We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector μ. We first formulate an effective approach for establishing the L-estimate pointwise in time between entropy solutions for μ 6= 0 and μ = 0, respectively, with respect to the flux parameter vector μ. Then we employ this approach and successfull...

We present an algorithm to estimate the configurational entropy S of a polymer. The algorithm uses the statistics of coincidences among random samples of configurations and is related to the catch-tag-release method for estimation of population sizes, and to the classic “birthday paradox”. Bias in the entropy estimation is decreased by grouping configurations in nearly equiprobable partitions b...

Abstract The long-standing problem of Shannon entropy estimation in data streams (assuming the strict Turnstile model) is now an easy task by using the technique proposed in this paper. Essentially speaking, in order to estimate the Shannon entropy with a guaranteed ν-additive accuracy, it suffices to estimate the αth frequency moment, where α = 1−∆, with a guaranteed ǫ-multiplicative accuracy,...

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and...

The mixing property is characterized by the metric entropy that is introduced by Kolmogorov for dynamical systems. The Kolmogorov entropy is infinite for a stochastic system. In this work a relative metric entropy is considered. The relative metric entropy allows to estimate the level of mixing in noisy dynamical systems. An algorithm for calculating the relative metric entropy is described and...

The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such approaches. Both have origins in statistical physics, but the relationship betwee...

We consider a problem in Mathematical Biology that leads to a question in Graph Theory, which can be solved using an old but not widely known upper estimate of the spectral radius of a nonnegative matrix. We provide a new proof of this estimate.

A Maximum Entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that de nes a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as linear combination of frame elements, the coe cients of the expansion are not unique. Frame theory guarant...