The Effective Potential, the Renormalisation Group and Vacuum Stability

We review the calculation of the the effective potential with particular emphasis on cases when the tree potential or the renormalisation-group-improved, radiatively corrected potential exhibits non-convex behaviour. We illustrate this in a simple Yukawa model which exhibits a novel kind of dimensional transmutation. We also review briefly earlier work on the Standard Model. We conclude that, despite some recent claims to the contrary, it can be possible to infer reliably that the tree vacuum does not represent the true ground state of the theory.Comment: 23 pages; 5 figures; v2 includes minor changes in text and additional reference

U-duality covariant membranes

We outline a formulation of membrane dynamics in D=8 which is fully covariant under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to fields in the eight-dimensional supergravity, which is constructed through Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric fluxes determine the membrane charges, and are conjectured to provide an interpretation of the variables occurring in the minimal representation of E_{6(6)} which appears in the context of automorphic membranes. We solve the relevant equations for the action for a restricted class of supergravity backgrounds. Some comments are made on supersymmetry and lower dimensions.Comment: LaTeX, 21 pages. v2: Minor changes in text, correction of a sign. v3: some changes in text, a sign convention changed; version to appear in JHE

Impurity induced resonant state in a pseudogap state of a high temperature superconductor

We predict a resonance impurity state generated by the substitution of one Cu atom with a nonmagnetic atom, such as Zn, in the pseudogap state of a high-T_c superconductor. The precise microscopic origin of the pseudogap is not important for this state to be formed, in particular this resonance will be present even in the absence of superconducting fluctuations in the normal state. In the presence of superconducting fluctuations, we predict the existence of a counterpart impurity peak on a symmetric bias. The nature of impurity resonance is similar to the previously studied resonance in the d-wave superconducting state.Comment: 4 pages, 2 figure

Power spectrum of many impurities in a d-wave superconductor

Recently the structure of the measured local density of states power spectrum of a small area of the \BSCCO (BSCCO) surface has been interpreted in terms of peaks at an "octet" of scattering wave vectors determined assuming weak, noninterfering scattering centers. Using analytical arguments and numerical solutions of the Bogoliubov-de Gennes equations, we discuss how the interference between many impurities in a d-wave superconductor alters this scenario. We propose that the peaks observed in the power spectrum are not the features identified in the simpler analyses, but rather "background" structures which disperse along with the octet vectors. We further consider how our results constrain the form of the actual disorder potential found in this material.Comment: 5 pages.2 figure

Performance of IMPACT, CRASH and Nijmegen models in predicting six month outcome of patients with severe or moderate TBI: An external validation study

Background: External validation on different TBI populations is important in order to assess the generalizability of prognostic models to different settings. We aimed to externally validate recently developed models for prediction of six month unfavourable outcome and six month mortality. Methods: The International Neurotrauma Research Organization - Prehospital dataset (INRO-PH) was collected within an observational study between 2009-2012 in Austria and includes 778 patients with TBI of GCS < = 12. Three sets of prognostic models were externally validated: the IMPACT core and extended models, CRASH basic models and the Nijmegen models developed by Jacobs et al - all for prediction of six month unfavourable outcome and six month mortality. The external validity of the models was assessed by discrimination (Area Under the receiver operating characteristic Curve, AUC) and calibration (calibration statistics and plots). Results: Median age in the validation cohort was 50 years and 44% had an admission GSC motor score of 1-3. Six-month mortality was 27%. Mortality could better be predicted (AUCs around 0.85) than unfavourable outcome (AUCs around 0.80). Calibration plots showed that the o

Membranes for Topological M-Theory

We formulate a theory of topological membranes on manifolds with G_2 holonomy. The BRST charges of the theories are the superspace Killing vectors (the generators of global supersymmetry) on the background with reduced holonomy G_2. In the absence of spinning formulations of supermembranes, the starting point is an N=2 target space supersymmetric membrane in seven euclidean dimensions. The reduction of the holonomy group implies a twisting of the rotations in the tangent bundle of the branes with ``R-symmetry'' rotations in the normal bundle, in contrast to the ordinary spinning formulation of topological strings, where twisting is performed with internal U(1) currents of the N=(2,2) superconformal algebra. The double dimensional reduction on a circle of the topological membrane gives the strings of the topological A-model (a by-product of this reduction is a Green-Schwarz formulation of topological strings). We conclude that the action is BRST-exact modulo topological terms and fermionic equations of motion. We discuss the role of topological membranes in topological M-theory and the relation of our work to recent work by Hitchin and by Dijkgraaf et al.Comment: 22 pp, plain tex. v2: refs. adde

