Related papers: Statistical Compactness
We propose a theory which describes the density relaxation of loosely packed, cohesionless granular material under mechanical tapping. Using the compactivity concept we develope a formalism of statistical mechanics which allows us to…
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…
One point compactification is studied in the light of ideal of subsets of $\mathbb{N}$. $\mathcal{I}$-proper map is introduced and showed that a continuous map can be extended continuously to the one point $\mathcal{I}$-compactification if…
We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…
It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points…
We present an overview of some results about characterization of compactness in which the concept of approximation scheme has had a role. In particular, we present several results that were proved by the second author, jointly with Luther,…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
In order to have a better description of homogenization for parabolic partial differential equations with periodic coefficients, we define the notion of parametric two-scale convergence. A compactness theorem is proved to justify this…
We introduce and investigate a topological version of St\"ackel's 1907 characterization of finite sets, with the goal of obtaining an interesting notion that characterizes usual compactness (or a close variant of it). Define a $T_2$…
Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics. Clustering is the process of grouping similar…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
The statistical convergence is handled for sequences with the natural density, in general. In a recent paper, the statistical convergence for nets in Riesz spaces has been studied and investigated by developing topology-free techniques in…
This work describes numerical methods that are useful in many areas: examples include statistical modelling (bioinformatics, computational biology), theoretical physics, and even pure mathematics. The methods are primarily useful for the…
This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence and continuity properties are investigated mostly (but not exclusively)…