Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries

The numerical analysis of spectral methods when non-constant coefficients appear in the equation, either due to the original statement of the equations or to take into account the deformed geometry, is presented. Particular attention is devoted to the optimality of the discretization even for low values of the discretization parameter. The effect of some overintegration is also addressed, in order to possibly improve the accuracy of the discretization

Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations

A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization

Spectral element methods: Algorithms and architectures

Spectral element methods are high-order weighted residual techniques for partial differential equations that combine the geometric flexibility of finite element methods with the rapid convergence of spectral techniques. Spectral element methods are described for the simulation of incompressible fluid flows, with special emphasis on implementation of spectral element techniques on medium-grained parallel processors. Two parallel architectures are considered: the first, a commercially available message-passing hypercube system; the second, a developmental reconfigurable architecture based on Geometry-Defining Processors. High parallel efficiency is obtained in hypercube spectral element computations, indicating that load balancing and communication issues can be successfully addressed by a high-order technique/medium-grained processor algorithm-architecture coupling

Sensitive Coverage Saves Lives: Improving media portrayal of suicidal behaviour

The report outlines the results of consultations with journalists, suicide prevention agencies and mental health groups conducted by the journalism ethics charity MediaWise. It makes recommendations for action by media organisations and suicide prevention agencies

Effects of simulated environmental changes on growth and growth form in a late snowbed population of pohlia wahlenbergii (Web. et Mohr) Andr

In a factorial field experiment we increased the temperature (OpenTop Chambers) and nutrients (nitrogen, phosphorus, and potassium[NPK]) to simulate predicted future climate changes and studiedthe growth response of the acrocarpous bryophyte Pohliawahlenbergii (Bryaceae) in a wet snowbed environment. The speciesshows a positive growth-length response to added nutrients andincreased temperature. The stronger response to nutrientsindicates a strong limitation of nutrients in the snowbedenvironment. There was an immediate response to nutrienttreatment, whereas the temperature response was delayed. Thegrowth response shows a clear interaction between temperature andnutrients. The immediate positive growth response is interpretedas a function of the wet habitat, since water makes the addednutrients immediately available to the plants. The growth formchanged toward a more lax (loose) and desiccation-intolerant formwith added nutrients. In a climate change scenario based on theseresults we hypothesize that bryophyte response will depend on thewater availability from precipitation and from meltwater. In adrier environment we predict that bryophytes will become moreconstrained toward areas with a high continuity of meltwater,whereas increased precipitation may compensate for any changes ingrowth form, which would be positive for bryophytes

Afterglow Light Curves and Broken Power Laws: A Statistical Study

In gamma-ray burst research it is quite common to fit the afterglow light curves with a broken power law to interpret the data. We apply this method to a computer simulated population of afterglows and find systematic differences between the known model parameters of the population and the ones derived from the power law fits. In general, the slope of the electron energy distribution is overestimated from the pre-break light curve slope while being underestimated from the post-break slope. We also find that the jet opening angle derived from the fits is overestimated in narrow jets and underestimated in wider ones. Results from fitting afterglow light curves with broken power laws must therefore be interpreted with caution since the uncertainties in the derived parameters might be larger than estimated from the fit. This may have implications for Hubble diagrams constructed using gamma-ray burst data.Comment: 4 pages, 5 figures, accepted for publication in ApJ Letter

Murine models of Alzheimer's disease and their use in developing immunotherapies

AbstractAlzheimer's disease (AD) is one of the categories of neurodegenerative diseases characterized by a conformational change of a normal protein into a pathological conformer with a high β-sheet content that renders it resistant to degradation and neurotoxic. In AD, the normal soluble amyloid β (sAβ) peptide is converted into oligomeric/fibrillar Aβ. The oligomeric forms of Aβ are thought to be the most toxic, while fibrillar Aβ becomes deposited as amyloid plaques and congophilic angiopathy, which both serve as neuropathological markers of the disease. An additional important feature of AD is the accumulation of abnormally phosphorylated tau as soluble toxic oligomers and as neurofibrillary tangles. Many therapeutic interventions are under investigation to prevent and treat AD. The testing of these diverse approaches to ameliorate AD pathology has been made possible by the existence of numerous transgenic mouse models which each mirror specific aspects of AD pathology. None of the current murine models is a perfect match of the human disease. Perhaps the most exciting of the therapeutic approaches being developed is immunomodulation targeting the aggregating proteins, Aβ and tau. This type of AD therapy is currently being assessed in many transgenic mouse models, and promising findings have led to clinical trials. However, there is a discrepancy between results in murine models and ongoing clinical trials, which highlight the limitations of these models and also of our understanding of the underlying etiology and pathogenesis of AD. Because of these uncertainties, Tg models for AD are continuously being refined with the aim to better understand the disease and to enhance the predictive validity of potential treatments such as immunotherapies

Parallelization in time through tensor-product space-time solvers

In this note, we extend the fast tensor-product algorithm for the simulation of time-dependent partial differential equations. We use the natural tensorization of the space-time domain to propose, after discretization, a set of independent problems, each one with the complexity of a single steady problem. This allows for an efficient parallel implementation that is already interesting on small architectures, but that can also be combined with standard domain-decomposition-based algorithms providing a further direction of parallelism on large computer platforms. Preliminary numerical simulations are presented for a one-dimensional unsteady heat equation