Monte Carlo Photon Transport On Shared Memory and Distributed Memory Parallel Processors

Parallelized Monte Carlo algorithms for analyzing photon transport in an inertially confined fusion (ICF) plasma are consid ered. Algorithms were developed for shared memory (vector and scalar) and distributed memory (scalar) parallel pro cessors. The shared memory algorithm was implemented on the IBM 3090/400, and timing results are presented for dedi cated runs with two, three, and four pro cessors. Two alternative distributed memory algorithms (replication and dis patching) were implemented on a hyper cube parallel processor (1 through 64 nodes). The replication algorithm yields essentially full efficiency for all cube sizes; with the 64-node configuration, the absolute performance is nearly the same as with the CRAY X-MP The dispatching algorithm also yields efficiencies above 80% in a large simulation for the 64-pro cessor configuration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67146/2/10.1177_109434208700100306.pd

Historical roots of Agile methods: where did “Agile thinking” come from?

The appearance of Agile methods has been the most noticeable change to software process thinking in the last fifteen years [16], but in fact many of the “Agile ideas” have been around since 70’s or even before. Many studies and reviews have been conducted about Agile methods which ascribe their emergence as a reaction against traditional methods. In this paper, we argue that although Agile methods are new as a whole, they have strong roots in the history of software engineering. In addition to the iterative and incremental approaches that have been in use since 1957 [21], people who criticised the traditional methods suggested alternative approaches which were actually Agile ideas such as the response to change, customer involvement, and working software over documentation. The authors of this paper believe that education about the history of Agile thinking will help to develop better understanding as well as promoting the use of Agile methods. We therefore present and discuss the reasons behind the development and introduction of Agile methods, as a reaction to traditional methods, as a result of people's experience, and in particular focusing on reusing ideas from histor

Spinorial cohomology and maximally supersymmetric theories

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an alpha' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the alpha'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity.Comment: 23 pp, plain tex. v2: Minor changes, references adde

Meixner class of non-commutative generalized stochastic processes with freely independent values I. A characterization

Let $T$ be an underlying space with a non-atomic measure $\sigma$ on it (e.g. $T=\mathbb R^d$ and $\sigma$ is the Lebesgue measure). We introduce and study a class of non-commutative generalized stochastic processes, indexed by points of $T$, with freely independent values. Such a process (field), $\omega=\omega(t)$, $t\in T$, is given a rigorous meaning through smearing out with test functions on $T$, with $\int_T \sigma(dt)f(t)\omega(t)$ being a (bounded) linear operator in a full Fock space. We define a set $\mathbf{CP}$ of all continuous polynomials of $\omega$, and then define a con-commutative $L^2$-space $L^2(\tau)$ by taking the closure of $\mathbf{CP}$ in the norm $\|P\|_{L^2(\tau)}:=\|P\Omega\|$, where $\Omega$ is the vacuum in the Fock space. Through procedure of orthogonalization of polynomials, we construct a unitary isomorphism between $L^2(\tau)$ and a (Fock-space-type) Hilbert space $\mathbb F=\mathbb R\oplus\bigoplus_{n=1}^\infty L^2(T^n,\gamma_n)$, with explicitly given measures $\gamma_n$. We identify the Meixner class as those processes for which the procedure of orthogonalization leaves the set $\mathbf {CP}$ invariant. (Note that, in the general case, the projection of a continuous monomial of oder $n$ onto the $n$-th chaos need not remain a continuous polynomial.) Each element of the Meixner class is characterized by two continuous functions $\lambda$ and $\eta\ge0$ on $T$, such that, in the $\mathbb F$ space, $\omega$ has representation \omega(t)=\di_t^\dag+\lambda(t)\di_t^\dag\di_t+\di_t+\eta(t)\di_t^\dag\di^2_t, where \di_t^\dag and \di_t are the usual creation and annihilation operators at point $t$