Related papers: Total positivity: tests and parametrizations
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
In this paper we parameterize non-negative matrices of sum one and rank at most two. More precisely, we give a family of parameterizations using the least possible number of parameters. We also show how these parameterizations relate to a…
Type inference refers to the task of inferring the data type of a given column of data. Current approaches often fail when data contains missing data and anomalies, which are found commonly in real-world data sets. In this paper, we propose…
Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
Motivated by applications to goodness of fit testing, the empirical likelihood approach is generalized to allow for the number of constraints to grow with the sample size and for the constraints to use estimated criteria functions. The…
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cp-factorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be used to show that every integral…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…
This is an introduction to some of the most probabilistic aspects of free probability theory.
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
A complete characterization of the asymptotic singularity probability of random circulant Bernoulli matrices is given for all values of the probability parameter.
The aim of this paper is to review some work conducted in the field of user testing that aims at specifying or clarifying the test procedures and at defining and developing tools to help conduct user tests. The topics that have been…
Considering a broad class of steady-state nonequilibrium systems for which some additive quantities are conserved by the dynamics, we introduce from a statistical approach intensive thermodynamic parameters (ITPs) conjugated to the…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
This article starts out with a detailed example illustrating the utility of applying quantum probability to psychology. Then it describes several alternative mathematical methods for mapping fundamental quantum concepts (such as state…