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Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…

Multiple Schramm-Loewner Evolutions (SLE) are conformally invariant random processes of several curves, whose construction by growth processes relies on partition functions: M\"obius covariant solutions to a system of second order partial…

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

This paper is concerned with the numerical approximation of stochastic mechanical systems with nonlinear holonomic constraints. Such systems are described by second order stochastic differential-algebraic equations involving an implicitly…

In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…

We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential…

Computer vision and machine learning tools offer an exciting new way for automatically analyzing and categorizing information from complex computer simulations. Here we design an ensemble machine learning framework that can independently…

This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

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…

It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure…

We disclose the origin of anisotropic percolation perimeters in terms of the Stochastic Loewner Evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multi-layered and directed…

We propose an online learning algorithm for a class of machine learning models under a separable stochastic approximation framework. The essence of our idea lies in the observation that certain parameters in the models are easier to…

Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor…

In this article we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of Support Points (SP), which was initially developed for finding the optimal…

The development of artificial intelligence (AI) provides opportunities for the promotion of deep neural network (DNN)-based applications. However, the large amount of parameters and computational complexity of DNN makes it difficult to…

There are a variety of approaches to obtain a vast receptive field with convolutional neural networks (CNNs), such as pooling or striding convolutions. Most of these approaches were initially designed for image classification and later…

Standard stochastic Loewner evolution (SLE) is driven by a continuous Brownian motion, which then produces a continuous fractal trace. If jumps are added to the driving function, the trace branches. We consider a generalized SLE driven by a…

A novel overlapping domain decomposition splitting algorithm based on a Crank-Nisolson method is developed for the stochastic nonlinear Schroedinger equation driven by a multiplicative noise with non-periodic boundary conditions. The…