A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Changes in gene expression in Arabidopsis shoots during phosphate starvation and the potential for developing smart plants

Our aim was to generate and prove the concept of "smart" plants to monitor plant phosphorus (P) status in Arabidopsis. Smart plants can be genetically engineered by transformation with a construct containing the promoter of a gene up-regulated specifically by P starvation in an accessible tissue upstream of a marker gene such as beta-glucuronidase (GUS). First, using microarrays, we identified genes whose expression changed more than 2.5-fold in shoots of plants growing hydroponically when P, but not N or K, was withheld from the nutrient solution. The transient changes in gene expression occurring immediately (4 h) after P withdrawal were highly variable, and many nonspecific, shock-induced genes were up-regulated during this period. However, two common putative cis-regulatory elements (a PHO-like element and a TATA box-like element) were present significantly more often in the promoters of genes whose expression increased 4 h after the withdrawal of P compared with their general occurrence in the promoters of all genes represented on the microarray. Surprisingly, the expression of only four genes differed between shoots of P-starved and -replete plants 28 h after P was withdrawn. This lull in differential gene expression preceded the differential expression of a new group of 61 genes 100 h after withdrawing P. A literature survey indicated that the expression of many of these "late" genes responded specifically to P starvation. Shoots had reduced P after 100 h, but growth was unaffected. The expression of SQD1, a gene involved in the synthesis of sulfolipids, responded specifically to P starvation and was increased 100 h after withdrawing P. Leaves of Arabidopsis bearing a SQD1::GUS construct showed increased GUS activity after P withdrawal, which was detectable before P starvation limited growth. Hence, smart plants can monitor plant P status. Transferring this technology to crops would allow precision management of P fertilization, thereby maintaining yields while reducing costs, conserving natural resources, and preventing pollution.

Statistical computations with AstroGrid and the Grid

We outline our first steps towards marrying two new and emerging technologies; the Virtual Observatory (e.g, Astro- Grid) and the computational grid. We discuss the construction of VOTechBroker, which is a modular software tool designed to abstract the tasks of submission and management of a large number of computational jobs to a distributed computer system. The broker will also interact with the AstroGrid workflow and MySpace environments. We present our planned usage of the VOTechBroker in computing a huge number of n–point correlation functions from the SDSS, as well as fitting over a million CMBfast models to the WMAP data.

Ubiquitous grid resource monitoring

In any wide-area distributed system there is a need to communicate and interact with a range of networked devices and services ranging from computer-based ones (CPU, memory and disk), to network components (hubs, routers, gateways) and specialised data sources (embedded devices, sensors, data-feeds). In order for the ensemble of underlying technologies to provide an environment suitable for virtual organisations to flourish, the resources that comprise the fabric of the Grid must be monitored in a seamless manner that abstracts away from the underlying complexity. Furthermore, as various competing Grid middleware offerings are released and evolve, an independent overarching monitoring service should act as a corner stone that ties these systems together. GridRM is a standards-based approach that is independent of any given middleware and that can utilise legacy and emerging resource-monitoring technologies. The main objective of the project is to produce a standardised and extensible architecture that provides seamless mechanisms to interact with native monitoring agents across heterogeneous resources.

GridRM: a resource monitoring architecture for the grid

Monitoring resources is an important aspect of the overall efficient usage and control of any distributed system. In this paper, we describe a generic open-source resource monitoring architecture that has been specifically designed for the Grid. The paper consists of three main sections. In the first section, we outline our motivation and briefly detail similar work in the area. In the second section, we describe the general monitoring architecture and its components. In the final section of the paper, we summarise the experiences so far and outline our future work.

Jini meets the Grid

There is an increasing interest in integrating Java-based, and in particular Jini systems, with the emerging Grid infrastructures. In this paper we explore various ways of integrating the key components of each architecture, their directory and information management services. In the first part of the paper we sketch out the Jini and Grid architectures and their services. We then review the components and services that Jini provides and compare these with those of the Grid. In the second part of the paper we critically explore four ways that Jini and the Grid could interact, here in particular we look at possible scenarios that can provide a seamless interface to a Jini environment for Grid clients and how to use Jini services from a Grid environment. In the final part of the paper we summarise our findings and report on future work being undertaken to integrate Jini and the Grid.

Coupling ensemble weather predictions based on TIGGE database with Grid-Xinanjiang model for flood forecast

The incorporation of numerical weather predictions (NWP) into a flood forecasting system can increase forecast lead times from a few hours to a few days. A single NWP forecast from a single forecast centre, however, is insufficient as it involves considerable non-predictable uncertainties and lead to a high number of false alarms. The availability of global ensemble numerical weather prediction systems through the THORPEX Interactive Grand Global Ensemble' (TIGGE) offers a new opportunity for flood forecast. The Grid-Xinanjiang distributed hydrological model, which is based on the Xinanjiang model theory and the topographical information of each grid cell extracted from the Digital Elevation Model (DEM), is coupled with ensemble weather predictions based on the TIGGE database (CMC, CMA, ECWMF, UKMO, NCEP) for flood forecast. This paper presents a case study using the coupled flood forecasting model on the Xixian catchment (a drainage area of 8826 km2) located in Henan province, China. A probabilistic discharge is provided as the end product of flood forecast. Results show that the association of the Grid-Xinanjiang model and the TIGGE database gives a promising tool for an early warning of flood events several days ahead.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.

People or machines? Assessing the impacts of smart meters and load controllers in Italian office spaces

Government initiatives in several developed and developing countries to roll-out smart meters call for research on the sustainability impacts of these devices. In principle smart meters bring about higher control over energy theft and lower consumption, but require a high level of engagement by end-users. An alternative consists of load controllers, which control the load according to pre-set parameters. To date, research has focused on the impacts of these two alternatives separately. This study compares the sustainability impacts of smart meters and load controllers in an occupied office building in Italy. The assessment is carried out on three different floors of the same building. Findings show that demand reductions associated with a smart meter device are 5.2% higher than demand reductions associated with the load controller.

Smart-phone based electrocardiogram wavelet decomposition and neural network classification

This paper discusses ECG classification after parametrizing the ECG waveforms in the wavelet domain. The aim of the work is to develop an accurate classification algorithm that can be used to diagnose cardiac beat abnormalities detected using a mobile platform such as smart-phones. Continuous time recurrent neural network classifiers are considered for this task. Records from the European ST-T Database are decomposed in the wavelet domain using discrete wavelet transform (DWT) filter banks and the resulting DWT coefficients are filtered and used as inputs for training the neural network classifier. Advantages of the proposed methodology are the reduced memory requirement for the signals which is of relevance to mobile applications as well as an improvement in the ability of the neural network in its generalization ability due to the more parsimonious representation of the signal to its inputs.

From harmonisation to better, smart and fit food law

As the European Union (EU) approaches its 60th anniversary, it is worth assessing progress towards a key objective – the abolition of barriers to the marketing of food in the EU. Food has always created particular problems for the EU as national differences in diets, culture and geography make standardisation impossible. Early attempts focussed on direct measures to harmonise requirements or, later, to create an ‘internal market’. Subsequently a changed emphasis brought about the need to focus more clearly on the harmonisation of food safety. More widely, the recent recognition that too much legislation can itself create barriers has led legislators to attempt to consider more carefully the impact of their efforts. This paper reflects on the various stages in the creation of harmonised food controls and considers how case law has impacted the process. Today there are still differences and complete barrier-free trade seems some way off.