相关论文: Discrepancy bounds for low-dimensional point sets

Convolutional Neural Networks (CNNs) can provide accurate object classification. They can be extended to perform object detection by iterating over dense or selected proposed object regions. However, the runtime of such detectors scales as…

Few-shot deep learning is a topical challenge area for scaling visual recognition to open ended growth of unseen new classes with limited labeled examples. A promising approach is based on metric learning, which trains a deep embedding to…

We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…

A concept of higher order neighborhood in complex networks, introduced previously (PRE \textbf{73}, 046101, (2006)), is systematically explored to investigate larger scale structures in complex networks. The basic idea is to consider each…

In this paper we give a formula for the classes (in the Grothendieck ring of complex quasi-projective varieties) of irreducible components of $(1,k)$-quasi-homogeneous Hilbert schemes of points on the plane. We find a new simple geometric…

Let $n,p,r$ be positive integers with $n \geq p\geq r$. A rank-$\overline{r}$ subset of $n$ by $p$ matrices (with entries in a field) is a subset in which every matrix has rank less than or equal to $r$. A classical theorem of Flanders…

The $\mathcal{L}_2$ discrepancy is one of several well-known quantitative measures for the equidistribution properties of point sets in the high-dimensional unit cube. The concept of weights was introduced by Sloan and Wo\'{z}niakowski to…

We give an explicit construction of two-dimensional point sets whose $L_p$ discrepancy is of best possible order for all $1\le p\le \infty$. It is provided by folding Hammersley point sets in base $b$ by means of the $b$-adic baker's…

Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…

We define a special network that exhibits the large embeddings in any class of similar algebras. With the aid of this network, we introduce a notion of distance that conceivably counts the minimum number of dissimilarities, in a sense,…

Most quasi-Monte Carlo research focuses on sampling from the unit cube. Many problems, especially in computer graphics, are defined via quadrature over the unit triangle. Quasi-Monte Carlo methods for the triangle have been developed by…

This article presents a novel and practically useful link between geometric integration, low-discrepancy sampling and code coupling for Lagrangian and Eulerian Vlasov-Poisson solvers. Low-discrepancy sequences, also called quasi-random…

We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in $[0,1]$. Similar notions have been considered for kernels; we extend them to more…

Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of…

Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…

Most of the real world networks such as the internet network, collaboration networks, brain networks, citation networks, powerline and airline networks are very large and to study their structure, and dynamics one often requires working…

Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods are classical approaches for the numerical integration of functions $f$ over $[0,1]^d$. While QMC methods can achieve faster convergence rates than MC in moderate dimensions, their…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

A concept of neighborhood in complex networks is addressed based on the criterion of the minimal number os steps to reach other vertices. This amounts to, starting from a given network $R_1$, generating a family of networks $R_\ell,…

Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…