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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonsplitting of the Hilbert Exact Sequence and the Principal Chebotarev Density Theorem
希尔伯特精确序列 主切 博塔列夫密度定理 非分裂
2023/4/18
Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
BASE CHANGE FOR BERNSTEIN CENTERS OF DEPTH ZERO PRINCIPAL SERIES BLOCKS
BERNSTEIN ZERO PRINCIPAL SERIES BLOCKS
2015/9/29
Let G be an unrami ed group over a p-adic eld. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal
series blocks for G and proves the corresponding base ...
ON HECKE ALGEBRA ISOMORPHISMS AND TYPES FOR DEPTH-ZERO PRINCIPAL SERIES
HECKE ALGEBRA ISOMORPHISMS DEPTH-ZERO PRINCIPAL SERIES
2015/9/29
These lectures describe Hecke algebra isomorphisms and types for depth-zero
principal series blocks, a.k.a. Bernstein components Rs(G) for s = sχ = [T, χe]G, where χ
is a depth-zero character on T(O...
Principal component models for sparse functional data
Functional data analysis Principal components Mixed effects model Reduced rank estimation Growth curve
2015/8/21
The elements of a multivariate data set are often curves rather than single points. Functional principal components can be used to describe the modes of variation of such curves. If one has complete m...
Sparse Principal Component Analysis
Arrays Gene expression Lasso/elastic net Multivariate analysis Singular value decomposition Thresholding
2015/8/21
Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However,PCA suffers from the fact that each principal component is a linear combination of all the or...
Prediction by Supervised Principal Components
Gene expression Microarray Regression Survival analysis
2015/8/21
In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called ...
In regression problems where the number of predictors greatly exceeds the number of observations, conventional regression techniques may produce unsatisfactory results. We describe a technique called ...
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of
data in the form of n observations (or cases) of a vector with p variables. Contemporary data sets
of...
ON THE DISTRIBUTION OF THE LARGEST EIGENVALUE IN PRINCIPAL COMPONENTS ANALYSIS
LARGEST EIGENVALUE PRINCIPAL COMPONENTS
2015/8/20
Let x1 denote the square of the largest singular value of an n × p
matrix X, all of whose entries are independent standard Gaussian varates. Equivalently, x1 is the largest principal component vari...
Investigating the multimodality of multivariate data with principal curves
Multimodality Principal curves
2015/8/20
We propose a simple method to assess the number of subpopulations in multivariate data
by projecting the data on its principal curve and then applying Silverman’s bandwidth test
to the resulting uni...
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
Dense Error Correction Low-Rank Matrices Principal Component Pursuit
2015/6/17
We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been sh...
Robust Principal Component Analysis?
Principal components robustness vis-a-vis outliers nuclear-norm minimization `1-norm minimization duality low-rank matrices sparsity video surveillance
2015/6/17
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove...
Principal Lyapunov Exp onent and Principal Flo quet Bundle of Sto chas tic/Ra ndom Para b olic Equations
Principal Lyapunov Exp onen Principal Flo quet Bundle
2015/4/3
Problem – Extension of Principal Eigenvalue/Principal
Eigenfunction Theory for Time Independent Parabolic
Equations to Random Parabolic Equations
I Principal Eigenvalue/Principal Eigenfunction Theo...
Semi-linear equations and principal eigenvalues in unbounded domains
Semi-linear equations principal eigenvalues unbounded domains
2015/4/3
Semi-linear equations and principal eigenvalues in unbounded domains.
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...