Related papers: Deep zero problems
We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.
We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued…
A new property, the strong singular value property, is introduced, developed, and utilized to study the problem of which lists of nonnegative real numbers occur as the singular values of a matrix with a prescribed zero-nonzero pattern.
We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…
We introduce the notion of soficity for locally compact groups and list a number of open problems.
This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.
A novel approach to complex problems has been previously applied to graph classification and the graph equivalence problem. Here we consider its applications to a wide set of NP complete problems, namely, those of finding a subgraph g…
We study extensions of the Election Isomorphism problem, focused on the existence of isomorphic subelections. Specifically, we propose the Subelection Isomorphism and the Maximum Common Subelection problems and study their computational…
We discuss to what extent the local techniques of resolution of singularities over fields of characteristic zero can be applied to improve singularities in general. For certain interesting classes of singularities, this leads to an embedded…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly…