Computable error bounds for approximate solutions of ordinary differential equations

PhD ThesisThis thesis is concerned with an error analysis of approximate methods for second order linear two point boundary value problems, in particular for the method of collocation using piecewise polynomial approximations. As in previous related work on strict error bounds an operator theoretic approach is taken. We consider operators acting between two spaces Xl and X2 with uniformly equivalent metrics. The concept of a "collectively compact sequence of operators" is examined in relation to "pointwise convergence" - relevant to many approximate numerical methods. The introduction of a finite dimensional projection operator permits considerable theoretical development which enables us to relate various inverse approximate operators directly to a certain inverse matrix. The application of this theory to the approximate solution of linear two point boundary value problems is then considered. It is demonstrated how the method of collocation can be expressed in terms of a projection method applied to a certain operator equation. The conditions required by the theory are expressed in terms of continuity requirements on the coefficients of the differential equation and in terms of the distribution of the collocation pOints. Various estimates of bounds on the inverse differential operator are presented and it is demonstrated that the "residual" can be a very useful error estimate. The use of a "weighted infinity norm" is shown to improve the applicability of the theory for "stiff" problems. Some real problems are then examined and a selection of numerical results illustrating the theory and application are presented. The thesis concludes with a brief review, outlining some of the deficiencies in the work and possible improvements and extensions of the analysis.Science Research Council

Analysis of power-saving techniques over a large multi-use cluster with variable workload

Reduction of power consumption for any computer system is now an important issue, although this should be carried out in a manner that is not detrimental to the users of that computer system. We present a number of policies that can be applied to multi-use clusters where computers are shared between interactive users and high-throughput computing. We evaluate policies by trace-driven simulations to determine the effects on power consumed by the high-throughput workload and impact on high-throughput users. We further evaluate these policies for higher workloads by synthetically generating workloads based around the profiled workload observed through our system. We demonstrate that these policies could save 55% of the currently used energy for our high-throughput jobs over our current cluster policies without affecting the high-throughput users’ experience

A novel process driving Alzheimer's disease validated in a mouse model: Therapeutic potential

Abstract Introduction The neuronal mechanism driving Alzheimer's disease (AD) is incompletely understood. Methods Immunohistochemistry, pharmacology, biochemistry, and behavioral testing are employed in two pathological contexts—AD and a transgenic mouse model—to investigate T14, a 14mer peptide, as a key signaling molecule in the neuropathology. Results T14 increases in AD brains as the disease progresses and is conspicuous in 5XFAD mice, where its immunoreactivity corresponds to that seen in AD: neurons immunoreactive for T14 in proximity to T14‐immunoreactive plaques. NBP14 is a cyclized version of T14, which dose‐dependently displaces binding of its linear counterpart to alpha‐7 nicotinic receptors in AD brains. In 5XFAD mice, intranasal NBP14 for 14 weeks decreases brain amyloid and restores novel object recognition to that in wild‐types. Discussion These findings indicate that the T14 system, for which the signaling pathway is described here, contributes to the neuropathological process and that NBP14 warrants consideration for its therapeutic potential