This study was prompted by investigations of models of traffic flow on a highway through analyses of the structure and properties of Poisson fields of random lines in a plane. It is possible to view the trajectory of a car produced by its time and space coordinates on the highway as a straight line in that plane if the car travels at a constant speed once it enters the highway and then never le...

Spring 2003 Le ture 7: Criti al behavior of the Erd} os-Renyi model Le turer: David Aldous S ribe: Andrej Bogdanov In this le ture we investigate the size of the giant omponent in the Erd} os-Renyi random graph model with edge probability p 1=n. In this model, the presen e of ea h edge in the graph is de ided by an independent oin ip with su ess probability p. We show that for p slightly bigger...

It is shown that the interactive error correction protocol ‘CASCADE’ should be analyzed taking the correlation between passes and finite length of sequence into account. Furthermore we mention some problems in quantifying the reduction of Renyi entropy by information announced during the error correction process.

Renyi entropies of a black hole are evaluated by counting the states of the Hawking radiation which fills a thin shell surrounding the horizon. The width of the shell is determined from its energy content and the corresponding mass defect. The Bekenstein-Hawking formula for the entropy of the black hole is correctly reproduced.

A universal approximation for the Renyi entropies of equilibrated pure states is presented, helping to understand how process thermalization consistent with unitarity in quantum chaotic systems and models evaporating black holes.

Entropy models have been recently adopted in many studies to evaluate the shear stress distribution open-channel flows. Although uncertainty of Shannon and Tsallis entropy were analyzed separately previous studies, other comparisons their reliability remain an open question. In this study, a new method is presented four models, Shannon, Shannon-Power Law (PL), Tsallis, Renyi, prediction circula...

We consider nonparametric estimation of L2, Rényi-α and Tsallis-α divergences between continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We show that these estimators achieve t...

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution ...

The main purpose of this note is to present a new approach to Poisson Approximations. Some bounds in Poisson Approximations in term of classical Le Cam’s inequalities for various row-wise triangular arrays of independent Poisson-binomial distributed random variables are established via probability distances based on Trotter-Renyi operators. Some analogous results related to random sums in Poiss...