Related papers: A critical assessment of the current implementatio…
Gaussian mixture models (GMMs) are fundamental tools in statistical and data sciences. We study the moments of multivariate Gaussians and GMMs. The $d$-th moment of an $n$-dimensional random variable is a symmetric $d$-way tensor of size…
The generator coordinate method of a microscopic cluster model is developed to treat the resonance and scattering of nuclear clusters with complex scaling. We consistently derive the formulation of the complex scaling for the microscopic…
Nuclear collisions at high energies produce a gluon field that can be described using the Colour Glass Condensate (CGC) effective theory at proper times $\tau \lesssim 1$ fm/c. The theory can be used to calculate the gluon energy-momentum…
The GW method is a many-body electronic structure technique capable of generating accurate quasiparticle properties for realistic systems spanning physics, chemistry, and materials science. Despite its power, GW is not routinely applied to…
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature,…
The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to…
We investigate properties of the Generator Coordinate Method (GCM) on a collective basis of Antisymmetrized Quasi-Cluster (AQC) states to describe the cluster-shell competition in $^{20}$Ne and $^{24}$Mg due to the spin-orbit interaction.…
We propose a new variational method for describing nuclear matter from nucleon-nucleon interaction. We use the unitary correlation operator method (UCOM) for central correlation to treat the short-range repulsion and further include the…
Quantum geometrodynamics (QGD) in extended phase space essentially distinguished from the Wheeler - DeWitt QGD is proposed. The grounds for constructing a new version of quantum geometrodynamics are briefly discussed. The main part in the…
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…
This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator…
We apply the optimized-basis generator coordinate method (OptGCM) to sd-shell nuclei, $^{20}$Ne, $^{24}$Mg, and $^{28}$Si. This method variationally optimizes both the basis Slater determinants in the generator coordinate method (GCM) and…
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…
Wave--current interaction (WCI) dynamics energizes and mixes the ocean thermocline by producing a combination of Langmuir circulation, internal waves and turbulent shear flows, which interact over a wide range of time scales. Two…
The improved quantum scheduling algorithm proposed by Grover has been generalized using the generalized quantum search algorithm, in which a unitary operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations replace the…
Perturbative and non-perturbative expansion methods already constitute a tool of choice to perform ab initio calculations over a significant part of the nuclear chart. In this context, the categories of accessible nuclei directly reflect…
An improved version of the Cascade-Exciton Model (CEM) of nuclear reactions contained in the code CEM2k and the Los Alamos version of the Quark-Gluon String Model (LAQGSM) are merged with the well-known sequential-binary-decay model GEMINI…
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically…
Identification of the causal relationship between multivariate time series is a ubiquitous problem in data science. Granger causality measure (GCM) and conditional Granger causality measure (cGCM) are widely used statistical methods for…
Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are…