Stationarity of a data set guarantees spatially invariant statistical properties, such as mean, variance, dip or spectrum. Many image processing schemes assume stationary data and consequently do not apply to nonstationary data. However, these processes can be generalized to apply to local-stationary data sets, a type of nonstationary data. We split the local-stationary data into its stationary...

Coupling is a useful tool in the analysis of the mixing time of Markov chains. The basic idea is that a Markov chain that is initialized to some arbitrary distribution can be compared via coupling with another Markov chain that is initialized to the stationary distribution. The two chains then progress simultaneously, and the distance between the two chains at any time indicates how close the r...

Under-determined blind source separation aims to separate N non-stationary sources from M (M<N) mixtures. Paper presents a time-frequency approach (TF) to under-determined blind source separation of N non-stationary sources from M mixtures(M<N).It is based on Wigner-Ville distribution and Khatri-Rao product. Improved method involves a two step approach which involves the estimation of the mixin...

In this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...

We present an evolving neural network model in which synapses appear and disappear stochastically according to bio-inspired probabilities. These are in general nonlinear functions of the local fields felt by neurons—akin to electrical stimulation—and of the global average field—representing total energy consumption. We find that initial degree distributions then evolve towards stationary states...

Based on quantum hydrodynamics theory (QHD), the propagation of nonlinear quantum dust-ion acoustic (QDIA) solitary waves in a ‎collision-less, unmagnetized four component quantum plasma consisting of electrons, positrons, ions and stationary negatively charged ‎dust grains with dust charge variation is investigated using reductive perturbation method. The charging current to the dust grains ca...

Consider a density-dependent birth-death process X N on a finite state space of size N . Let PN be the law (on D.[0; T ]/ where T > 0 is arbitrary) of the density process XN =N and let 5N be the unique stationary distribution (on [0,1]) of X N =N , if it exists. Typically, these distributions converge weakly to a degenerate distribution as N ! 1, so the probability of sets not containing the de...

Suppose a certain variable Xt is measured at discrete equally spaced time points t = 1, ... , T and we want to make assertions on the energy distribution of the frequencies in a harmonic analysis. This energy distribution may for example be used to code the data if Xt is a speech signal or to make a prediction if the Xt are economic data. Instead of using a deterministic approach applied scient...

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic process. A standard way to compute this distribution for a random walk on a finite set of states is to compute the Perron vector of the associated transition ...