Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

The benefits of a compute cluster approach to high spatial resolution biodiversity richness modelling: projecting the impact of climate change on Mediterranean flora

High spatial resolution environmental data gives us a better understanding of the environmental factors affecting plant distributions at fine spatial scales. However, large environmental datasets dramatically increase compute times and output species model size stimulating the need for an alternative computing solution. Cluster computing offers such a solution, by allowing both multiple plant species Environmental Niche Models (ENMs) and individual tiles of high spatial resolution models to be computed concurrently on the same compute cluster. We apply our methodology to a case study of 4,209 species of Mediterranean flora (around 17% of species believed present in the biome). We demonstrate a 16 times speed-up of ENM computation time when 16 CPUs were used on the compute cluster. Our custom Java ‘Merge’ and ‘Downsize’ programs reduce ENM output files sizes by 94%. The median 0.98 test AUC score of species ENMs is aided by various species occurrence data filtering techniques. Finally, by calculating the percentage change of individual grid cell values, we map the projected percentages of plant species vulnerable to climate change in the Mediterranean region between 1950–2000 and 2020.

Substitutional and orientational disorder in organic crystals: a symmetry-adapted ensemble model

Modelling of disorder in organic crystals is highly desirable since it would allow thermodynamic stabilities and other disorder-sensitive properties to be estimated for such systems. Two disordered organic molecular systems are modeled using a symmetry-adapted ensemble approach, in which the disordered system is treated as an ensemble of the configurations of a supercell with respect to substitution of one disorder component for another. Computation time is kept manageable by performing calculations only on the symmetrically inequivalent configurations. Calculations are presented on a substitutionally disordered system, the dichloro/dibromobenzene solid solution, and on an orientationally disordered system, eniluracil, and the resultant free energies, disorder patterns, and system properties are discussed. The results are found to be in agreement with experiment following manual removal of physically implausible configurations from ensemble averages, highlighting the dangers of a completely automated approach to organic crystal thermodynamics which ignores the barriers to equilibration once the crystal has been formed.

Modelling negative feedback networks for activating transcription factor 3 predicts a dominant role for miRNAs in immediate early gene regulation

Activating transcription factor 3 (Atf3) is rapidly and transiently upregulated in numerous systems, and is associated with various disease states. Atf3 is required for negative feedback regulation of other genes, but is itself subject to negative feedback regulation possibly by autorepression. In cardiomyocytes, Atf3 and Egr1 mRNAs are upregulated via ERK1/2 signalling and Atf3 suppresses Egr1 expression. We previously developed a mathematical model for the Atf3-Egr1 system. Here, we adjusted and extended the model to explore mechanisms of Atf3 feedback regulation. Introduction of an autorepressive loop for Atf3 tuned down its expression and inhibition of Egr1 was lost, demonstrating that negative feedback regulation of Atf3 by Atf3 itself is implausible in this context. Experimentally, signals downstream from ERK1/2 suppress Atf3 expression. Mathematical modelling indicated that this cannot occur by phosphorylation of pre-existing inhibitory transcriptional regulators because the time delay is too short. De novo synthesis of an inhibitory transcription factor (ITF) with a high affinity for the Atf3 promoter could suppress Atf3 expression, but (as with the Atf3 autorepression loop) inhibition of Egr1 was lost. Developing the model to include newly-synthesised miRNAs very efficiently terminated Atf3 protein expression and, with a 4-fold increase in the rate of degradation of mRNA from the mRNA/miRNA complex, profiles for Atf3 mRNA, Atf3 protein and Egr1 mRNA approximated to the experimental data. Combining the ITF model with that of the miRNA did not improve the profiles suggesting that miRNAs are likely to play a dominant role in switching off Atf3 expression post-induction.

The development of a data-driven application benchmarking approach to performance modelling

Performance modelling is a useful tool in the lifeycle of high performance scientific software, such as weather and climate models, especially as a means of ensuring efficient use of available computing resources. In particular, sufficiently accurate performance prediction could reduce the effort and experimental computer time required when porting and optimising a climate model to a new machine. In this paper, traditional techniques are used to predict the computation time of a simple shallow water model which is illustrative of the computation (and communication) involved in climate models. These models are compared with real execution data gathered on AMD Opteron-based systems, including several phases of the U.K. academic community HPC resource, HECToR. Some success is had in relating source code to achieved performance for the K10 series of Opterons, but the method is found to be inadequate for the next-generation Interlagos processor. The experience leads to the investigation of a data-driven application benchmarking approach to performance modelling. Results for an early version of the approach are presented using the shallow model as an example.

Estimate of the cutoff errors in the Ewald summation for dipolar systems

Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.

Anticipatory engineering: anticipation in sensory-motor systems of human

In visual tracking experiments, distributions of the relative phase be-tween target and tracer showed positive relative phase indicating that the tracer precedes the target position. We found a mode transition from the reactive to anticipatory mode. The proposed integrated model provides a framework to understand the antici-patory behaviour of human, focusing on the integration of visual and soma-tosensory information. The time delays in visual processing and somatosensory feedback are explicitly treated in the simultaneous differential equations. The anticipatory behaviour observed in the visual tracking experiments can be ex-plained by the feedforward term of target velocity, internal dynamics, and time delay in somatosensory feedback.

