Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Swashplate feedback control for tilt-rotor aircraft

Changes in angle of attack in system were sensed indirectly by gages which responded to strains induced in wing structure. Output signals were amplified, filtered, and used to activate swashplate actuators. System provided significant reduction in blade loads and desirable changes in hub forces and moments

Ultracold atoms at unitarity within quantum Monte Carlo

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. The ratio of the energy of the interacting to the non-interacting gas for a system of 128 particles is calculated to be 0.4517(3) in VMC and 0.4339(1) in the more accurate DMC method. The spherically-averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, but the two-body density matrices and condensate fractions show some differences. Our best estimate of the condensate fraction of 0.51 is a little smaller than values from other quantum Monte Carlo calculations

Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics

We analyse two classes of $(1+2)$ evolution equations which are of special interest in Financial Mathematics, namely the Two-dimensional Black-Scholes Equation and the equation for the Two-factor Commodities Problem. Our approach is that of Lie Symmetry Analysis. We study these equations for the case in which they are autonomous and for the case in which the parameters of the equations are unspecified functions of time. For the autonomous Black-Scholes Equation we find that the symmetry is maximal and so the equation is reducible to the $(1+2)$ Classical Heat Equation. This is not the case for the nonautonomous equation for which the number of symmetries is submaximal. In the case of the two-factor equation the number of symmetries is submaximal in both autonomous and nonautonomous cases. When the solution symmetries are used to reduce each equation to a $(1+1)$ equation, the resulting equation is of maximal symmetry and so equivalent to the $(1+1)$ Classical Heat Equation.Comment: 15 pages, 1 figure, to be published in Mathematics in the Special issue "Mathematical Finance

Orthotic management of cerebral palsy : recommendations from a consensus conference

An international multidisciplinary group of healthcare professionals and researchers participated in a consensus conference on the management of cerebral palsy, convened by the International Society for Prosthetics and Orthotics. Participants reviewed the evidence and considered contemporary thinking on a range of treatment options including physical and occupational therapy, and medical, surgical and orthotic interventions. The quality of many of the reviewed papers was compromised by inadequate reporting and lack of transparency, in particular regarding the types of patients and the design of the interventions being evaluated. Substantial evidence suggests that ankle-foot orthoses (AFOs) that control the foot and ankle in stance and swing phases can improve gait efficiency in ambulant children (GMFCS levels I-III). By contrast, little high quality evidence exists to support the use of orthoses for the hip, spine or upper limb. Where the evidence for orthosis use was not compelling consensus was reached on recommendations for orthotic intervention. Subsequent group discussions identified recommendations for future research. The evidence to support using orthoses is generally limited by the brevity of follow-up periods in research studies; hence the extent to which orthoses may prevent deformities developing over time remains unclear. The full report of the conference can be accessed free of charge at www.ispoint.org

The growth and decline of the semiconductor industry within the U.K. 1950-1985

This thesis reviews the history of the semiconductor industry during the period 1950 to 1985 and identifies the major factors governing its development. It also analyses the reasons for the failure of British manufacturing companies to develop on a more competitive scale. The development of the British semiconductor industry, almost from the start, took place within an environment dominated by large foreign multinational companies. Operating under conditions of technical lag and with increasing penetration of its markets, it concentrated, aided by funding from the Ministry of Defence, on producing specialised solid-state components for the much smaller military market. Because of its size, this market was not sufficiently large to initiate the pump-priming action which was such an important feature in bringing about the success of its American counterpart. Generous Government inducements, aimed at attracting multinational companies to British shores, did little to assist the development of the indigenous industry, which, underfunded, underprotected and increasingly restricted to niche markets by competitors, soon fell into relative decline. Direct Governmental assistance to the ailing commercial sector of the British semiconductor industry came too late substantially to affect the situation. Both inconsistency and lack of continuity in policy towards the industry, under successive Governments, did not improve the confidence of industrial management, nor encourage a more long-term outlook. It is argued within this thesis that the best chance of industrial success would have been to adopt a national policy towards the industry at an early stage, with substantial funding on a long-term basis, together with adequate import controls. The epilogue concludes that only within a European framework might it now be possible to build a semiconductor manufacturing industry, eventually capable of competing on equal terms with overseas rivals

Microarray sub-grid detection: A novel algorithm

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Taylor & Francis LtdA novel algorithm for detecting microarray subgrids is proposed. The only input to the algorithm is the raw microarray image, which can be of any resolution, and the subgrid detection is performed with no prior assumptions. The algorithm consists of a series of methods of spot shape detection, spot filtering, spot spacing estimation, and subgrid shape detection. It is shown to be able to divide images of varying quality into subgrid regions with no manual interaction. The algorithm is robust against high levels of noise and high percentages of poorly expressed or missing spots. In addition, it is proved to be effective in locating regular groupings of primitives in a set of non-microarray images, suggesting potential application in the general area of image processing