Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Computing regular equivalence: practical and theoretical issues

Social network analysts have tried to capture the idea of social role explicitly by proposing a framework that precisely gives conditions under which group actors are playing equivalent roles. They term these methods positional analysis techniques. The most general definition is regular equivalence which captures the idea that equivalent actors are related in a similar way to equivalent alters. Regular equivalence gives rise to a whole class of partitions on a network. Given a network we have two different computational problems. The first is how to find a particular regular equivalence. An algorithm exists to find the largest regular partition but there are not efficient algorithms to test whether there is a regular k-partition. That is a partition in k groups that is regular. In addition, when dealing with real data, it is unlikely that any regular partitions exist. To overcome this problem relaxations of regular equivalence have been proposed along with optimisation techniques to find nearly regular partitions. In this paper we review the algorithms that have developed to find particular regular equivalences and look at some of the recent theoretical results which give an insight into the complexity of finding regular partitions.

AC & DC magnetic levitation and semi-levitation modelling

This work presents computation analysis of levitated liquid thermal and flow fields with free surface oscillations in AC and DC magnetic fields. The volume electromagnetic force distribution is continuously updated with the shape and position change. The oscillation frequency spectra are analysed for droplets levitation against gravity in AC and DC magnetic fields at various combinations. For larger volume liquid metal confinement and melting the semi-levitation induction skull melting process is simulated with the same numerical model. Applications are aimed at pure electromagnetic material processing techniques and the material properties measurements in uncontaminated conditions.

The semi-automatic parallelisation of scientific application codes using a computer aided parallelisation toolkit

The shared-memory programming model can be an effective way to achieve parallelism on shared memory parallel computers. Historically however, the lack of a programming standard using directives and the limited scalability have affected its take-up. Recent advances in hardware and software technologies have resulted in improvements to both the performance of parallel programs with compiler directives and the issue of portability with the introduction of OpenMP. In this study, the Computer Aided Parallelisation Toolkit has been extended to automatically generate OpenMP-based parallel programs with nominal user assistance. We categorize the different loop types and show how efficient directives can be placed using the toolkit's in-depth interprocedural analysis. Examples are taken from the NAS parallel benchmarks and a number of real-world application codes. This demonstrates the great potential of using the toolkit to quickly parallelise serial programs as well as the good performance achievable on up to 300 processors for hybrid message passing-directive parallelisations.

Semi-Parametric Analysis of Extreme Forest Fires

Forest fires can cause extensive damage to natural resources and properties. They can also destroy wildlife habitat, affect the forest ecosystem and threaten human lives. In this paper incidences of extreme wildland fires are modelled by a point process model which incorporates time-trend. A model based on a generalised Pareto distribution is used to model data on acres of wildland burnt by extreme fire in the US since 1825. A semi-parametric smoothing approach, which is very useful in exploratory analysis of changes in extremes, is illustrated with the maximum likelihood method to estimate model parameters.

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results

'Re-using an existing wheel' developing data architecture for cooperating autonomous and semi-autonomous, agent-based web services

This short position paper considers issues in developing Data Architecture for the Internet of Things (IoT) through the medium of an exemplar project, Domain Expertise Capture in Authoring and Development ­Environments (DECADE). A brief discussion sets the background for IoT, and the development of the ­distinction between things and computers. The paper makes a strong argument to avoid reinvention of the wheel, and to reuse approaches to distributed heterogeneous data architectures and the lessons learned from that work, and apply them to this situation. DECADE requires an autonomous recording system, ­local data storage, semi-autonomous verification model, sign-off mechanism, qualitative and ­quantitative ­analysis ­carried out when and where required through web-service architecture, based on ontology and analytic agents, with a self-maintaining ontology model. To develop this, we describe a web-service ­architecture, ­combining a distributed data warehouse, web services for analysis agents, ontology agents and a ­verification engine, with a centrally verified outcome database maintained by certifying body for qualification/­professional status.

A method for semi-automated objective quantification of linear bedforms from multi-scale Digital Elevation Models

The increasing availability of large, detailed digital representations of the Earth’s surface demands the application of objective and quantitative analyses. Given recent advances in the understanding of the mechanisms of formation of linear bedform features from a range of environments, objective measurement of their wavelength, orientation, crest and trough positions, height and asymmetry is highly desirable. These parameters are also of use when determining observation-based parameters for use in many applications such as numerical modelling, surface classification and sediment transport pathway analysis. Here, we (i) adapt and extend extant techniques to provide a suite of semi-automatic tools which calculate crest orientation, wavelength, height, asymmetry direction and asymmetry ratios of bedforms, and then (ii) undertake sensitivity tests on synthetic data, increasingly complex seabeds and a very large-scale (39 000km2) aeolian dune system. The automated results are compared with traditional, manually derived,measurements at each stage. This new approach successfully analyses different types of topographic data (from aeolian and marine environments) from a range of sources, with tens of millions of data points being processed in a semi-automated and objective manner within minutes rather than hours or days. The results from these analyses show there is significant variability in all measurable parameters in what might otherwise be considered uniform bedform fields. For example, the dunes of the Rub’ al Khali on the Arabian peninsula are shown to exhibit deviations in dimensions from global trends. Morphological and dune asymmetry analysis of the Rub’ al Khali suggests parts of the sand sea may be adjusting to a changed wind regime from that during their formation 100 to 10 ka BP.