Representation Theory of Twisted Group Double

This text collects useful results concerning the quasi-Hopf algebra \D . We give a review of issues related to its use in conformal theories and physical mathematics. Existence of such algebras based on 3-cocycles with values in ${R} / {Z}$ which mimic for finite groups Chern-Simons terms of gauge theories, open wide perspectives in the so called "classification program". The modularisation theorem proved for quasi-Hopf algebras by two authors some years ago makes the computation of topological invariants possible. An updated, although partial, bibliography of recent developments is provided.Comment: 15 pages, no figur

Generalised Fermat Hypermaps and Galois Orbits

We consider families of quasiplatonic Riemann surfaces characterised by the fact that -- as in the case of Fermat curves of exponent $n$ -- their underlying regular (Walsh) hypermap is the complete bipartite graph $K_{n,n}$, where $n$ is an odd prime power. We will show that all these surfaces, regarded as algebraic curves, are defined over abelian number fields. We will determine the orbits under the action of the absolute Galois group, their minimal fields of definition, and in some easier cases also their defining equations. The paper relies on group-- and graph--theoretic results by G. A. Jones, R. Nedela and M.\v{S}koviera about regular embeddings of the graphs $K_{n,n}$ [JN\v{S}] and generalises the analogous question for maps treated in [JStW], partly using different methods.Comment: 14 pages, new version with extended introduction, minor corrections and updated reference

Resonant Magnetic Vortices

By using the complex angular momentum method, we provide a semiclassical analysis of electron scattering by a magnetic vortex of Aharonov-Bohm-type. Regge poles of the $S$-matrix are associated with surface waves orbiting around the vortex and supported by a magnetic field discontinuity. Rapid variations of sharp characteristic shapes can be observed on scattering cross sections. They correspond to quasibound states which are Breit-Wigner-type resonances associated with surface waves and which can be considered as quantum analogues of acoustic whispering-gallery modes. Such a resonant magnetic vortex could provide a new kind of artificial atom while the semiclassical approach developed here could be profitably extended in various areas of the physics of vortices.Comment: 6 pages, 7 figure

Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.Comment: 8 page

Red-Shifted Firefly Luciferase Optimized for Candida albicans In vivo Bioluminescence Imaging.

Candida albicans is a major fungal pathogen causing life-threatening diseases in immuno-compromised patients. The efficacy of current drugs to combat C. albicans infections is limited, as these infections have a 40-60% mortality rate. There is a real need for novel therapeutic approaches, but such advances require a detailed knowledge of C. albicans and its in vivo pathogenesis. Additionally, any novel antifungal drugs against C. albicans infections will need to be tested for their in vivo efficacy over time. Fungal pathogenesis and drug-mediated resolution studies can both be evaluated using non-invasive in vivo imaging technologies. In the work presented here, we used a codon-optimized firefly luciferase reporter system for detecting C. albicans in mice. We adapted the firefly luciferase in order to improve its maximum emission intensity in the red light range (600-700 nm) as well as to improve its thermostability in mice. All non-invasive in vivo imaging of experimental animals was performed with a multimodal imaging system able to detect luminescent reporters and capture both reflectance and X-ray images. The modified firefly luciferase expressed in C. albicans (Mut2) was found to significantly increase the sensitivity of bioluminescence imaging (BLI) in systemic infections as compared to unmodified luciferase (Mut0). The same modified bioluminescence reporter system was used in an oropharyngeal candidiasis model. In both animal models, fungal loads could be correlated to the intensity of emitted light. Antifungal treatment efficacies were also evaluated on the basis of BLI signal intensity. In conclusion, BLI with a red-shifted firefly luciferase was found to be a powerful tool for testing the fate of C. albicans in various mice infection models

Tame Functions with strongly isolated singularities at infinity: a tame version of a Parusinski's Theorem

Let f be a definable function, enough differentiable. Under the condition of having strongly isolated singularities at infinity at a regular value c we give a sufficient condition expressed in terms of the total absolute curvature function to ensure the local triviality of the function f over a neighbourhood of c and doing so providing the tame version of Parusinski's Theorem on complex polynomials with isolated singularities at infinity.Comment: 20 page

Examining the virulence of Candida albicans transcription factor mutants using Galleria mellonella and mouse infection models.

The aim of the present study was to identify Candida albicans transcription factors (TFs) involved in virulence. Although mice are considered the gold-standard model to study fungal virulence, mini-host infection models have been increasingly used. Here, barcoded TF mutants were first screened in mice by pools of strains and fungal burdens (FBs) quantified in kidneys. Mutants of unannotated genes which generated a kidney FB significantly different from that of wild-type were selected and individually examined in Galleria mellonella. In addition, mutants that could not be detected in mice were also tested in G. mellonella. Only 25% of these mutants displayed matching phenotypes in both hosts, highlighting a significant discrepancy between the two models. To address the basis of this difference (pool or host effects), a set of 19 mutants tested in G. mellonella were also injected individually into mice. Matching FB phenotypes were observed in 50% of the cases, highlighting the bias due to host effects. In contrast, 33.4% concordance was observed between pool and single strain infections in mice, thereby highlighting the bias introduced by the "pool effect." After filtering the results obtained from the two infection models, mutants for MBF1 and ZCF6 were selected. Independent marker-free mutants were subsequently tested in both hosts to validate previous results. The MBF1 mutant showed impaired infection in both models, while the ZCF6 mutant was only significant in mice infections. The two mutants showed no obvious in vitro phenotypes compared with the wild-type, indicating that these genes might be specifically involved in in vivo adapt

Spatial Mixing and Non-local Markov chains

We consider spin systems with nearest-neighbor interactions on an $n$-vertex $d$-dimensional cube of the integer lattice graph $\mathbb{Z}^d$. We study the effects that exponential decay with distance of spin correlations, specifically the strong spatial mixing condition (SSM), has on the rate of convergence to equilibrium distribution of non-local Markov chains. We prove that SSM implies $O(\log n)$ mixing of a block dynamics whose steps can be implemented efficiently. We then develop a methodology, consisting of several new comparison inequalities concerning various block dynamics, that allow us to extend this result to other non-local dynamics. As a first application of our method we prove that, if SSM holds, then the relaxation time (i.e., the inverse spectral gap) of general block dynamics is $O(r)$, where $r$ is the number of blocks. A second application of our technology concerns the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models. We show that SSM implies an $O(1)$ bound for the relaxation time. As a by-product of this implication we observe that the relaxation time of the Swendsen-Wang dynamics in square boxes of $\mathbb{Z}^2$ is $O(1)$ throughout the subcritical regime of the $q$-state Potts model, for all $q \ge 2$. We also prove that for monotone spin systems SSM implies that the mixing time of systematic scan dynamics is $O(\log n (\log \log n)^2)$. Systematic scan dynamics are widely employed in practice but have proved hard to analyze. Our proofs use a variety of techniques for the analysis of Markov chains including coupling, functional analysis and linear algebra