Algorithms for estimating the integral over hyper-rectangular regions are discussed. Solving this problem in high dimensions is usually considered a domain of Monte Carlo and quasi-Monte Carlo methods, because their power degrades little with increasing dimension. These algorithms are compared to integration routines based on interpolatory cubature rules, which are usually only used in low dime...

We present an efficient new Monte Carlo method which couples path integrals for finite temperature protons with quantum Monte Carlo calculations for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher...

We present an iterative Monte Carlo path integral methodology for evaluating thermally averaged real-time correlation functions. Standard path integral Monte Carlo methods are used to sample paths along the imaginary time contour. Propagation of the density matrix is performed iteratively on a grid composed of the end points of the sampled paths. Minimally oscillatory propagators are constructe...

The Monte Carlo method is an important numerical simulation tool in many applied fields such as economics, finance, statistical physics, and optimization. One of the most useful aspects of this method is in numerical integration of higher dimensions. For integrals of higher dimensions, the common numerical methods such as Simpson’s method, fail because the total number of grid points needed to ...

Convolutional neural networks (CNNs) have recently achieved remarkable performance in positron emission tomography (PET) image reconstruction. In particular, CNN-based direct PET reconstruction, which directly generates the reconstructed from sinogram, has potential applicability to enhancements because it does not require reconstruction algorithms, often produce some artifacts. However, these ...

background: palladium-103 (103pd) is a brachytherapy source for cancer treatment. the monte carlo codes are usually applied for dose distribution and effect of shieldings. monte carlo calculation of dose distribution in water phantom due to a med3633 103pd source is presented in this work. materials and methods: the dose distribution around the 103pd model med3633 located in the center of 30×30...

Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations...