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.

Rerum cognoscere causas: part II - opportunities generated by the agency/structure debate and suggestions for clarifying the social theoretic position of system dynamics

This is the second half of a two-part paper dealing with the social theoretic assumptions underlying system dynamics. In the first half it was concluded that analysing system dynamics using traditional, paradigm-based social theories is highly problematic. An innovative and potentially fruitful resolution is now proposed to these problems. In the first section it is argued that in order to find an appropriate social theoretic home for system dynamics it is necessary to look to a key exchange in contemporary social science: the agency/structure debate. This debate aims to move beyond both the theories based only on the actions of individual human agents, and those theories that emphasise only structural influences. Emerging from this debate are various theories that instead aim to unite the human agent view of the social realm with views that concentrate solely on system structure. It is argued that system dynamics is best viewed as being implicitly grounded in such theories. The main conclusion is therefore that system dynamics can contribute to an important part of social thinking by providing a formal approach for explicating social mechanisms. This conclusion is of general significance for system dynamics. However, the over-arching aim of the two-part paper is to increase the understanding of system dynamics in related disciplines. Four suggestions are therefore offered for how the system dynamics method might be extended further into the social sciences. It is argued that, presented in the right way, the formal yet contingent feedback causality thinking of system dynamics should diffuse widely in the social sciences and make a distinctive and important contribution to them. Felix qui potuit rerum cognoscere causas Happy is he who comes to know the causes of things Virgil - Georgics, Book II, line 490. 29 BCE

Word position and stress effects in consonant cluster perception and production

The aim of the present study was to investigate whether the saliency effect for word beginnings reported in children with Dyslexia (Marshall & van der Lely, 2009) can be found also in TD children. Thirty-four TD Italian children aged 8-10 completed two specifically designed tasks: a production task and a perception task. Both tasks used nonwords containing clusters consisting of plosive plus liquid (eg. pl). Clusters could be either in a stressed or in an unstressed syllable, and could be either in initial position (first syllable) or in medial position (second syllable). In the production task children were asked to repeat the non-words. In the perception task, the children were asked to discriminate between two nonwords differing in one phoneme belonging to a cluster by reporting whether two repetitions were the same or different. Results from the production task showed that children are more accurate in repeating stressed than unstressed syllables, but there was no difference with respect to position of the cluster. Results from the perception task showed that children performed more accurately when discriminating word initial contrasts than when discriminating word medial contrasts, especially if the cluster was unstressed. Implications of this finding for clinical assessments are discussed.

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.

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.

Word length and landing position effects during reading in children and adults

The present study examined the effects of word length on children’s eye movement behaviour when other variables were carefully controlled. Importantly, the results showed that word length influenced children’s reading times and fixation positions on words. Furthermore, children exhibited stronger word length effects than adults in gaze durations and refixations. Adults and children generally did not differ in initial landing positions, but did differ in refixation behaviour. Overall, the results indicated that while adults and children show similar effects of word length for early measures of eye movement behaviour, differences emerge in later measures.

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.

Gendered struggles over land: shifting inheritance practices among the Serer in rural Senegal

Although women's land rights are often affirmed unequivocally in constitutions and international human rights conventions in many African countries, customary practices usually prevail on the ground and often deny women's land inheritance. Yet land inheritance often goes unnoticed in wider policy and development initiatives to promote women's equal access to land. This paper draws on feminist ethnographic research among the Serer ethnic group in two contrasting rural communities in Senegal. Through analysis of land governance, power relations and 'technologies of the self', this article shows how land inheritance rights are contingent on the specific effects of intersectionality in particular places. The contradictions of legal pluralism, greater adherence to Islam and decentralisation led to greater application of patrilineal inheritance practices. Gender, religion and ethnicity intersected with individuals' marital position, status, generation and socio-ecological change to constrain land inheritance rights for women, particularly daughters, and widows who had been in polygamous unions and who remarried. Although some women were aware that they were legally entitled to inherit a share of the land, they tended not to 'demand their rights'. In participatory workshops, micro-scale shifts in women's and men's positionings reveal a recognition of the gender discriminatory nature of customary and Islamic law and a desire to 'change with the times'. While the effects of 'reverse' discourses are ambiguous and potentially reinforce prevailing patriarchal power regimes, 'counter' discourses, which emerged in participatory spaces, may challenge customary practices and move closer to a rights-based approach to gender equality and women's land inheritance.

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.

On competitive bidding: scoring and position probability graphs

Iso-score curves graph (iSCG) and mathematical relationships between Scoring Parameters (SP) and Forecasting Parameters (FP) can be used in Economic Scoring Formulas (ESF) used in tendering to distribute the score among bidders in the economic part of a proposal. Each contracting authority must set an ESF when publishing tender specifications and the strategy of each bidder will differ depending on the ESF selected and the weight of the overall proposal scoring. The various mathematical relationships and density distributions that describe the main SPs and FPs, and the representation of tendering data by means of iSCGs, enable the generation of two new types of graphs that can be very useful for bidders who want to be more competitive: the scoring and position probability graphs.

Modeling bidding competitiveness and position performance in multi-attribute construction auctions

Currently, multi-attribute auctions are becoming widespread awarding mechanisms for contracts in construction, and in these auctions, criteria other than price are taken into account for ranking bidder proposals. Therefore, being the lowest-price bidder is no longer a guarantee of being awarded, thus increasing the importance of measuring any bidder’s performance when not only the first position (lowest price) matters. Modeling position performance allows a tender manager to calculate the probability curves related to the more likely positions to be occupied by any bidder who enters a competitive auction irrespective of the actual number of future participating bidders. This paper details a practical methodology based on simple statistical calculations for modeling the performance of a single bidder or a group of bidders, constituting a useful resource for analyzing one’s own success while benchmarking potential bidding competitors.

ESC Working Group on Myocardial Function Position Paper: how to study the right ventricle in experimental models

The right ventricle has become an increasing focus in cardiovascular research. In this position paper, we give a brief overview of the specific pathophysiological features of the right ventricle, with particular emphasis on functional and molecular modifications as well as therapeutic strategies in chronic overload, highlighting the differences from the left ventricle. Importantly, we put together recommendations on promising topics of research in the field, experimental study design, and functional evaluation of the right ventricle in experimental models, from non-invasive methodologies to haemodynamic evaluation and ex vivo set-ups.