For an irreducible symmetric Markov process on a, not necessarily compact, state space associated with a symmetric Dirichlet form, we give Poincaré type inequalities. As an application of the inequalities, we consider a time inhomogeneous diffusion process obtained by a time dependent drift transformation from a diffusion process and give general conditions for the transience or recurrence of s...

the release of fe from soil solid phases into soil solution is a dynamic process that regulates the continuous supply of this element to growing plants. to ascertain the pattern of fe release, the kinetics of fe release from six soils by diethylenetriaminepentaacetic acid (dtpa) solution were investigated using soil samples taken from two different agroclimatic regions of iran. all soils were c...

There has been recent work [Louis STOC 2015] to analyze the spectral properties of hypergraphs with respect to edge expansion. In particular, a diffusion process is defined on a hypergraph such that within each hyperedge, measure flows from nodes having maximum weighted measure to those having minimum. The diffusion process determines a Laplacian, whose spectral properties are related to the ed...

Ionic transport in conventional ionic solids is generally considered to proceed via independent diffusion events or "hops." This assumption leads to well-known Arrhenius expressions for transport coefficients, and is equivalent to assuming diffusion is a Poisson process. Using molecular dynamics simulations of the low-temperature B1, B3, and B4 AgI polymorphs, we have compared rates of ion hopp...

It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the innitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the innitesimal cov...

The main reason to study random diffusions is that this class of processes combines two key features of modern probability theory. On the one hand they are semi-martingales so the whole Itô theory of stochastic integration applies, but on the other hand they are also strong Markov processes. The combination of techniques from those two worlds enables us to have an in-depth look at their behavio...

A diffusion process model of the frequency of a mutation • Reversibility of a 1-dimensional diffusion process • Frequency spectrum and age of a mutation General binary coalescent trees • Combinatorial derivation of the age of a mutation • Ewens' sampling formula, a combinatorial derivation • Coalescent lineage distributions Gene trees and Coalescent trees • DNA sequences and the infinitely-many...

Modeling the diffusion of information on social media has mainly been treated as a diffusion process on known graphs, and under closed world assumptions. We introduce here a new approach to this problem whose principle is to learn a mapping of the observed interacting users onto a latent representation space in such a way that information diffusion can be modeled efficiently using a heat diffus...

The reaction of fly ash with a KOH solution was used to synthesize Linde F(K) zeolite, following which Fourier transform infrared spectroscopy were used to characterize the crystalline material. The competitive adsorption of Cu, Ni, Pb, and Cd onto this zeolite was subsequently studied in quaternary solution systems. The results show that the metal removal rates gradually increase with incr...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...