Integrable lattice equations with vertex and bond variables

We present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables. In some of the models the vertex dynamics is independent of the evolution of the bond variables, and one can write the equations as non-autonomous "Yang-Baxter maps". We also present a model in which the vertex and bond variables are fully coupled. Integrability is tested with algebraic entropy as well as multidimensional consistencyComment: 15 pages, remarks added, other minor change

On the complexity of some birational transformations

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions

On the Symmetries of Integrability

We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition $q^n=1$ so often mentioned in the theory of quantum groups, when no $q$ parameter is available.Comment: 23 page

Complexity and integrability in 4D bi-rational maps with two invariants

In this letter we give fourth-order autonomous recurrence relations with two invariants, whose degree growth is cubic or exponential. These examples contradict the common belief that maps with sufficiently many invariants can have at most quadratic growth. Cubic growth may reflect the existence of non-elliptic fibrations of invariants, whereas we conjecture that the exponentially growing cases lack the necessary conditions for the applicability of the discrete Liouville theorem.Comment: 16 pages, 2 figure

Random Matrix Theory and higher genus integrability: the quantum chiral Potts model

We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of ``higher genus integrability''.Comment: 23 pages and 10 figure

A combinatorial model for reversible rational maps over finite fields

We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e., map-independent) distribution function R(x)=1-e^{-x}(1+x) has been conjectured to exist, for the normalized cycle lengths of the reduced map in the large field limit (J. A. G. Roberts and F. Vivaldi, Nonlinearity 18 (2005) 2171-2192). We show that these statistics correspond to those of a composition of two random involutions, having an appropriate number of fixed points. This model also explains the experimental observation that, asymptotically, almost all cycles are symmetrical, and that the probability of occurrence of repeated periods is governed by a Poisson law.Comment: LaTeX, 19 pages with 1 figure; to be published in Nonlinearit

The AVuPUR project (Assessing the Vulnerabiliy of Peri-Urbans Rivers): experimental set up, modelling strategy and first results

International audienceLe projet AVuPUR a pour objectif de progresser sur la compréhension et la modélisation des flux d'eau dans les bassins versants péri-urbains. Il s'agit plus particulièrement de fournir des outils permettant de quantifier l'impact d'objets anthropiques tels que zones urbaines, routes, fossés sur les régimes hydrologiques des cours d'eau dans ces bassins. Cet article présente la stratégie expérimentale et de collecte de données mise en ½uvre dans le projet et les pistes proposées pour l'amélioration des outils de modélisation existants et le développement d'outils novateurs. Enfin, nous présentons comment ces outils seront utilisés pour simuler et quantifier l'impact des modifications d'occupation des sols et/ou du climat sur les régimes hydrologiques des bassins étudiés. / The aim of the AVuPUR project is to enhance our understanding and modelling capacity of water fluxes within suburban watersheds. In particular, the objective is to deliver tools allowing to quantify the impact of anthropogenic elements such as urban areas, roads, ditches on the hydrological regime of suburban rivers. This paper presents the observation and data collection strategy set up by the project, and the directions for improving existing modelling tools or proposing innovative ones. Finally, we present how these tools will be used to simulate and quantify the impact of land use and climate changes on the hydrological regimes of the studied catchments

Evaluation of neuroendocrine markers in renal cell carcinoma

<p>Abstract</p> <p>Background</p> <p>The purpose of the study was to examine serotonin, CD56, neurone-specific enolase (NSE), chromogranin A and synaptophysin by immunohistochemistry in renal cell carcinomas (RCCs) with special emphasis on patient outcome.</p> <p>Methods</p> <p>We studied 152 patients with primary RCCs who underwent surgery for the removal of kidney tumours between 1990 and 1999. The mean follow-up was 90 months. The expression of neuroendocrine (NE) markers was determined by immunohistochemical staining using commercially available monoclonal antibodies. Results were correlated with patient age, clinical stage, Fuhrman grade and patient outcome.</p> <p>Results</p> <p>Eight percent of tumours were positive for serotonin, 18% for CD56 and 48% for NSE. Chromogranin A immunostaining was negative and only 1% of the tumours were synaptophysin immunopositive. The NSE immunopositivity was more common in clear cell RCCs than in other subtypes (<it>p </it>= 0.01). The other NE markers did not show any association with the histological subtype. Tumours with an immunopositivity for serotonin had a longer RCC-specific survival and tumours with an immunopositivity for CD56 and NSE had a shorter RCC-specific survival but the difference was not significant. There was no relationship between stage or Fuhrman grade and immunoreactivity for serotonin, CD56 and NSE.</p> <p>Conclusions</p> <p>Serotonin, CD56 and NSE but not synaptophysin and chromogranin A are expressed in RCCs. However, the prognostic potential of these markers remains obscure.</p

Discrete integrable systems and Poisson algebras from cluster maps

We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1. Such quivers were completely classified by Fordy and Marsh, who characterised them in terms of the skew-symmetric matrix that defines the quiver. The associated nonlinear recurrences are equivalent to birational maps, and we explain how these maps can be endowed with an invariant Poisson bracket and/or presymplectic structure. Upon applying the algebraic entropy test, we are led to a series of conjectures which imply that the entropy of the cluster maps can be determined from their tropical analogues, which leads to a sharp classification result. Only four special families of these maps should have zero entropy. These families are examined in detail, with many explicit examples given, and we show how they lead to discrete dynamics that is integrable in the Liouville-Arnold sense.Comment: 49 pages, 3 figures. Reduced to satisfy journal page restrictions. Sections 2.4, 4.5, 6.3, 7 and 8 removed. All other results remain, with minor editin

Monitoring of Gene Expression in Bacteria during Infections Using an Adaptable Set of Bioluminescent, Fluorescent and Colorigenic Fusion Vectors

A family of versatile promoter-probe plasmids for gene expression analysis was developed based on a modular expression plasmid system (pZ). The vectors contain different replicons with exchangeable antibiotic cassettes to allow compatibility and expression analysis on a low-, midi- and high-copy number basis. Suicide vector variants also permit chromosomal integration of the reporter fusion and stable vector derivatives can be used for in vivo or in situ expression studies under non-selective conditions. Transcriptional and translational fusions to the reporter genes gfpmut3.1, amCyan, dsRed2, luxCDABE, phoA or lacZ can be constructed, and presence of identical multiple cloning sites in the vector system facilitates the interchange of promoters or reporter genes between the plasmids of the series. The promoter of the constitutively expressed gapA gene of Escherichia coli was included to obtain fluorescent and bioluminescent expression constructs. A combination of the plasmids allows simultaneous detection and gene expression analysis in individual bacteria, e.g. in bacterial communities or during mouse infections. To test our vector system, we analyzed and quantified expression of Yersinia pseudotuberculosis virulence genes under laboratory conditions, in association with cells and during the infection process