Related papers: Tensor decomposition methods for correlated electr…
Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of…
The gravitational waves (GW) from core-collapse supernovae (CCSN) have been proposed as a probe to investigate physical properties inside of the supernova. However, how to search and extract the GW signals from core-collapse supernovae…
Over recent years it has become well accepted that user interest is not static or immutable. There are a variety of contextual factors, such as time of day, the weather or the user's mood, that influence the current interests of the user.…
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…
This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the…
We show that the uniform measure-theoretic ergodic decomposition of a countable Borel equivalence relation $(X, E)$ may be realized as the topological ergodic decomposition of a continuous action of a countable group $\Gamma…
We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial…
We consider the radiative properties of a system of two identical correlated atoms interacting with the electromagnetic field in its vacuum state in the presence of a generic dielectric environment. We suppose that the two emitters are…
This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…
A truncated partial wave analysis for the photoproduction of two pseudoscalar mesons on a nucleon is discussed with respect to the determination of a complete set of observables. For the selection of such a set we have applied a criterion…
A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described…
We present results on the reconstruction of electromagnetic (EM) activity from photons produced in charged current $\nu_{\mu}$ interactions with final state $\pi^0$s. We employ a fully-automated reconstruction chain capable of identifying…
We give efficient algorithms for finding power-sum decomposition of an input polynomial $P(x)= \sum_{i\leq m} p_i(x)^d$ with component $p_i$s. The case of linear $p_i$s is equivalent to the well-studied tensor decomposition problem while…
The long-standing resolution of the Abraham--Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…