We consider the symmetric exclusion process on $d$-dimensional lattice with translational invariant and ergodic initial data. It is then known that as $t$ diverges distribution of at time converges to a Bernoulli product measure. Assuming summable decay correlations data, we prove quantitative version this convergence by obtaining an explicit bound Ornstein $\bar d$-distance. The proof based an...

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative relationship from conservation of energy, assuming that system be non-ergodic at large length scales and relying on averaging in both space time homogenize behavior. Explicit criteria are obtained define stationary conditions: (1) there can no net change for exten...

Understanding the seizure initiation process and its propagation pattern(s) is a critical task in epilepsy research. Characteristics of the pre-seizure electroencephalograms (EEGs) such as oscillating powers and high-frequency activities are believed to be indicative of the seizure onset and spread patterns. In this article, we analyze epileptic EEG time series using nonparametric spectral esti...