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Minicourse——Purity of Brauer groups: application of perfectoids
北大 Purity of Brauer groups application of perfectoids
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2023/6/16
Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Application of algebraic curve theory to integrable systems
代数曲线理论 可积系统 紧黎曼曲面
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2023/5/5
We first consider the basic theory of algebraic curves, including the compact Riemann surface, Riemann-Hurwitz formula, Baker-Akhiezer function, three kinds of Abelian differentials, the construction ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Critical Allard regularity in dimension two and its application
二维中临界 阿拉德规律性 欧几里得空间
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2023/5/5
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some special cases of the three dimensional Kakeya conjecture and their application to the restriction conjecture
三维Kakeya猜想 特殊情况 限制猜想
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2023/5/9
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（III）
多项式方法 多项式划分 关联几何
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2023/5/10
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（II）
多项式方法 应用 代数
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2023/5/17
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Regularization methods for high-dimensional instrumental variables regression with an application to genetical genomics
Causal inference Confounding Endogeneity Sparse regression
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2016/1/25
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expres...
Regularization methods for high-dimensional instrumental variables regression with an application to genetical genomics
Causal inference Confounding Endogeneity Sparse regression
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2016/1/20
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expres...
GENERALIZED SPARSE SIGNAL MIXING MODEL AND APPLICATION TO NOISY BLIND SOURCE SEPARATION
GENERALIZED SPARSE SIGNAL MIXING MODEL NOISY BLIND SOURCE SEPARATION
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2015/9/29
Sparse constraints on signal decompositions are justified bytypical sensor data used in a variety of signal processing fields such as acoustics, medical imaging, or wireless, but moreover can lead to ...
THE METHOD OF SPREADING CUMULATIVE TWIST AND ITS APPLICATION TO THE RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
SPREADING CUMULATIVE TWIST RESTRICTED CIRCULAR PLANAR THREE BODY PROBLEM
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2015/9/25
The purpose of this paper is twofold. First we show that the dynamics ofa Sun-Jupiter-Comet system and under some simplifying assumptions has a semi-infiniteregion of instability. This is done by redu...
Analysis of a Non-linear Partial Difference Equation, and Its Application to Cardiac Dynamics
Partial difference equation Non-linear Cardiac dynamics Singular perturbation method Spatial bifurcations
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2015/8/27
A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on th...
Regularized linear discriminant analysis and its application in microarrays
Regularized linear discriminant analysis microarrays
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2015/8/21
In this paper, we introduce a modified version of linear discriminant analysis, called the “shrunken centroids regularized discriminant analysis” (SCRDA). This method generalizes the idea of the “near...
One Sketch For All:Theory and Application of Conditional Random Sampling
One Sketch For All Theory and Application Conditional Random Sampling
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2015/8/21
Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise (l2, l1) distances, in static, large-scale, and sparse data. This study modifies the original CRS and exten...
A Quantitative Approach to Incentives: Application to Voting Rules
Voting Rules Quantitative
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2015/7/15
We present a general approach to quantifying a mechanism’s susceptibility to
strategic manipulation, based on the premise that agents report their preferences
truthfully if the potential gain from b...
FAST ALGORITHM FOR EXTRACTING THE DIAGONAL OF THE INVERSE MATRIX WITH APPLICATION TO THE ELECTRONIC STRUCTURE ANALYSIS OF METALLIC SYSTEMS
Diagonal extraction hierarchical Schur complement electronic structure calculation
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2015/7/14
We propose an algorithm for extracting the diagonal of the inverse matrices arising from electronic structure calculation. The proposed algorithm uses a hierarchical decomposition ofthe computational ...