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Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…

Probability · Mathematics 2019-09-25 Haozhe Shan , Rubén Moreno-Bote , Jan Drugowitsch

An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of…

Soft Condensed Matter · Physics 2016-09-21 I. A. Zaluzhnyy , R. P. Kurta , A. P. Menushenkov , B. I. Ostrovskii , I. A. Vartanyants

A shift-invariant system is a collection of functions $\{g_{m,n}\}$ of the form $g_{m,n}(k) = g_m(k-an)$. Such systems play an important role in time-frequency analysis and digital signal processing. A principal problem is to find a dual…

Numerical Analysis · Mathematics 2025-10-20 Thomas Strohmer

While second and higher order correlations of the light distribution have received extensive study, the lowest order probability distribution function (PDF) -- the probability that a unit volume of space will emit a given amount of light --…

Astrophysics · Physics 2009-11-07 Jeremiah P. Ostriker , Kentaro Nagamine , Renyue Cen , Masataka Fukugita

There has been overwhelming evidence that coherent structures play a critical role in determining the overall transport in a variety of systems. We compute the probability distribution function (PDF) tails of momentum flux and heat flux in…

Plasma Physics · Physics 2009-11-13 Johan Anderson , Eun-jin Kim

We propose a regression model for non-central $\chi$ (NC-$\chi$) distributed functional magnetic resonance imaging (fMRI) and diffusion weighted imaging (DWI) data, with the heteroscedastic Rician regression model as a prominent special…

Applications · Statistics 2016-12-22 Bertil Wegmann , Anders Eklund , Mattias Villani

We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…

Mathematical Physics · Physics 2013-11-13 Gernot Akemann , Jesper R. Ipsen , Mario Kieburg

The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These…

Plasma Physics · Physics 2010-03-12 Johan Anderson , Eun-jin Kim

We analysis the performances for the dual-hop fixed gain amplify-and-forward (AF) relay systems operating over mixed radio-frequency (RF) and free-space optical (FSO) links. The RF link is subject to Rician fading and the FSO link…

Signal Processing · Electrical Eng. & Systems 2017-11-28 Chao Wei , Zaichen Zhang

In this letter we derive the $(n-1)$-dimensional distribution corresponding to a $n$-dimensional i.i.d. Normal standard vector $Z=(Z_1,Z_2,\ldots,Z_n)$ subjected to the weighted sum constraint $\sum_{i=1}^n w_i Z_i=c$, $w_i\neq 0$. We first…

Probability · Mathematics 2018-01-22 Frédéric Vrins

The research presents a procedure of the closed-form average bit error rate evaluation for wireless communication systems in the presence of multipath fading. A generalization of the classical moment generating function is applied, and a…

Information Theory · Computer Science 2022-08-01 Aleksey S. Gvozdarev

This work is devoted to the analysis of a regenerative multi-node dual-hop cooperative system over enriched multipath fading channels. Novel analytic expressions are derived for the symbol-error-rate for $M{-}$ary quadrature modulated…

Information Theory · Computer Science 2016-12-30 Mulugeta K. Fikadu , Paschalis C. Sofotasios , Qimei Cui , Mikko Valkama

Meta-surfaces intend to improve significantly the performance of future wireless networks by controlling the wireless propagation and shaping the radio waves according to the generalized Snell's law. A recent application of meta-surfaces is…

Cahill-Glauber C(s)-correspondence is employed to construct Quasi-Probability Distribution Functions (QPDFs) for optical-polarization in phase space following equivalent description of polarization in Classical Optics. The proposed scheme…

Quantum Physics · Physics 2012-11-05 Ravi S. Singh , Sunil P. Singh , Gyaneshwar K. Gupta

We examine the probability distribution function (pdf) of energy injection rate (power) in numerical simulations of stationary two--dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an…

Statistical Mechanics · Physics 2009-11-13 M. Bandi , C. Connaughton

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…

Signal Processing · Electrical Eng. & Systems 2023-01-20 Günther Koliander , Yousef El-Laham , Petar M. Djurić , Franz Hlawatsch

An opportunistic DF-AF selection relaying scheme with maximal received signal-to-noise ratio (SNR) at the destination is investigated in this paper. The outage probability of the opportunistic DF-AF selection relaying scheme over Nakagami-m…

Information Theory · Computer Science 2016-11-17 Tian Zhang , Wei Chen , Zhigang Cao

The outage probability of maximal-ratio combining (MRC) for a multiple-input multiple-output (MIMO) wireless communications system under Rician fading is given by the cumulative distribution function (CDF) for the largest eigenvalue of a…

Statistics Theory · Mathematics 2018-05-01 Fadil Habibi Danufane , Katsuyoshi Ohara , Nobuki Takayama , Constantin Siriteanu

This paper deals with the secrecy capacity of the radio channel in interference-limited regime. We assume that interferers are uniformly scattered over the network area according to a Point Poisson Process and the channel model consists of…

Information Theory · Computer Science 2015-06-23 Hirley Alves , Carlos H. M. de Lima , Pedro. H. J. Nardelli , Richard Demo Souza , Matti Latva-aho

Complete active space self-consistent field (CASSCF) computations can be realized at polynomial cost via the variational optimization of the active-space two-electron reduced-density matrix (2-RDM). Like conventional approaches to CASSCF,…

Chemical Physics · Physics 2018-12-10 Mohammad Mostafanejad , A. Eugene DePrince