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The object-oriented middleware standard, CORBA, is a very useful platform for distributed computing, and in particular for sharing a workload among a collection of possibly polymorphic computers. CORBA has, however, received relatively little attention from the scientific computing community. In this article we demonstrate how CORBA and Java can be used to implement a distributed multi-dimensional Monte Carlo integration algorithm which runs on the internet.

Monte Carlo estimates of virial coefficients up to the sixth for the Hard Gaussian Overlap (HGO) model are presented for values of the aspect ratio parameter κ of the model ranging from 0.05 to 10. The sixth coefficients are new and the lower coefficients are improvements on previous numerical estimates. The second virials are found to be in excellent agreement with an analytical integration reported in the literature. Padé (3, 3) approximations to the pressure and residual Helmholtz energy were constructed. Attempts to represent coefficients in these approximations by analytical functions of κ were not successful due to singularities in these functions. In the approximate range of 4.5≤κ≤ 5.5, the (3, 3) Padé approximations were found to be no better than lower ones. Comparisons with available Monte Carlo simulated pressures for moderately aspherical fluids were found to be good.

In this paper we propose a forward time update algorithm to recursively estimate subset vector autoregressive models (including an intercept term) with a forgetting factor, using the exact window case. The proposed recursions cover, for the first time, subset vector autoregressive models (VAR) with a forgetting factor and an intercept variable. We then present two applications. In the first application we apply the proposed estimation algorithm to the quarterly aluminium prices on the London Metal Exchange. The findings show that the proposed algorithm can improve the forecasting performance. In the second application a bivariate system investigates the relationship between the Australian's All Ordinaries Share Price Index (SPI) futures and BHP share price (BHP). The proposed algorithm also introduces the Monte Carlo Integration approach into the proposed algorithm to generate error bands for the impulse responses. These results confirm that the SPI Granger causes BHP, but not vice versa.

By using a cosmographic analysis of the redshift data of type Ia supernovae, we are able to get the expansion of the scale factor, obtaining the current values of the Hubble, deceleration, jerk and snap parameters. Our data is then used to compare the fitness of various proposed alternative cosmological models. Since our method assumes only the validity of general relativity at the cosmic scale, along with the isotropy and homogeneity of the universe, they are very useful for comparison between different cosmological models, including the fitness of ΛCDM model. Our method is based on the order expansion of the scale factor present in the FRW metric and using a Monte Carlo integration to find the best fit order parameters of the scale factor to reproduce the observed data, we make use of parallel paradigm to improve the computational time behind the model. We find the known result of an accelerated expansion of the universe. With access to better measurements of type Ia supernovae redshifts and more data, the cosmographic results will be significantly improved.

Whenever a Bayesian procedure that involves the numerical evaluation of multi-dimensional integrals is contemplated, a decision as to whether proceed with a computer implementation of the procedure will often depend on the ease with which the software may be written. The ease with which the software may be written will, in turn, depend not only programming language chosen but also a programmer's knowledge of the language. Because the author has had rather extensive experience in using the programming language, APL, which, among other things, is known for ease with which succinct code may be written to process complex arrays, it was known at the outset that the software to program Bayesian structure outlined in this paper could written and validated with relative ease. Furthermore, it seems likely that any other programming language with array processing capabilities could also be used to write code the implement the ideas presented in this paper. Consequently, a decision was made to organize the ideas in a precise mathematical form as a first step to writing computer code in any programming language chosen by an investigator. One of the outstanding problems in using the Bayesian paradigm to estimate unknown parameters and make statistical inferences, using stochastic models of HIV/AIDS epidemics, was that of developing a methodology for drawing sample from the joint conditional posterior distribution of the parameters and the stochastic process, given the data. Chapter 6 in the recent book by (Tan, 2000) may be consulted for technical details. Among other things, this paper contains a novel procedure, depending on the ease with which large arrays may be processed in a computer, for drawing random samples from the posterior of the parameters and the process, given a sample of data.

Higher-order perturbative calculations in Quantum (Field) Theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines two new coefficients are obtained corresponding to a 4- and 5-loop calculation.