Integrability as a consequence of discrete holomorphicity: the Z_N model

It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star-triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde

Study and modelling of the effect of herbicides pulse exposure on freshwater microalgae

De plus en plus de substances chimiques sont émises et détectées dans l'environnement.Parmi ces substances, on trouve les herbicides qui sont utilisés en agriculture pour luttercontre la présence des mauvaises herbes. Après leur application sur les sols, les herbicidespeuvent être entrainés par les eaux de pluie jusque dans les ruisseaux et les rivières. Lesconcentrations de ces substances varient donc de manière importante dans les systèmesaquatiques en période de pluie ou en période de temps sec. Des pics élevés de concentrationssont suivis de période de concentrations très faibles ou nulles. Les herbicides présents dans lescours d'eau peuvent engendrer des effets toxiques sur les algues et les plantes aquatiques. Orles tests classiques d'écotoxicologie effectués en laboratoire sont réalisés en exposant lesespèces vivantes à des polluants de manière continue. Ils ne permettent donc pas d'évaluer leseffets des concentrations fluctuantes comme celles des herbicides. Le but de cette thèse estd'étudier et de modéliser les effets des concentrations fluctuantes d'herbicide sur les espècesde microalgues vertes Scenedesmus vacuolatus et Pseudokirchneriella subcapitata. Desexpériences en laboratoire ont également été effectuées dans le but de valider le modèle.Quatre herbicides ont été testés. Il s'agit de l'atrazine (utilisé jusqu'à récemment pour lemaïs), du diuron (utilisé dans la vigne), de l'isoproturon (utilisé pour les céréales) et du Smétolachlore(utilisé pour le maïs). Les résultats de ce travail de thèse indiquent que les effetsdes concentrations fluctuantes d'herbicide peuvent être modélisés sur des algues d'eau douce.Le modèle est relativement simple pour les inhibiteurs de la photosynthèse tels que l'atrazine,le diuron ou l'isoproturon. Il nécessite la connaissance de deux paramètres, le taux decroissance de l'algue sans polluant et la courbe dose-réponse pour chaque substance.Cependant, des expériences supplémentaires doivent être réalisées si la substance étudiéeinduit un délai de l'effet et du rétablissement ou si une algue est cultivée avec une autre alguedans le même milieu de croissance. Le modèle pourrait également être adapté pour tenircompte des mélanges de substances. Appliqué pour prédire les effets sur les algues descénarios réels, le modèle montre que les longs pics de concentrations jouent le rôle le plusimportant. Il est donc crucial de les mesurer lors du monitoring des cours d'eau. D'autre part,une évaluation du risque effectuée avec ce modèle montre que l'impact des pics deconcentrations sur les espèces les plus sensibles est total. Cela met en évidence, une fois deplus, l'importance de tenir compte de ces concentrations fluctuantes dans l'évaluation durisque environnemental des herbicides, mais également des autres polluants

HyperGal: hyperspectral scene modeling for supernova typing with the Integral Field Spectrograph SEDmachine

Recent developments in time domain astronomy, like the Zwicky Transient Facility, have made possible a daily scan of the entire visible sky, leading to the discovery of hundreds of new transients every night. Among them, 10 to 15 are supernovae (SNe), which have to be classified prior to cosmological use. The Spectral Energy Distribution machine (SEDm), a low resolution Integral Field Spectrograph, has been designed, built, and operated to spectroscopically classify targets detected by the ZTF main camera. The current Pysedm pipeline is limited by contamination when the transient is too close to its host galaxy core; this can lead to an incorrect typing and ultimately bias the cosmological analyses, and affect the SN sample homogeneity in terms of local environment properties. We present a new scene modeler to extract the transient spectrum from its structured background, aiming at improving the typing efficiency of the SEDm. HyperGal is a fully chromatic scene modeler, which uses pre-transient photometric images to generate a hyperspectral model of the host galaxy; it is based on the CIGALE SED fitter used as a physically-motivated spectral interpolator. The galaxy model, complemented by a point source and a diffuse background component, is projected onto the SEDm spectro-spatial observation space and adjusted to observations. The full procedure is validated on 5000 simulated cubes. We introduce the contrast as the transient-to-total flux ratio at SN location. From estimated contrast distribution of real SEDm observations, we show that HyperGal correctly classifies ~95% of SNe Ia. Compared to the standard extraction method, HyperGal correctly classifies 10% more SNe Ia. The false positive rate is less than 2%, half as much as the standard extraction method. Assuming a similar contrast distribution for core-collapse SNe, HyperGal classifies 14% (11%) additional SNe II (Ibc).Comment: 14 pages, 17 figures, submitted to Astronomy & Astrophysic

Bridge Decomposition of Restriction Measures

Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros.Comment: 24 pages, 2 figures. Final version incorporates minor revisions suggested by the referee, to appear in Jour. Stat. Phy

A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference

OASIS High-Resolution Integral Field Spectroscopy of the SAURON Ellipticals and Lenticulars

We present a summary of high-spatial resolution follow-up observations of the elliptical (E) and lenticular (S0) galaxies in the SAURON survey using the OASIS integral field spectrograph. The OASIS observations explore the central 8x10" regions of these galaxies using a spatial sampling four times higher than SAURON, often revealing previously undiscovered features. Around 75% (31/48) of the SAURON E/S0s with central velocity dispersion >= 120 km/s were observed with OASIS, covering well the original SAURON representative sample. We present here an overview of this follow-up survey, and some preliminary results on individual objects, including a previously unreported counter-rotating core in NGC 4382; the decoupled stellar and gas velocity fields of NGC 2768; and the strong age gradient towards the centre of NGC 3489.Comment: 4 pages, 5 figures. Accepted for publication in Astron. Nachr. as refereed proceedings of Euro3D Science Workshop, IoA Cambridge, May 200

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721