an important need in radiation therapy is a fast and accurate treatment planning system. this system using ct data and characteristics of the radiation beam, calculates the dose in all points of the patient’s volume. two main factors in planning system are “accuracy” and “speed”. according to these factors, various generation of treatment planning systems are developed.   this article is the re...

We study equal weight numerical integration, or Quasi Monte Carlo (QMC) rules, for functions in a Sobolev space Hs(Sd) with smoothness parameter s > d/2 defined over the unit sphere Sd in Rd+1. Focusing on N-point configurations that achieve optimal order QMC error bounds (as is the case for efficient spherical designs), we are led to introduce the concept of QMC designs: these are sequences of...

Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on each processor can potentially ruin the adaptive behaviour. Using the popular VEGAS-Algorithm as an example an economic method of semi-micro parallelization w...

We performed Bayesian model comparison on mass spectra from CH 4 rf process plasmas to detect radicals produced in the plasma. The key ingredient for its implementation is the highdimensional evidence integral. We apply Gauss approximation to evaluate the evidence. The results were compared with those calculated by the thermodynamic integration method using Markov Chain Monte Carlo technique. I...

We develop multivariate extensions to two variance reduction techniques { nonlinear control variates for estimating expected values, and concomitants of order statistics for estimating a distribution (including expected values, probabilities, and percentiles). We allow the relationship between Y and the X variables to be nonlinear, and consider two cases { where the relationship is additive, an...

Learning a function of many arguments is viewed from the perspective of high– dimensional numerical quadrature. It is shown that many of the popular ensemble learning procedures can be cast in this framework. In particular randomized methods, including bagging and random forests, are seen to correspond to random Monte Carlo integration methods each based on particular importance sampling strate...

In this review paper, we outline the principles of Monte Carlo simulation of fluid mixtures, with emphasis on methods for calculation of free energies and phase equilibria. We begin with a brief introduction to common intermolecular potential models. We discuss density-dependent potentials that can accurately represent properties over a wide range of densities. A number of Monte Carlo technique...

Recently quasi-Monte Carlo algorithms have been successfully used for multivariate integration of high dimension d, and were signiicantly more eecient than Monte Carlo algorithms. The existing theory of the worst case error bounds of quasi-Monte Carlo algorithms does not explain this phenomenon. This paper presents a partial answer to why quasi-Monte Carlo algorithms can work well for arbitrari...

Formulation is given for the Gibbs-Duhem integration (GDI) method in the semigrand canonical (SGC) ensemble, in which the total number of particles N is fixed with the specified chemical potential differences between species ∆μ i (≡μ i -∆μ1;i =2,3,...). Demonstration of the SGC Monte Carlo simulation with the GDI technique is given for a pseudo-binary semiconductor alloy, In x Ga 1-x N.

We analyze the error introduced by approximately calculating the s-dimensional Lebesgue measure of a Jordan-measurable subset of Is = [0, 1)s. We give an upper bound for the error of a method using a (t,m, s)-net, which is a set with a very regular distribution behavior. When the subset of Is is defined by some function of bounded variation on Īs−1, the error is estimated by means of the variat...