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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the L2 rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation
哈特里到弗拉索夫 泊松方程 极限 L2收敛率
2023/4/13
We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global and Local Convergence-Rate Analysis of an Inexact Newton Augmented Lagrangian Method for Zero-One Composite Optimization
零一复合优化 不精确 牛顿增强拉格朗日方法 收敛率分析
2023/4/14
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, non- convex optimization problems and it has attracted much attention recently. Augmented Lagrangian Method (ALM) has stood out a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence analysis of one-point large deviations rate functions of numerical methods for stochastic wave equations with small noise
小噪声 随机波动方程 数值方法 单点大偏差率 函数收敛分析
2023/4/21
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
QUASI-OPTIMAL CONVERGENCE RATE OF AN ADAPTIVE DISCONTINUOUS GALERKIN METHOD
Discontinuous Galerkin interior penalty nonconforming meshes
2015/12/11
We analyze an adaptive discontinuous finite element method (ADFEM) for symmetric
second order linear elliptic operators. The method is formulated on nonconforming meshes made
of simplices or q...
Energy-Efficient Power and Rate Control with QoS Constraints:A Game-Theoretic Approach
Energy-Efficient Power Rate Control QoS Constraints Game-Theoretic Approach
2015/9/29
A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each us...
Adapting to Unknown Sparsity by controlling the False Discovery Rate
Thresholding Wavelet Denoising Minimax Estimation
2015/8/21
We attempt to recover a high-dimensional vector observed in white noise, where
the vector is known to be sparse, but the degree of sparsity is unknown. We consider
three di®erent ways of deˉnin...
Asymptotic Minimaxity of False Discovery Rate Thresholding for Sparse Exponential Data
Minimax Decision theory Minimax Bayes estimation
2015/8/21
Control of the False Discovery Rate (FDR) is a recent innovation in multiple hypothesis
testing, allowing the user to limit the fraction of rejected null hypotheses which correspond to
false rejecti...
ESTABLISHING STRONG CONTROL OF FAMILYWISE ERROR RATE FOR ITERATIVE STEP-DOWN TESTS
ESTABLISHING STRONG ITERATIVE STEP-DOWN TESTS
2015/3/18
A long-standing problem concerning the iterative analysis of orthogonal
saturated designs has b een resolved. Consider an unreplicated factorial design
yielding indep endent, normally distributed es...
Uniform Convergence and Rate Adaptive Estimation of a Convex Function
Adaptive estimate B-splines convex regression minimax risk
2012/5/9
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates vario...
Tree Codes Improve Convergence Rate of Consensus Over Erasure Channels
Tree Codes Convergence Rate of Consensus Erasure Channels Optimization and Control
2012/4/17
We study the problem of achieving average consensus between a group of agents over a network with erasure links. In the context of consensus problems, the unreliability of communication links between ...
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Consensus consensus+innovations performance analysis random network convergence in probability exponential rate
2012/3/1
Distributed consensus and other linear systems with system stochastic matrices $W_k$ emerge in various settings, like opinion formation in social networks, rendezvous of robots, and distributed infere...
On the rate of convergence to equilibrium for a non-isothermal viscous Cahn-Hilliard equation
Partial differential equation Cahn-Hilliard equation Maxwell-Cattaneo's law convergence rate
2011/10/14
In this short note, a model describing non-isothermal fast phase separation processes taking place in a three-dimensional bounded domain is considered. The model consists of a viscous Cahn-Hilliard eq...
Convergence and Rate Analysis of Neural Networks for Sparse Approximation
Locally Competitive Algorithm sparse approximation global stability exponential convergence non-smooth objective
2011/9/23
Abstract: We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that solves sparse approximation problems (e.g., approximating a vector from a dictionary u...
Singular limit and exact decay rate of a nonlinear elliptic equation
existence of solution nonlinear elliptic equations singular limit exact decay rate Yamabe flow
2011/9/6
Abstract: For any $n\ge 3$, $00$, $\beta>0$, $\alpha$, satisfying $\alpha\le\beta(n-2)/m$, we prove the existence of radially symmetric solution of $\frac{n-1}{m}\D...
Improvement of the Han-Kobayashi Rate Region for General Interference Channel-v2
Interference channel Input correlation Binning scheme
2011/2/28
Allowing the input auxiliary random variables to be correlated and using the binning scheme, the Han-Kobayashi (HK) rate region for general interference channel is partially improved. The obtained par...