Related papers: Maximum Entropy Framework for a Universal Rank Ord…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
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,…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents…
The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
This paper considers the problem of inference after ranking. In our setting, we are interested in any population whose rank according to some random quantity, such as an estimated treatment effect, a measure of value-added, or benefit (net…
Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum entropy choice, and provide a motivating example applicable…
The Beta Rank Function (BRF) $x(u) =A(1-u)^b/u^a$, where $u$ is the normalized and continuous rank of an observation $x$, has wide applications in fitting real-world data from social science to biological phenomena. The underlying…
It is supposed that the exponential multiplier in the method of the non-equilibrium statistical operator (Zubarev`s approach) can be considered as a distribution density of the past lifetime of the system, and can be replaced by an…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
Entropy serves as a central observable which indicates uncertainty in many chemical, thermodynamical, biological and ecological systems, and the principle of the maximum entropy (MaxEnt) is widely supported in natural science. Recently,…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…