Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu + ω 2 u = 0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua’s theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximations.

Inferring the biggest and best: a measurement model for applying recognition to evoke consideration sets and judge between multiple alternatives

It has long been supposed that preference judgments between sets of to-be-considered possibilities are made by means of initially winnowing down the most promising-looking alternatives to form smaller “consideration sets” (Howard, 1963; Wright & Barbour, 1977). In preference choices with >2 options, it is standard to assume that a “consideration set”, based upon some simple criterion, is established to reduce the options available. Inferential judgments, in contrast, have more frequently been investigated in situations in which only two possibilities need to be considered (e.g., which of these two cities is the larger?) Proponents of the “fast and frugal” approach to decision-making suggest that such judgments are also made on the basis of limited, simple criteria. For example, if only one of two cities is recognized and the task is to judge which city has the larger population, the recognition heuristic states that the recognized city should be selected. A multinomial processing tree model is outlined which provides the basis for estimating the extent to which recognition is used as a criterion in establishing a consideration set for inferential judgments between three possible options.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

Rossby number expansions, slaving principles, and balance dynamics

We consider the problem of constructing balance dynamics for rapidly rotating fluid systems. It is argued that the conventional Rossby number expansion—namely expanding all variables in a series in Rossby number—is secular for all but the simplest flows. In particular, the higher-order terms in the expansion grow exponentially on average, and for moderate values of the Rossby number the expansion is, at best, useful only for times of the order of the doubling times of the instabilities of the underlying quasi-geostrophic dynamics. Similar arguments apply in a wide class of problems involving a small parameter and sufficiently complex zeroth-order dynamics. A modified procedure is proposed which involves expanding only the fast modes of the system; this is equivalent to an asymptotic approximation of the slaving relation that relates the fast modes to the slow modes. The procedure is systematic and thus capable, at least in principle, of being carried to any order—unlike procedures based on truncations. We apply the procedure to construct higher-order balance approximations of the shallow-water equations. At the lowest order quasi-geostrophy emerges. At the next order the system incorporates gradient-wind balance, although the balance relations themselves involve only linear inversions and hence are easily applied. There is a large class of reduced systems associated with various choices for the slow variables, but the simplest ones appear to be those based on potential vorticity.

Visualizing probabilistic flood forecast information: expert preferences and perceptions of best practice in uncertainty communication

The aim of this article is to improve the communication of the probabilistic flood forecasts generated by hydrological ensemble prediction systems (HEPS) by understanding perceptions of different methods of visualizing probabilistic forecast information. This study focuses on interexpert communication and accounts for differences in visualization requirements based on the information content necessary for individual users. The perceptions of the expert group addressed in this study are important because they are the designers and primary users of existing HEPS. Nevertheless, they have sometimes resisted the release of uncertainty information to the general public because of doubts about whether it can be successfully communicated in ways that would be readily understood to nonexperts. In this article, we explore the strengths and weaknesses of existing HEPS visualization methods and thereby formulate some wider recommendations about the best practice for HEPS visualization and communication. We suggest that specific training on probabilistic forecasting would foster use of probabilistic forecasts with a wider range of applications. The result of a case study exercise showed that there is no overarching agreement between experts on how to display probabilistic forecasts and what they consider the essential information that should accompany plots and diagrams. In this article, we propose a list of minimum properties that, if consistently displayed with probabilistic forecasts, would make the products more easily understandable. Copyright © 2012 John Wiley & Sons, Ltd.

Best practice in the training, appointment and remuneration of members of dispute boards for large infrastructure projects

This paper reports part of a qualitative study into evolving practice in the implementation of the Dispute Adjudication Board (DAB) construction dispute resolution technique, a variant of the Dispute Review Board (DRB) concept used in the US and Canada. Data was collected through a focus group interview of 20 highly experienced dispute resolution practitioners from engineering and the law. The group was assembled from members of FIDIC-NET with direct experience of project DABs. The part reported here concerns practice and procedure for establishing DABs. The main findings are that: constitution of the DABs is often delayed because of either project owners' ignorance of the DAB process or deterrence by the cost of the DABs; such owners also tend to insist on appointing DAB members from local engineers and lawyers without sufficient understanding of the DAB process; rates of remuneration of DAB members vary widely; the training provision for DAB membership and advocacy skills is inadequate; the process of selecting candidates for DAB membership and negotiating the tripartite agreement between each member and the contractual parties needs to be navigated with great care to avoid raising ethical problems. The research contribution is threefold. First, it highlights the importance of realistic fees for DAB members within a standard framework in achieving timely establishment of a board that works well as a team. Second, it illustrates the use of qualitative focus group interview to study the impact of new contract terms from multiple stakeholder perspectives. Finally, it identifies areas where further research is needed.

Can profitable trading strategies be derived from investment best-sellers?

A glance along the finance shelves at any bookshop reveals a large number of books that seek to show readers how to ‘make a million’ or ‘beat the market’ with allegedly highly profitable equity trading strategies. This paper investigates whether useful trading strategies can be derived from popular books of investment strategy, with What Works on Wall Street by James P. O'Shaughnessy used as an example. Specifically, we test whether this strategy would have produced a similarly spectacular performance in the UK context as was demonstrated by the author for the US market. As part of our investigation, we highlight a general methodology for determining whether the observed superior performance of a trading rule could be attributed in part or in entirety to data mining. Overall, we find that the O'Shaughnessy rule performs reasonably well in the UK equity market, yielding higher returns than the FTSE All-Share Index, but lower returns than an equally weighted benchmark

Knowledge intensive processes characteristics and improvement: a banking best practice example

This paper identifies characteristics of knowledge intensive processes and a method to improve their performance based on analysis of investment banking front office processes. The inability to improve these processes using standard process improvement techniques confirmed that much of the process was not codified and depended on tacit knowledge and skills. This led to the use of a semi-structured analysis of the characteristics of the processes via a questionnaire to identify knowledge intensive processes characteristics that adds to existing theory. Further work identified innovative process analysis and change techniques that could generate improvements based on an analysis of their properties and the issue drivers. An improvement methodology was developed to harness a number of techniques that were found to effective in resolving the issue drivers and improving these knowledge intensive processes.

Sustainable social housing: examination of global best practice

This report reviews best social housing schemes from around the world, and makes recommendations for a more sustainable approach.

The importance of anisotropic Coulomb interaction in LaMnO3

In low-temperature anti-ferromagnetic LaMnO3, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund’s coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO3. The best parameter values for LaMnO3 within the DFT(PBEsol)+U framework are determined to be U = 8 eV and J = 1.9 eV.