Related papers: On mean-sets
Metric mean dimension is a metric invariant of dynamical systems. It is a dynamical analogue of Minkowski dimension of metric spaces. We explain that old ideas of Bowen (1972) can be used for clarifying the local nature of metric mean…
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
We give a characterization of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. This includes the converse of an inequality of Beardon's for subharmonic functions. We also obtain integral inequalities…
Several primal and dual characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
Concentration of measure is studied, and obtained, for stable and related random vectors.
In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.
We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…
Extending the notion of projective means we first generalize an invariance identity related to the Carlson log given in a recent paper of P. Kahlig and J. Matkowski, and then, more generally, given a bivariate symmetric, homogeneous and…
In this paper we define the concepts of $g.\Lambda_s$-sets and $g.V_s$-sets and we use them in order to obtain new characterizations of semi-T_1-, semi-R_0- and semi-T_{1/2}-spaces.
We are developing techniques to generate summary descriptions of sets of objects. In this paper, we present and evaluate a rule-based NLG technique for summarising sets of bibliographical references in academic papers. This extends our…
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
We consider two relations on a $\cap$-semigroup of partial functions of a given set: the inclusion of domains and the semiadjacencity (i.e., the inclusion of the image of the first function into the domain of the second), which…
We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.
We introduce Domain-specific Masks for Generalization, a model for improving both in-domain and out-of-domain generalization performance. For domain generalization, the goal is to learn from a set of source domains to produce a single model…
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a…
We introduce a way to represent word pairs instantiating arbitrary semantic relations that keeps track of the contexts in which the words in the pair occur both together and independently. The resulting features are of sufficient generality…