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AVERAGING OF HAMILTONIAN FLOWS WITH AN ERGODIC COMPONENT
ERGODIC COMPONENT Unperturbed flow
2015/9/29
We consider a process on T2, which consists of fast motion along the
stream lines of an incompressible periodic vector field perturbed by white
noise. It gives rise to a process on the graph n...
Suppose G(R) is a real reductive group, with L-group ∨GΓ, and φ : WR →∨G Γ is an L-homomorphism.There is a close relationship between the Lpacket associated to φ and characters the component group of ...
Averaging of Hamiltonian Flows with an Ergodic Component
Rapid movement white noise the vector field perturbation function
2015/9/28
We consider a process on T 2, which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise to a process on the grap...
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...
A Desingularization of the Main Component of the Moduli Space of Genus-One Stable Maps into P n
Genus-One Stable Maps Moduli
2015/7/14
We construct a natural smooth compacti cation of the space of smooth genus-one curves with
k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth
compacti ca...
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...
Geometric Ergodicity & Scanning Strategies For Two-Component Gibbs Samplers
Geometric Ergodicity Scanning Strategies Two-Component Gibbs Samplers
2012/11/23
In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate i...
Independent component analysis via nonparametric maximum likelihood estimation
Blind source separation density estimation independent component analysis log-concave projection
2012/6/19
Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector $X = AS$, where $A$ is a non-singular matrix and $S$ has in...
Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes
nonlinear hyperbolic equations Multi-component coupling multidimensional well-balanced schemes Analysis of PDEs
2012/6/14
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated ...
Approximation Bounds for Sparse Principal Component Analysis
Sparse PCA convex relaxation semidefinite programming approximation bounds detection
2012/5/9
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testi...
The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws
Two-Component Camassa-Holm Equations CH(2,1) CH(2,2) First-Order Integrating Factors Conservation Laws Exactly Solvable and Integrable Systems
2012/4/26
Recently, Holm and Ivanov, proposed and studied a class of multi-component generalisations of the Camassa-Holm equations [D D Holm and R I Ivanov, Multi-component generalizations of the CH equation: g...
Prime component-preservingly amphicheiral link with odd minimal crossing number
component-preservingly amphicheiral link minimal crossing number Tait's conjecture
2012/3/1
For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with minimal crossing number $c$.
Anatomy of the giant component: The strictly supercritical regime
Anatomy giant component strictly supercritical regime
2012/2/29
In a recent work of the authors and Kim, we derived a complete description of the largest component of the Erd\H{o}s-R\'enyi random graph $G(n,p)$ as it emerges from the critical window, i.e. for $p =...