Related papers: On mean-sets
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Natural Language Processing prides itself to be an empirically-minded, if not outright empiricist field, and yet lately it seems to get itself into essentialist debates on issues of meaning and measurement ("Do Large Language Models…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent…
While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…
We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
In this paper, we give corrected and improved definitions of the sets $S$ and $\Delta$ compared to [1]. By using these new definitions, we go throughout the proof of the main result in [1], and we correct it.
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…