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.

Modelling the torsional interaction of wire and polyester fibre ropes used for offshore moorings

Oil rig mooring lines have traditionally consisted of chain and wire rope. As production has moved into deeper water it has proved advantageous to incorporate sections of fibre rope into the mooring lines. However, this has highlighted torsional interaction problems that can occur when ropes of different types are joined together. This paper describes a method by which the torsional properties of ropes can be modelled and can then be used to calculate the rotation and torque for two ropes connected in series. The method uses numerical representations of the torsional characteristics of both the ropes, and equates the torque generated in each rope under load to determine the rotation at the connection point. Data from rope torsional characterization tests have been analysed to derive constants used in the numerical model. Constants are presented for: a six-strand wire rope; a torque-balanced fibre rope; and a fibre rope that has been designed to be torque-matched to stranded wire rope. The calculation method has been verified by comparing predicted rotations with measured test values. Worked examples are given for a six-strand wire rope connected, firstly, to a torque-balanced fibre rope that offers little rotational restraint, and, secondly, to a fibre rope whose torsional properties are matched to that of the wire rope.

Modelling fatigue damage distribution to inform slip and cut policy for riser tensioner ropes

The paper describes a method whereby the distribution of fatigue damage along riser tensioner ropes is calculated, taking account of heave motion, set tension, system geometry, tidal range and rope specification. From these data the distribution of damage along the rope is calculated for a given time period using a Miner’s summation method. This information can then be used to help the operator decide on the length of rope to ‘slip and cut’ whereby a length from the end of the rope is removed and the rope moved through the system from a storage drum such that sections of rope that have already suffered significant fatigue damage are not moved to positions where there is another peak in the distribution. There are two main advantages to be gained by using the fatigue damage model. The first is that it shows the amount of fatigue damage accumulating at different points along the rope, enabling the most highly damaged section to be removed well before failure. The second is that it makes for greater efficiency, as damage can be spread more evenly along the rope over time, avoiding the need to scrap long sections of undamaged rope.

Promotion carryover as a missing data problem

An important feature of agribusiness promotion programs is their lagged impact on consumption. Efficient investment in advertising requires reliable estimates of these lagged responses and it is desirable from both applied and theoretical standpoints to have a flexible method for estimating them. This note derives an alternative Bayesian methodology for estimating lagged responses when investments occur intermittently within a time series. The method exploits a latent-variable extension of the natural-conjugate, normal-linear model, Gibbs sampling and data augmentation. It is applied to a monthly time series on Turkish pasta consumption (1993:5-1998:3) and three, nonconsecutive promotion campaigns (1996:3, 1997:3, 1997:10). The results suggest that responses were greatest to the second campaign, which allocated its entire budget to television media; that its impact peaked in the sixth month following expenditure; and that the rate of return (measured in metric tons additional consumption per thousand dollars expended) was around a factor of 20.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

Cross-correlations and cross-bicorrelations in Sterling exchange rates

This paper proposes two new tests for linear and nonlinear lead/lag relationships between time series based on the concepts of cross-correlations and cross-bicorrelations, respectively. The tests are then applied to a set of Sterling-denominated exchange rates. Our analysis indicates that there existed periods during the post-Bretton Woods era where the temporal relationship between different exchange rates was strong, although these periods have become less frequent over the past 20 years. In particular, our results demonstrate the episodic nature of the nonlinearity, and have implications for the speed of flow of information between financial series. The method generalises recently proposed tests for nonlinearity to the multivariate context.

A time-series method to identify and correct range sidelobes in meteorological radar data

The use of pulse compression techniques to improve the sensitivity of meteorological radars has become increasingly common in recent years. An unavoidable side-effect of such techniques is the formation of ‘range sidelobes’ which lead to spreading of information across several range gates. These artefacts are particularly troublesome in regions where there is a sharp gradient in the power backscattered to the antenna as a function of range. In this article we present a simple method for identifying and correcting range sidelobe artefacts. We make use of the fact that meteorological targets produce an echo which fluctuates at random, and that this echo, like a fingerprint, is unique to each range gate. By cross-correlating the echo time series from pairs of gates therefore we can identify whether information from one gate has spread into another, and hence flag regions of contamination. In addition we show that the correlation coefficients contain quantitative information about the fraction of power leaked from one range gate to another, and we propose a simple algorithm to correct the corrupted reflectivity profile.

