Related papers: A Gauss Elimination Method for Resonances
For a theoretical understanding of the reactivity of complex chemical systems, relative energies of stationary points on potential energy hypersurfaces need to be calculated to high accuracy. Due to the large number of intermediates present…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.
These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a…
Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
We introduce a new analysis method to deal with stationary non-Gaussian noises in gravitational wave detectors in terms of the independent component analysis. First, we consider the simplest case where the detector outputs are linear…
The semiclassical backreaction equations are solved in closed Robertson-Walker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stress-energy tensor results in…
We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…