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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
HYPERSPECTRAL IMAGE DENOISING USING A NONLOCAL SPECTRAL SPATIAL PRINCIPAL COMPONENT ANALYSIS
Hyperspectral Images Noise Reduction Nonlocal Similarity Spectral Spatial Information Principal Component Analysis
2018/5/14
Hyperspectral images (HSIs) denoising is a critical research area in image processing duo to its importance in improving the quality of HSIs, which has a negative impact on object detection and classi...
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...
Potential reasons for ionospheric anomalies detected by nonlinear principal component analysis just before the China Wenchuan earthquake, and their relationship to source conditions
Nonlinear Principal Component Analysis (NLPCA) Principal Component Analysis (PCA) Total Electron Content (TEC),
2015/8/27
Nonlinear principal component analysis (NLPCA) was performed to examine the total electron content (TEC) anomalies for the China Wenchuan earthquake of May 12, 2008 (= 7.9). This was applied to global...
Ionospheric perturbations associated with two huge earthquakes in Japan, using principal component analysis for multiple subionospheric VLF/LF propagation paths
Ionospheric perturbations Earthquakes Subionospheric VLF/LF propagation
2015/8/24
The presence of ionospheric perturbations in possible association with two huge earthquakes (Noto-hanto peninsula and Niigata-chuetu-oki earthquakes) in 2007 was studied on the basis of a conventional...
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 ...
A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
Canonical correlation analysis DNA copy number Integrative genomic analysis L1 Matrix decomposition Principal component analysis Sparse principal component analysis SVD.
2015/8/21
We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as X ˆ = k K=1 dkukvk T , where dk, uk, and vk m...
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...
MULTIVARIATE MATHEMATICAL MORPHOLOGY BASED ON PRINCIPAL COMPONENT ANALYSIS: INITIAL RESULTS IN BUILDING EXTRACTION
Multichannel image processing colour morphology vector ordering principal component analysis urban analysis
2015/7/30
Today, colour or multichannel satellite and aerial images are increasingly becoming available due to the commercial availability of
multispectral digital sensors and pansharpening function of the co...