Arithmetic harmonic analysis on character and quiver varieties

We present a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the character varieties of representations of the fundamental group of a Riemann surface of genus g to GL_n(C) with fixed generic semi-simple conjugacy classes at k punctures. Using the character table of GL_n(F_q) we calculate the E-polynomial of these character varieties and confirm that it is as predicted by our main conjecture. Then, using the character table of gl_n(F_q), we calculate the E-polynomial of certain associated comet-shaped quiver varieties, the additive analogues of our character variety, and find that it is the pure part of our conjectured mixed Hodge polynomial. Finally, we observe that the pure part of our conjectured mixed Hodge polynomial also equals certain multiplicities in the tensor product of irreducible representations of GL_n(F_q). This implies a curious connection between the representation theory of GL_n(F_q) and Kac-Moody algebras associated with comet-shaped, typically wild, quivers.Comment: To appear in Duke Math. Journal + a section with examples is adde

Topology of character varieties and representations of quivers

In arXiv:0810.2076 we presented a conjecture generalizing the Cauchy formula for Macdonald polynomials. This conjecture encodes the mixed Hodge polynomials of the representation varieties of Riemann surfaces with semi-simple conjugacy classes at the punctures. We proved several results which support this conjecture. Here we announce new results which are consequences of those of arXiv:0810.2076

Nonlinear Analysis of Irregular Variables

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been developed for analyzing irregular stellar light or radial velocity variations, and we describe what useful physical and astronomical information can be gained from their use.Comment: 31 pages, to appear as a chapter in `Nonlinear Stellar Pulsation' in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselo

Observability of dynamical networks from graphic and symbolic approaches

A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore, it is of the utmost importance to determine a reduced set of variables providing all the required information for non-ambiguously distinguish its different states. Inherited from control theory, one possible approach is based on the use of the observability matrix defined as the Jacobian matrix of the change of coordinates between the original state space and the space reconstructed from the measured variables. The observability of a given system can be accurately assessed by symbolically computing the complexity of the determinant of the observability matrix and quantified by symbolic observability coefficients. In this work, we extend the symbolic observability, previously developed for dynamical systems, to networks made of coupled $d$-dimensional node dynamics ($d>1$). From the observability of the node dynamics, the coupling function between the nodes, and the adjacency matrix, it is indeed possible to construct the observability of a large network with an arbitrary topology.Comment: 12 pages, 4 figures made from 12 eps file

Residual contamination detection and serovar distribution of Listeria monocytogenes isolates in pork slaughterhouse and cutting facilities in province of Quebec

L. monocytogenes (L. mono) is recognised as a zoonotic foodborne pathogen. Its control is focused on the “Readyto Eat” food production level. Recently, Health Canada had reinforced its “Policy on L. mono in Ready-to-Eat Foods”, highlighting environmental surveillance and control of meat processing facilities as important risk reduction tools. The industry wants to improve its management of L. mono risk, taking into account previous steps of meat production. Nowadays, few information are available on the presence, distribution and types of strains in the environments concerning this pathogen in pork slaughterhouses and cutting facilities in Canada. Our objective was to detect and described residual L. mono contamination and analyse serovars distribution in different areas in the pork production continuum in and between slaughterhouses and cutting facilities in province of Quebec, during a one year period. Such data are a pre-requisite to achieve the optimization of the management measures by the industrials

Molecular serotyping and virulence potential of Listeria monocytogenes isolated from bovine, swine and human in the province of Quebec

Listeria monocytogenes (L mono) cause rare but critical diseases, particularly for at risk population that include pregnant women. Food-borne origin of listeriosis is clearly recognised only since 1984. Since then, a great number of grouped cases occurred and milk or meat products, particularly pork meat, were implicated. Management of this zoonotic pathogen considers all strains as at equal risk. Recently a new perspective for characterisation of strain virulence was allowed since unaltered sequence of InlA was recognised as a key for strain virulence

Risk factors associated with presence of Salmonella in pigs in Canada

Carriers of Salmonella in finishing pigs are believed to be a main source of carcass and pork contamination at the slaughterhouse and during meat processing. To better control the presence of Salmonella at the farm and slaughter, it is important to adequately identify on-farm risk factors associated with presence of these bacteria in animals

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

Symphonie massively parallel computer, modelling and design

The goal of this paper is to present an embedded calculator for image processing SYMPHONIE and the methodology used for its realization. In this calculator we could have up to 1024 processors . Its first application will take place in the french Rafale Aircraft as core of the infra-red system . For this application, low size and low consumption will be very important and an ASIC of a million gates has been developped . To succeed in this realization we used a VHDL model allowing simulations on the full system . Then we used VHDL synthesis methods for the conception of the ASIC . We will conclude this paper by a presentation of some perfomances of the system in some applications fields .L'objectif de cet article est de présenter le calculateur embarqué de traitement d'image SYMPHONIE, ainsi que la méthodologie mise en oeuvre pour sa réalisation. Ce calculateur dont une des applications se situe au coeur du système de veille infrarouge de l'avion Rafale pourra comporter jusqu'à 1024 processeurs. Afin de tenir compte des contraintes de volume et de consommation, un ASIC d'un million de portes a été développé. Pour réussir cette réalisation un modèle VHDL a été écrit permettant des simulations de l'ensemble du système. Par ailleurs, ce modèle a permis d'aborder la réalisation du circuit ASIC en faisant appel aux outils de synthèse VHDL. Nous terminerons cette présentation par quelques performances dans différents domaines d'applications