Backwards analysis, first popularized by Seidel, is often the simplest most elegant way of analyzing a randomized algorithm. It applies to incremental algorithms where elements are added incrementally, following some random permutation, e.g., incremental Delauney triangulation of a pointset, where points are added one by one, and where we always maintain the Delauney triangulation of the points...

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error...

Maria Eugénia Mata 1,† and Jose Tenreiro Machado 2,*,† 1 Faculdade de Economia, Nova School of Business and Economics, Campus de Campolide, Lisbon 1099-032, Portugal; [email protected] 2 Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto, Porto 4249-015, Portugal * Correspondence: [email protected]; Tel.: +351-22-8340500 † These authors contributed equa...

This is a companion to Robert Niven’s block 4, 2007lectures. I point to an alternative way of deriving the MaxEnt and the MinXEnt-distributions which is claimed to be more fundamental as well as technically a good deal simpler than the standard method via Lagrange multipliers (sic, still what you find in many (any ?) textbook you may pick up in this field). I hope you, the students in Robert’s ...

Abstract: Multiscale entropy (MSE) was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i) a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii) the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE)—based on the same steps as MSE—also exists. Compared ...

We provide an entropy analysis for light storage and light retrieval. In this analysis, entropy extraction and reduction in a typical light storage experiment are identified. The spatiotemporal behavior of entropy is presented for D1 transition in cold sodium atoms. The governing equations are the reduced Maxwell field equations and the Liouville–von Neumann equation for the density matrix of t...

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the...

In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numeric...