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We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…
The fuzzy linear regression (FLR) modeling was first proposed making use of linear programming and then followed by many improvements in a variety of ways. In almost all approaches changing the meters, objective function, and restrictions…
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl-von K\'arm\'an…
In this article we study the trapped motion of a molecule undergoing diffusivity fluctuations inside a harmonic potential. For the same diffusing-diffusivity process, we investigate two possible interpretations. Depending on whether…
In this paper, we provide a global framework analysis of a dual-hop mixed Radio Frequency (RF)/Free Space Optical (FSO) system with multiple branches/relays wherein the first and second hops, respectively, consist of RF and FSO channels. To…
There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this…
Subcritical transition of an inhomogeneous plasma where turbulences with different characteristic space-time scales coexist is analyzed with methods of statistical physics of turbulences. We derived the development equations of the…
We have discovered analytical expressions for the probability density function (PDF) of photons that are multiply scattered in relativistic flows, under the assumption of isotropic and inelastic scattering. These expressions characterize…
In this paper, we derive a generalized second fluctuation-dissipation theorem (FDT) for stochastic dynamical systems in the steady state. The established theory is built upon the Mori-type generalized Langevin equation for stochastic…
A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…
This paper proposes a unified framework for the effective rate analysis over arbitrary correlated and not necessarily identical multiple inputs single output (MISO) fading channels, which uses moment generating function (MGF) based approach…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
This paper considers the distribution of the mutual information of frequency-selective spatially-uncorrelated Rayleigh fading MIMO channels. Results are presented for OFDM-based spatial multiplexing. New exact closed-form expressions are…
Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In…
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation…
The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a \emph{minimal} ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the Fluctuation…
In previous papers of this series, we presented a formalism able to account for both statistical equilibrium of a multilevel atom and coherent and incoherent scatterings (partial redistribution). aims: This paper provides theoretical…
In this paper, a generalized Brownian motion model has been applied to describe the relative particle dispersion problem in more realistic turbulent flows. The fluctuating pressure forces acting on a fluid particle are taken to be a colored…