Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Atmospheric electric fields during the Carrington flare

Karen Aplin and Giles Harrison examine international records of the 1859 Carrington flare and consider what they mean for our understanding of space weather today. Space weather is increasingly recognized as a hazard to modern societies, and one way to assess the extent of its possible impact is through analysis of historic space weather events. One such event was the massive solar storm of late August and early September 1859. This is now widely known as the “Carrington flare” or “Carrington event” after the visual solar emissions on 1 September first reported by the Victorian astronomer Richard Carrington from his observatory in Redhill, Surrey (Carrington 1859). The related aurorae and subsequent effects on telegraph networks are well documented (e.g. Clark 2007, Boteler 2006), but use of modern techniques, such as analysis of nitrates produced by solar protons in ice cores to retrospectively assess the nature of the solar flare, has proved problematic (Wolff et al. 2012). This means that there is still very little quantitative information about the flare beyond magnetic observations (e.g. Viljanen et al. 2014).

What is outside? The early years foundation stage in England: outdoor facilities, organisation and staff attitudes

The purpose of this paper is to report on the facilities available, organisation of, and staff attitudes to early years outdoor education from schools within the south east of England, focusing on provision for children aged three to five. One component of the successful education of the child involves providing an ‘environment for learning’, including the facilities, layout and routines. This paper presents findings concerning the type and variety of facilities available outside; the various styles of organisation of the space; staff attitudes about: their roles, their aims for the environment, children’s behaviour and learning, and perceived drawbacks to practice. This paper draws on empirical data collected from schools within the University of Reading partnership. The findings suggest that although all early years settings must adhere to the statutory framework there are a range of facilities available, and there are a number of ways this environment is organised. Further there appears to be uncertainty about the adult role outside and the aims for activities. The conclusions drawn indicate that staff do not appear to be linking their aims for outdoor education to the facilities provided or to their actions outside. This means there is not a clear link between what staff provide outside and the declared ambitions for learning. This study is important as all educators need to be certain about their aims for education to ensure best outcomes for children. The implications of these findings for early years teachers are that they need to be able to articulate their aims for outdoor education and to provide the correct facilities to achieve these aims. Finally this study was undertaken to raise debate, posit questions and to ascertain the parameters for further research about the early years outdoor environment.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The Phantom Carriage (1921)

The reputation of The Phantom Carriage (Körkarlen) as one of the major films of Swedish silent cinema is in some respects securely established. Yet the film has attracted surprisingly little detailed discussion. It may be that its most striking stylistic features have deflected or discouraged closer scrutiny. Tom Gunning, for instance, in making the case for Sjöström’s Masterman, argues that ‘Körkarlen wears its technique on its sleeve, overtly displays its unquestionable mastery of superimposition and complex narrative structure. Mästerman tucks its mastery of editing and composition up its sleeve, so to speak’. This article makes an argument for a different evaluation of The Phantom Carriage, bringing a critical and interpretative understanding of the film’s style into conversation with the historical accounts of film form which predominate in the scholarship around silent cinema. It suggests that the film achieves ‘mastery of editing and composition’ with a flexibility and fluidity in the construction of dramatic space that is in itself remarkable for its period, but that Sjöström’s achievements extend well beyond his handling of film space. Specifically, it discusses a segment which is in several respects at the heart of the film: the first meeting between the two central characters, David Holm (Victor Sjöström) and Sister Edit (Astrid Holm); it spans the film’s exact mid-point; and at almost twelve and a half minutes it is the longest uninterrupted passage to take place in a single setting. The chapter argues that the dramatic and structural centrality of the hostel segment is paralleled by its remarkably rich articulation of the relationships between action, character and space. We show how Sjöström’s creation of a three-dimensional filmic space - with no hint of frontality - becomes the basis for a reciprocal relationship between spatial naturalism and performance style, and for a mise-en-scene that can take on discrete interpretive force. The argument also places the hostel sequences within the film as a whole in order to show how relationships articulated through the detailed decisions in this section take on their full resonance within patterns and motifs that develop across the film.

Concepts for a geostationary-like polar missions

An evidence-led scientific case for development of a space-based polar remote sensing platform at geostationary-like (GEO-like) altitudes is developed through methods including a data user survey. Whilst a GEO platform provides a nearstatic perspective, multiple platforms are required to provide circumferential coverage. Systems for achieving GEO-like polar observation likewise require multiple platforms however the perspective is non-stationery. A key choice is between designs that provide complete polar view from a single platform at any given instant, and designs where this is obtained by compositing partial views from multiple sensors. Users foresee an increased challenge in extracting geophysical information from composite images and consider the use of non-composited images advantageous. Users also find the placement of apogee over the pole to be preferable to the alternative scenarios. Thus, a clear majority of data users find the “Taranis” orbit concept to be better than a critical inclination orbit, due to the improved perspective offered. The geophysical products that would benefit from a GEO-like polar platform are mainly estimated from radiances in the visible/near infrared and thermal parts of the electromagnetic spectrum, which is consistent with currently proven technologies from GEO. Based on the survey results, needs analysis, and current technology proven from GEO, scientific and observation requirements are developed along with two instrument concepts with eight and four channels, based on Flexible Combined Imager heritage. It is found that an operational system could, mostly likely, be deployed from an Ariane 5 ES to a 16-hour orbit, while a proof-of-concept system could be deployed from a Soyuz launch to the same orbit.

Designing in caves: using immersive visualisations in design practice

This paper describes a study of the use of immersive Virtual reality technologies in the design of a new hospital. It uses Schön’s concept of reflective practice and video-based methods to analyse the ways design teams approach and employ a full scale 3D immersive environment – a CAVE – in collaborative design work. The analysis describes four themes relating to reflective practice occurring in the setting: orienting to the CAVE technology itself, orienting to the representation of the specific design within the CAVE, activities accounting for, or exploring alternatives within the design for the use and users of the space, and more strategic interactions around how to best represent the design and model to the client within the CAVE setting. The analysis also reveals some unique aspects of design work in this environment. Perhaps most significantly, rather than enhancing or adding to an existing understanding of design through paper based or non-immersive digital representations, it is often acting to challenge or surprise the participants as they experience the immersive, full scale version of their own design.

Phase 1

Exhibition investigating the role of different methods of drawing in the visualization of architectural space

Green infrastructure and ecosystem services - is the devil in the detail?

Background - Green infrastructure is a strategic network of green spaces designed to deliver ecosystem services to human communities. Green infrastructure is a convenient concept for urban policy makers, but the term is used too-generically and with limited understanding of the relative values or benefits of different types of green space and how these complement one another. At a finer scale/more practical level– little consideration is given to the composition of the plant-communities, yet this is what ultimately defines extent of service provision. This paper calls for greater attention to be paid to urban plantings with respect to ecosystem service delivery and for plant science to engage more-fully in identifying those plants that promote various services. Scope - Many urban plantings are designed based on aesthetics alone, with limited thought on how plant choice/composition provides other ecosystem services. Research is beginning to demonstrate, however, that landscape plants provide a range of important services, such as helping mitigate floods and alleviating heat islands, but that not all species are equally effective. The paper reviews a number of important services and demonstrates how genotype choice radically affects service delivery. Conclusions – Although research is in its infancy, data is being generated that relates plant traits to specific services; thereby helping identify genotypes that optimise service delivery. The urban environment, however, will become exceedingly bland if future planting is simply restricted to monocultures of a few ‘functional’ genotypes. Therefore, further information is required on how to design plant communities where the plants identified:- a/ provide more than a single benefit (multi-functionality) b/ complement each other in maximising the range of benefits that can be delivered in one location and c/ continue to maintain public acceptance through diversity. The identification/development of functional landscape plants is an exciting and potentially high impact arena for plant science.

A Plant Needs Ants like a Dog Needs Fleas: Myrmelachista schumanni Ants Gall Many Tree Species to Create Housing

Hundreds of tropical plant species house ant colonies in specialized chambers called domatia. When, in 1873, Richard Spruce likened plant-ants to fleas and asserted that domatia are ant-created galls, he incited a debate that lasted almost a century. Although we now know that domatia are not galls and that most ant-plant interactions are mutualisms and not parasitisms, we revisit Spruce`s suggestion that ants can gall in light of our observations of the plant-ant Myrmelachista schumanni, which creates clearings in the Amazonian rain forest called ""supay-chakras,"" or ""devil`s gardens."" We observed swollen scars on the trunks of nonmyrmecophytic canopy trees surrounding supay-chakras, and within these swellings, we found networks of cavities inhabited by M. schumanni. Here, we summarize the evidence supporting the hypothesis that M. schumanni ants make these galls, and we hypothesize that the adaptive benefit of galling is to increase the amount of nesting space available to M. schumanni colonies.

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass mu not equal 0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy-momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g(mu,nu)rho with rho > 0, thus providing a concrete quantum field theoretic model of the cosmological constant. This rho represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p <= 0. (C) 2009 Elsevier Inc. All rights reserved.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

Piano Performance at a New York Trade School Commencement

Six piano players spread across the front of the stage at the New York Trade School perform at a commencement ceremony. The graduates can be seen sitting in the first few rows of the auditorium with guests filling up the rest of the space. On the dais several administrators from the New York Trade School are shown. Black and white photograph.