And yet it moves: Recovery of volitional control after spinal cord injury

Preclinical and clinical neurophysiological and neurorehabilitation research has generated rather surprising levels of recovery of volitional sensory-motor function in persons with chronic motor paralysis following a spinal cord injury. The key factor in this recovery is largely activity-dependent plasticity of spinal and supraspinal networks. This key factor can be triggered by neuromodulation of these networks with electrical and pharmacological interventions. This review addresses some of the systems-level physiological mechanisms that might explain the effects of electrical modulation and how repetitive training facilitates the recovery of volitional motor control. In particular, we substantiate the hypotheses that: (1) in the majority of spinal lesions, a critical number and type of neurons in the region of the injury survive, but cannot conduct action potentials, and thus are electrically non-responsive; (2) these neuronal networks within the lesioned area can be neuromodulated to a transformed state of electrical competency; (3) these two factors enable the potential for extensive activity-dependent reorganization of neuronal networks in the spinal cord and brain, and (4) propriospinal networks play a critical role in driving this activity-dependent reorganization after injury. Real-time proprioceptive input to spinal networks provides the template for reorganization of spinal networks that play a leading role in the level of coordination of motor pools required to perform a given functional task. Repetitive exposure of multi-segmental sensory-motor networks to the dynamics of task-specific sensory input as occurs with repetitive training can functionally reshape spinal and supraspinal connectivity thus re-enabling one to perform complex motor tasks, even years post injury

Sampling of quantum dynamics at long time

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the parameters of the calculation) over previous schemes is achieved. Novel perspectives for theoretical calculations in coherent many-body systems are opened.Comment: Revised versio

The Generalized Star Product and the Factorization of Scattering Matrices on Graphs

In this article we continue our analysis of Schr\"odinger operators on arbitrary graphs given as certain Laplace operators. In the present paper we give the proof of the composition rule for the scattering matrices. This composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs. We perform a detailed analysis of the generalized star product for arbitrary unitary matrices. The relation to the theory of transfer matrices is also discussed

Kirchhoff's Rule for Quantum Wires

In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the vertices. This results in a scattering theory with $n$ channels. The corresponding on-shell S-matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy $E>0$ is explicitly given in terms of the boundary conditions and the lengths of the internal lines. It is shown to be unitary, which may be viewed as the quantum version of Kirchhoff's law. We exhibit covariance and symmetry properties. It is symmetric if the boundary conditions are real. Also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory. Finally we provide a composition rule by which the on-shell S-matrix of a graph is factorizable in terms of the S-matrices of its subgraphs. All proofs only use known facts from the theory of self-adjoint extensions, standard linear algebra, complex function theory and elementary arguments from the theory of Hermitean symplectic forms.Comment: 40 page

