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We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the…
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of…
In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…
We study the one-point probability distribution functions (PDFs) of the peculiar velocity and the density fluctuation in a cosmological fluid. Within the perturbative approach to the structure formation scenario, the effect of ``pressure''…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
The paper considers the propagation of Laguerre-Gaussian beams in a turbulent gas medium. As demonstrated by numerical modelling and the decomposition of Laguerre-Gaussian modes according to the basis of orthogonal Zernike polynomials,…
A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This…
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature…
Feature selection is fundamental to robust data-centric AI, but most existing methods optimize predictive performance under a single data distribution. This often selects spurious features that fail under distribution shifts. Motivated by…
Velocity distributions in a vibrated granular monolayer are investigated experimentally. Non-Gaussian velocity distributions are observed at low vibration amplitudes but cross over smoothly to Gaussian distributions as the amplitude is…
We compute a novel type of large non-Gaussianity due to small periodic features in general single field inflationary models. We show that the non-Bunch-Davies vacuum component generated by features, although has a very small amplitude, can…
Gaussian graphical models (GGMs) are well-established tools for probabilistic exploration of dependence structures using precision matrices. We develop a Bayesian method to incorporate covariate information in this GGMs setup in a nonlinear…
Model equations for describing and efficiently computing the radiation profiles of tightly spherically-focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point…
In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution, formulated on the basis of the single-particle Courant-Snyder (CS) invariants, has served as a fundamental theoretical basis for the analyses of the…
We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We…