Oving Eigenvalues and Eigenvectors

The Office of Naval Research Department Of The Navy Contract No. N 00014-67-A-0305-0010 ; Project No. NR 064-183/5-28-70(439

Wave Propagation in an Elastic Half Space Due to Couples Applied at a Point Beneath the Surface

Office of Naval Research. Department of the Navy: Contract No. N00014-67-A-0305-0010; Project No. NR 064-183U.S. Army Research Office - Durham: Project No. D0161102B33G, Proposal No. D-5

The Analgesia-Enhancing Component of\ud Ingested Amniotic Fluid Does Not Affect\ud Nicotine-Induced Antinociception in\ud Naltrexone-Treated Rats

Ingestion of amniotic fluid and placenta by rats has been shown to enhance opioid-mediated antinociception but not affect the nonopioid-mediated antinociception produced by aspirin, suggesting spccificity for opioid-mediated processes. However, enhancement by the active substance(s) in amniotic fluid and placenta1 (POEF, for placental opioid-enhancing factor) of antinociception produced by other nonopioid mechanisms has yet to be examined. The present experiments tested whether ingestion of amniotic fluid enhances the antinociception produced by nicotine injection. In Experiment IA, Enhancement of morphine-mediated antinociception by ingestion of amniotic fluid was demonstrated in a hot-plate assay. In Experiment IB, rats pretreated with naltrexone were given an orogastric infusion of amniotic fluid or control (0.25 ml), then injected with nicotine (0, 0.075, 0.125, or 0.225 mg/kg subcutaneously), then tested for antinociception in a hot-plate assay. Amniotic fluid ingestion did not enhance the antinociception produced by various doses of nicotine. In Experiment 2, rats pretreated with naltrexone were given an orogastric infusion of amniotic fluid (0, 0.125,\ud 0.25, or 0.50 ml) and then injectcd with 0.125 mg/kg nicotine. None of the doses of amniotic fluid enhanced the nicotine-induced antinociception. The findings of these experiments lend support to our contention that the enhancement by POEF of antinociception is specific to opioid-mediated processes

Non-perturbative QEG Corrections to the Yang-Mills Beta Function

We discuss the non-perturbative renormalization group evolution of the gauge coupling constant by using a truncated form of the functional flow equation for the effective average action of the Yang-Mills-gravity system. Our result is consistent with the conjecture that Quantum Einstein Gravity (QEG) is asymptotically safe and has a vanishing gauge coupling constant at the non-trivial fixed point.Comment: To appear in the proceedings of CORFU 200

Population Dynamics and Non-Hermitian Localization

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.Comment: 19 pages, 11 figure

Sharp version of the Goldberg-Sachs theorem

We reexamine from first principles the classical Goldberg-Sachs theorem from General Relativity. We cast it into the form valid for complex metrics, as well as real metrics of any signature. We obtain the sharpest conditions on the derivatives of the curvature that are sufficient for the implication (integrability of a field of alpha planes)$\Rightarrow$(algebraic degeneracy of the Weyl tensor). With every integrable field of alpha planes we associate a natural connection, in terms of which these conditions have a very simple form.Comment: In this version we made a minor change in Remark 5.5 and simplified Section 6, starting at Theorem 6.

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to anotherComment: 16 pages, talk delivered at the Geilo Winter School 201

Establishing and Prioritising Research Questions for the Treatment of Alopecia Areata: The Alopecia Areata Priority Setting Partnership

BACKGROUND: Alopecia areata is a common hair loss disorder that results in patchy to complete hair loss. Many uncertainties exist around the most effective treatments for this condition. OBJECTIVES: To identify uncertainties in alopecia areata management and treatment that are important to both service users (people with hair loss, carers and relatives) and healthcare professionals. METHODS: An alopecia areata priority setting partnership was established between patients, their carers and relatives, and healthcare professionals to identify the most important uncertainties in alopecia areata. The methodology of the James Lind Alliance was followed to ensure a balanced, inclusive and transparent process. RESULTS: In total 2747 treatment uncertainties were submitted by 912 participants, of which 1012 uncertainties relating to alopecia areata (and variants) were analyzed. Questions were combined into "indicative uncertainties" following a structured format. A series of ranking exercises further reduced this list to a top 25 that were taken to a final prioritization workshop where the top 10 priorities were agreed. CONCLUSIONS: We present the top 10 research priorities for alopecia areata to guide researchers and funding bodies to support studies important to both patients and clinicians. This article is protected by copyright. All rights reserved

Flux-branes and the Dielectric Effect in String Theory

We consider the generalization to String and M-theory of the Melvin solution. These are flux p-branes which have (p+1)-dimensional Poincare invariance and are associated to an electric (p+1)-form field strength along their worldvolume. When a stack of Dp-branes is placed along the worldvolume of a flux (p+3)-brane it will expand to a spherical D(p+2)-brane due to the dielectric effect. This provides a new setup to consider the gauge theory/gravity duality. Compactifying M-theory on a circle we find the exact gravity solution of the type IIA theory describing the dielectric expansion of N D4-branes into a spherical bound state of D4-D6-branes, due to the presence of a flux 7-brane. In the decoupling limit, the deformation of the dual field theory associated with the presence of the flux brane is irrelevant in the UV. We calculate the gravitational radius and energy of the dielectric brane which give, respectively, a prediction for the VEV of scalars and vacuum energy of the dual field theory. Consideration of a spherical D6-brane probe with n units of D4-brane charge in the dielectric brane geometry suggests that the dual theory arises as the Scherk-Schwarz reduction of the M5-branes (2,0) conformal field theory. The probe potential has one minimum placed at the locus of the bulk dielectric brane and another associated to an inner dielectric brane shell.Comment: v2 Major Additions: dielectric radius in gravity solution matches exactly stable and unstable points of Myers probe potential, as well as the upper bound on D-brane charge. New section probing dielectric brane that clarifies dual field theory discussion and is consistent with Scherk-Schwarz reduction of (2,0) M5-brane theory. References added. 43 pages, 4 figure

Structure of self-organized Fe clusters grown on Au(111) analyzed by Grazing Incidence X-Ray Diffraction

We report a detailed investigation of the first stages of the growth of self-organized Fe clusters on the reconstructed Au(111) surface by grazing incidence X-ray diffraction. Below one monolayer coverage, the Fe clusters are in "local epitaxy" whereas the subsequent layers adopt first a strained fcc lattice and then a partly relaxed bcc(110) phase in a Kurdjumov-Sachs epitaxial relationship. The structural evolution is discussed in relation with the magnetic properties of the Fe clusters.Comment: 7 pages, 6 figures, submitted to Physical Review B September 200