Estimation of the Rate-Distortion Function

Motivated by questions in lossy data compression and by theoretical considerations, we examine the problem of estimating the rate-distortion function of an unknown (not necessarily discrete-valued) source from empirical data. Our focus is the behavior of the so-called "plug-in" estimator, which is simply the rate-distortion function of the empirical distribution of the observed data. Sufficient conditions are given for its consistency, and examples are provided to demonstrate that in certain cases it fails to converge to the true rate-distortion function. The analysis of its performance is complicated by the fact that the rate-distortion function is not continuous in the source distribution; the underlying mathematical problem is closely related to the classical problem of establishing the consistency of maximum likelihood estimators. General consistency results are given for the plug-in estimator applied to a broad class of sources, including all stationary and ergodic ones. A more general class of estimation problems is also considered, arising in the context of lossy data compression when the allowed class of coding distributions is restricted; analogous results are developed for the plug-in estimator in that case. Finally, consistency theorems are formulated for modified (e.g., penalized) versions of the plug-in, and for estimating the optimal reproduction distribution.Comment: 18 pages, no figures [v2: removed an example with an error; corrected typos; a shortened version will appear in IEEE Trans. Inform. Theory

Backing the horse or the jockey? Due diligence, agency costs, information and the evaluation of risk by business angel investors

This paper explores the argument that business angel investors are more concerned with managing and minimising agency risk than market risk. Based on data on the due diligence process from a survey of business angels in the UK, the paper concludes that business angels do view entrepreneur characteristics and experience as having the greatest impact on the perceived riskiness of an investment opportunity. Further, they emphasise personal and informal over formal sources of information in the due diligence process, and seek information on both the entrepreneur and the venture in determining valuation. Indeed, the reliance of business angels on short-term and subjective information to value investment opportunities leads to the conclusion that their approach to valuation is not a function of the conventional protocols of financial analysis, but of personal relations and assessment

Approximate methods for the solution of quantum wires and dots : Connection rules between pyramidal, cuboidal, and cubic dots

Energy eigenvalues of the electronic ground state are calculated for rectangular and triangular GaAs/Ga(0.6)Al(0.4)As quantum wires as well as for cuboidal and pyramidal quantum dots of the same material. The wire (dot) geometries are approximated by a superposition of perpendicular independent finite one-dimensional potential wells. A perturbation is added to the system to improve the approximation. Excellent agreement with more complex treatments is obtained. The method is applied to investigate the ground state energy dependence on volume and aspect ratio for finite barrier cubic, cuboidal, and pyramidal quantum dots. It is shown that the energy eigenvalues of cubes are equal to those of cuboids of the same volume and aspect ratio similar to one. In addition, a relationship has been found between the volumes of pyramidal quantum dots (often the result of self-assembling in strain layered epitaxy) and cuboidal dots with the same ground state energy and aspect ratios close to one. © 1999 American Institute of Physics

An unexpected oxidation : NaK5Cl2(S2O6)2 revisited

Acknowledgements We thank the EPSRC National Crystallography Service (University of Southampton) for the X-ray data collection.Peer reviewedPublisher PD

Streamlined life cycle assessment of transparent silica aerogel made by supercritical drying

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 ElsevierWhen developing sustainable building fabric technologies, it is essential that the energy use and CO2 burden arising from manufacture does not outweigh the respective in-use savings. This study investigates this paradigm by carrying out a streamlined life cycle assessment (LCA) of silica aerogel. This unique, nanoporous translucent insulation material has the lowest thermal conductivity of any solid, retaining up to four times as much heat as conventional insulation, whilst being highly transparent to light and solar radiation. Monolithic silica aerogel has been cited as the ‘holy grail’ of future glazing technology. Alternatively, translucent granular aerogel is now being produced on a commercial scale. In each case, many solvents are used in production, often accompanied by intensive drying processes, which may consume large amounts of energy and CO2. To date, there has been no peer-reviewed LCA of this material conducted to the ISO 14000 standard. Primary data for this ‘cradle-to-factory gate’ LCA is collected for silica aerogel made by low and high temperature supercritical drying. In both cases, the mass of raw materials and electricity usage for each process is monitored to determine the total energy use and CO2 burden. Findings are compared against the predicted operational savings arising from retrofitting translucent silica aerogel to a single glazed window to upgrade its thermal performance. Results should be treated as a conservative estimate as the aerogel is produced in a laboratory, which has not been developed for mass manufacture or refined to reduce its environmental impact. Furthermore, the samples are small and assumptions to upscale the manufacturing volume occur without major changes to production steps or equipment used. Despite this, parity between the CO2 burden and CO2 savings is achieved in less than 2 years, indicating that silica aerogel can provide a measurable environmental benefit.This work is funded by the EPSRC, Brunel University and Buro Happold Ltd, the University of Bath is funded by the EPSRC grant EP/F018622/1

Designing probiotic therapies with broad-spectrum activity against a wildlife pathogen

Host-associated microbes form an important component of immunity that protect against infection by pathogens. Treating wild individuals with these protective microbes, known as probiotics, can reduce rates of infection and disease in both wild and captive settings. However, the utility of probiotics for tackling wildlife disease requires that they offer consistent protection across the broad genomic variation of the pathogen that hosts can encounter in natural settings. Here we develop multi-isolate probiotic consortia with the aim of effecting broad-spectrum inhibition of growth of the lethal amphibian pathogen Batrachochytrium dendrobatidis (Bd) when tested against nine Bd isolates from two distinct lineages. Though we achieved strong growth inhibition between 70 and 100% for seven Bd isolates, two isolates appeared consistently resistant to inhibition, irrespective of probiotic strategy employed. We found no evidence that genomic relatedness of the chytrid predicted similarity of inhibition scores, nor that increasing the genetic diversity of the bacterial consortia could offer stronger inhibition of pathogen growth, even for the two resistant isolates. Our findings have important consequences for the application of probiotics to mitigate wildlife diseases in the face of extensive pathogen genomic variation

Keck IR Spectroscopy of WZ Sge: Detection of Molecular Emission from the Accretion Disk

Time-resolved IR spectroscopy of WZ Sge was obtained using NIRSPEC on Keck II. We detect CO and H$_{\rm 2}$ emission from the accretion disk placing WZ Sge into a rarefied class of astronomical objects including YSOs and high luminosity early-type stars. During the eclipse phase, the molecular emission greatly weakens but no firm evidence for the secondary star is seen allowing new limits on its luminosity to be determined. The detection of molecular emission provides physical properties within the outer disk of T=3000K and N$_H$$>10^{10}$ cm$^{-3}$. Such a cool, dense region, not associated with areas of H I and He I emission, provides the first observational confirmation of predictions made by accretion disk models.Comment: 10 pages, 3 figures. Accepted for publication in ApJ Letter

Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field

Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov–Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium

Clear air turbulence

Research on forecasting, detection, and incidents of clear air turbulenc