The Vaginal Microbiome of Mares on the Post-Foaling Day Under Field Conditions.

The vaginal bacteria are critical for neonatal immunity, as well as for further infections and pathologies in foals and mares during the postpartum period. The vaginal microbiota was examined in six mares. Swabs were taken from the vaginal caudal wall within 12 h after natural delivery.

Parameter estimation of the fractional Ornstein-Uhlenbeck process based on quadratic variation.

Modern experiments routinely produce extensive data of the diffusive dynamics of tracer particles in a large range of systems. Often, the measured diffusion turns out to deviate from the laws of Brownian motion, i.e.

Stochastic representation of processes with resetting.

In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or nonrandom point. Our approach is based on stochastic differential equations called jump-diffusion models.

Lévy walks with rests: Long-time analysis.

In this paper we analyze the asymptotic behavior of Lévy walks with rests. Applying recent results in the field of functional convergence of continuous-time random walks we find the corresponding limiting processes. Depending on the parameters of the model, we show that in the limit we can obtain standard Lévy walk or the process describing competition between subdiffusion and Lévy flights.

Stochastic modeling of Lévy-like human eye movements.

The standard model of visual search dynamics is Brownian motion. However, recent research in cognitive science reveals that standard diffusion processes seem not to be the appropriate models of human looking behavior. In particular, experimental results confirm that the superdiffusive Lévy-type dynamics appears in this context.

Insight into the intestinal microbiome of farrowing sows following the administration of garlic (Allium sativum) extract and probiotic bacteria cultures under farming conditions.

Background: Due to the tendency to reduce antibiotic use in humans and animals, more attention is paid to feed additives as their replacement. Crucial role of feed additives is to improve the health status, production efficiency and performance. In this original research, we estimate the potential influence of garlic (Allium sativum) extract and probiotic formula including Enterococcus faecium, Lactobacillus rhamnosus and Lactobacillus fermentum on the intestinal microbiota of sows, using the next generation sequencing method (NGS).

Nonlinear dynamics of continuous-time random walks in inhomogeneous medium.

Continuous-time random walks (CTRWs) are an elementary model for particle motion subject to randomized waiting times. In this paper, we consider the case where the distribution of waiting times depends on the location of the particle. In particular, we analyze the case where the medium exhibits a bounded trapping region in which the particle is subject to CTRW with power-law waiting times and regular diffusion elsewhere.

Statistical analysis of superstatistical fractional Brownian motion and applications.

Recent advances in experimental techniques for complex systems and the corresponding theoretical findings show that in many cases random parametrization of the diffusion coefficients gives adequate descriptions of the observed fractional dynamics. In this paper we introduce two statistical methods which can be effectively applied to analyze and estimate parameters of superstatistical fractional Brownian motion with random scale parameter. The first method is based on the analysis of the increments of the process, the second one takes advantage of the variation of the trajectories of the process.

Aging ballistic Lévy walks.

Aging can be observed for numerous physical systems. In such systems statistical properties [like probability distribution, mean square displacement (MSD), first-passage time] depend on a time span t_{a} between the initialization and the beginning of observations. In this paper we study aging properties of ballistic Lévy walks and two closely related jump models: wait-first and jump-first.

Explicit densities of multidimensional ballistic Lévy walks.

Lévy walks have proved to be useful models of stochastic dynamics with a number of applications in the modeling of real-life phenomena. In this paper we derive explicit formulas for densities of the two- (2D) and three-dimensional (3D) ballistic Lévy walks, which are most important in applications. It turns out that in the 3D case the densities are given by elementary functions.

Asymptotic behaviour of random walks with correlated temporal structure.

We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions.

Correlated continuous-time random walks in external force fields.

We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T_{i} is equal to the previous waiting time T_{i-1} plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced.

Anomalous diffusion: testing ergodicity breaking in experimental data.

Recent advances in single-molecule experiments show that various complex systems display nonergodic behavior. In this paper, we show how to test ergodicity and ergodicity breaking in experimental data. Exploiting the so-called dynamical functional, we introduce a simple test which allows us to verify ergodic properties of a real-life process.

