相关论文: Mosaic-skeleton approximation is all you need for …

Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…

Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle…

We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…

This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classic approach the mean-field Smoluchowski coagulation is used. However, the…

Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…

The work discusses a new low-rank Monte Carlo technique to solve Smoluchowski-like kinetic equations. It drastically decreases the computational complexity of modeling of size-polydisperse systems. For the studied systems it can outperform…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…

Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…

Efficient and accurate low-rank approximations of multiple data sources are essential in the era of big data. The scaling of kernel-based learning algorithms to large datasets is limited by the O(n^2) computation and storage complexity of…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…

Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…

We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to…

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…

Motivated by the need for efficient and accurate simulation of the dynamics of the polar ice sheets, we design high-order finite element discretizations and scalable solvers for the solution of nonlinear incompressible Stokes equations. We…

Recent advances in the joint processing of images have certainly shown its advantages over individual processing. Different from the existing works geared towards co-segmentation or co-localization, in this paper, we explore a new joint…

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…