Related papers: Free complement method with Gaussian expanded comp…
The complement functions in the free complement (FC) method are constructed by decontracting the Gaussian expansions of the Slater functions formed by the initial wavefunction and the $g$ functions. The helium ground state is used to…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We present a spectrally accurate, efficient FFT-based method for the three-dimensional free-space Poisson equation with smooth, compactly supported sources. The method adopts a super-potential formulation: we first compute the convolution…
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…
Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure…
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling…
We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…
In the analysis of High-Energy Physics data, it is frequently desired to separate resonant signals from a smooth, non-resonant background. This paper introduces a new technique - functional decomposition (FD) - to accomplish this task. It…
In this work, we extend the x-ray constrained wavefunction fitting approach, a key method in quantum crystallography for charge density reconstruction, to incorporate experimental observables beyond x-ray diffraction. Unlike traditional…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
This paper develops an enhanced finite element method for approximating a class of variational problems which exhibit the \textit{Lavrentiev gap phenomenon} in the sense that the minimum values of the energy functional have a nontrivial gap…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
The explicit solution of the discrete time filtering problems with exponential criteria for a general Gaussian signal is obtained through an approach based on a conditional Cameron-Martin type formula. This key formula is derived for…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…
The Gaussian free field (GFF) is considered in the background of random iso-height islands which is modeled by the site percolation with the occupation probability $p$. To realize GFF, we consider the Poisson equation in the presence of…
The feedback particle filter (FPF), a resampling-free algorithm proposed over a decade ago, modifies the particle filter (PF) by incorporating a feedback structure. Each particle in FPF is regulated via a feedback gain function (lacking a…
The feedback particle filter (FPF) is an innovative, control-oriented and resampling-free adaptation of the traditional particle filter (PF). In the FPF, individual particles are regulated via a feedback gain, and the corresponding gain…
In this work we present an extension of the popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework. Although we used in this work the recently introduced one-parameter correlation factor [E. Giner,…
Confounder selection, namely choosing a set of covariates to control for confounding between a treatment and an outcome, is arguably the most important step in the design of an observational study. Previous methods, such as Pearl's…