相关论文: Partitions of Equiangular Tight Frames

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

We introduce the $\star_G$ tensor algebra, in which any finite group $G$ defines the multiplication rule, making equivariance an intrinsic algebraic property rather than an architectural constraint. The framework rests on three…

We introduce a projective Riesz $s$-kernel for the unit sphere $\mathbb{S}^{d-1}$ and investigate properties of $N$-point energy minimizing configurations for such a kernel. We show that these configurations, for $s$ and $N$ sufficiently…

This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other…

When constructing finite frames for a given application, the most important consideration is the spectrum of the frame operator. Indeed, the minimum and maximum eigenvalues of the frame operator are the optimal frame bounds, and the frame…

In this paper, we propose new extragradient algorithms for solving a split equilibrium and nonexpansive mapping SEPNM($C, Q, A, f, g, S, T)$ where $C, Q$ are nonempty closed convex subsets in real Hilbert spaces $\mathcal{H}_1,…

We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the traditional problem of expressing the index class in K-theory in terms of…

Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear elliptic partial differential equations. The proposed scheme…

Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of…

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…

This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…

We introduce an effective field theory (EFT) for conformal impurity by considering a pair of transversely displaced impurities and integrating out modes with mass inversely proportional to the separation distance. This EFT captures the…

The soft bootstrap program aims to construct consistent effective field theories (EFT's) by recursively imposing the desired soft limit on tree-level scattering amplitudes through on-shell recursion relations. A prime example is the leading…

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

Let M be a foliated manifold and G a discrete group acting on M by diffeomorphisms mapping leaves to leaves. Then G naturally acts by automorphisms on the algebra of Heisenberg pseudodifferential operators on the foliation. Our main result…

The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge…

Electrostatic potential fitting method (ESPF) is a powerful way of defining atomic charges derived from quantum density matrices fitted to reproduce a quantum mechanical charge distribution in the presence of an external electrostatic…

Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…

In this paper, we consider optimization problems over closed embedded submanifolds of $\mathbb{R}^n$, which are defined by the constraints $c(x) = 0$. We propose a class of constraint dissolving approaches for these Riemannian optimization…

A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…