In machine learning, the model is not as complicated as possible. Good generalization
ability means that the model not only performs well on the training data set, but also can …

We investigate a family of regression problems in a semisupervised setting. The task is to
assign real-valued labels to a set of n sample points provided a small training subset of N …

In this paper we introduce a new family of partial difference operators on graphs and study
equations involving these operators. This family covers local variational p-Laplacian, ∞ …

Abstract Let G=(V, E) be a finite graph. We consider the existence of solutions to a
generalized Chern–Simons–Higgs equation Δ u=-λ eg (u) eg (u)-1 2+ 4 π∑ j= 1 N δ pj on G …

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn
(AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics …

We consider the nonlinear Schrödinger equation-Δ u+(λ a (x)+ 1) u=| u| p-1 u on a locally
finite graph G=(V, E). We prove via the Nehari method that if a (x) satisfies certain …

Partial difference equations (PDEs) and variational methods for image processing on
Euclidean domains spaces are very well established because they permit to solve a large …

We prove H\" older estimates for viscosity solutions of a class of possibly degenerate and
singular equations modelled by the fractional $ p $-Laplace equation $$\text {PV}\int …

In this paper by exploiting the theory of wavelet transform, a solution of Laplace equation,
after changing certain initial conditions in terms of wavelet transformation is obtained. We …

With the advance of three-dimensional (3-D) scanning technology, the cultural heritage
community is increasingly interested in 3-D scans of cultural objects such as antiques …