INTERNET PARA OS GANHOS DOS ESTUDANTES: LOCAL DE TRABALHO OU ESPAÇO DE COMUNICAÇÃO

La sobrecarga de trabajo de los docentes puede ocasionar desafíos para los docentes que provoquen agotamiento a largo plazo si no se abordan. En consecuencia, el presente estudio tiene como objetivo examinar las fuentes de prevención del agotamiento desde las perspectivas de los supervisores EFL (inglés como lengua extranjera). Los participantes fueron 85 supervisores de EFL iraníes cuyo trabajo consistía en observar y dar retroalimentación a los maestros sobre su desempeño docente en varios niveles de dominio del idioma, desde los niveles de primaria hasta los avanzados. En este estudio se empleó un diseño secuencial de método mixto. Primero, la recopilación de datos cualitativos se realizó mediante entrevistas con 30 participantes para determinar las fuentes de prevención del agotamiento desde la perspectiva de los supervisores. A continuación, se diseñó un cuestionario de prevención de agotamiento utilizando los resultados de las entrevistas, después de lo cual se administró a los participantes restantes. Los datos recopilados fueron analizados por factores para identificar los componentes de la construcción de prevención de agotamiento. Los resultados del análisis de contenido de los datos de la entrevista indicaron que el apoyo de los maestros por parte de sus colegas, la situación menos estresante y la satisfacción laboral fueron las principales fuentes de prevención del agotamiento. El análisis factorial mostró las mismas fuentes de agotamiento que los componentes principales de la construcción de prevención de agotamiento. Los hallazgos de este estudio enfatizan la contribución del apoyo educativo y emocional de los maestros, proporcionando un lugar de trabajo constructivo y saludable, así como ingresos deseables como formas de prevención del agotamiento en los maestros de EFL.Teacher work overload can cause challenges for teachers leading to burnout in the long term if not addressed. Consequently, the present study aims at examining the sources of burnout prevention from EFL (English as a foreign Language) supervisors’ perspectives. The participants were 85 Iranian EFL supervisors whose job was observing and giving feedback to teachers about their teaching performance at various levels of language proficiencies from elementary to advanced levels. A sequential mixed method design was employed in this study. First, collection of qualitative data was performed using interviews with 30 participants in order to determine the sources of burnout prevention from supervisors’ perspectives. Next, a burnout prevention questionnaire was designed using the results of the interviews, after which it was administered to the remaining participants. The collected data were factor analyzed to identify the components of burnout prevention construct. Results of content analysis of the interview data indicated that teachers’ support from their colleagues, less stressful situation, and job satisfaction were the main sources of burnout prevention. Factor analysis showed the same sources of burnout as the main components of the burnout prevention construct. The findings of this study emphasize on the contribution of teachers’ educational and emotional support, providing constructive and healthy working place, as well as desirable income as ways for prevention of burnout in EFL teachers.A sobrecarga de trabalho do professor pode causar desafios para os professores, levando a esgotamento a longo prazo, se não forem abordados. Consequentemente, o presente estudo tem como objetivo examinar as fontes de prevenção de burnout das perspectivas dos supervisores de EFL (inglês como língua estrangeira). Os participantes foram 85 supervisores iranianos de EFL, cujo trabalho era observar e dar feedback aos professores sobre seu desempenho no ensino em vários níveis de proficiência linguística, do nível básico ao avançado. Um método misto sequencial foi empregado neste estudo. Primeiro, a coleta de dados qualitativos foi realizada por meio de entrevistas com 30 participantes, a fim de determinar as fontes de prevenção de burnout na perspectiva dos supervisores. Em seguida, foi elaborado um questionário de prevenção de burnout, utilizando os resultados das entrevistas, após o qual foi aplicado aos demais participantes. Os dados coletados foram analisados por fatores para identificar os componentes do construto de prevenção de burnout. Os resultados da análise de conteúdo dos dados da entrevista indicaram que o apoio dos professores de seus colegas, a situação menos estressante e a satisfação no trabalho foram as principais fontes de prevenção de burnout. A análise fatorial mostrou as mesmas fontes de burnout que os principais componentes do construto de prevenção de burnout. As conclusões deste estudo enfatizam a contribuição do apoio educacional e emocional dos professores, proporcionando um local de trabalho construtivo e saudável, bem como a renda desejável como formas de prevenção do esgotamento nos professores de EFL

Scattering theory on graphs (2): the Friedel sum rule

We consider the Friedel sum rule in the context of the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We generalize the Smith formula for graphs. We give several examples of graphs where the state counting method given by the Friedel sum rule is not working. The reason for the failure of the Friedel sum rule to count the states is the existence of states localized in the graph and not coupled to the leads, which occurs if the spectrum is degenerate and the number of leads too small.Comment: 20 pages, LaTeX, 6 eps figure

Weakly coupled states on branching graphs

We consider a Schr\"odinger particle on a graph consisting of $\,N\,$ links joined at a single point. Each link supports a real locally integrable potential $\,V_j\,$; the self--adjointness is ensured by the $\,\delta\,$ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as $\,x^{-1-\epsilon}$ along each of them, is non--repulsive in the mean and weak enough, the corresponding Schr\"odinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the $\,\delta\,$ coupling constant may be interpreted in terms of a family of squeezed potentials.Comment: LaTeX file, 7 pages, no figure

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure

A single-mode quantum transport in serial-structure geometric scatterers

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit $N\to\infty$. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. A detailed discussion is presented for a finite-periodic "comb"; we show how the resonance poles can be computed within the Krein formula approach. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart of the resonances coming from the decoupled-surface eigenvalues such scatterers exhibit the high-energy behavior typical for the delta' interaction for the physically interesting couplings.Comment: 36 pages, a LaTeX source file with 2 TeX drawings, 3 ps and 3 jpeg figures attache