by combining single cell transcriptome and chromatin accessibility data. TENET+ predicts target genes and open chromatin regions associated with transcription factors (TFs) and links the target regions to their corresponding target gene. As a result, TENET+ can infer regulatory triplets of TF, target gene, and enhancer. By applying TENET+ to a paired scRNAseq and scATACseq dataset of human peripheral blood mononuclear cells, we found critical regulators and their epigenetic regulations for the differentiations of CD4 T cells, CD8 T cells, B cells and monocytes. Interestingly, not only did TENET+ predict several top regulators of each cell type which were not predicted by the motif-based tool SCENIC, but we also found that TENET+ outperformed SCENIC in prioritizing critical regulators by using a cell type associated gene list. Furthermore, utilizing and modeling regulatory triplets, we can infer a comprehensive epigenetic GRN. In sum, TENET+ is a tool predicting epigenetic gene regulatory programs for various types of datasets in an unbiased way, suggesting that novel epigenetic regulations can be identified by TENET+.

2024-01-20 / 14:00 ~ 16:00

학과 세미나/콜로퀴엄 - 응용수학 세미나:

by ()

In the past couple of decades, mathematical fluid dynamics has been highlighted by numerous constructions of solutions to fluid equations that exhibit pathological or wild behavior. These include the loss of the energy balance, non-uniqueness, singularity formation, and dissipation anomaly. Interesting from the mathematical point of view, providing counterexamples to various well-posedness results in supercritical spaces, such constructions are becoming more and more relevant from the physical point of view as well. Indeed, a fundamental physical property of turbulent flows is the existence of the energy cascade. Conjectured by Kolmogorov, it has been observed both experimentally and numerically, but had been difficult to produce analytically. In this talk I will overview new developments in discovering not only pathological mathematically, but also physically realistic solutions of fluid equations.

2024-01-16 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Average flat-size in complex-representable matroids

by Matthew Kroeker(University of Waterloo)

Melchior’s Inequality (1941) implies that, in a rank-3 real-representable matroid, the average number of points in a line is less than three. This was extended to the complex-representable matroids by Hirzebruch in 1983 with the slightly weaker bound of four. In this talk, we discuss and sketch the proof of the recent result that, in a rank-4 complex-representable matroid which is not the direct-sum of two lines, the average number of points in a plane is bounded above by an absolute constant. Consequently, the average number of points in a flat in a rank-4 complex-representable matroid is bounded above by an absolute constant. Extensions of these results to higher dimensions will also be discussed. In particular, the following quantities are bounded in terms of k and r respectively: the average number of points in a rank-k flat in a complex-representable matroid of rank at least 2k-1, and the average number of points in a flat in a rank-r complex-representable matroid. Our techniques rely on a theorem of Ben Lund which approximates the number of flats of a given rank. This talk is based on joint work with Rutger Campbell and Jim Geelen.

2024-01-23 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Convex polytopes in non-elongated point sets in $R^d$

by Zichao Dong(IBS 극단조합및확률그룹)

For any finite point set $P \subset \mathbb{R}^d$, we denote by $\text{diam}(P)$ the ratio of the largest to the smallest distances between pairs of points in $P$. Let $c_{d, \alpha}(n)$ be the largest integer $c$ such that any $n$-point set $P \subset \mathbb{R}^d$ in general position, satisfying $\text{diam}(P) < \alpha\sqrt[d]{n}$ (informally speaking, `non-elongated'), contains a convex $c$-polytope. Valtr proved that $c_{2, \alpha}(n) \approx \sqrt[3]{n}$, which is asymptotically tight in the plane. We generalize the results by establishing $c_{d, \alpha}(n) \approx n^{\frac{d-1}{d+1}}$. Along the way we generalize the definitions and analysis of convex cups and caps to higher dimensions, which may be of independent interest. Joint work with Boris Bukh.

Events for the 취소된 행사 포함