PURPOSE The Monte Carlo method is an accurate model for time-resolved quantitative fluorescence tomography. However, this method suffers from low computational efficiency due to the large number of photons required for reliable statistics. This paper presents a comparison study on the computational efficiency of three Monte Carlo-based methods for time-domain fluorescence molecular tomography. ...

Path integral Monte Carlo with Green’s function analysis allows the sampling of quantum mechanical properties of molecules at finite temperature. While a high-precision computation of the energy of the Born-Oppenheimer surface from path integral Monte Carlo is quite costly, we can extract many properties without explicitly calculating the electronic energies. We demonstrate how physically relev...

A new method is proposed for Monte Carlo integration. This method is more efficient with wider coverage, including improper integrals, while the classical Monte Carlo integration can only handle bounded domain integrals. To implement this method in computer programming, you only need a random number generator. Unlike the deterministic numerical integration methods, the expected error of this me...

In this article we describe Monte Carlo methods for computing two intimately related quantities, the capacitance of a conducting body the diffusion-limited reaction rate. Both quantities can be represented as integral functionals of the solution to an integral equation on the surface of an object. The Monte Carlo methods we describe are derived by using “random walk on the boundary” Markov chai...

Path integral Monte Carlo (PIMC) simulations have become an important tool for the investigation of the statistical mechanics of quantum systems. I discuss some of the history of applying the Monte Carlo method to non-relativistic quantum systems in path-integral representation. The principle feasibility of the method was well established by the early eighties, a number of algorithmic improveme...

A generative model’s partition function is typically expressed as an intractable multi-dimensional integral, whose approximation presents a challenge to numerical and Monte Carlo integration. In this work, we propose a new estimation method for intractable partition functions, based on distilling an intractable generative model into a tractable approximation thereof, and using the latter for pr...

A newly developed method for systematically improving the convergence of path integrals for transition amplitudes, introduced in Phys. is here applied to the efficient calculation of energy spectra. We show how the derived hierarchies of effective actions lead to substantial speedup of the standard path integral Monte Carlo evaluation of energy levels. The general results and the ensuing increa...