Intertwining Symmetry Algebras of Quantum Superintegrable Systems

We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or $(su(p,q),so(2p,2q))$. The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness

Anyons, group theory and planar physics

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell groups.Comment: 22 pages, journal reference added, bibliography update

Towards a Virtuosity of School Leadership: clinical support and supervision as professional learning

This paper introduces an innovative clinical support and supervision project that has its origins in the concern for how senior school leaders are increasingly being expected to manage the escalating demand to care for pupils, families and often the wider community. In response to these pressures we offer a three-stage professional learning model of supervision which encompasses collaboration, reflection and dialogue, while facilitating the development of professional skills within a non-judgmental space for personal and professional reflexivity. Alongside providing the service, the authors undertook two phases of qualitative research over a five-year period. Our findings indicate that support and supervision has been wholly beneficial identifying a positive impact across three broad themes: Professional learning, health and well-being, and wider school culture. The process facilitates headteachers making professionally situated decisions grounded in an understanding of educational purpose. We call for a virtuosity of school leadership – a practice of educational leadership where decision-making is informed by good educational judgments and not by standardisation and punitive accountability measures. Distinctively, clinical support and supervision promotes a virtuosity of school leadership while also meeting the moral obligation to care for school leaders and in doing so those in their care

Lava flow susceptibility map of mt etna based on numerical simulations

We constructed maps of probability of lava inundation using computer simulations considering the past eruptive behaviour of the Mt. Etna volcano and data deriving from monitoring networks. The basic a priori assumption is that new volcanoes will not form far from existing ones and that such a distribution can be performed using a Cauchy kernel. Geophysical data are useful to update or fine tune the initial Cauchy kernel to better reflect the distribution of future volcanism. In order to obtain a final susceptibility map, a statistical analysis permits a classification of Etna’s flank eruptions into twelve types. The simulation method consists of creating a probability surface of the location of future eruption vents and segmenting the region according to the most likely historical eruption on which to base the simulation. The paths of lava flows were calculated using the MAGFLOW Cellular Automata (CA) model, allowing us to simulate the discharge rate dependent spread of lava as a function of time

Synaptic Depression Influences Inspiratory-Expiratory Phase Transition in Dbx1 Interneurons of the preBotzinger Complex in Neonatal Mice

The brainstem preBotzinger complex (preBotC) generates the rhythm underlying inspiratory breathing movements and its core interneurons are derived from Dbx1-expressing precursors. Recurrent synaptic excitation is required to initiate inspiratory bursts, but whether excitatory synaptic mechanisms also contribute to inspiratory-expiratory phase transition is unknown. Here, we examined the role of short-term synaptic depression using a rhythmically active neonatal mouse brainstem slice preparation. We show that afferent axonal projections to Dbx1 preBotC neurons undergo activity-dependent depression and we identify a refractory period (similar to 2 s) after endogenous inspiratory bursts that precludes light-evoked bursts in channelrhodopsin-expressing Dbx1 preBotC neurons. We demonstrate that the duration of the refractory period-but neither the cycle period nor the magnitude of endogenous inspiratory bursts-is sensitive to changes in extracellular Ca2+. Further, we show that postsynaptic factors are unlikely to explain the refractory period or its modulation by Ca2+. Our findings are consistent with the hypothesis that short-term synaptic depression in Dbx1 preBotC neurons influences the inspiratory-expiratory phase transition during respiratory rhythmogenesis

Assessment and modeling of lava flow hazard on Mt. Etna volcano

A methodology for constructing a probability map of lava inundation by considering the past eruptive behavior of the Mt. Etna volcano is described. The basic a priori assumption is that new vents will not form far from existing ones and that such a distribution can be performed using a Gaussian kernel. The methodology follows several steps: computation of a susceptibility map that provides the spatial probability of vent opening; evaluation of the temporal probability for the occurrence of the hazard during the considered time interval; characterization of the expected eruptions; numerical simulations of lava flow paths and elaboration of the hazard map. The application of MAGFLOW code, a physical-mathematical model, for simulating the lava flow paths represents the central part of this methodology for the hazard assessment at Mt. Etna. The simulation approach, to assess lava flow hazard, provides a more robust and locally accurate analysis than a simple probabilistic approach and accounts for the influence of the actual topography on the path of future lava flows

Modelling lava flows by Cellular Nonlinear Networks (CNN): preliminary results

International audienceThe forecasting of lava flow paths is a complex problem in which temperature, rheology and flux-rate all vary with space and time. The problem is more difficult to solve when lava runs down a real topography, considering that the relations between characteristic parameters of flow are typically nonlinear. An alternative approach to this problem that does not use standard differential equation methods is Cellular Nonlinear Networks (CNNs). The CNN paradigm is a natural and flexible framework for describing locally interconnected, simple, dynamic systems that have a lattice-like structure. They consist of arrays of essentially simple, nonlinearly coupled dynamic circuits containing linear and non-linear elements able to process large amounts of information in real time. Two different approaches have been implemented in simulating some lava flows. Firstly, a typical technique of the CNNs to analyze spatio-temporal phenomena (as Autowaves) in 2-D and in 3-D has been utilized. Secondly, the CNNs have been used as solvers of partial differential equations of the Navier-Stokes treatment of Newtonian flow

Assessment and modeling of lava flow hazard on Etna volcano

A methodology for constructing a probability map of lava inundation by considering the past eruptive behavior of the Mt Etna volcano is described. The basic a priori assumption is that new vents will not form far from existing ones and that such a distribution can be performed using a Gaussian kernel. The methodology is based on several steps: computation of susceptibility map that provides the spatial probability of vent opening; evaluation of the temporal probability for the occurrence of the hazard during the considered time interval; characterization of the expected eruptions; numerical simulations of lava flow paths, and elaboration of the hazard map. The application of MAGFLOW code, a physical-mathematical model, for simulating the lava flow paths represents the central part of this methodology for the hazard assessment at Etna. The simulation approach, to assess lava flow hazard, provides a more robust and locally accurate analysis than a simple probabilistic approach and accounts for the influence of the actual topography on the path of future lava flows

Peripartum cardiomyopathy (PPCM): anesthetic and obstetric monitoring, management and medico-legal aspects

Peripartum Cardiomyopathy (PPCM): anesthetic and obstetric monitoring, management and medico-legal aspect