相关论文: A Fuzzy Decomposition Method to Establish Function…

The goal of this note is to give the unified approach to the solutions of a class of isoperimetric problems by relating them to the exterior differential systems studied by R.~Bryant and P.~Griffiths. In this note we list several classical…

The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…

This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…

We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upwinding Petrov-Galerkin discretization based on bubble…

Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds…

We define fully coupled forward-backward stochastic differential equations on spaces related to continuous time, finite state Markov Chains. Existence and uniqueness results of the fully coupled forward-backward stochastic differential…

Langevin diffusions are rapidly convergent under appropriate functional inequality assumptions. Hence, it is natural to expect that with additional smoothness conditions to handle the discretization errors, their discretizations like the…

We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property…

We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry \'Emery…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

There has been a recent surge of powerful tools to show rapid mixing of Markov chains, via functional inequalities such as Poincar\'e inequalities. In many situations, Markov chains fail to mix rapidly from a worst-case initialization, yet…

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control…

We introduce a universal approach for applying the partition rank method, an extension of Tao's slice rank polynomial method, to tensors that are not diagonal. This is accomplished by generalizing Naslund's distinctness indicator to what we…

In this paper, we give sharp Rusak- and Markov-type inequalities for rational functions on several intervals when the system of intervals is a \textquotedblleft rational function inverse image\textquotedblright\, of an interval and those…

The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and…

An algorithm for estimating quasi-stationary distribution of finite state space Markov chains has been proven in a previous paper. Now this paper proves a similar algorithm that works for general state space Markov chains under very general…

A classical problem for Markov chains is determining their stationary (or steady-state) distribution. This problem has an equally classical solution based on eigenvectors and linear equation systems. However, this approach does not scale to…

We study the effects of adding a local perturbation in a pattern forming system, taking as an example the Ginzburg-Landau equation with a small localized inhomogeneity in two dimensions. Measuring the response through the linearization at a…