Non-homogeneous processes and, in particular, base compositional non-stationarity have long been recognized as a critical source of systematic error. But only a small fraction of current molecular systematic studies methodically examine and effectively account for the potentially confounding effect of non-stationarity. The problem is especially overlooked in multi-locus or phylogenomic scale an...

Previous epidemiological studies on SIS model have only considered the dynamic evolution of the mean value and the variance of the infected individuals. In this paper, through cumulant neglection, we use the dynamic equations of all the moments of infected individuals to develop a recursive method to compute the equilibria manifold of the moment closure ODE's. Specifically, we use the stable eq...

Dynamics of brain signals such as electroencephalogram (EEG) can be characterized as a sequence of quasi-stable patterns. Such patterns in the brain signals can be associated with coordinated neural oscillations, which can be modeled by non-linear systems. Further, these patterns can be quantified through dynamical non-stationarity based on detection of qualitative changes in the state of the s...

Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are believed to be stationary. Although stationarity of the underlying process is typically crucial to ensure desirable properties or even validity of statistical estimators, there are numerous time series models for which this stationarity is not yet proven. A major barrier...

In recent years, some investigations have been carried out to examine the assumptions like stationarity, symmetry and separability of spatio-temporal covariance function which would considerably simplify fitting a valid covariance model to the data by parametric and nonparametric methods. In this article, assuming a Gaussian random field, we consider the likelihood ratio separability test, a va...