相关论文: Total positivity: tests and parametrizations
In this exploratory note we ask the question of what a measure of performance for all tasks is like if we use a weighting of tasks based on a difficulty function. This difficulty function depends on the complexity of the (acceptable)…
A general and relatively simple method for construction of multivariate goodness-of-fit tests is introduced. The proposed test is applied to elliptical distributions. The method is based on a characterization of probability distributions…
This article explores the extension of well-known F1 score used for assessing the performance of binary classifiers. We propose the new metric using probabilistic interpretation of precision, recall, specificity, and negative predictive…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
We propose a numerical method, based on the shift-and-invert power iteration, that answers whether a symmetric matrix is positive definite ("yes") or not ("no"). Our method uses randomization. But, it returns the correct answer with high…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A=BB^T. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
This article has two interpenetrating motifs. One is an exposition of some major ideas and techniques behind the use of block matrices, and especially their positivity properties. This is done by focussing on one major problem:…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
We give a pedagogical introduction to the theory of resonances, focusing specifically on the spectrum of excited strongly interacting particles. After providing historical context starting from the atomic theory, we summarize the status of…
Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…
This work proposes a taxonomy for diagnosis computation methods which allows their standardized assessment, classification and comparison. The aim is to (i) give researchers and practitioners an impression of the diverse landscape of…
In the paper, the authors introduce a matrix-parametrized generalization of the multinomial probability mass function that involves a ratio of several multivariate gamma functions. They show the logarithmic complete monotonicity of this…