Related papers: Best multi-valued approximants via multi-designs

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

In the first part of this paper, we define a deep convolutional neural network connected with the fractional Fourier transform (FrFT) using the $\theta$-translation operator, the translation operator associated with the FrFT. Subsequently,…

Given a finite sequence of vectors $\mathcal F_0$ in $\C^d$ we characterize in a complete and explicit way the optimal completions of $\mathcal F_0$ obtained by adding a finite sequence of vectors with prescribed norms, where optimality is…

We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…

We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the…

We present an analysis of the approximation error for a $d$-dimensional quasiperiodic function $f$ with Diophantine frequencies, approximated by a periodic function with the fundamental domain $[0,L_1)\times [0,L_2)\times \cdots…

For a fixed finite collection of graphs ${\cal F}$, the ${\cal F}$-M-DELETION problem asks, given an $n$-vertex input graph $G,$ for the minimum number of vertices that intersect all minor models in $G$ of the graphs in ${\cal F}$. by…

The main aim of this paper is to show that the nonlinear Choquet integral can be used to construct nonlinear approximation operators, exactly as by the use in probability of the Lebesgue-type integral, linear and positive approximation…

Let $T\subset\mathbb{R}$, $M$ be a metric space with metric $d$, and $M^T$ be the set of all functions mapping $T$ into $M$. Given $f\in M^T$, we study the properties of the approximate variation $\{V_\varepsilon(f)\}_{\varepsilon>0}$,…

We study the least squares regression problem \begin{align*} \min_{\Theta \in \mathcal{S}_{\odot D,R}} \|A\Theta-b\|_2, \end{align*} where $\mathcal{S}_{\odot D,R}$ is the set of $\Theta$ for which $\Theta = \sum_{r=1}^{R} \theta_1^{(r)}…

In this paper we analyze the convergence of the following type of series \begin{equation*} T_N f(x)=\sum_{j=N_1}^{N_2} v_j\Big(\mathcal{P}_{a_{j+1}} f(x)-\mathcal{P}_{a_{j}} f(x)\Big),\quad x\in \mathbb R_+, \end{equation*} where…

In this article, we study a class of non-archimedean pseudo-differential operators associated via Fourier transform to the Bessel potentials. These operators (which we will denote as $J^{\alpha },$ $\alpha >n$) are of the form (J^{\alpha…

For any integers $d, n \geq 2$ and $1/({\min\{n,d\}})^{0.4999} < \varepsilon<1$, we show the existence of a set of $n$ vectors $X\subset \mathbb{R}^d$ such that any embedding $f:X\rightarrow \mathbb{R}^m$ satisfying $$ \forall x,y\in X,\…

We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…

In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework…

A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an…

In this paper we study the classical problem of throughput maximization. In this problem we have a collection $J$ of $n$ jobs, each having a release time $r_j$, deadline $d_j$, and processing time $p_j$. They have to be scheduled…

We develop a finite difference approximation of order $\alpha$ for the $\alpha$-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Gr\"unwald scheme. In particular,…

We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…

For a field $\mathbb{F}$ and integers $d$ and $k$, a set ${\cal A} \subseteq \mathbb{F}^d$ is called $k$-nearly orthogonal if its members are non-self-orthogonal and every $k+1$ vectors of ${\cal A}$ include an orthogonal pair. We prove…