Related papers: The use of entropy to measure structural diversity
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…
The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is…
The container methods are powerful tools to bound the number of independent sets of graphs and hypergraphs, and they have been extremely influential in the area of extremal and probabilistic combinatorics. We will focus on more specialized…
Selective prediction systems can mitigate harms resulting from language model hallucinations by abstaining from answering in high-risk cases. Uncertainty quantification techniques are often employed to identify such cases, but are rarely…
Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can be different, we develop a model to interpolate between…
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…
The classical Maximum-Entropy Principle (MEP) based on Shannon entropy is widely used to construct least-biased probability distributions from partial information. However, the Shore-Johnson axioms that single out the Shannon functional…
Increased deployment of residential smart meters has made it possible to record energy consumption data on short intervals. These data, if used efficiently, carry valuable information for managing power demand and increasing energy…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the plug-in estimator of a wide class of indices, including…
Nestedness is a property of interaction networks widely observed in natural mutualistic communities. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several metrics aiming at…
A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…
Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy,…
Diversity can be broadly defined as the presence of meaningful variation across elements, which can be viewed from multiple perspectives, including statistical variation and geometric structural richness in the dataset. Existing diversity…