Mathematical modelling of the refractive index reconstruction through global optimization

We examine a mathematical model of non-destructive testing of planar waveguides, based on numerical solution of a nonlinear integral equation. Such problem is ill-posed, and the method of Tikhonov regularization is applied. To minimize Tikhonov functional, and find the parameters of the waveguide, we use two new optimization methods: the cutting angle method of global optimization, and the discrete gradient method of nonsmooth local optimization. We examine how the noise in the experimental data influences the solution, and how the regularization parameter has to be chosen. We show that even with significant noise in the data, the numerical solution is of high accuracy, and the method can be used to process real experimental da.ta..

Concurrent execution of multiple NAS parallel programs on a cluster

Currently, coordinated scheduling of multiple parallel applications across computers has been considered as the critical factor to achieve high execution performance. We claim in this report that the performance and costs of the execution of parallel applications could be improved if not only dedicated clusters but also non-dedicated clusters were used and several parallel applications were executed concurreontly. To support this claim we carried out experimental study into the performance of multiple NAS parallel programs executing concurrently on a non-dedicated cluster.

Developing formal mathematical assessment for 4-to-8-year-olds

The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children's mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.

Extraction of structured programs from specification proofs

We present a method using an extended logical system for obtaining programs from specifications written in a sublanguage of CASL. These programs are “correct” in the sense that they satisfy their specifications. The technique we use is to extract programs from proofs in formal logic by techniques due to Curry and Howard. The logical calculus, however, is novel because it adds structural rules corresponding to the standard ways of modifying specifications: translating (renaming), taking unions, and hiding signatures. Although programs extracted by the Curry-Howard process can be very cumbersome, we use a number of simplifications that ensure that the programs extracted are in a language close to a standard high-level programming language. We use this to produce an executable refinement of a given specification and we then provide a method for producing a program module that maximally respects the original structure of the specification. Throughout the paper we demonstrate the technique with a simple example.

Micro-credit programs and land distribution: a note

"Micro-credit" has come to refer to a popular extension strategy---usually in the agricultural sector---whereby a government or NGO extends credit at favorable rates to poorer borrowers, with repayment being supported by some kind of mortgage on the borrower's social capital. In the commonest case, eligibility is determined by the borrower's wealth, as indexed by his/her landholding. This note shows that, with an imperfect land market, the response to such a program will be to fragment landholdings which are smaller than a certain threshold, while larger holdings remain unaffected. Thus the pattern of landholding will tend to become more polarized.