Related papers: A note on tempered measures
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
Is there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.
In this note we examine the relationship between two-dimensional Coulomb systems and the thermal equilibrium measure, such as defined in the lecture notes [arXiv:2407.21194v1], pointing out some of its discrepancies with respect to the…
With the increasing capabilities of LLMs, recent studies focus on understanding whose opinions are represented by them and how to effectively extract aligned opinion distributions. We conducted an empirical analysis of three straightforward…
In this paper is discussed an application of signed measures (charges) to description of segment and chord length distributions in nonconvex bodies. The signed distribution may naturally appears due to definition via derivatives of…
Probabilities of measurement outcomes of two-particle entangled states give a physically transparent interpretation of the concurrence and of the I-concurrence as entanglement measures. The (I)-concurrence can thus be measured…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak…
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
Sentiment analysis is one of the most widely used techniques in text analysis. Recent advancements with Large Language Models have made it more accurate and accessible than ever, allowing researchers to classify text with only a plain…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functional analysts, this approach is rarely known by…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
Purity and coherence of a quantum state are recognized as useful resources for various information processing tasks. In this article, we propose a fidelity based valid measure of purity and coherence monotone and establish a relationship…
There is a big gap between the charming principles ideas and the real implementation of a diagnostic. In this lecture we review some details that make the difference between a good and bad measurement, highlighting also the relation between…