The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from n log n to n, if the entropy of the...

Consider the linear regression model y = X + u in the usual notation. In many applications the design matrix X is frequently subject to severe multicollinearity. In this paper an alternative estimation methodology, maximum entropy is given and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We described the generalized maximum entropy (GME) ...

We demonstrate an efficient formula to compute the entropy rate H(μ) of a hidden Markov process with q output symbols where at least one symbol is unambiguously received. Using an approximation to H(μ) to the first N terms we give a O(Nq) algorithm to compute the entropy rate of the hidden Markov model. We use the algorithm to estimate the entropy rate when the parameters of the hidden Markov m...

Hyperbolic systems of conservation laws augumented with an entropy inequality are studied. It is shown that such systems can be written in a (quasilinear) skewselfndjoint form. Centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered. Employing the above formulation...

In the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel. Under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed (i.i.d.) random variables plus a perturbation which is asymptotic...

Our XMM-Newton observations of Abell 85 confirm the extended 4 Mpc filament first detected with ROSAT, which has an X-ray temperature of about ∼ 2 keV and is probably made of groups falling on to the cluster. A comparison of the temperature map with numerical simulations show that Abell 85 had intense merging activity in the past and is not fully relaxed, even in the central region. Finally, a ...

We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) b...

Data on 'neural coding' have frequently been analyzed using information-theoretic measures. These formulations involve the fundamental and generally difficult statistical problem of estimating entropy. We review briefly several methods that have been advanced to estimate entropy and highlight a method, the coverage-adjusted entropy estimator (CAE), due to Chao and Shen that appeared recently in...

The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We...