Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

Multi-Hamiltonian structures for r-matrix systems

For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral curves and sheaves supported on them; (c) Symmetric products of a surface. We have, at each level, a linear space of compatible Poisson structures, and the maps relating the levels are Poisson. This leads in a natural way to Nijenhuis coordinates for these spaces. At level (b), there are Hamiltonian systems on these spaces which are integrable for each Poisson structure in the family, and which are such that the Lagrangian leaves are the intersections of the symplective leaves over the Poisson structures in the family. Specific examples include many of the well-known integrable systems.Comment: 26 pages, Plain Te

Noncoding RNAs in Duchenne and Becker muscular dystrophies: role in pathogenesis and future prognostic and therapeutic perspectives

Noncoding RNAs (ncRNAs), such as miRNAs and long noncoding RNAs, are key regulators of gene expression at the post-transcriptional level and represent promising therapeutic targets and biomarkers for several human diseases, including Duchenne and Becker muscular dystrophies (DMD/BMD). A role for ncRNAs in the pathogenesis of muscular dystrophies has been suggested, even if it is still incompletely understood. Here, we discuss current progress leading towards the clinical utility of ncRNAs for DMD/BMD. Long and short noncoding RNAs are differentially expressed in DMD/BMD and have a mechanism of action via targeting mRNAs. A subset of muscle-enriched miRNAs, the so-called myomiRs (miR-1, miR-133, and miR-206), are increased in the serum of patients with DMD and in dystrophin-defective animal models. Interestingly, myomiRs might be used as biomarkers, given that their levels can be corrected after dystrophin restoration in dystrophic mice. Remarkably, further evidence demonstrates that ncRNAs also play a role in dystrophin expression; thus, their modulations might represent a potential therapeutic strategy with the aim of upregulating the dystrophin protein in combination with other oligonucleotides/gene therapy approaches

A Novel Hierarchy of Integrable Lattices

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalisation. We also solve the associated spectral problem and explicity contruct action-angle variables through the r-matrix approach.Comment: Latex fil

Engineering Silicon Nanocrystals: Theoretical study of the effect of Codoping with Boron and Phosphorus

We show that the optical and electronic properties of nanocrystalline silicon can be efficiently tuned using impurity doping. In particular, we give evidence, by means of ab-initio calculations, that by properly controlling the doping with either one or two atomic species, a significant modification of both the absorption and the emission of light can be achieved. We have considered impurities, either boron or phosphorous (doping) or both (codoping), located at different substitutional sites of silicon nanocrystals with size ranging from 1.1 nm to 1.8 nm in diameter. We have found that the codoped nanocrystals have the lowest impurity formation energies when the two impurities occupy nearest neighbor sites near the surface. In addition, such systems present band-edge states localized on the impurities giving rise to a red-shift of the absorption thresholds with respect to that of undoped nanocrystals. Our detailed theoretical analysis shows that the creation of an electron-hole pair due to light absorption determines a geometry distortion that in turn results in a Stokes shift between adsorption and emission spectra. In order to give a deeper insight in this effect, in one case we have calculated the absorption and emission spectra going beyond the single-particle approach showing the important role played by many-body effects. The entire set of results we have collected in this work give a strong indication that with the doping it is possible to tune the optical properties of silicon nanocrystals.Comment: 14 pages 19 figure

Vertex Operator Superalgebras and Odd Trace Functions

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call `odd trace functions'. We examine the case of the N=1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.Comment: 13 pages, 0 figures. To appear in Conference Proceedings `Advances in Lie Superalgebras

Marked pseudoepitheliomatous hyperplasia secondary to a red-pigmented tattoo. a case report

Tattooing is gaining increasing popularity in developed countries in recent years. Adverse cutaneous reactions of many different types against coumponds in tattoo inks are being reported more and more often in medical literature,especially against red-pigmented tattoo. Delayed immune-mediated reactions can manifest in several ways and different histological patterns have been described This article is protected by copyright. All rights reserved

Ophthalmoplegia due to Miller Fisher syndrome in a patient with myasthenia gravis

Here, we describe a 79-year-old man, admitted to our unit for worsening diplopia and fatigue, started a few weeks after an episode of bronchitis and flu vaccination. Past medical history includes myasthenia gravis (MG), well-controlled by Pyridostigmine, Azathioprine, and Prednisone. During the first days, the patient developed progressive ocular movement abnormalities up to complete external ophthalmoplegia, severe limb and gait ataxia, and mild dysarthria. Deep tendon reflexes were absent in lower limbs. Since not all the symptoms were explainable with the previous diagnosis of myasthenia gravis, other etiologies were investigated. Brain MRI and cerebrospinal fluid analysis were normal. Electromyography showed a pattern of predominantly sensory multiple radiculoneuritis. Suspecting Miller Fisher syndrome (MFS), the patient was treated with plasmapheresis with subsequent clinical improvement. Antibodies against GQ1b turned out to be positive. MFS is an immune-mediated neuropathy presenting with ophthalmoplegia, ataxia, and areflexia. Even if only a few cases of MFS overlapping with MG have been described so far, the coexistence of two different autoimmune disorders can occur. It is always important to evaluate possible differential diagnosis even in case of known compatible diseases, especially when some clinical features seem atypical

Dispersionless integrable equations as coisotropic deformations. Extensions and reductions

Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systems is discussed. Several generalizations are considered. Stationary reductions of the dispersionless integrable equations are shown to be connected with the dynamical systems on the plane completely integrable on a fixed energy level. ems is discussed. Several generalizations are considered. Stationary reductions of the dispersionless integrable equations are shown to be connected with the dynamical systems on the plane completely integrable on a fixed energy level.Comment: 21 pages, misprints correcte

On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page