Related papers: Variational free complement method with Gaussian c…
A simplified mathematical approach is presented and used to find a suitable free-field Lagrangian to complete previous work on constructing a gauge theory of CPT transformations. The new Lagrangian is a slight but important modification of…
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 Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. The goal of these lecture notes is to describe some aspects of…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
The Gaussian wavefunctional approach is developed in thermofield dynamics. We manufacture thermal vacuum wavefunctional, its creation as well as annihilation operators,and accordingly thermo-particle excited states. For a (D+1)-dimensional…
We apply a formalism recently developed to carry out Generator Coordinate Method calculations using a set of Hartree- Fock- Bogoliubov wave functions, where each of the members of the set can be expanded in an arbitrary basis. In this paper…
We present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, $P$, and conformal Casimir,…
We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
The unitary gauge fixing technique is applied to the QCD hamiltonian formulated in terms of angular variables. It is demonstrated that in this formulation projections on the physical Hilbert space are unnecessary to separate physical and…
Free-particle Green's function plays a central role in the theoretical description of electron scattering and autoionization processes in quantum physics and chemistry. Recently, Gaussian basis set approaches have become increasingly…
We introduce a training-free method for feature field rendering in Gaussian splatting. Our approach back-projects 2D features into pre-trained 3D Gaussians, using a weighted sum based on each Gaussian's influence in the final rendering.…
Accurately simulating the atmospheric turbulence behaviour is always challenging. The well-known FFT based method falls short in correctly predicting both the low and high frequency behaviours. Sub-harmonic compensation aids in…
A general method for focusing of waves, based on phase and amplitude compensation, is applied to monochromatic, polychromatic and diffusive waves. Monochromatic waves may form spatially localized waves in free space, whereas polychromatic…
A method of deriving quadrature rules has been developed which gives nodes and weights for a Gaussian-type rule which integrates functions of the form: f(x,y,t) = a(x,y,t)/((x-t)^2+y^2) + b(x,y,t)/([(x-t)^2+y^2]^{1/2}) +…
The $f(R,T)$ gravity models, for which $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor, elevate the degrees of freedom of the renowned $f(R)$ theories, by making the Einstein field equations of the theory to also…
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…
A fluorescence correlation spectroscopy (FCS) system based on two independent measurement volumes is presented. The optical setup and data acquisition hardware are detailed, as well as a complete protocol to control the location, size and…
A version of the Gaussian self-consistent (GSC) method, which avoids the use of the Edwards' virial expansion, is presented. Instead, the mean energy is evaluated directly via a convolution of the attractive part of the pair-wise non-bonded…
We present an analytical and numerical solution of the calculation of the transition moments for the exact semi-classical light-matter interaction for wavefunctions expanded in a Gaussian basis. By a simple manipulation we show that the…