Integrality of Homfly (1,1)-tangle invariants

Given an invariant J(K) of a knot K, the corresponding (1,1)-tangle invariant J'(K)=J(K)/J(U) is defined as the quotient of J(K) by its value J(U) on the unknot U. We prove here that J' is always an integer 2-variable Laurent polynomial when J is the Homfly satellite invariant determined by decorating K with any eigenvector of the meridian map in the Homfly skein of the annulus. Specialisation of the 2-variable polynomials for suitable choices of eigenvector shows that the (1,1)-tangle irreducible quantum sl(N) invariants of K are integer 1-variable Laurent polynomials.Comment: 10 pages, including several interspersed figure

Linear and nonlinear interpretation of the direct strike lightning response of the NASA F106B thunderstorm research aircraft

The objective of the work reported here is to develop a methodology by which electromagnetic measurements of inflight lightning strike data can be understood and extended to other aircraft. A linear and time invariant approach based on a combination of Fourier transform and three dimensional finite difference techniques is demonstrated. This approach can obtain the lightning channel current in the absence of the aircraft for given channel characteristic impedance and resistive loading. The model is applied to several measurements from the NASA F106B lightning research program. A non-linear three dimensional finite difference code has also been developed to study the response of the F106B to a lightning leader attachment. This model includes three species air chemistry and fluid continuity equations and can incorporate an experimentally based streamer formulation. Calculated responses are presented for various attachment locations and leader parameters. The results are compared qualitatively with measured inflight data

Entanglement and the Thermodynamic Arrow of Time

We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We describe a hierarchy of arrows that arises from the different correlations allowed in a quantum state and examine these features in the context of Maxwell's Demon. We examine in detail the case of three qubits, and also propose some simple experimental demonstrations possible with small numbers of qubits.Comment: 10 pages with 9 figure

A quantum protocol for cheat-sensitive weak coin flipping

We present a quantum protocol for the task of weak coin flipping. We find that, for one choice of parameters in the protocol, the maximum probability of a dishonest party winning the coin flip if the other party is honest is 1/sqrt(2). We also show that if parties restrict themselves to strategies wherein they cannot be caught cheating, their maximum probability of winning can be even smaller. As such, the protocol offers additional security in the form of cheat sensitivity.Comment: 4 pages RevTex. Differs from the journal version only in that the sentences: "The ordering of the authors on this paper was chosen by a coin flip implemented by a trusted third party. TR lost." have not been remove

Further results on the cross norm criterion for separability

In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that the greatest cross norm criterion induces a novel computable separability criterion for bipartite systems. This new criterion is a necessary but in general not a sufficient criterion for separability. It is shown, however, that for all pure states, for Bell diagonal states, for Werner states in dimension d=2 and for isotropic states in arbitrary dimensions the new criterion is necessary and sufficient. Moreover, it is shown that for Werner states in higher dimensions (d greater than 2), the new criterion is only necessary.Comment: REVTeX, 19 page

Poisson smooth structures on stratified symplectic spaces

In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a stratified symplectic Poisson algebra introduced by Sjamaar and Lerman. We show that these smooth spaces possess several important properties, e.g. the existence of smooth partitions of unity. Furthermore, under mild conditions many properties of a symplectic manifold can be extended to a symplectic stratified space provided with a smooth Poisson structure, e.g. the existence and uniqueness of a Hamiltonian flow, the isomorphism between the Brylinski-Poisson homology and the de Rham homology, the existence of a Leftschetz decomposition on a symplectic stratified space. We give many examples of stratified symplectic spaces possessing a Poisson smooth structure which is also weakly symplectic.Comment: 21 page, final version, to appear in the Proceedings of the 6-th World Conference on 21st Century Mathematic

Interpretation of F106B and CV580 in-flight lightning data and form factor determination

Two topics of in-flight aircraft/lightning interaction are addressed. The first is the analysis of measured data from the NASA F106B Thunderstorm Research Aircraft and the CV580 research program run by the FAA and Wright-Patterson Air Force Base. The CV580 data was investigated in a mostly qualitative sense, while the F106B data was subjected to both statistical and quantitative analysis using linear triggered lightning finite difference models. The second main topic is the analysis of field mill data and the calibration of the field mill systems. The calibration of the F106B field mill system was investigated using an improved finite difference model of the aircraft having a spatial resolution of one-quarter meter. The calibration was applied to measured field mill data acquired during the 1985 thunderstorm season. The experimental determination of form factors useful for field mill calibration was also investigated both experimentally and analytically. The experimental effort involved the use of conducting scale models and an electrolytic tank. An analytic technique was developed to aid in the understanding of the experimental results

