Tuesday, January 31, 2023

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2023-02-03 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI’s efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.
2023-02-07 / 11:00 ~ 12:00
IBS-KAIST 세미나 - 대수기하학: The Martens-Mumford Theorem and the Green-Lazarsfeld Secant Conjecture 인쇄
by Daniele Agostini(Eberhard Karls Universität Tübingen)
The syzygies of a curve are the algebraic relation amongst the equation defining it. They are an algebraic concept but they have surprising applications to geometry. For example, the Green-Lazarsfeld secant conjecture predicts that the syzygies of a curve of sufficiently high degree are controlled by its special secants. We prove this conjecture for all curves of Clifford index at least two and not bielliptic and for all line bundles of a certain degree. Our proof is based on a classic result of Martens and Mumford on Brill-Noether varieties and on a simple vanishing criterion that comes from the interpretation of syzygies through symmetric products of curves.
2023-01-31 / 16:30 ~ 17:30
IBS-KAIST 세미나 - 이산수학: A proof of the Erdős–Faber–Lovász conjecture 인쇄
by Abhishek Methuku(ETH Zürich)
The Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on n vertices is at most n. In this talk, I will sketch a proof of this conjecture for every large n. Joint work with D.Kang, T. Kelly, D. Kühn and D. Osthus.
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