Related papers: On the mathematical modelling of measurement
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
There are compelling historical and mathematical reasons why we ended up, among others in Physics, with using the scalars given by the real or the complex numbers. Recently, however, infinitely many easy to construct and use other algebras…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…
In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms,…
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…
We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.
The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power some of these methods have become prominent and central to modern data analysis.…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…