Parallel pipelined array architectures for real-time histogram computation in consumer devices

The real-time parallel computation of histograms using an array of pipelined cells is proposed and prototyped in this paper with application to consumer imaging products. The array operates in two modes: histogram computation and histogram reading. The proposed parallel computation method does not use any memory blocks. The resulting histogram bins can be stored into an external memory block in a pipelined fashion for subsequent reading or streaming of the results. The array of cells can be tuned to accommodate the required data path width in a VLSI image processing engine as present in many imaging consumer devices. Synthesis of the architectures presented in this paper in FPGA are shown to compute the real-time histogram of images streamed at over 36 megapixels at 30 frames/s by processing in parallel 1, 2 or 4 pixels per clock cycle.

Inheritance of time to flowering in cowpea (Vigna unguiculata (L.) Walp.)

Time to flowering and maturity is an important adaptive feature in annual crops, including cowpeas (Vigna unguiculata (L.) Walp.). In West and Central Africa, photoperiod is the most important environmental variable affecting time to flowering in cowpea. The inheritance of time from sowing to flowering (f) in cowpeas was studied by crossing a photoperiod-sensitive genotype Kanannnado to a photoperiod-insensitive variety IT97D-941-1. Sufficient seed of F-1, F-2, F-3 and backcross populations were generated. The parental, F-1, F-2, F-3 and the backcross populations were screened for f under long natural days (mean daylength 13.4 h per day) in the field and the parents, F-1, F-2 and backcross populations under short day (10 h per day) conditions. The result of the screening showed that photoperiod in the field was long enough to delay flowering of photoperiod-sensitive genotypes. Photoperiod-sensitivity was found to be partially dominant to insensitivity. Frequency distribution of the trait in the various populations indicated quantitative inheritance. Additive (d) and additive x dominance (j) interactions were the most important gene actions conditioning time to flowering. A narrow sense heritability of 86% was estimated for this trait. This will result in 26 days gain in time to flowering with 5% selection intensity from the F-2 to F-3 generation. At least seven major gene pairs, with an average delay of 6 days each, were estimated to control time to flowering in this cross.

The effects of a pre-movement delay on the kinematics of prehension in middle childhood

The present study examined the effects of a pre-movement delay on the kinematics of prehension in middle childhood. Twenty-five children between the ages of 5 and 11 years made visually open-loop reaches to two different sized objects at two different distances along the midline. Reaches took place either (i) immediately, or (ii) 2 s after the occlusion of the stimulus. In all age groups, reaches following the pre-movement delay were characterised by longer movement durations, lower peak velocities, larger peak grip apertures and longer time spent in the final slow phase of the movement. This pattern of results suggests that the representations that control the transport and grasp component are affected similarly by delay, and is consistent with the results previously reported for adults. Such representations therefore appear to develop before the age of 5. (C) 2004 Elsevier B.V. All rights reserved.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Delay analysis of enhanced relay-enabled distributed coordination function

This paper analyzes the delay performance of Enhanced relay-enabled Distributed Coordination Function (ErDCF) for wireless ad hoc networks under ideal condition and in the presence of transmission errors. Relays are nodes capable of supporting high data rates for other low data rate nodes. In ideal channel ErDCF achieves higher throughput and reduced energy consumption compared to IEEE 802.11 Distributed Coordination Function (DCF). This gain is still maintained in the presence of errors. It is also expected of relays to reduce the delay. However, the impact on the delay behavior of ErDCF under transmission errors is not known. In this work, we have presented the impact of transmission errors on delay. It turns out that under transmission errors of sufficient magnitude to increase dropped packets, packet delay is reduced. This is due to increase in the probability of failure. As a result the packet drop time increases, thus reflecting the throughput degradation.

Wavelet filtered modelling applied to measurements of a waveguide's THz time domain response

A quasi-optical de-embedding technique for characterizing waveguides is demonstrated using wideband time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time domain responses were discretised and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an ARX as well as with a state space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize signal distortion and the noise propagating in the ARX and subspace models. The model identification procedure requires isolation of the phase delay in the structure and therefore the time-domain signatures must be firstly aligned with respect to each other before they are compared. An initial estimate of the number of propagating modes was provided by comparing the measured phase delay in the structure with theoretical calculations that take into account the physical dimensions of the waveguide. Models derived from measurements of THz transients in a precision WR-8 waveguide adjustable short will be presented.

The impact on housing supply in England of planning delay and uncertainty

The time taken to consider development proposals within the English planning system continues to provoke great policy concern despite a decade of inquiry and policy change. The results of an extensive site-based survey and hedonic modelling exercise across 45 local authorities are reported here. The analysis reveals a slow, uncertain system. It identifies planning delay as a serious problem for housing supply and its ability to respond to increases in demand. Only a relatively limited set of factors seem relevant in explaining differences in times and the results suggest that 80% of councils’ performances are statistically indistinguishable from each other. These findings question the policy emphasis put on rankings of local authorities, though some influence from local politics is apparent. Development control is consistently a lengthy and uncertain process due to its complexity. Therefore, success in lowering planning delay is only likely through radical simplification.

Change, rigidity & delay in the UK system of land-use development control

The British system of development control is time-consuming and uncertain in outcome. Moreover, it is becoming increasingly overloaded as it has gradually switched away from being centred on a traditional ‘is it an appropriate land-use?’ type approach to one based on multi-faceted inspections of projects and negotiations over the distribution of the potential financial gains arising from them. Recent policy developments have centred on improving the operation of development control. This paper argues that more fundamental issues may be a stake as well. Important market changes have increased workloads. Furthermore, the UK planning system's institutional framework encourages change to move in specific directions, which is not always helpful. If expectations of increased long-term housing supply are to be met more substantial changes to development control may be essential but hard to achieve.