Concepts and implementation of the Cuba library for multidimensional numerical integration are elucidated. 1. Overview Cuba [1] is a library for multidimensional numerical integration. It features four integration algorithms with interfaces for Fortran, C/C++, and Mathematica. All four can integrate vector integrands and their invocation is quite similar to make it easy to switch routines for c...

Problems in many disciplines, such as physics, chemistry, and finance, can be modelled as integrals of high dimensions (hundreds or even thousands). Quasi-Monte Carlo (QMC) methods, which perform sampling using a more uniform point set than that used in MC, have been successfully used to approximate multivariate integrals with an error bound of size O((logN)kN−1) or even O((logN)kN−3/2), where ...

The significant increase in using reservoir simulation models poses significant challenges in the design and calibration of models. Moreover, conventional model calibration, history matching, is usually performed using a trial and error process of adjusting model parameters until a satisfactory match is obtained. In addition, history matching is an inverse problem, and hence it may have non-uni...

A standard assumption in stated preferences modelling is the independence between repeated responses from an interviewee. The rationale for this strong assumption is that the mathematical treatment of the choices becomes rather cumbersome when dependency is incorporated in the analysis. Assuming dependence between the various responses given by one individual is known as the repeated observatio...

The Voronoi tessellation in a plane or in a space has recently aroused renewed interest due to its applications in various areas ranging from astrophysics (see refs. [ 1,2 ] ) to the representation of properties of materials (see ref. [ 31). It turns out that some typical parameters like the area distribution in two dimensions and the volume distribution in three dimensions depend strongly on t...

We investigate the propagation of probabilistic uncertainty through the action potential mechanism in nerve cells. Using the Hodgkin-Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an accurate probabilistic interpretation of the deterministic dynamics of the transmembrane potential and gating variables. Using Sobol indices, out of the 11 uncertain parameters in the H-H ...

Hybrids of equidistribution and Monte Carlo methods of integration can achieve the superior accuracy of the former while allowing the simple error estimation methods of the latter. In particular randomized (0; m; s)-nets in base b produce unbiased estimates of the integral, have a variance that tends to zero faster than 1=n for any square integrable integrand, and have a variance that for nite ...

in a recent paper in this journal, yang et al. [feng yang, dexiang wu,liang liang, gongbing bi & desheng dash wu (2009), supply chaindea:production possibility set and performance evaluation model] definedtwo types of supply chain production possibility set which were proved to beequivalent to each other. they also proposed a new model for evaluatingsupply chains. there are, however, some short...