A practical comparison of blinded methods for sample size reviews in survival data clinical trials.

This paper presents practical approaches to the problem of sample size re-estimation in the case of clinical trials with survival data when proportional hazards can be assumed. When data are readily available at the time of the review, on a full range of survival experiences across the recruited patients, it is shown that, as expected, performing a blinded re-estimation procedure is straightforward and can help to maintain the trial's pre-specified error rates. Two alternative methods for dealing with the situation where limited survival experiences are available at the time of the sample size review are then presented and compared. In this instance, extrapolation is required in order to undertake the sample size re-estimation. Worked examples, together with results from a simulation study are described. It is concluded that, as in the standard case, use of either extrapolation approach successfully protects the trial error rates. Copyright © 2012 John Wiley & Sons, Ltd.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Pianos for the people: the manufacture, marketing and sale of pianos as consumer durables, 1850-1914

During the second half of the nineteenth century, British society experienced a rise in real incomes and a change in its composition, with the expansion of the middle classes. These two factors led to a consumer revolution, with a growing, but still segmented, demand for household goods that could express status and aspiration. At the same time technological changes and new ways of marketing and selling goods made these goods more affordable. This paper analyzes these themes and the process of mediation that took place between producers, retailers, and consumers, by looking at the most culturally symbolic of nineteenth century consumer goods, the piano.

Variations in the mainstreaming of sustainability: a case study approach

The construction sector has a major role to play in delivering the transition to a low carbon economy and in contributing to sustainable development; however, integrating sustainability into everyday business remains a major challenge for the sector. This research explores the experience of three large construction and engineering consultancy firms in mainstreaming sustainability. The aim of the paper is to identify and explain variations in firm level strategies for mainstreaming sustainability. The three cases vary in the way in which sustainability is ramed – as a problem of risk, business opportunity or culture – and in its location within the firm. The research postulates that the mainstreaming of sustainability is not the uniform linear process often articulated in theories of strategic change and management, but varies with the dominant organisational culture and history of each firm. he paper concludes with a reflection on the implications of this analysis for management theories and for firm level strategies.

Updated estimate of aerosol direct radiative forcing from satellite observations and comparison against the Hadley Centre climate model

The fourth assessment report of the Intergovernmental Panel on Climate Change (IPCC) includes a comparison of observation-based and modeling-based estimates of the aerosol direct radiative forcing. In this comparison, satellite-based studies suggest a more negative aerosol direct radiative forcing than modeling studies. A previous satellite-based study, part of the IPCC comparison, uses aerosol optical depths and accumulation-mode fractions retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) at collection 4. The latest version of MODIS products, named collection 5, improves aerosol retrievals. Using these products, the direct forcing in the shortwave spectrum defined with respect to present-day natural aerosols is now estimated at −1.30 and −0.65 Wm−2 on a global clear-sky and all-sky average, respectively, for 2002. These values are still significantly more negative than the numbers reported by modeling studies. By accounting for differences between present-day natural and preindustrial aerosol concentrations, sampling biases, and investigating the impact of differences in the zonal distribution of anthropogenic aerosols, good agreement is reached between the direct forcing derived from MODIS and the Hadley Centre climate model HadGEM2-A over clear-sky oceans. Results also suggest that satellite estimates of anthropogenic aerosol optical depth over land should be coupled with a robust validation strategy in order to refine the observation-based estimate of aerosol direct radiative forcing. In addition, the complex problem of deriving the aerosol direct radiative forcing when aerosols are located above cloud still needs to be addressed.

Excise taxes and commodity promotion bayesian retrieval of the optimum

This article shows how the solution to the promotion problem—the problem of locating the optimal level of advertising in a downstream market—can be derived simply, empirically, and robustly through the application of some simple calculus and Bayesian econometrics. We derive the complete distribution of the level of promotion that maximizes producer surplus and generate recommendations about patterns as well as levels of expenditure that increase net returns. The theory and methods are applied to quarterly series (1978:2S1988:4) on red meats promotion by the Australian Meat and Live-Stock Corporation. A slightly different pattern of expenditure would have profited lamb producers

The application of Regional Climate Model output for the simulation of high-mountain permafrost scenarios

This study investigates the possibilities and limitations of using Regional Climate Model (RCM) output for the simulation of alpine permafrost scenarios. It focuses on the general problem of scale mismatch between RCMs and impact models and, in particular, the special challenges that arise when driving an impact model in topographically complex high-mountain environments with the output of an RCM. Two approaches are introduced that take into account the special difficulties in such areas, and thus enable the use of RCM for alpine permafrost scenario modelling. Intended as an initial example, they are applied at the area of Corvatsch (Upper Engadine, Switzerland) in order to demonstrate and discuss the application of the two approaches, rather than to provide an assessment of future changes in permafrost occurrence. There are still many uncertainties and inaccuracies inherent in climate and impact models, which increase when driving one model with the output of the other. Nevertheless, our study shows that the use of RCMs offers new and promising perspectives for the simulation of high-mountain permafrost scenarios

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

Design of a forecasting system for ECMWF

As laid out in its convention there are 8 different objectives for ECMWF. One of the major objectives will consist of the preparation, on a regular basis, of the data necessary for the preparation of medium-range weather forecasts. The interpretation of this item is that the Centre will make forecasts once a day for a prediction period of up to 10 days. It is also evident that the Centre should not carry out any real weather forecasting but merely disseminate to the member countries the basic forecasting parameters with an appropriate resolution in space and time. It follows from this that the forecasting system at the Centre must from the operational point of view be functionally integrated with the Weather Services of the Member Countries. The operational interface between ECMWF and the Member Countries must be properly specified in order to get a reasonable flexibility for both systems. The problem of making numerical atmospheric predictions for periods beyond 4-5 days differs substantially from 2-3 days forecasting. From the physical point we can define a medium range forecast as a forecast where the initial disturbances have lost their individual structure. However we are still interested to predict the atmosphere in a similar way as in short range forecasting which means that the model must be able to predict the dissipation and decay of the initial phenomena and the creation of new ones. With this definition, medium range forecasting is indeed very difficult and generally regarded as more difficult than extended forecasts, where we usually only predict time and space mean values. The predictability of atmospheric flow has been extensively studied during the last years in theoretical investigations and by numerical experiments. As has been discussed elsewhere in this publication (see pp 338 and 431) a 10-day forecast is apparently on the fringe of predictability.

A study of the microstructure and condition of thin sheets of painting support ivory using SEM and ESEM

This paper outlines a study of the microstructure of thin sheets of ivory used as a painting support for portrait miniatures. Warping of the ivory support is one of the main problems commonly found in portrait miniatures from the late eighteenth century and early nineteenth century. Portrait miniatures from this period are painted on very thin sheets of ivory that are often only 0.2 mm in thickness. Warping can lead to cracking of the ivory and can also accentuate flaking of the paint layer. The problem of warping in ivory has thus been of long-term interest to conservators who deal with portrait miniatures, including those at the Victoria and Albert (V&A) Museum. The causes of warping are complex. However, it should be noted that artists normally stuck the thin ivory sheets onto paper or card before commencing the painting. The possible causes of warping therefore are thought to relate to the differential reactions of the ivory/adhesive/paper or card layers to changes in relative humidity (RH). It is well known that ivory is hygroscopic and anisotropic.1 However, only a few scientific studies have been carried out related to this subject and systematic analyses of the morphological and microstructural changes due to changes in RH or moisture in such thin sheets of ivory have yet to be investigated.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot