Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

People or machines? Assessing the impacts of smart meters and load controllers in Italian office spaces

Government initiatives in several developed and developing countries to roll-out smart meters call for research on the sustainability impacts of these devices. In principle smart meters bring about higher control over energy theft and lower consumption, but require a high level of engagement by end-users. An alternative consists of load controllers, which control the load according to pre-set parameters. To date, research has focused on the impacts of these two alternatives separately. This study compares the sustainability impacts of smart meters and load controllers in an occupied office building in Italy. The assessment is carried out on three different floors of the same building. Findings show that demand reductions associated with a smart meter device are 5.2% higher than demand reductions associated with the load controller.

Parameter spaces of environmental fields responsible for cyclone development from tropics to extratropics

Objective cyclone tracking applied to a 30-yr reanalysis dataset shows that cyclone development in the summer and autumn seasons is active in the tropics and extratropics and inactive in the subtropics. To understand this geographically bimodal distribution of cyclone development associated with tropical and extratropical cyclones quantitatively, the direct relationship between cyclone types and their environments are assessed by using a parameter space of environmental variables [environmental parameter space (EPS)]. The number of cyclones is analyzed in terms of two different factors: the environmental conditions favorable for cyclone development and the area size that satisfies the favorable condition. The EPS analysis is mainly conducted for two representative environmental parameters that are commonly used for cyclone analysis: potential intensity for tropical cyclones and baroclinicity for extratropical cyclones. The geographically bimodal distribution is attributed to the high sensitivity of the cyclone development to the change in the environmental fields from tropics to extratropics. In addition, the bimodal distribution is partly attributed to the rapid change in the environmental fields from tropics to extratropics. The EPS analysis also shows that other environmental parameters, including relative humidity and vertical velocity, may enhance the contrast between the tropics (extratropics) and subtropics, whereas they are not essential for determining cyclone types. The relationship between cyclones and their environments is found to be similar between the hemispheres in the EPS, although the geographical distribution, particularly the longitudinal uniformity, is markedly different between the hemispheres.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

The spaces of the Wednesday Play (BBC TV 1964–1970): production, technology and style

The BBC television drama anthology The Wednesday Play, broadcast from 1964-70 on the BBC1 channel, was high-profile and often controversial in its time and has since been central to accounts of British television’s ‘golden age’. This article demonstrates that production technologies and methods were more diverse at that time than is now acknowledged, and that The Wednesday Play dramas drew both approving but also very critical responses from contemporary viewers and professional reviewers. This article analyses the ways that the physical spaces of production for different dramas in the series, and the different technologies of shooting and recording that were adopted in these production spaces, are associated with but do not determine aesthetic style. The adoption of single-camera location filming rather than the established production method of multi-camera studio videotaping in some of the dramas in the series has been important to The Wednesday Play’s significance, but each production method was used in different ways. The dramas drew their dramatic forms and aesthetic emphases from both theatre and cinema, as well as connecting with debates about the nature of drama for television. Institutional and regulatory frameworks such as control over staff working away from base, budgetary considerations and union agreements also impacted on decisions about how programmes were made. The article makes use of records from the BBC Written Archives Centre, as well as published scholarship. By placing The Wednesday Play in a range of overlapping historical contexts, its identity can be understood as transitional, differentiated and contested.

Writers' rooms: theories of contemporary authorship in portraits of creative spaces

This article analyzes two series of photographs and essays on writers’ rooms published in England and Canada in 2007 and 2008. The Guardian’s Writers Rooms series, with photographs by Eamon McCabe, ran in 2007. In the summer of 2008, The Vancouver International Writers and Readers Festival began to post its own version of The Guardian column on its website by displaying, each week leading up to the Festival in September, a different writer’s “writing space” and an accompanying paragraph. I argue that these images of writers’ rooms, which suggest a cultural fascination with authors’ private compositional practices and materials, reveal a great deal about theoretical constructions of authorship implicit in contemporary literary culture. Far from possessing the museum quality of dead authors’ spaces, rooms that are still being used, incorporating new forms of writing technology, and having drafts of manuscripts scattered around them, can offer insight into such well-worn and ineffable areas of speculation as inspiration, singular authorial genius, and literary productivity.

Rapid preconditioning of data for accelerating convex hull algorithms

Given a dataset of two-dimensional points in the plane with integer coordinates, the method proposed reduces a set of n points down to a set of s points s ≤ n, such that the convex hull on the set of s points is the same as the convex hull of the original set of n points. The method is O(n). It helps any convex hull algorithm run faster. The empirical analysis of a practical case shows a percentage reduction in points of over 98%, that is reflected as a faster computation with a speedup factor of at least 4.

Local spaces: open minds - inspirational ideas for managing lowland commons and other green spaces

The Chiltern commons are typical of those in the south east of England: small and numerous, but with the potential to provide important natural green space whilst contributing to environmental sustainability. In order to keep commons in good heart, they need to be managed. However, as activities such as grazing and coppicing become unviable on the commons, owners need to find sustainable roles beyond traditional agricultural and silvicultural practices. This paper examines ways of making management pay. It begins by exploring the economic, social and environmental challenges of sustainable management within the context of contemporary life. Section 2 identifies the different ways in which revenue contributions might be made towards the management of commons. Section 3 examines the relevant legal and other restrictions and Section 4 offers insights into where management proposals might offer multiple positive benefits, but also where there is the potential to cause conflict with environmental and social interests. Section 5 explores alternative funding streams for commons. Finally, Section 6 concludes with practical tips for the owners and managers of commons in the Chilterns and identifies areas for further research. Full references, links and resources are provided in the footnotes and appendix.

Objective Empirical Mode Decomposition metric

Empirical Mode Decomposition (EMD) is a data driven technique for extraction of oscillatory components from data. Although it has been introduced over 15 years ago, its mathematical foundations are still missing which also implies lack of objective metrics for decomposed set evaluation. Most common technique for assessing results of EMD is their visual inspection, which is very subjective. This article provides objective measures for assessing EMD results based on the original definition of oscillatory components.

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

Promenades in Enlightenment Madrid: the tapestry cartoons and new social spaces

Discusses how the painters of the Royal Tapestry Factory of Santa Barbara in Madrid depicted the new social spaces of the capital in the cartoons designed to be turned into tapestries for Royal apartments. The cultural and sociological role of the 'paseo' or 'promenade' is also considered.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.