Gaussian limits for multidimensional random sequential packing at saturation (extended version)

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is asymptotically normal as $\lambda \to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page

The Integrability of Pauli System in Lorentz Violating Background

We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.Comment: 19 page

Strings on pp-waves and Hadrons in (softly broken) N=1 gauge theories

We study the Penrose limit of Type IIB duals of softly broken N=1 SU(N) gauge theories in four dimensions, obtained as deformations of the Maldacena-Nunez and Klebanov-Strassler backgrounds. We extract the string spectrum on the resulting pp-wave backgrounds and discuss some properties of the conjectured dual gauge theory hadrons, the so called "Annulons". The string zero-point energy on the light-cone is nontrivial, due to the loss of linearly realized worldsheet supersymmetry, and negative, even in the unbroken supersymmetric case. This causes the appearance of non-perturbative corrections to the hadronic mass spectrum. We briefly discuss the thermodynamic behavior of these string models, calculating the corresponding Hagedorn temperatures.Comment: 20 page

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud \ud \ud We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions

Penrose Limits, Deformed pp-Waves and the String Duals of N=1 Large n Gauge Theory

A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a description as an infra-red fixed point obtained by deforming the N=4 supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral multiplets. We study the Penrose limit of the supergravity dual of the large n limit of this N=1 gauge theory. The limit gives a pp-wave with R-R five-form flux and both R-R and NS-NS three-form flux. We discover that this new solution preserves twenty supercharges and that, in the light-cone gauge, string theory on this background is exactly solvable. Correspondingly, this latter is the stringy dual of a particular large charge limit of the large n gauge theory. We are able to identify which operators in the field theory survive the limit to form the string's ground state and some of the spacetime excitations. The full string model, which we exhibit, contains a family of non-trivial predictions for the properties of the gauge theory operators which survive the limit.Comment: 39 pages, Late

Glueballs of Super Yang-Mills from Wrapped Branes

In this paper we study qualitative features of glueballs in N=1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0++ is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularization procedure needed to make these states normalizable.Comment: 22 pages plus a appendixes, 2 figure

Breaking down the mussel (Mytilus edulis) shell: Which layers affect Oystercatchers' (Haematopus ostralegus) prey selection?

Copyright © 2011 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Experimental Marine Biology and Ecology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Experimental Marine Biology and Ecology, 2011, Vol. 405, Issue 1-2, pp. 87 – 92 DOI: http://dx.doi.org/10.1016/j.jembe.2011.05.021Predators are able to identify fine characteristic features of prey and use them to maximise the profitability of foraging. Oystercatchers Haematopus ostralegus select thin-shelled mussels Mytilus edulis to hammer through because they are easier to crack than thick-shelled mussels. But mussel shells are composite structures, so we need to ask what it is about these thin-shelled mussels that make them vulnerable. Here we show that the mussels damaged by Oystercatchers were mainly distinguished by having a significantly thinner prismatic layer than undamaged mussels. Regression analysis indicated that the Oystercatchers' shell selection was independently influenced by the thickness of the prismatic and nacreous layers, but the coefficient for the thickness of the prismatic layer was almost one and a half times that for the nacreous layer. Thus the thickness of the prismatic layer largely determines the vulnerability of the mussel shells. Oystercatchers were more likely to attack mussels by the right valve than the left, and this tendency was accentuated in larger mussels and those with a thicker nacreous layer

Examining the Cascade of Participant Attrition in a Genomic Medicine Research Study: Barriers and Facilitators to Achieving Diversity

Background/Aims: Recent genomic medicine initiatives underscore the importance of including diverse participants in research. Considerable literature has identified barriers to and facilitators of increasing diversity, yet disparities in recruiting and retaining adequate numbers of participants from diverse groups continue to limit the generalizability of clinical genomic research. Methods: The North Carolina Clinical Genomic Evaluation by Next-gen Exome Sequencing study employed evidence-based strategies to enhance the participation of under-represented minority patients. In this study, we evaluate the impact of our efforts by systematically analyzing the "cascade" of attrition of participants throughout study interactions. Results: Although successful in recruiting a cohort that included ~30% non-Caucasian patients overall, the study still enrolled and retained a lower proportion of minorities compared to the pool of eligible patients who were nominated. We evaluated sociodemographic characteristics and related variables as potential factors associated with attrition throughout these phases of the study. Conclusions: These results suggest that varied approaches will be needed to increase participation in genomic medicine research. Our findings highlight factors to consider when developing strategies to address this critical need. Failing to include a broad range of populations in research studies will exacerbate existing disparities in the translation of genomic sequencing to medical care

'Education, education, education' : legal, moral and clinical

This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students