Status epilepticus affects the gigantocellular network of the pontine reticular formation

Background  

The impairment of the pontine reticular formation (PRF) has recently been revealed to be histopathologically connected with focal-cortical seizure induced generalized convulsive status epilepticus. To elucidate whether the impairment of the PRF is a general phenomenon during status epilepticus, the focal-cortical 4-aminopyridine (4-AP) application was compared with other epilepsy models. The presence of "dark" neurons in the PRF was investigated by the sensitive silver method of Gallyas in rats sacrificed at 3 h after focal 4-AP crystal or systemic 4-AP, pilocarpine, or kainic acid application. The behavioral signs of the developing epileptic seizures were scored in all rats. The EEG activity was recorded in eight rats.     

Polarization control of the nonlinear emission of semiconductor microcavities

The degree of circular polarization ( Weierstrass p ) of the nonlinear emission in semiconductor microcavities is controlled by changing the exciton-cavity detuning. The polariton relaxation towards K approximately 0 cavitylike states is governed by final-state stimulated scattering. The helicity of the emission is selected due to the lifting of the degeneracy of the +/-1 spin levels at K approximately 0. At short times after a pulsed excitation Weierstrass p reaches very large values, either positive or negative, as a result of stimulated scattering to the spin level of lowest energy (+1/-1 spin for positive/negative detuning).     

Longitudinal focusing and cooling of a molecular beam

A neutral polar molecule experiences a force in an inhomogeneous electric field. This electric field can be designed such that a beam of polar molecules is exposed to a harmonic potential in the forward direction. In this potential the longitudinal phase-space distribution of the ensemble of molecules is rotated uniformly. This property is used to longitudinally focus a pulsed beam of ammonia molecules and to produce a beam with a longitudinal velocity spread of 0.76 m/s, corresponding to a temperature of 250 mu K.     

The Spectrum of the Cubic Oscillator

We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E _n (β)} _{n ≥ 0} labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case.     

Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations

Hierarchical tensors can be regarded as a generalisation, preserving many crucial features, of the singular value decomposition to higher-order tensors. For a given tensor product space, a recursive decomposition of the set of coordinates into a dimension tree gives a hierarchy of nested subspaces and corresponding nested bases. The dimensions of these subspaces yield a notion of multilinear rank. This rank tuple, as well as quasi-optimal low-rank approximations by rank truncation, can be obtained by a hierarchical singular value decomposition. For fixed multilinear ranks, the storage and operation complexity of these hierarchical representations scale only linearly in the order of the tensor. As in the matrix case, the set of hierarchical tensors of a given multilinear rank is not a convex set, but forms an open smooth manifold. A number of techniques for the computation of hierarchical low-rank approximations have been developed, including local optimisation techniques on Riemannian manifolds as well as truncated iteration methods, which can be applied for solving high-dimensional partial differential equations. This article gives a survey of these developments. We also discuss applications to problems in uncertainty quantification, to the solution of the electronic Schrödinger equation in the strongly correlated regime, and to the computation of metastable states in molecular dynamics.     

Passivation of aluminium–n+ silicon contacts for solar cells by ultrathin Al2O3 and SiO2 dielectric layers

Ultra‐thin thermally grown SiO₂ and atomic‐layer‐deposited (ALD) Al₂O₃ films are trialled as passivating dielectrics for metal–insulator–semiconductor (MIS) type contacts on top of phosphorus diffused regions applicable to high efficiency silicon solar cells. An investigation of the optimum insulator thickness in terms of contact recombination factor J_{0_cont} and contact resistivity ρ_c is undertaken on 85 Ω/□ and 103 Ω/□ diffusions. An optimum ALD Al₂O₃ thickness of ～22 Å produces a J_{0_cont} of ～300 fAcm^–2 whilst maintaining a ρ_c lower than 1 mΩ cm² for the 103 Ω/□ diffusion. This has the potential to improve the open‐circuit voltage by a maximum 15 mV. The thermally grown SiO₂ fails to achieve equivalently low J_{0_cont} values but exhibits greater thermal stability, resulting in slight improvements in ρ_c when annealed for 10 minutes at 300 °C without significant changes in J_{0_cont}. The after‐anneal J_{0_cont} reaches ～600 fAcm^–2 with a ρ_c of ～2.5 mΩ cm² for the 85 Ω/□ diffusion amounting to a maximum gain in open‐circuit voltage of 6 mV. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A New Inertia Theorem for Stein Equations,Inertia of Invertible Hermitian Block Toeplitz Matrices and Matrix Orthogonal Polynomials

In this paper we present an inertia result for Stein equations with an indefinite right hand side. This result is applied to establish connnections between the inertia of invertible hermitian block Toeplitz matrices and associated orthogonal polynomials.     

A Combined Experimental and Theoretical Study on the Formation of Ag Filaments on β‐Ag2MoO4 Induced by Electron Irradiation

A combined experimental and theoretical study is presented to understand the novel observed nucleation and early evolution of Ag filaments on β‐Ag₂MoO₄ crystals, driven by an accelerated electron beam from an electronic microscope under high vacuum. The growth process, chemical composition, and the element distribution in these filaments are analyzed in depth at the nanoscale level using field‐emission scanning electron microscopy (FE‐SEM) and transmission electron microscopy (TEM) with energy‐dispersive spectroscopy (EDS) characterization. To complement experimental results, chemical stability, structural and electronic aspects have been studied systematically using first‐principles electronic structure theory within a quantum theory of atoms in molecules (QTAIM) framework. The Ag nucleation and formation on β‐Ag₂MoO₄ are a result of structural and electronic changes of the AgO₄ tetrahedral cluster as a constituent building block of β‐Ag₂MoO₄, consistent with Ag metallic formation. The formation of Ag filament transforms the β‐Ag₂MoO₄ semiconductor from n‐ to p‐type concomitant with the appearance of Ag defects.     

Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials p_k(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑ_m(x) p_n(x;q), where ϑ_m(x) is x^mor (x;q)_m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.