Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

Dynamic trust models for ubiquitous computing environments

A significant characteristic of ubiquitous computing is the need for interactions of highly mobile entities to be secure: secure both for the entity and the environment in which the entity operates. Moreover, ubiquitous computing is also characterised by partial views over the state of the global environment, implying that we cannot guarantee that an environment can always verify the properties of the mobile entity that it has just received. Secure in this context encompasses both the need for cryptographic security and the need for trust, on the part of both parties, that the interaction is functioning as expected. In this paper we make a broad assumption that trust and cryptographic security can be considered as orthogonal concerns (i.e. an entity might encrypt a deliberately incorrect answer to a legitimate request). We assume the existence of reliable encryption techniques and focus on the characteristics of a model that supports the management of the trust relationships between two entities during an interaction in a ubiquitous environment

The SECURE collaboration model

The SECURE project has shown how trust can be made computationally tractable while retaining a reasonable connection with human and social notions of trust. SECURE has produced a well-founded theory of trust that has been tested and refined through use in real software such as collaborative spam filtering and electronic purse. The software comprises the SECURE kernel with extensions for policy specification by application developers. It has yet to be applied to large-scale, multi-domain distributed systems taking different application contexts into account. The project has not considered privacy in evidence distribution, a crucial issue for many application domains, including public services such as healthcare and police. The SECURE collaboration model has similarities with the trust domain concept, embodying the interaction set of a principal, but SECURE is primarily concerned with pseudonymous entities rather than domain-structured systems

Retrograde Accretion and Merging Supermassive Black Holes

We investigate whether a circumbinary gas disc can coalesce a supermassive black hole binary system in the centre of a galaxy. This is known to be problematic for a prograde disc. We show that in contrast, interaction with a retrograde circumbinary disc is considerably more effective in shrinking the binary because there are no orbital resonances. The binary directly absorbs negative angular momentum from the circumbinary disc by capturing gas into a disc around the secondary black hole, or discs around both holes if the binary mass ratio is close to unity. In many cases the binary orbit becomes eccentric, shortening the pericentre distance as the eccentricity grows. In all cases the binary coalesces once it has absorbed the angular momentum of a gas mass comparable to that of the secondary black hole. Importantly, this conclusion is unaffected even if the gas inflow rate through the disc is formally super--Eddington for either hole. The coalescence timescale is therefore always $\sim M_2/\dot M$, where $M_2$ is the secondary black hole mass and $\dot M$ the inflow rate through the circumbinary disc.Comment: 8 pages, 4 figures. Accepted for publication in MNRAS. Movies of the simulations can be found at: http://www.astro.le.ac.uk/users/cjn12/RetroBinaryMovies.htm

50 Years of Spaceflight with Fourier Transform Spectrometers (FTS) Built at NASA GSFC

Over the past 50 years, NASA Goddard Space Flight Center (GSFC) has been developing, building, testing and flying a series of Fourier Transform Spectrometers (FTS). This began with the IRIS instruments on the Earth-orbiting Nimbus satellites and progressed to more sophisticated designs optimized for interplanetary spacecraft sent to Mars and later to the outer solar system. Adaptions have been made over time, including progressively higher spectral resolution, sensitivity, numbers of detectors and complexity. Instrument operating temperatures have decreased to enable remote sensing of the cold giant planet systems. In this paper we describe the historical evolution of this instrument line, comparing and contrasting different aspects such as optical design and materials, detector types and data handling. We conclude by looking towards the future. At present the CIRS-Lite prototype is being tested at NASA GSFC for potential use on a future mission to the ice giants, Uranus and Neptune. Surpassing the previous performance of the Voyager IRIS instruments remains challenging, and new technologies that could enable these measurements are discussed

Methods of editing cloud and atmospheric layer affected pixels from satellite data

Subvisible cirrus clouds (SCi) were easily distinguished in mid-infrared (MIR) TIROS-N daytime data from south Texas and northeast Mexico. The MIR (3.55-3.93 micrometer) pixel digital count means of the SCi affected areas were more than 3.5 standard deviations on the cold side of the scene means. (These standard deviations were made free of the effects of unusual instrument error by factoring out the Ch 3 MIR noise on the basis of detailed examination of noisy and noise-free pixels). SCi affected areas in the IR Ch 4 (10.5-11.5 micrometer) appeared cooler than the general scene, but were not as prominent as in Ch 3, being less than 2 standard deviations from the scene mean. Ch 3 and 4 standard deviations and coefficients of variation are not reliable indicators, by themselves, of the presence of SCi because land features can have similar statistical properties

Randomised, controlled trial of alternating pressure mattresses compared with alternating pressure overlays for the prevention of pressure ulcers : PRESSURE (pressure relieving support surfaces) trial

Objective To compare whether differences exist between alternating pressure overlays and alternating pressure mattresses in the development of new pressure ulcers, healing of existing pressure ulcers, and patient acceptability. Design Pragmatic, open, multicentre, randomised controlled trial. Setting 11 hospitals in six NHS trusts. Participants 1972 people admitted to hospital as acute or elective patients. Interventions Participants were randomised to an alternating pressure mattress (n = 982) of- an alternating pressure overlay (n = 990). Main outcome measures The proportion of participants developing a new pressure ulcer of grade 2 or worse; time to development of new pressure ulcers; proportions of participants developing a new ulcer within 30 days; healing of existing pressure ulcers; and patient acceptability Results Intention to treat analysis found no difference in the proportions of participants developing a new pressure ulcer of grade 2 or worse (10.7% overlay patients, 10.3% mattress patients; difference 0.4%, 95% confidence interval - 23% to 3.1%, P = 0.75). More overlay patients requested change owing to dissatisfaction (23.3%) than mattress patients (18.9%, P = 0.02). Conclusion No difference was found between alternating pressure mattresses and alternating pressure overlays in the proportion of people who develop a pressure ulcer

Methods of editing cloud and atmospheric layer affected pixels from satellite data

The location and migration of cloud, land and water features were examined in spectral space (reflective VIS vs. emissive IR). Daytime HCMM data showed two distinct types of cloud affected pixels in the south Texas test area. High altitude cirrus and/or cirrostratus and "subvisible cirrus" (SCi) reflected the same or only slightly more than land features. In the emissive band, the digital counts ranged from 1 to over 75 and overlapped land features. Pixels consisting of cumulus clouds, or of mixed cumulus and landscape, clustered in a different area of spectral space than the high altitude cloud pixels. Cumulus affected pixels were more reflective than land and water pixels. In August the high altitude clouds and SCi were more emissive than similar clouds were in July. Four-channel TIROS-N data were examined with the objective of developing a multispectral screening technique for removing SCi contaminated data