Traditional measures of diversity, namely the number of species as well as Simpson's and Shannon's indices, are particular cases of Tsallis entropy. Entropy decomposition, i.e. decomposing gamma entropy into alpha and beta components, has been previously derived in the literature. We propose a generalization of the additive decomposition of Shannon entropy applied to Tsallis entropy. We obtain ...

Let T be a precompact subset of a Hilbert space. The metric entropy of the convex hull of T is estimated in terms of the metric entropy of T , when the latter is of order α = 2. The estimate is best possible. Thus, it answers a question left open in [LL] and [CKP]. 0.

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

Abstract. The number of possible activity patterns in a population of neurons grows exponentially with the size of the population. Typical experiments explore only a tiny fraction of the large space of possible activity patterns in the case of populations with more than 10 or 20 neurons. It is thus impossible, in this undersampled regime, to estimate the probabilities with which most of the act...

We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem 1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li–Yau’s gradient estimate. As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also show that the equalit...

Uncertainty theory is a branch of axiomatic mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. In uncertainty theory this paper proposes a definition of quadratic cross entropy and the principle of minimum quadratic cross entropy. Based on the principle, an application in statistics and a numerical algorithm to estimate uncertain dis...

In a reward-free environment, what is suitable intrinsic objective for an agent to pursue so that it can learn optimal task-agnostic exploration policy? this paper, we argue the entropy of state distribution induced by finite-horizon trajectories sensible target. Especially, present novel and practical policy-search algorithm, Maximum Entropy POLicy optimization (MEPOL), policy maximizes non-pa...

The entropic component of the free energy of assembly for multiparticle hydrogen-bonded aggregates is analyzed using a model based on balls connected by rigid rods or flexible strings. The entropy of assembly, ∆S, is partitioned into translational, rotational, vibrational, and conformational components. While previously reported theoretical treatments of rotational and vibrational entropies for...

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial BV bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in L1 of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochas...

Market volatility remains one of the most important research fields in agricultural economics.Interestingly, price transmission mechanism seems to be symmetric in sectors that are likely to be of high political power.This paper analyzes the price transmission effects from international markets to domestic markets for corn in Iran. For this purpose, we estimate the elasticity of substitution bet...