Wednesday, October 20, 2021

2021-10-27 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 정수론: On the Kottwitz conjecture for local shtuka spaces

by David Hansen(Max Planck Institute for Mathematics)

The cohomology of local Shimura varieties, and of more general spaces of local shtukas, is of fundamental interest in the Langlands program. On the one hand, it is supposed to realize instances of the local Langlands correspondence. On the other hand, there is a tight relationship with the cohomology of global Shimura varieties. In recent joint work with Kaletha and Weinstein, we proved the first general results towards the Kottwitz conjecture, which predicts how supercuspidal L-packets contribute to the cohomology of local shtuka spaces. I will review this whole story, and give some overview of the ideas which enter into our proof. The key idea in our argument - namely, that the Kottwitz conjecture should follow from some form of the Lefschetz-Verdier fixed point formula - was already formulated by Michael Harris in the '90s. However, executing this idea brings substantial technical challenges. I will try to emphasize the new ingredients which allow us to implement this idea in full generality.

2021-10-26 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: 𝝘-graphic delta-matroids and their applications

by 김동규(KAIST & IBS 이산수학그룹)

Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define a $\Gamma$-graphic delta-matroid for an abelian group $\Gamma$, which generalizes a graphic delta-matroid. For an abelian group $\Gamma$, a $\Gamma$-labelled graph is a graph whose vertices are labelled by elements of $\Gamma$. We prove that a certain collection of edge sets of a $\Gamma$-labelled graph forms a delta-matroid, which we call a $\Gamma$-graphic delta-matroid, and provide a polynomial-time algorithm to solve the separation problem, which allows us to apply the symmetric greedy algorithm of Bouchet (1987) to find a maximum weight feasible set in such a delta-matroid. We also prove that a $\Gamma$-graphic delta-matroid is a graphic delta-matroid if and only if it is even. We prove that every $\mathbb{Z}_p^k$-graphic delta matroid is represented by some symmetric matrix over a field of characteristic of order $p^k$, and if every $\Gamma$-graphic delta-matroid is representable over a finite field $\mathbb{F}$, then $\Gamma$ is isomorphic to $\mathbb{Z}_p^k$ and $\mathbb{F}$ is a field of order $p^\ell$ for some prime $p$ and positive integers $k$ and $\ell$. This is joint work with Duksang Lee and Sang-il Oum.

2021-10-25 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 계산수학 세미나: Color image enhancement based on retinex theory

by 강명민(충남대학교)

In the first part, I introduce a novel variational model for the joint enhancement and restoration of dark images corrupted by blurring and/or noise. The model decomposes a given dark image into reflectance and illumination images that are recovered from blurring and/or noise. In addition, our approach utilizes non-convex total variation regularization on all variables. This allows us to adequately denoise homogeneous regions while preserving the details and edges in both reflectance and illumination images, which leads to clean and sharp final enhanced images. Experimental results demonstrate the effectiveness of the proposed model when compared to other state-of-the-art methods in terms of both visual aspect and image quality measures. In the second part, I propose a novel variational model for the restoration of a single color image degenerated by haze. The model extends the total variation based model, by inserting an inter-channel correlation term. This additional term permits both color and gray-valued transmission maps, which enable broader applications of the proposed model. Numerical experiments validate the outstanding performance of the proposed model compared to the state-of-the-art methods.

2021-10-27 / 17:00 ~ 18:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Chronotherapeutics- that is administering drugs following the patient’s biological rhythms over the 24 h span- may largely impact on both drug toxicities and efficacy in various pathologies including cancer [1]. However, recent findings highlight the critical need of personalizing circadian delivery according to the patient sex, genetic background or chronotype. Chronotherapy personalization requires to reliably account for the temporal dynamics of molecular pathways of patient’s response to drug administration [2]. In a context where clinical molecular data is usually minimal in individual patients, multi-scale- from preclinical to clinical- systems pharmacology stands as an adapted solution to describe gene and protein networks driving circadian rhythms of treatment efficacy and side effects and allow for the design of personalized chronotherapies. Such a multiscale approach is being undertaken for personalizing the circadian administration of irinotecan, one of the cornerstones of chemotherapies against digestive cancers. Irinotecan molecular chronopharmacology was studied at the cellular level in an in vitro/in silico investigation. Large transcription rhythms of period T= 28 h 06 min (SD 1 h 41 min) moderated drug bioactivation, detoxification, transport, and target in synchronized Caco-2 colorectal cancer cell cultures. These molecular rhythms translated into statistically significant changes according to drug timing in irinotecan pharmacokinetics, pharmacodynamics, and drug-induced apoptosis. Clock silencing through siBMAL1 exposure ablated all the chronopharmacology mechanisms. Mathematical modeling highlighted circadian bioactivation and detoxification as the most critical determinants of irinotecan chronopharmacology [3]. The cellular model of irinotecan chronoPK-PD was further tested on SW480 and SW620 cell lines, and connected to a new clock model to investigate the feasibility of irinotecan timing personalization solely based on clock gene expression monitoring (Hesse, Martinelli et al., under review). To step towards the clinics, on one side, mathematical models of irinotecan, oxaliplatin and 5-fluorouracil pharmacokinetics were designed to precisely compute the exposure concentration of tissue over time after complex chronomodulated drug administration through programmable pumps [4]. On the other side, we aimed to design a model learning methodology predicting from non-invasively measured circadian biomarkers (e.g. rest-activity, body temperature, cortisol, food intake, melatonin), the patient peripheral circadian clocks and associated optimal drug timing [5]. We investigated at the molecular scale the influence of systemic regulators on peripheral clocks in four classes of mice (2 strains, 2 sexes). Best models involved a modulation of either Bmal1 or Per2 transcription most likely by temperature or nutrient exposure cycles. The strengths of systemic regulations were found to be significantly different according to mouse sex and genetic background. References 1. Ballesta, A., et al., Systems Chronotherapeutics. Pharmacol Rev, 2017. 69(2): p. 161-199. 2. Sancar, A. and R.N. Van Gelder, Clocks, cancer, and chronochemotherapy. Science, 2021. 371(6524). 3. Dulong, S., et al., Identification of Circadian Determinants of Cancer Chronotherapy through In Vitro Chronopharmacology and Mathematical Modeling. Mol Cancer Ther, 2015. 4. Hill, R.J.W., et al., Optimizing circadian drug infusion schedules towards personalized cancer chronotherapy. PLoS Comput Biol, 2020. 16(1): p. e1007218. 5. Martinelli, J., et al., Model learning to identify systemic regulators of the peripheral circadian clock. 2021.

2021-10-21 / 11:00 ~ 12:00

IBS-KAIST 세미나 - 수리생물학:

by ()

Within a given species, fluctuations in egg or embryo size is unavoidable. Despite this, the gene expression pattern and hence the embryonic structure often scale in proportion with the body length. This scaling phenomenon is very common in development and regeneration and has long fascinated scientists. I will first discuss a generic theoretical framework to show how scaling gene expression pattern can emerge from non-scaling morphogen gradients. I will then demonstrate that the Drosophila gap gene system achieves scaling in a way that is entirely consistent with our theory. Remarkably, a parameter-free model based on the theory quantitatively accounts for the gap gene expression pattern in nearly all morphogen mutants. Furthermore, the regulation logic and the coding/decoding strategy of the gap gene system can be revealed. Our work provides a general theoretical framework on a large class of problems where scaling output is induced by non-scaling input, as well as a unified understanding of scaling, mutants’ behavior and regulation in the Drosophila gap gene and related systems.

Events for the 취소된 행사 포함