Related papers: Explicitly correlated Gaussians with tensor pre-fa…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…
Drachmann's regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems. Earlier applications of drachmannized relativistic corrections for molecular systems were hindered due to the…
We study the properties of a non-Gaussian density matrix for a O(N) scalar field in the context of the incomplete description picture. This is of relevance for studies of decoherence and entropy production in quantum field theory. In…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
We point out that confusion sometimes arises when using a chemical potential in plasma with Coulomb interactions. The results of our consideration are applied to the discussion of nuclear reactions screening. Finally, we present a…
We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
This study deals with the missing link prediction problem: the problem of predicting the existence of missing connections between entities of interest. We address link prediction using coupled analysis of relational datasets represented as…
A covariant formalism is used in order to examine the status of Maxwell equations and to unify the concept of balances, for all chemical engineering applications in relation with electrodynamics. The resulting formal structure serves as a…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
We propose a principled way to define Gaussian process priors on various sets of unweighted graphs: directed or undirected, with or without loops. We endow each of these sets with a geometric structure, inducing the notions of closeness and…
Exploiting final-state interactions and/or identity interference, analysis of anisotropic correlations of particles at low-relative velocities yields information on the anisotropy of emission sources in heavy-ion reactions. We show that the…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions…
This work presents a detailed covariance and correlation matrix analysis for experimentally measured cross sections obtained using the activation technique. Both statistical and systematic contributions to the covariance matrix were…
Given an orthonormal basis in a $d$-dimensional Hilbert space and a unital quantum operation $\cal E$ acting on it one can define a non-linear mapping that associates to $\cal E$ a $d\times d$ real-valued matrix that we call the Coherence…
The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional…
The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…