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许多复杂生物系统可以由高维非线性动力系统描述,对原始数据进行降维有助于对这些系统进行有效分析。然而以一种可解释的方式进行极致低尺度的降维仍然是一个具有挑战性的问题。基于Takens延迟嵌入理论,将高维空间信息转换为低维时间信息,我们开发了极致低降维算法stPCA,并将其应用于重症监护医疗信息管理系统MIMIC-IIIMIMIC-IV数据集,提出了ICU病人的出院决策。stPCA基于ICU患者的高...
In this talk, we introduce occupation fields for vertices and oriented edges and compute their distributions. More precisely, under the Markov loop measure, the expected number for crossings of an ori...
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
We considers the adaptive stabilization problem for a basic class of linear-quadratic non-cooperative stochastic differential games when the systems matrices are unknown to the regulator and the playe...
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Dirac方程最初是Dirac为解决Minkowski时空中Klein—Gordon方程的粒子的负几率与负能问题建立的。1980年,Weinberg和Witten证明了引力无法量子化,所以为了将引力引入量子场论中,数学和物理学家将平直时空的Dirac方程推广到弯曲时空的Dirac方程,弯曲时空Dirac方程表示了任一自由费米子物质场在时空背景所应满足的场方程,是宇宙学研究的核心问题。2000年Fi...
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
This talk is concerned with a direct sampling method for imaging the support of a frequency-dependent source term embedded in a homogeneous and isotropic medium. The source term is given by the Fourie...
Causal inference is a permanent challenge topic in statistics, data science, and many other applied fields. Existing machine learning methods often focus on the correlations in the data and ignore the...

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