Related papers: A general method for rotational averages
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
Unlike with the energy, which is a scalar property, machine learning (ML) predictions of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. If the…
We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic…
The paper analyzes the rotation averaging problem as a minimization problem for a potential function of the corresponding gradient system. This dynamical system is one generalization of the famous Kuramoto model on special orthogonal group…
Tensorial curvature measures are tensor-valued generalizations of the curvature measures of convex bodies. We prove a complete set of kinematic formulae for such tensorial curvature measures on convex bodies and for their (nonsmooth)…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
The spectral decomposition of a symmetric, second-order tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a…
The aim of this article is a comprehensive description of normal modes of molecular vibrations. The starting point is chosen to be a general molecular system with separated center of mass and an arbitrary embedding of body-fixed axes. This…
In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly…
We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
The purpose of this article is to discuss the circle method and its quantitative role in understanding pointwise almost everywhere convergence phenomena for polynomial ergodic averaging operators. Specifically, we will use the circle method…
A brief review of the search for variation of the fine structure constant in quasar absorption spectra is presented. Special consideration is given to the role of atomic calculations in the analysis of the observed data. A range of methods…
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor…
Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…