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...

Time-changed Lévy processes include the fractional Poisson process, and the scaling limit of a continuous time random walk. They are obtained by replacing the deterministic time variable by a positive non-decreasing random process. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as the correlation function. This paper provides the...

Objective There is a growing interest in the customers’ innovation in the realm of tourism studies. In the new global business ecosystem where individuals, organizations, governments and economy work together as an integrated network, we need a new innovation model. The model should be set at a level in which internal, external, cooperative and co-creative ideas can converge to create organiza...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

this study aimed at investigating the effect of learners’ gender on their preferences for corrective feedback. learners’ prefer- ences which were investigated included the necessity, frequency, timing, type, method, and delivering agent of error treatment. to this end, a questionnaire was administered to a random sample of 100 participants (50 males and 50 females) studying english (efl) at shi...

The stability properties of the bandwidth allocation algorithm first fit are analyzed for the distributions concentrated on three sizes for the requests. We give the explicit expression of the ergodicity condition of this model; it involves a quadratic functional of the input parameters. The stochastic processes describing these systems are string valued Markov processes. The notion of a smooth...

We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length k is a constant, depending only on k and the alphabet size `. We give a recurrence that allows us to determine these constants with any required precision. This also allows us to evaluate the expected pe...

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order and this order is at most 4, we prove that ...

We consider the sensitivity of real zeros structured polynomial systems to pertubations their coefficients. In particular, we provide explicit estimates for condition numbers random and extend these smoothed analysis setting.

The Nisan-Wigderson pseudo-random generator [NW94] was constructed to derandomize probabilistic algorithms under the assumption that there exist explicit functions which are hard for small circuits. We give the first explicit construction of a pseudo-random generator with asymptotically optimal seed length even when given a function which is hard for relatively small circuits. Generators with o...