Related papers: Group characterizable entropy functions
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…
By 'informational entropy', we understand an inherent boundary to knowability, due e.g. to perceptual, theoretical, evidential or linguistic limits. In this paper, we discuss a logical framework in which this boundary is incorporated into…
In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and…
The total entropy production fluctuations are studied in some exactly solvable models. For these systems, the detailed fluctuation theorem holds even in the transient state, provided initially the system is prepared in thermal equilibrium.…
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…
Sofic entropy theory is a generalization of the classical Kolmogorov-Sinai entropy theory to actions of large class of non-amenable groups called sofic groups. This is a short introduction with a guide to the literature.
The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these…
The traditional approach to the quantitative study of segregation is to employ indices that are selected by ``desirable properties''. Here, we detail how information theory underpins entropy-based indices and demonstrate how desirable…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
We develop cycle index generating functions for orthogonal groups in even characteristic, and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic…
This book chapter is an introduction to and an overview of the information-theoretic, task independent utility function "Empowerment", which is defined as the channel capacity between an agent's actions and an agent's sensors. It quantifies…
Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and…
A new notion of partition-determined functions is introduced, and several basic inequalities are developed for the entropy of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these…
In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information…
Pairwise interactions between individuals are taken as fundamental drivers of collective behavior responsible for group cohesion and decision-making. While an individual directly influences only a few neighbors, over time indirect…
Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…
We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the interval to closed subsets of the interval. We view these set-valued functions, via…