相关论文: Highly asymmetric electrolytes in the primitive mo…

The correlation entropy as a functional of radial distribution function $g(r)$ (or the total correlation function $h(r)=g(r)-1$) in classical fluids has been obtained from the second Legendre transform of the grand potential. We focus on…

Edge computing is highly demanded to achieve their full potentials Internet of Things (IoT), since various IoT systems have been generating big data facilitating modern latency-sensitive applications. As a basic problem, network dismantling…

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…

Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space…

We present a nonlinear (in the sense of McKean) generalization of Hamiltonian Monte Carlo (HMC) termed nonlinear HMC (nHMC) capable of sampling from nonlinear probability measures of mean-field type. When the underlying confinement…

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…

Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different…

Solutions of interacting linear polymers are mapped onto a system of ``soft'' spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only…

This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differential equations, specifically linear advection-reaction…

Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were…

Osmotic coefficients, individual and mean activity coefficients of primitive model electrolyte solutions are computed at different molar concentrations using the symmetric Poisson-Boltzmann and modified Poisson-Boltzmann theories. The…

We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…

We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which…

Correlated {\em ab initio} electronic structure calculations are reported for the polymers lithium hydride chain $[LiH]_{\infty}$ and beryllium hydride $[Be_{2}H_{4}]_{\infty}$. First, employing a Wannier-function-based approach, the…

The nonrelativistic many-electron system in the forward, exchange and BCS approximation is considered. In this approximation, which is still quartic in the annihilation and creation operators, the model is explicitly solvable for arbitrary…

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…

This paper investigates the self-similar solutions of the Einstein-axion-dilaton configuration from type IIB string theory and the global SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the scale transformation is…

We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair interaction forms comprising a hard core and a combination of…

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic…

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how…