Related papers: Splitting algorithm and normed convergence for dra…
This article analyses the convergence of the Lie-Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order…
Let \phi(G) be the minimum conductance of an undirected graph G, and let 0=\lambda_1 <= \lambda_2 <=... <= \lambda_n <= 2 be the eigenvalues of the normalized Laplacian matrix of G. We prove that for any graph G and any k >= 2, \phi(G) =…
We prove the unexpected result that almost uniform sampling of independent sets in graphs is possible via a probabilistic polynomial time algorithm. Note that our sampling algorithm (if correct) has extremely surprising consequences; the…
Given a length $n$ sample from $\mathbb{R}^d$ and a neural network with a fixed architecture with $W$ weights, $k$ neurons, linear threshold activation functions, and binary outputs on each neuron, we study the problem of uniformly sampling…
We prove the optimal strong convergence rate of a fully discrete scheme, based on a splitting approach, for a stochastic nonlinear Schr\"odinger (NLS) equation. The main novelty of our method lies on the uniform a priori estimate and…
We prove that a "first-order" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\kappa_R)^k$, where $\kappa_R$ is the condition number of the Riemannian…
The pseudo-inverse of a graph Laplacian matrix, denoted as $L^\dagger$, finds extensive application in various graph analysis tasks. Notable examples include the calculation of electrical closeness centrality, determination of Kemeny's…
Let $M_n$ be a simple triangulation of the sphere $S^2$, drawn uniformly at random from all such triangulations with n vertices. Endow $M_n$ with the uniform probability measure on its vertices. After rescaling graph distance on $V(M_n)$ by…
We consider an initial-boundary value problem for a 2D time-dependent Schr\"odinger equation on a semi-infinite strip. For the Numerov-Crank-Nicolson finite-difference scheme with discrete transparent boundary conditions, the Strang-type…
We give the first L_1-sketching algorithm for integer vectors which produces nearly optimal sized sketches in nearly linear time. This answers the first open problem in the list of open problems from the 2006 IITK Workshop on Algorithms for…
We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…
We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of L\^e (2020). This approach allows one to exploit regularization by noise effects…
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of…
In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak ergodic and weak convergence of the sequence generated by the…
We survey recent developments in the field of complexity of pathwise approximation in $p$-th mean of the solution of a stochastic differential equation at the final time based on finitely many evaluations of the driving Brownian motion.…
The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be…
In this paper, we investigate a class of nonconvex and nonsmooth fractional programming problems, where the numerator composed of two parts: a convex, nonsmooth function and a differentiable, nonconvex function, and the denominator consists…
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
We introduce a general technique for proving estimates for certain random planar maps which belong to the $\gamma$-Liouville quantum gravity (LQG) universality class for $\gamma \in (0,2)$. The family of random planar maps we consider are…