Kramers' escape problem for fractional Klein-Kramers equation with tempered α-stable waiting times.

In this paper we extend the subdiffusive Klein-Kramers model, in which the waiting times are modeled by the α-stable laws, to the case of waiting times belonging to the class of tempered α-stable distributions. We introduce a generalized version of the Klein-Kramers equation, in which the fractional Riemman-Liouville derivative is replaced with a more general integro-differential operator. This allows a transition from the initial subdiffusive character of motion to the standard diffusion for long times to be modeled.

Generalization of the Khinchin theorem to Lévy flights.

One of the most fundamental theorems in statistical mechanics is the Khinchin ergodic theorem, which links the ergodicity of a physical system with the irreversibility of the corresponding autocorrelation function. However, the Khinchin theorem cannot be successfully applied to processes with infinite second moment, in particular, to the relevant class of Lévy flights. Here, we solve this challenging problem.

Detecting origins of subdiffusion: P-variation test for confined systems.

In this paper, we propose a method to distinguish between mechanisms leading to single molecule subdiffusion in confinement. We show that the method of p-variation, introduced in the recent paper [M. Magdziarz, Phys.

Fractional Fokker-Planck equation with tempered α-stable waiting times: langevin picture and computer simulation.

In this paper we introduce a Langevin-type model of subdiffusion with tempered α-stable waiting times. We consider the case of space-dependent external force fields. The model displays subdiffusive behavior for small times and it converges to standard Gaussian diffusion for large time scales.

Overshooting and undershooting subordination scenario for fractional two-power-law relaxation responses.

In this paper, we propose a transparent subordination approach to anomalous diffusion processes underlying the nonexponential relaxation. We investigate properties of a coupled continuous-time random walk that follows from modeling the occurrence of jumps with compound counting processes. As a result, two different diffusion processes corresponding to over- and undershooting operational times, respectively, have been found.

Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics.

Fractional Brownian motion with Hurst index less then 1/2 and continuous-time random walk with heavy tailed waiting times (and the corresponding fractional Fokker-Planck equation) are two different processes that lead to a subdiffusive behavior widespread in complex systems. We propose a simple test, based on the analysis of the so-called p variations, which allows distinguishing between the two models on the basis of one realization of the unknown process. We apply the test to the data of Golding and Cox [Phys.

Equivalence of the fractional Fokker-Planck and subordinated Langevin equations: the case of a time-dependent force.

A century after the celebrated Langevin paper [C.R. Seances Acad.

Modeling of subdiffusion in space-time-dependent force fields beyond the fractional Fokker-Planck equation.

In this paper we attack the challenging problem of modeling subdiffusion with an arbitrary space-time-dependent driving. Our method is based on a combination of the Langevin-type dynamics with subordination techniques. For the case of a purely time-dependent force, we recover the death of linear response and field-induced dispersion -- two significant physical properties well-known from the studies based on the fractional Fokker-Planck equation.

Numerical approach to the fractional Klein-Kramers equation.

Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation.

First passage times of Lévy flights coexisting with subdiffusion.

We investigate both analytically and numerically the first passage time (FPT) problem in one dimension for anomalous diffusion processes in which Lévy flights and subdiffusion coexist. We analyze the FPT for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index mu, 0 View Article and Find Full Text PDF

Competition between subdiffusion and Lévy flights: a Monte Carlo approach.

In this paper we answer positively a question raised by Metzler and Klafter [Phys. Rep. 339, 1 (2000)]: can one see a competition between subdiffusion and Lévy flights in the framework of the fractional Fokker-Planck dynamics? Our method of Monte Carlo simulations demonstrates the competition on the level of realizations as well as on the level of probability density functions of the anomalous diffusion process.

Fractional Fokker-Planck dynamics: stochastic representation and computer simulation.

A computer algorithm for the visualization of sample paths of anomalous diffusion processes is developed. It is based on the stochastic representation of the fractional Fokker-Planck equation describing anomalous diffusion in a nonconstant potential. Monte Carlo methods employing the introduced algorithm will surely provide tools for studying many relevant statistical characteristics of the fractional Fokker-Planck dynamics.