Related papers: SHarmonic: A fast and accurate implementation of s…
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…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and…
Spherical Harmonic Transforms (SHT) are at the heart of many scientific and practical applications ranging from climate modelling to cosmological observations. In many of these areas new, cutting-edge science goals have been recently…
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…
SPARC is an accurate, efficient, and scalable real-space electronic structure code for performing ab initio Kohn-Sham density functional theory calculations. Version 2.0.0 of the software provides increased efficiency, and includes…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
Development of quantum architectures during the last decade has inspired hybrid classical-quantum algorithms in physics and quantum chemistry that promise simulations of fermionic systems beyond the capability of modern classical computers,…
This study proposes an approach toward the first principles electronic structure calculation with the aid of symbolic-numeric solving. The symbolic computation enables us to express the Hartree-Fock-Roothaan equation and the molecular…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
We consider the problem of distributedly computing a general class of functions, referred to as gradient-type computation, while maintaining the privacy of the input dataset. Gradient-type computation evaluates the sum of some `partial…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
Efficient methods are proposed, for computing integrals appeaing in electronic structure calculations. The methods consist of two parts: the first part is to represent the integrals as contour integrals and the second one is to evaluate the…
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
By the collective name of {\it lattice counting} we refer to a setup introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between arithmetic and randomness in the context of affine symmetric spaces. In this paper we extend…
This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a…