Related papers: Filtering a distribution simultaneously in real an…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from…
This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an…
Recent research has shown a weak convergence - convergence in distribution - of particle filtering methods under certain assumptions. However, some applications of particle filtering methods, such as radiation source localization problems,…
Consider the problem when $X_1,X_2,..., X_n$ are distributed on a circle following an unknown distribution $F$ on $S^1$. In this article we have consider the absolute general set-up where the density can have local features such as…
This paper examines filtering on a sphere, by first examining the roles of spherical harmonic magnitude and phase. We show that phase is more important than magnitude in determining the structure of a spherical function. We examine the…
Handling the massive number of devices needed in numerous applications such as smart cities is a major challenge given the scarcity of spectrum resources. Dynamic spectrum access (DSA) is seen as a potential candidate to support the…
The creation of optimal samplers can be a challenging task, especially in the presence of constraints on the support of parameters. One way of mitigating the severity of this challenge is to work with transformed variables, where the…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…
A rectangular enclosure has such an even distribution of resonances that it can be accurately and efficiently modelled using a feedback delay network. Conversely, a non rectangular shape such as a sphere has a distribution of resonances…
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
We study the Brownian motion of a particle in a bounded circular 2-dimensional domain, in search for a stationary target on the boundary of the domain. The process switches between two modes: one where it performs a two-dimensional…
The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…
This paper proposes a theoretical framework for modeling and optimizing the bounded functions based on the Fourier series approximation and Ricci flow. Specifically, the initial manifold, $\mathcal{M}_0$ is approximated using Fourier series…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
Sliced optimal transport reduces optimal transport on multi-dimensional domains to transport on the line. More precisely, sliced optimal transport is the concatenation of the well-known Radon transform and the cumulative density transform,…