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A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields…
This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the…
This paper introduces a noise-tolerant computing method for over-the-air computation (AirComp) aimed at weighted averaging, which is critical in various Internet of Things (IoT) applications such as environmental monitoring. Traditional…
We introduce a class of algorithms for constructing Fourier representations of Gaussian processes in $1$ dimension that are valid over ranges of hyperparameter values. The scaling and frequencies of the Fourier basis functions are evaluated…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
We propose a reconstruction of vortex beams based on the implementation of quadratic transformations in the orbital angular momentum. The information is encoded in a superposition of Bessel-like nondiffracting beams. The measurement of the…
The radiation transfer equation is widely used for simulating such as heat transfer in engineering, diffuse optical tomography in healthcare, and radiation hydrodynamics in astrophysics. By combining the lattice Boltzmann method, we propose…
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…
A solution of the radiative-transfer problem in arbitrary velocity fields introduced in a previous paper, has limitations in its applicability. For large-scale applications, the methods described also require large memory sets that are…
A fast and accurate algorithm for the computation of Gauss-Hermite and generalized Gauss-Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's method with carefully selected initial guesses for the nodes and…
We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…
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…
We extend Gaussian perturbation models in classical functional data analysis to the three-dimensional rotational group where a zero-mean Gaussian process in the Lie algebra under the Lie exponential spreads multiplicatively around a central…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
One of the key challenges in the area of signal processing on graphs is to design transforms and dictionaries methods to identify and exploit structure in signals on weighted graphs. In this paper, we first generalize graph Fourier…
Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…
Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the…
We study the efficiency of quantum algorithms which aim at obtaining phase space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions,…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
We present the first extension of the special-relativistic Lattice-Boltzmann Method for radiative transport developed by Weih et al. (2020), to solve the radiative-transfer equation in curved spacetimes. The novel approach is based on the…