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The problem of low-rank matrix reconstruction arises in various applications in communications and signal processing. The state of the art research largely focuses on the recovery techniques that utilize affine maps satisfying the…

We study the problem of recovering a collection of $n$ numbers from the evaluation of $m$ power sums. This yields a system of polynomial equations, which can be underconstrained ($m < n$), square ($m = n$), or overconstrained ($m > n$).…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

Motivated by applications in polymer-based data storage, we study the problem of reconstructing a string from part of its composition multiset. We give a full description of the structure of the strings that cannot be uniquely reconstructed…

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…

Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the…

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…

Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

A finite subset $M \subset \mathbb{R}^d$ is basic, if for any function $f \colon M \to \mathbb{R}$ there exists a collection of functions $f_1, \ldots, f_d \colon \mathbb{R} \to \mathbb{R}$ such that for each element $(x_1, \ldots, x_d)\in…

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case…

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…

We generalize the problem of reconstructing strings from their substring compositions first introduced by Acharya et al. in 2015 motivated by polymer-based advanced data storage systems utilizing mass spectrometry. Namely, we see strings as…

We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…

We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…

We carefully evaluate a number of algorithms for learning in a federated environment, and test their utility for a variety of image classification tasks. We consider many issues that have not been adequately considered before: whether…

We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of…

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…