Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.Comment: 56 pages, 4 eps figures, LaTeX, uses eps

Empty nose syndrome

SummaryEmpty nose syndrome (ENS) is a clinical entity without consensual definition; it is a rare complication of nose or sinus surgery, and of inferior turbinectomy in particular. Physiopathology remains unclear, but probably involves disorder caused by excessive nasal permeability affecting neurosensitive receptors and inhaled air humidification and conditioning functions. Neuropsychological involvement is suspected. Symptomatology is variable and changeable, the most common sign being paradoxical nasal obstruction. Diagnosis is founded on: (1) a range of symptoms that need to be precisely collated; (2) broad post-surgical nasal permeability. Management is problematic, deploying the full range of simple nasal cavity hygiene and humidification techniques, with surgery reserved for the most severe cases; whatever the technique, surgery aims at partial filling of the nasal airway. Prevention is the most important strategy, and seeks (1) to check, before any surgery is envisaged, the reality of nasal dyspermeability resistant to medical treatment; and (2) to prefer the most conservative surgical techniques

IL-1α and TNF-α Down-Regulate CRH Receptor-2 mRNA Expression in the Mouse Heart

Two receptors (CRH receptor type 1 and CRH receptor type 2) have been identified for the stress-induced neuropeptide, CRH and related peptides, urocortin, and urocortin II. We previously found marked down-regulation of cardiac CRH receptor type 2 expression following administration of bacterial endotoxin, lipopolysaccharide, a model of systemic immune activation, and inflammation. We postulated that inflammatory cytokines may regulate CRH receptor type 2. We show that systemic IL-1α administration significantly down-regulates CRH receptor type 2 mRNA in mouse heart. In addition, TNFα treatment also reduces CRH receptor type 2 mRNA expression, although the effect was not as marked as with IL-1α. However, CRH receptor type 2 mRNA expression is not altered in adult mouse ventricular cardiomyocytes stimulated in vitro with TNFα or IL-1α. Thus, cytokine regulation may be indirect. Exogenous administration of corticosterone in vivo or acute restraint stress also reduces cardiac CRH receptor type 2 mRNA expression, but like cytokines, in vitro corticosterone treatment does not modulate expression in cardiomyocytes. Interestingly, treatment with urocortin significantly decreases CRH receptor type 2 mRNA in cultured cardiomyocytes. We speculate that in vivo, inflammatory mediators such as lipopolysaccharide and/or cytokines may increase urocortin, which in turn down-regulates CRH receptor type 2 expression in the heart. Because CRH and urocortin increase cardiac contractility and coronary blood flow, impaired CRH receptor type 2 function during systemic inflammation may ultimately diminish the adaptive cardiac response to adverse conditions

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

Collecting cometary soil samples? Development of the ROSETTA sample acquisition system

In the reference scenario of the ROSETTA CNRS mission, the Sample Acquisition System is mounted on the Comet Lander. Its tasks are to acquire three kinds of cometary samples and to transfer them to the Earth Return Capsule. Operations are to be performed in vacuum and microgravity, on a probably rough and dusty surface, in a largely unknown material, at temperatures in the order of 100 K. The concept and operation of the Sample Acquisition System are presented. The design of the prototype corer and surface sampling tool, and of the equipment for testing them at cryogenic temperatures in ambient conditions and in vacuum in various materials representing cometary soil, are described. Results of recent preliminary tests performed in low temperature thermal vacuum in a cometary analog ice-dust mixture are provided

Four-strand hamstring tendon autograft for ACL reconstruction in patients aged 50years or older

SummaryIntroductionReconstruction of the anterior cruciate ligament using a four-strand hamstring tendon autograft in symptomatic patients aged 50years or older is an accepted treatment option.HypotesisFour-strand hamstring tendon autograft although not universally utilized in patients who are at least 50years old is an efficient procedure to control knee instability.Material and methodsIn this retrospective, we analyzed the clinical outcomes of 18patients treated from September 1998 to September 2003. Criteria for inclusion were the following: age above 50years at surgery, chronic anterior laxity associated or not with meniscal damage; one or more episodes of knee instability and no prior ligament surgery on the involved knee. A same operative technique (arthroscopic single-bundle four-strand hamstring reconstruction, blind femoral tunnel, through anteromedial portals), a same fixation type (absorbable interference screws in femur and tibia) and a same rehabilitation protocol were used for all these knees. The IKDC 93scores were determined pre- and postoperatively combined with anteroposterior and lateral views, single leg stance, 30° flexion stance, and passive Lachman test (Telos) postoperatively.ResultsAt mean 30month-follow-up (range 12–59months), there were no graft failure and no loss of extension for any of these knees. Three patients complained of hypoesthesia in the medial saphenous nerve territory and one patient experienced posterior knee pain. All patients graded their knee as normal or nearly normal, all were satisfied or very satisfied with their operation. None of the patients reported instability. The Lachman-Trillat test was noted “firm end point” in 14knees and “delayed firm end point” in four. The pivot-shift test was negative in 16knees and mild positive in two. The mean residual differential laxity was 3.1mm (0 to +6mm) for the passive Lachman test. At last follow-up, the overall IKDC score was 7A, 7B, 3C, and 1 D. Patients with preserved meniscus (nine patients) reported a lesser degree of pain and a better residual laxity control compared with patients who had undergone a meniscectomy.ConclusionAge over 50years is not a contraindication to select a hamstring tendon autograft for ACL reconstruction. This surgery can restore knee stability but does not modify the pain pattern in patients, who had a medial meniscectomy prior to the ACL reconstruction.Level of evidence: level IV, therapeutic study

Cutoff for the Ising model on the lattice

Introduced in 1963, Glauber dynamics is one of the most practiced and extensively studied methods for sampling the Ising model on lattices. It is well known that at high temperatures, the time it takes this chain to mix in $L^1$ on a system of size $n$ is $O(\log n)$. Whether in this regime there is cutoff, i.e. a sharp transition in the $L^1$-convergence to equilibrium, is a fundamental open problem: If so, as conjectured by Peres, it would imply that mixing occurs abruptly at $(c+o(1))\log n$ for some fixed $c>0$, thus providing a rigorous stopping rule for this MCMC sampler. However, obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple Markov chains. Already for the one-dimensional Ising model, showing cutoff is a longstanding open problem. We settle the above by establishing cutoff and its location at the high temperature regime of the Ising model on the lattice with periodic boundary conditions. Our results hold for any dimension and at any temperature where there is strong spatial mixing: For $\Z^2$ this carries all the way to the critical temperature. Specifically, for fixed $d\geq 1$, the continuous-time Glauber dynamics for the Ising model on $(\Z/n\Z)^d$ with periodic boundary conditions has cutoff at $(d/2\lambda_\infty)\log n$, where $\lambda_\infty$ is the spectral gap of the dynamics on the infinite-volume lattice. To our knowledge, this is the first time where cutoff is shown for a Markov chain where even understanding its stationary distribution is limited. The proof hinges on a new technique for translating $L^1$ to $L^2$ mixing which enables the application of log-Sobolev inequalities. The technique is general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure