Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

Neural networks and flexible approximations

Email: cuny{at}cardiff.ac.uk This paper supports the view that neural networks are best seenas devices that can approximate a wide range of functions. Theauthors argue the need to consider the precise details of howthe approximations operate in practice. The paper shows howstandard network models can be regarded as polynomial functions,obtained from expanding exponential terms. Multivariate Taylor-seriesexpansions, obtained through the MAPLE software package, areused for this purpose. The expansions serve to cast light onthe role of the hidden nodes. Also considered is the relativedifficulty of fitting different types of function. Quadraticfunctions are compared with Gaussian shapes.     

The Z-transform and linear multistep stability

^** Email: mapjjc{at}maths.bath.ac.uk^*** Corresponding author. Email: ath{at}maths.bath.ac.uk^**** Email: hl{at}maths.bath.ac.uk This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods.     

Control consolidation with a threshold: an algorithm

Email: ariane.chapelle{at}ulb.ac.be Corresponding author. Email: aszafarz{at}ulb.ac.be Received on 14 October 2005. Accepted on 21 November 2006. Besides multiple voting rights, board representation and shareholders’monitoring, control tunnelling over firms can be reached throughpyramids, cross-ownership and other complex features. This phenomenonis frequent in Europe and Asia. However, the theoretical literaturehas not yet converged towards a well-defined and robust measurementof integrated control that takes into account the thresholdfor control as applied in practice. Based on graph theory, thispaper aims at filling this gap and proposes a new algorithmfor evaluating the control tunnelling exerted by the firms’ultimate shareholders. Then, the paper discusses the variousforms of control existing next to voting shares, like multiplevoting rights, board representation and active monitoring, beforesuggesting ways to include them into the modelling of control.     

Lattice Boltzmann simulations of complex fluids

Email: j.yeomansl{at}physics.oxford.ac.uk We discuss how lattice Boltzmann simulations can be used tomodel the self-assembly and flow properties of complex fluids.The aim is to include both the hydrodynamic (viscous, diffusive)and the equilibrium (phase ordering, interface profiles) fluidproperties. Examples include the decomposition of a dropletunder extensional flow and phase separation of binary and lamellarfluids.     

The dynamic control of risk in optimised portfolios

E-mail: c.j.adcock{at}sheffield.ac.uk or adcock{at}intonet.co.uk This paper presents a theoretical treatment of the statisticalproperties of optimal portfolios. The results demonstrate theway in which the statistical properties of forecast returnsaffect the performance of optimised portfolios. The paper thenindicates how these methods may be used in principle to controlthe performance of an optimised portfolio. This is exemplifiedby an optimal portfolio of foreign currencies.     

Computation and parametrization of periodic and connecting orbits

Email: g.moore{at}ma.ic.ac.uk or na.gmoore New algorithms for the computation of periodic and connectingorbits of autonomous differential equations are developed. Previousmethods have parametrized these curves by the independent timevariable, but our procedure is based on the canonical arclengthparametrization.     

Estimation and decomposition of cost efficiency in the health care food service sector: an extended stochastic frontier approach

K. M. Matawie School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith South DC NSW 1797, Australia Email: a.assaf{at}uws.edu.au Corresponding author. Email: k.matawie{at}uws.edu.au Received on 11 February 2007. Accepted on 14 September 2007. This paper introduces and implements an extended stochasticfrontier model to estimate and decompose cost efficiency (CE)in the health care foodservice sector. The interesting featureof this model is that it allows differentiation between thethree different types of efficiency: technical efficiency (TE),allocative efficiency (AE) and their associated CE. A completeillustration of these efficiencies is presented using a cross-sectionalsample of 101 hospital foodservice operations. Results showedthat the model and all its parameter coefficients were plausible,significant and satisfy all theoretical requirements. It wasalso clear that the average efficiency scores were lower forTE (80%) than AE (88%), indicating that TE is the main sourceof CE and requires further attention.     

Multiple criteria models for evaluation of competitive bids

Email: slliu{at}mail.east.net.cnAuthor for correspondence Email: mskklai{at}cityu.edu.hkEmail: sywang{at}iss02.iss.ac.cn In this paper, two general bidding systems are proposed to aidan owner to select one contractor based on multiple-attributedecision making models. They are named the general multiple-attributelower-bidder system and the general multiple-attribute average-bid system and are an extension (and refreshment) of the multiparameterbidding system and the average-bid method, respectively. Thepreference of the owner over the criteria (or attributes) relevantto construction work award is incorporated into the two newsystems if necessary and required by the owner. The values ofthe attributes (excluding the cost) required to be determinedby the owner in the multiparameter bidding system are not necessarilydetermined in the general multiple-attribute lower-bidder system.This reduces the burden to the owner. The two new bidding systemsare demonstrated via an example, and are compared with the multiparameterbidding system and the average-bid method. The comparisons showthat the preference of the owner in regard to the attributesrelevant to selection of contractors has a significant effecton bid evaluation. The two new systems preserve the form ofthe competitive bidding concept and can easily be applied topractice.     

Graphical association models for road accident characteristics

Email: R.Tunaru{at}mdx.ac.uk Governments and local authorities spend large sums of moneycollecting information about road accidents. Statistical modelsare applied to extract valuable information that can be subsequentlyused to design safety measures and safety policies. Two largesubsets of data are explored using graphical modelling. It isshown how to overcome some difficulties due to the nature ofroad accident data and how to reduce the dimensionality of theanalysis without having any problem with Simpson's paradox.This type of analysis is new in this area of research and specificproblems are discussed.     

Predicting stock returns and assessing prediction performance

Email: r.d.baker{at}salford.ac.uk Received on 1 November 2006. Accepted on 15 March 2007. We use regression methods to predict the expected monthly returnon stocks and the covariance matrix of returns, the predictorvariables being a company's ‘fundamentals’, suchas dividend yield and the history of previous returns. Predictionsare evaluated out of sample for shares traded on the LondonStock Exchange from 1976 to 2005. We explore and evaluate manymodelling and inferential approaches, including the use of weightedregression, discounted regression, shrinkage of regression coefficientsand the transformation to normality of predictor variables.We also investigate alternative covariance matrix models, suchas a two-index model and a shrinkage model. Using suitable statisticsto enable the out-of-sample performance of competing methodologiesto be compared is crucial, and we develop some new statisticsand a graphical aid for this purpose. What is original in thispaper is an evaluation of many modelling and inferential proceduresfor which conflicting claims have been made in the literatureand the development of new measures of portfolio performance.     

An a posteriori error indicator for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

^** Email: paul.houston{at}nottingham.ac.uk^*** Corresponding author. Email: ilaria.perugia{at}unipv.it^**** Email: schoetzau{at}math.ubc.ca We introduce a residual-based a posteriori error indicator fordiscontinuous Galerkin discretizations of H(curl; )-ellipticboundary value problems that arise in eddy current models. Weshow that the indicator is both reliable and efficient withrespect to the approximation error measured in terms of a naturalenergy norm. We validate the performance of the indicator withinan adaptive mesh refinement procedure and show its asymptoticexactness for a range of test problems.     

Minimal equivalence of differential IO systems

Differential algebraic controllability, observability, and minimalrealization are considered further, upon which a new equivalenceproblem, i.e. the minimal equivalence of two given differentialinput-output (IO) systems through state-space realization isconsidered. Some criteria for equivalence and minimal equivalenceof two IO systems are given. The algorithm for checking minimalequivalence of two IO systems with single input is implementedwith MACSYMA. Email: xyl{at}sun.engg.le.ac.uk David.Bell{at}umist.ac.uk     

Singular value decomposition expansion for electrical demand analysis

Email: fan.li{at}ngc.co.uk To analyse electricity-demand data, appropriate mathematicalmodels and algorithms have been developed. Some theoreticalproperties of the singular value decomposition (SVD) and SVDexpansion have been found very useful during these developments.These properties, which have generic implications in data miningand numerical analysis, are presented in this paper. Followinga discussion of the theoretical development, this paper reportsapplications of the SVD expansion in demand analysis and forecastingwith three illustrative practical algorithms, that have beendeveloped by the National Grid Company in recent years.     

An inventory model for stock with advertising sensitive demand

K. S. Chaudhuri Department of Mathematics, Jadavpur University, Kolkata-700 032, West Bengal, India Corresponding author. Email: shib_sankar{at}yahoo.com Email: k_s_chaudhuri{at}yahoo.com The effect of advertising media and sales effort on future demandof merchandize is considered. In an oligopolistic marketingsystem, it is quite natural to boost sales by using advertisingand sales effort to earn more money from a business sector.Determination of demand and costs due to advertising and saleseffort is quite difficult. The approach in this paper is toconcentrate on investment for the purpose of advertising andincreasing sales effort in order to maximize profit. The paperextends an inventory model over finite and infinite time horizonswhere demand is influenced by the level of stock, advertisingmedia and sales effort. The associated profit maximization problemis solved by the ‘Euler–Lagrange method’.The model is illustrated with a numerical example.     

An adaptive boundary element method for the exterior Stokes problem in three dimensions

^** Email: vjervin{at}clemson.edu^*** Email: norbert.heuer{at}brunel.ac.uk We present an adaptive refinement strategy for the h-versionof the boundary element method with weakly singular operatorson surfaces. The model problem deals with the exterior Stokesproblem, and thus considers vector functions. Our error indicatorsare computed by local projections onto 1D subspaces definedby mesh refinement. These indicators measure the error separatelyfor the vector components and allow for component-independentadaption. Assuming a saturation condition, the indicators giverise to an efficient and reliable error estimator. Also we describehow to deal with meshes containing quadrilaterals which arenot shape regular. The theoretical results are underlined bynumerical experiments. To justify the saturation assumption,in the Appendix we prove optimal lower a priori error estimatesfor edge singularities on uniform and graded meshes.     

A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

^** Corresponding author. Email: l.elalaoui{at}imperial.ac.uk^*** Email: ern{at}cermics.enpc.fr^**** Email: erik.burman{at}epfl.ch We analyse a non-conforming finite-element method to approximateadvection–diffusion–reaction equations. The methodis stabilized by penalizing the jumps of the solution and thoseof its advective derivative across mesh interfaces. The a priorierror analysis leads to (quasi-)optimal estimates in the meshsize (sub-optimal by order in the L²-norm and optimal in thebroken graph norm for quasi-uniform meshes) keeping the Pécletnumber fixed. Then, we investigate a residual a posteriori errorestimator for the method. The estimator is semi-robust in thesense that it yields lower and upper bounds of the error whichdiffer by a factor equal at most to the square root of the Pécletnumber. Finally, to illustrate the theory we present numericalresults including adaptively generated meshes.     

Bayesian networks applied to credit scoring

Email: kchang{at}gmu.eduEmail: RobertFung{at}Fairlsaac.comEmail: alan.lucas{at}hotmail.com^¶Email: BobOliver{at}Fairlsaac.com^||Email: NShikaloff{at}Fairlsaac.com The objectives of this paper are to apply the theory and numericalalgorithms of Bayesian networks to risk scoring, and comparethe results with traditional methods for computing scores andposterior predictions of performance variables. Model identification,inference, and prediction of random variables using Bayesiannetworks have been successfully applied in a number of areas,including medical diagnosis, equipment failure, informationretrieval, rare-event prediction, and pattern recognition. Theability to graphically represent conditional dependencies andindependencies among random variables may also be useful incredit scoring. Although several papers have already appearedin the literature which use graphical models for model identification,as far as we know there have been no explicit experimental resultsthat compare a traditionally computed risk score with predictionsbased on Bayesian learning algorithms. In this paper, we examine a database of credit-card applicantsand attempt to ‘learn’ the graphical structure ofthe characteristics or variables that make up the database.We identify representative Bayesian networks in a developmentsample as well as the associated Markov blankets and cliquestructures within the Markov blanket. Once we obtain the structureof the underlying conditional independencies, we are able toestimate the probabilities of each node conditional on its directpredecessor node(s). We then calculate the posterior probabilitiesand scores of a performance variable for the development sample.Finally, we calculate the receiver operating characteristic(ROC) curves and relative profitability of scorecards basedon these identifications. The results of the different modelsand methods are compared with both development and validationsamples. Finally, we report on a statistical entropy calculationthat measures the degree to which cliques identified in theBayesian network are independent of one another.     

A spatial model of antipredator vigilance

The authors are also members of the Centre for the Study of Evolution at the University of Sussex (Email: C.J.Proctor{at}sussex.ac.uk and M.Broom{at}sussex.ac.uk) Many species of animals have to perform two contradictozy tasks:feeding, and avoiding becoming food for others. A large numberof theoretical and empirical studies have investigated the trade-offbetween feeding and antipredator vigilance, especially in birds.An important factor which has been neglected in these studiesis that of the area occupied by the flock. If individuals feedclose together, competition increases and feeding rates decrease.However, if individuals space themselves widely, then vigilanceefficiency goes down and there is an increased predation risk.We develop a vigilance model which allows birds to control thearea the flock occupies as well as their vigilance rate. Theoptimal strategy is found for the birds under a variety of environmentalconditions. In particular the effect of each environmental parameteron this optimum is considered in turn. How the model can beadapted for different bird species is also investigated.