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A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
The gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory.…
Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…
We numerically investigate the influence of self-attraction on the critical behaviour of a polymer in two dimensions, by means of an analysis of finite-size results of transfer-matrix calculations. The transfer matrix is constructed on the…
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
A ``forward walking'' Quantum Monte Carlo (QMC) algorithm has been developed to calculate correlation functions for the Hamiltonian lattice formulation of U(1) Yang-Mills theory in (2+1) dimensions. It is shown that Wilson loops can be…
A Monte Carlo based computer model is presented to comprehend the contrasting observations of Mazumder et al. [Phys. Rev. Lett. 93, 255704 (2004) and Phys. Rev. B 72, 224208 (2005)], based on neutron-scattering measurements, on temporal…
We compare the integration error of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods for approximating the normalizing constant of posterior distributions and certain marginal likelihoods. In doing so, we characterize the dependency of…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…
We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase…
We present novel Monte Carlo methods for treating the interacting shell model that allow exact calculations much larger than those heretofore possible. The two-body interaction is linearized by an auxiliary field; Monte Carlo evaluation of…
We develop new tools for isolating CFTs using the numerical bootstrap. A "cutting surface" algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale…
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of Chemistry, Biology and Atmospheric Science.…
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective…