Related papers: Detecting discrete integrability: the singularity …
Intrusion detection systems (IDS) help detect unauthorized activities or intrusions that may compromise the confidentiality, integrity or availability of a resource. This paper presents a general overview of IDSs, the way they are…
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is…
A good deal of current research in complex networks involves the characterization and/or classification of the topological properties of given structures, which has motivated several respective measurements. This letter proposes a framework…
We consider the numerical evaluation of a class of double integrals with respect to a pair of self-similar measures over a self-similar fractal set (the attractor of an iterated function system), with a weakly singular integrand of…
This work proposes and evaluates a novel approach to determine interesting categorical attributes for lists of entities. Once identified, such categories are of immense value to allow constraining (filtering) a current view of a user to…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…
The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…
The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these…
We introduce graded, enriched characteristic cycles as a method for encoding Morse modules of strata with respect to a constructible complex of sheaves. Using this new device, we obtain results for arbitrary complex analytic functions on…
We are concerned with the Calder\'on inverse inclusion problem, where one intends to recover the shape of an inhomogeneous conductive inclusion embedded in a homogeneous conductivity by the associated boundary measurements. We consider the…
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
Nowadays, there are outstanding strides towards a future with autonomous vehicles on our roads. While the perception of autonomous vehicles performs well under closed-set conditions, they still struggle to handle the unexpected. This survey…
This work establishes simple criteria for detecting higher rational singularities via the intersection Du Bois complex and the irrationality complex of a normal variety over the complex numbers.
Analyzing singular patterns in vector fields is a fundamental problem in theoretical and practical domains due to the ability of such patterns to detect the intrinsic characteristics of vector fields. In this study, we propose an approach…
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.