Current state of knowledge of freshwater malacostracans of Chile

Indexación: ScieloLa fauna de crustáceos malacostráceos limnéticos, en el territorio de Chile continental, está compuesta por seis especies de camarones, i.e., cinco parastácidos de los géneros Parastacus, Samastacus y Virilastacus y un palemónido del género Cryphiops, 18 especies de anomuros del género Aegla, siete especies de anfípodos gamarídeos del género Hyallela y una especie de isópodo aselotano del género Heterias. La distribución conjunta abarca desde Arica a Punta Arenas, pero la mayor parte de las especies tiene rango geográfico restringido. La mayor densidad de taxa ocurre entre las regiones VIII y X, donde el número de taxa por Región varía entre 11 y 15, siendo la X Región la que tiene el número mayor. Índices derivados de un estudio sobre relaciones filogenéticas de las especies chilenas de Aegla, combinados con criterios propuestos por IUCN (2001), calificó a A. concepcionensis y A. expansa como especies Extintas y a A. papudo, A. l. laevis y A. spectabilis como Críticamente Amenazadas. Además, asignó máxima prioridad de conservación a la zona comprendida entre las cuencas del río Tucapel y del río Toltén. El estado de conservación de las especies de Parastacidae fue establecido por Bahamonde et al. (1998) y complementado por Rudolph & Crandall (2005). El estado de conservación de las especies de Hyalella y del isópodo Heterias exul no ha sido determinado. Se percibe que las amenazas a la conservación de las especies de malacostráceos limnéticos en Chile derivan principalmente de perturbaciones antropogénicas de la integridad y salud ambiental de las cuencas hidrográficas, particularmente entre las Regiones IV a VIII. Palabras claves: Malacostráceos, diversidad, conservación, Amphipoda, Isopoda, Decapoda, Chile, limnología. -------------------------------------------------------------------------------- ABSTRACT The continental Chilean limnetic malacostracan fauna is currently composed of six species of crayfish / shrimp, i.e., five parastacids in the genus Parastacus, Samastacus and Virilastacus, and one palaemonid in the genus Cryphiops, eighteen species of anomuran crabs in the genus Aegla, seven species of gammaridean amphipods in the genus Hyalella, and one species of asellotan isopod in the genus Heterias. The distribution of the set of thirty one species of malacostracans spans from Arica in the north to Magallanes in the far south. However, most species have a restricted geographic range, comprising one or a few hydrographical contiguous basins along the latitudinal gradient. The largest concentration of malacostracan species is found between the VIII and X Administrative Regions of Chile; being the X the largest with fifteen taxa. Indices derived from a phylogenetic study concerning the relationship of the Chilean species of Aegla, and considering the conservation criteria proposed by UICN (2001), qualified A. concepcionensis and A. expansa as Extinct in the Wild, and A. papudo, A. l. laevis and A. spectabilis as Critically Endangered species. Furthermore, it assigned maximum conservation priority to the coastal area between the Tucapel and the Tolten rivers. The conservation status of the species of Parastacidae was established by Bahamonde et al. (1998), and supplemented by Rudolph & Crandall (2005). The conservation status of Hyalella and Heterias species has not yet been determined. It is apparent that threats to the conservation of a large number of limnetic malacostracan species in Chile arise from non quantified anthropogenic perturbations of the limnetic environment, particularly between the IV and VIII Regions. Keywords: Malacostracans, diversity, conservation, Amphipoda, Isopoda, Decapoda, Chile, limnology

Algorithms (X,sigma,eta) : quasi-random mutations for Evolution Strategies

International audienceRandomization is an efficient tool for global optimization. We here define a method which keeps : - the order 0 of evolutionary algorithms (no gradient) ; - the stochastic aspect of evolutionary algorithms ; - the efficiency of so-called "low-dispersion" points ; and which ensures under mild assumptions global convergence with linear convergence rate. We use i) sampling on a ball instead of Gaussian sampling (in a way inspired by trust regions), ii) an original rule for step-size adaptation ; iii) quasi-monte-carlo sampling (low dispersion points) instead of Monte-Carlo sampling. We prove in this framework linear convergence rates i) for global optimization and not only local optimization ; ii) under very mild assumptions on the regularity of the function (existence of derivatives is not required). Though the main scope of this paper is theoretical, numerical experiments are made to backup the mathematical results. Algorithm XSE: quasi-random mutations for evolution strategies. A. Auger, M. Jebalia, O. Teytaud. Proceedings of EA'2005