Related papers: Recursive Harmonic Analysis for Computational of H…
We introduce $Recursive~Jigsaw~Reconstruction$, a technique for analyzing reconstructed particle interactions in the presence of kinematic and combinatoric unknowns associated with unmeasured and indistinguishable particles, respectively.…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
We propose an algorithm for evaluation of the cumulative bivariate normal distribution, building upon Marsaglia's ideas for evaluation of the cumulative univariate normal distribution. The algorithm is mathematically transparent, delivers…
This paper presents a method for the accurate and efficient computations on scalar, vector and tensor fields in three-dimensional spherical polar coordinates. The methods uses spin-weighted spherical harmonics in the angular directions and…
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
We demonstrate a simple method to improve the Lewenstein model for the description of high-order harmonic generation (HHG). It is shown that HHG spectra can be expressed as the product of a returning electron wave packet and the…
In this paper, we propose a recursive method for finding Costas arrays that relies on a particular formation of Costas arrays from similar patterns of smaller size. By using such an idea, the proposed algorithm is able to dramatically…
An aggregated recursive K-index is proposed as a new scientometric indicator of added value and scientific research output of individual publications. This index can be used instead of or in addition to the H-index (J.E. Hirsch. An index to…
We present a new Fortran library to evaluate all harmonic polylogarithms up to weight four numerically for any complex argument. The algorithm is based on a reduction of harmonic polylogarithms up to weight four to a minimal set of basis…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
We demonstrate a conditional autoregressive pipeline for efficient music recomposition, based on methods presented in van den Oord et al.(2017). Recomposition (Casal & Casey, 2010) focuses on reworking existing musical pieces, adhering to…
In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…
We demonstrate numerical refocusing in coherent confocal laser scanning microscopy based on synthetic optical holography. This physics-based approach implements a computational propagation on the complex signal recovered in synthetic…
In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…
A method for the analytical evaluation of layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for piecewise flat boundary elements with polynomial shape functions. The…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
A numerical explicit method to evaluates transient solutions of linear partial differential non-homogeneous equation with constant coefficients is proposed.