(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation

Using methods of math.DG/0304245 and [I.S.Krasil'shchik and P.H.M.Kersten, Symmetries and recursion operators for classical and supersymmetric differential equations, Kluwer, 2000], we accomplish an extensive study of the N=1 supersymmetric Korteweg-de Vries equation. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, five hierarchies of symmetries, the corresponding hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. We stress that the main point of the paper is not just the results on super-KdV equation itself, but merely exposition of the efficiency of the geometrical approach and of the computational algorithms based on it.Comment: 16 pages, AMS-LaTeX, Xy-pic, dvi-file to be processed by dvips. v2: nonessential improvements of exposition, title change

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic

Potential involvement of IL-9 and Th9 cells in the pathogenesis of rheumatoid arthritis

Objective. IL-9 has been shown to be upregulated before the clinical onset of articular disease in RA. The exact role of IL-9 and Th9 cells in RA, however, has not yet been adequately studied. The aim of this study was to evaluate the expression of IL-9 and IL-9-expressing cells in RA patients. Methods. IL-9, IL-9R, PU.1, IL-9, thymic stromal lymphopoietin (TSLP), IL-4 and TGF-β expression was assessed by real-time-PCR in the synovial tissues of RA and OA patients. IL-9, IL-9R, IL-4, TSLP and TGF-β were also investigated by immunohistochemistry. Peripheral CD4+ T cell subsets were studied by flow cytometry analysis before and after incubation with citrullinated peptides. Results. IL-9 was overexpressed in RA synovial tissues and correlated with the degree of histological organization of B and T cells in ectopic lymphoid structures. The majority of IL-9-producing cells were identified as CD3+ cells. Increased mRNA and protein expression of IL-9R, IL-4, TSLP and TGF-β was also observed in RA synovial tissue. Blood peripheral Th9 cells were expanded by citrullinated peptides. Conclusion. These results indicate that Th9 cells and IL-9 were frequently detected in peripheral blood mononuclear cells and synovia of RA patients. A possible pathogenic role for Th9 in RA is discussed

Numerical convergence of the block-maxima approach to the Generalized Extreme Value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. [2006] have found analytical results.Comment: 34 pages, 7 figures; Journal of Statistical Physics 201

A possible cause of misdiagnosis in tumors of the axilla: schwannoma of the brachial plexus

The Authors report a rare case of a 57 years old man affected by a left radial nerve schwannoma that occurred as an asymptomatic lesion of the axilla. At clinical examination the lump was undistinguishable from the most common axillary lymphadenopathy. A lymphoadenopathy was erroneously diagnosed with ultrasonography (US). This mistake was due to the low specificity of the instrumental methodology and to the rarity of an asymptomatic schwannoma of the infraclavicular brachial plexus. The neoplasia was excised without using the microscope. In the early post-operative follow up, a “falling” attitude of the wirst, the hand and the fingers appeared, peculiar for a lesion of the radial nerve. Furthermore a hypoaesthesia of the skin of first finger and of the first interosseus space was associated. The sensitive and motor electromyography showed a radial nerve suffering. The “stupor” of the nerve trunk was treated with steroid therapy for 7 days and the patient underwent to some series of neuro-rehabilitative physical therapy for 12 weeks. The postoperative total body CT, showed that the lesion was unique: therefore it was possible to exclude the diagnosis of neurofibromatosis. After 28 months electromyography and axillary US were performed showing the complete resolution of the motor and sensitive deficit and the absence of local recurrence

Heads in the cloud:innovation in data and model dissemination

Utilising environmental data to better support decision making is a complex task. The Environmental Virtual Observatory pilot project has demonstrated that a multidisciplinary approach to making integrated data and modelling services available via new cloud technologies offers a way forward

A Spatial Survey of Environmental Indicators for Kazakhstan: An Examination of Current Conditions and Future Needs

The Republic of Kazakhstan, located in Central Asia, has experienced many years of environmental degradation, largely as a result of the poor management of its significant natural resources. In this survey, data relating to different environmental factors are critically analysed in order to understand the state of the environment. It was found that: warming trends are seen in sensitive areas (e.g. the steppe and near glaciers); drying trends are seen where there is already water stress (e.g. the Aral Sea); air quality has been declining recently (following improvements on the decadal timescale) in major urban centres, particularly Almaty; water quality appears to be improving in some areas (e.g. important lakes in the Aktobe and Zhambyl regions); and levels of exposure to radioactivity are below internationally recommended levels (where data have been found). More generally, there is an issue with data availability and quality, which requires attention if Kazakhstan is going to make the best use of its increasing investment in environmental actions. Current policies are reviewed and recommendations are made for future interventions

Numerical-Experimental Assessment of a Hybrid FE-MB Model of an Aircraft Seat Sled Test

This paper deals with the development of an established hybrid finite element multibody (FE-MB) model for the simulation of an experimental sled test of a single row of a double passenger seat placed in front of a fuselage bulkhead, by considering a single anthropomorphic Hybrid II 50th dummy arranged on one of the seat places. The numerical investigation has been carried out by focusing on the passenger passive safety. Specifically, the occupant injury assessment has been quantitatively monitored by means of the head injury criterion (HIC), which, based on the average value of the dummy head acceleration during a crash event, should not exceed, according to the standards, the value of 1000. Numerical results provided by the hybrid model have been compared with the experimental ones provided by the Geven S.p.A. company and with the results carried out by a full FE model. The hybrid model simulates with a good level of accuracy the experimental test and allows reducing significantly the computing time with respect to the full FE one