Related papers: Factorization of network reliability with perfect …
The two-terminal reliability, known as the pair connectedness or connectivity function in percolation theory, may actually be expressed as a product of transfer matrices in which the probability of operation of each link and site is exactly…
It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditions, and that there is a small set of…
Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, universal broadcast, universal summation) that can be critical…
We prove that it is NP-complete to decide whether a given string can be factored into palindromes that are each unique in the factorization.
In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…
We generalize the notion of complete binary relation on complete lattice to residuated lattice valued ordered sets and show its properties. Then we focus on complete fuzzy tolerances on fuzzy complete lattices and prove they are in…
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
We discuss an open problem and its converse first posed by Dougherty and Faber in [3], "Network routing on regular directed graphs from spanning factorizations." Does every vertex transitive digraph have a spanning 1=factorization? We show…
Various real-life applications, for example, Internet of Things, wireless sensor networks, smart grids, transportation networks, communication networks, social networks, and computer grid systems, are always modeled as network structures.…
We establish a factorisation theorem for invertible, cross-symmetric, totally nonnegative matrices, and illustrate the theory by verifying that certain cases of Holte's Amazing Matrix are totally nonnegative.
We establish two general theorems on the local properties of the absolute summability of factored Fourier series by applying a recently defined absolute summability, $\left\vert A,\alpha_{n}\right\vert _{k}$ summability, and the class…
In this note we describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a factorization of dynamics in…
This paper addresses the large-scale acquisition of end-to-end network performance. We made two distinct contributions: ordinal rating of network performance and inference by matrix completion. The former reduces measurement costs and…
In the paper Compositionality of Component Fault Trees, we present a discussion of the compositionality of correctness of component fault trees. In this technical report, we present the formal proof of the central theorem of the…
We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
This paper contains a stronger version of a final identification theorem for the `generic' groups of finite Morley rank.
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…