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The problem of matrix factorization motivated by diffraction or elasticity is studied. A powerful tool for analyzing its solutions is introduced, namely analytical continuation formulae are derived. Necessary condition for commutative…
We present an algorithm for factoring linear differential operators with coefficients in a finite separable extension of F p (x). Our methods rely on specific tools arising in positive characteristic: p-curvature, structure of simple…
It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in the other the entries are products of powers. These results…
We study the existence of the product of two weighted modulation spaces. For this purpose we discuss two different strategies. The more simple one allows transparent proofs in various situations. However, our second method allows a closer…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
We introduce $p$-derivations and give a few basic ways in which they act like derivatives by numbers.
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…