Related papers: On mean-sets
This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5)…
Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches…
In classification, it is usual to observe that models trained on a given set of classes can generalize to previously unseen ones, suggesting the ability to learn beyond the initial task. This ability is often leveraged in the context of…
Motivated by recent results on beta-type functions, a new family of means, which are of logarithmic Cauchy quotient type, are determined and characterized.
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…
A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are…
We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning,…
In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,...,x_n):=(f_1+...+f_n)^{-1}(f_1(x_1)+...+f_n(x_n))$, where $f_1,...,f_n:I\to\mathbb{R}$ are strictly increasing and continuous functions.…
The evolution of a measured system and an experimental apparatus is presented in an unified form. Conditions under which the state of such a total system forms, evaluates and declines from a superposition of states are defined. The problem…
We characterize continuous, symmetric and homogeneous means $M$ that can be represented in the form \begin{equation*} \frac{1}{M(x,y)}=\int_0^1 \frac{dt}{N\left(\tfrac{x+y}{2}-t\tfrac{x-y}{2},\tfrac{x+y}{2}+t\tfrac{x-y}{2}\right)}.…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of excluded middle, the law of non-contradiction, the…