Evaluation of the S(T) assimilation method with the Argo dataset

Recent observations from the Argo dataset of temperature and salinity profiles are used to evaluate a series of 3-year data assimilation experiments in a global ice–ocean general circulation model. The experiments are designed to evaluate a new data assimilation system whereby salinity is assimilated along isotherms, S(T ). In addition, the role of a balancing salinity increment to maintain water mass properties is investigated. This balancing increment is found to effectively prevent spurious mixing in tropical regions induced by univariate temperature assimilation, allowing the correction of isotherm geometries without adversely influencing temperature–salinity relationships. In addition, the balancing increment is able to correct a fresh bias associated with a weak subtropical gyre in the North Atlantic using only temperature observations. The S(T ) assimilation method is found to provide an important improvement over conventional depth level assimilation, with lower root-mean-squared forecast errors over the upper 500 m in the tropical Atlantic and Pacific Oceans. An additional set of experiments is performed whereby Argo data are withheld and used for independent evaluation. The most significant improvements from Argo assimilation are found in less well-observed regions (Indian, South Atlantic and South Pacific Oceans). When Argo salinity data are assimilated in addition to temperature, improvements to modelled temperature fields are obtained due to corrections to model density gradients and the resulting circulation. It is found that observations from the Argo array provide an invaluable tool for both correcting modelled water mass properties through data assimilation and for evaluating the assimilation methods themselves.

Stopping clinical trials because of treatment ineffectiveness: a comparison of a futility design with a method of stochastic curtailment

This paper introduces a simple futility design that allows a comparative clinical trial to be stopped due to lack of effect at any of a series of planned interim analyses. Stopping due to apparent benefit is not permitted. The design is for use when any positive claim should be based on the maximum sample size, for example to allow subgroup analyses or the evaluation of safety or secondary efficacy responses. A final frequentist analysis can be performed that is valid for the type of design employed. Here the design is described and its properties are presented. Its advantages and disadvantages relative to the use of stochastic curtailment are discussed. Copyright (C) 2003 John Wiley Sons, Ltd.

A preliminary evaluation of cognitive-behaviour therapy for clinical perfectionism: a case series

Objective: The construct of 'clinical perfectionism' has been developed in response to criticisms that other approaches have failed to yield advances in the treatment of the type of self-oriented perfectionism that poses a clinical problem. The primary aim of this study was to conduct a preliminary investigation into the efficacy of a theory-driven, cognitive-behavioural intervention for 'clinical perfectionism'. Design. A multiple baseline single case series design was used. Method: A specific, 10-session cognitive-behavioural intervention to address clinical perfectionism in eating disorders was adapted to allow its use in nine patients referred with a range of axis I disorders and clinical perfectionism. Results: The intervention led to clinically significant improvements in self-referential perfectionism from pretreatment to follow-up for six of the nine participants on two perfectionism measures and for three of the nine participants on the measure of clinical perfectionism. Statistically significant improvements from pre- to post-intervention for the group as a whole were found on all three measures. The improvements were maintained at follow-up. Conclusions: The finding that clinical perfectionism is improved in the majority of participants is particularly encouraging given that perfectionism has traditionally been viewed as a personality characteristic resistant to change. These preliminary findings warrant replication in a larger study.

Enhancing dominant modes in nonstationary time series by means of the symbolic resonance analysis

We present the symbolic resonance analysis (SRA) as a viable method for addressing the problem of enhancing a weakly dominant mode in a mixture of impulse responses obtained from a nonlinear dynamical system. We demonstrate this using results from a numerical simulation with Duffing oscillators in different domains of their parameter space, and by analyzing event-related brain potentials (ERPs) from a language processing experiment in German as a representative application. In this paradigm, the averaged ERPs exhibit an N400 followed by a sentence final negativity. Contemporary sentence processing models predict a late positivity (P600) as well. We show that the SRA is able to unveil the P600 evoked by the critical stimuli as a weakly dominant mode from the covering sentence final negativity. (c) 2007 American Institute of Physics. (c) 2007 American Institute of Physics.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Modelling of surface identifying characteristics using Fourier series

Texture and small-scale surface details are widely recognised as playing an important role in the haptic identification of objects. In order to simulate realistic textures in haptic virtual environments, it has become increasingly necessary to identify a robust technique for modelling of surface profiles. This paper describes a method whereby Fourier series spectral analysis is employed in order to describe the measured surface profiles of several characteristic surfaces. The results presented suggest that a bandlimited Fourier series can be used to provide a realistic approximation to surface amplitude profiles.