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We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…

General Relativity and Quantum Cosmology · Physics 2015-06-05 J. Manuel Garcia-Islas

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

Disordered Systems and Neural Networks · Physics 2013-05-30 James West , Lucas Lacasa , Simone Severini , Andrew Teschendorff

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…

Information Theory · Computer Science 2024-04-15 Paolo Perrone

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information Theory · Computer Science 2011-04-05 Paul M. B. Vitányi

The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…

Combinatorics · Mathematics 2021-09-01 Yanni Dong , Maximilien Gadouleau , Pengfei Wan , Shenggui Zhang

We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…

Quantum Physics · Physics 2021-10-04 Alexander McKinlay

The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information, for a class of structured spiking neuronal network. In…

Neurons and Cognition · Quantitative Biology 2019-12-04 Wenjie Li , Yao Li

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

Quantum Physics · Physics 2009-06-28 Nilanjana Datta , Renato Renner

Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…

Disordered Systems and Neural Networks · Physics 2013-09-17 Ekaterina S. Roberts , Anthonius C. C. Coolen

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…

Quantum Physics · Physics 2018-05-30 Alexey E. Rastegin

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Probability · Mathematics 2018-01-23 Alois Pichler , Ruben Schlotter

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

Information Theory · Computer Science 2018-01-16 Mihai-Alin Badiu , Justin P. Coon

Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…

Information Theory · Computer Science 2019-08-22 Amos Lapidoth , Christoph Pfister

We propose a new way to measure inequalities such as the glass ceiling effect in attributed networks. Existing measures typically rely solely on node degree distribution or degree assortativity, but our approach goes beyond these measures…

Social and Information Networks · Computer Science 2023-03-20 Rui Luo , Buddhika Nettasinghe , Vikram Krishnamurthy

The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…

Quantum Physics · Physics 2014-01-28 Martin Müller-Lennert , Frédéric Dupuis , Oleg Szehr , Serge Fehr , Marco Tomamichel

This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…

Physics and Society · Physics 2025-03-27 Yujie Shi , Alex Jie Yang , Sanhong Deng

The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…

Methodology · Statistics 2017-03-20 Linda Altieri , Daniela Cocchi , Giulia Roli

We consider an isomorphism invariant for measure-preserving systems - types of generalized entropy convergence rates. We show the connections of this invariant with the types of Shannon entropy convergence rates. In the case when they…

Dynamical Systems · Mathematics 2013-09-25 Fryderyk Falniowski

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…

Statistical Mechanics · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

A wide range of tasks in network analysis, such as clustering network populations or identifying anomalies in temporal graph streams, require a measure of the similarity between two graphs. To provide a meaningful data summary for…

Physics and Society · Physics 2024-10-15 Helcio Felippe , Federico Battiston , Alec Kirkley