Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Regulation of GABA(A) and glutamate receptor expression, synaptic facilitation and long-term potentiation in the hippocampus of prion mutant mice

Background: Prionopathies are characterized by spongiform brain degeneration, myoclonia, dementia, and periodic electroencephalographic (EEG) disturbances. The hallmark of prioniopathies is the presence of an abnormal conformational isoform (PrP(sc)) of the natural cellular prion protein (PrP(c)) encoded by the Prnp gene. Although several roles have been attributed to PrP(c), its putative functions in neuronal excitability are unknown. Although early studies of the behavior of Prnp knockout mice described minor changes, later studies report altered behavior. To date, most functional PrP(c) studies on synaptic plasticity have been performed in vitro. To our knowledge, only one electrophysiological study has been performed in vivo in anesthetized mice, by Curtis and coworkers. They reported no significant differences in paired-pulse facilitation or LTP in the CA1 region after Schaffer collateral/commissural pathway stimulation. Principal Findings: Here we explore the role of PrP(c) expression in neurotransmission and neural excitability using wild-type, Prnp -/- and PrP(c)-overexpressing mice (Tg20 strain). By correlating histopathology with electrophysiology in living behaving mice, we demonstrate that both Prnp -/- mice but, more relevantly Tg20 mice show increased susceptibility to KA, leading to significant cell death in the hippocampus. This finding correlates with enhanced synaptic facilitation in paired-pulse experiments and hippocampal LTP in living behaving mutant mice. Gene expression profiling using Illumina microarrays and Ingenuity pathways analysis showed that 129 genes involved in canonical pathways such as Ubiquitination or Neurotransmission were co-regulated in Prnp -/- and Tg20 mice. Lastly, RT-qPCR of neurotransmission-related genes indicated that subunits of GABA(A) and AMPA-kainate receptors are co-regulated in both Prnp -/- and Tg20 mice. Conclusions/Significance: Present results demonstrate that PrP(c) is necessary for the proper homeostatic functioning of hippocampal circuits, because of its relationships with GABA(A) and AMPA-Kainate neurotransmission. New PrP(c) functions have recently been described, which point to PrP(c) as a target for putative therapies in Alzheimer's disease. However, our results indicate that a "gain of function" strategy in Alzheimer's disease, or a "loss of function" in prionopathies, may impair PrP(c) function, with devastating effects. In conclusion, we believe that present data should be taken into account in the development of future therapies.

Podocalyxin is a novel polysialylated neural adhesion protein with multiple roles in neural development and synapse formation

Neural development and plasticity are regulated by neural adhesion proteins, including the polysialylated form of NCAM (PSA-NCAM). Podocalyxin (PC) is a renal PSA-containing protein that has been reported to function as an anti-adhesin in kidney podocytes. Here we show that PC is widely expressed in neurons during neural development. Neural PC interacts with the ERM protein family, and with NHERF1/2 and RhoA/G. Experiments in vitro and phenotypic analyses of podxl-deficient mice indicate that PC is involved in neurite growth, branching and axonal fasciculation, and that PC loss-of-function reduces the number of synapses in the CNS and in the neuromuscular system. We also show that whereas some of the brain PC functions require PSA, others depend on PC per se. Our results show that PC, the second highly sialylated neural adhesion protein, plays multiple roles in neural development.

Low-loss rib waveguides containing Si nanocrystals embedded in SiO2

We report on the study and modeling of the structural and optical properties of rib-loaded waveguides working in the 600-900-nm spectral range. A Si nanocrystal (Si-nc) rich SiO2 layer with nominal Si excess ranging from 10% to 20% was produced by quadrupole ion implantation of Si into thermal SiO2 formed on a silicon substrate. Si-ncs were precipitated by annealing at 1100°C, forming a 0.4-um-thick core layer in the waveguide. The Si content, the Si-nc density and size, the Si-nc emission, and the active layer effective refractive index were determined by dedicated experiments using x-ray photoelectron spectroscopy, Raman spectroscopy, energy-filtered transmission electron microscopy, photoluminescence and m-lines spectroscopy. Rib-loaded waveguides were fabricated by photolithographic and reactive ion etching processes, with patterned rib widths ranging from 1¿to¿8¿¿m. Light propagation in the waveguide was observed and losses of 11dB/cm at 633 and 780 nm were measured, modeled and interpreted.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Computation of arbitrarily constrained synthetic discriminant functions

An algorithm for computing correlation filters based on synthetic discriminant functions that can be displayed on current spatial light modulators is presented. The procedure is nondivergent, computationally feasible, and capable of producing multiple solutions, thus overcoming some of the pitfalls of previous methods.

Perturbation theory for classical thermodynamic Green's functions

A systematic time-dependent perturbation scheme for classical canonical systems is developed based on a Wick's theorem for thermal averages of time-ordered products. The occurrence of the derivatives with respect to the canonical variables noted by Martin, Siggia, and Rose implies that two types of Green's functions have to be considered, the propagator and the response function. The diagrams resulting from Wick's theorem are "double graphs" analogous to those introduced by Dyson and also by Kawasaki, in which the response-function lines form a "tree structure" completed by propagator lines. The implication of a fluctuation-dissipation theorem on the self-energies is analyzed and compared with recent results by Deker and Haake.

Finite-size effects in nonequilibrium correlation functions

We have shown that finite-size effects in the correlation functions away from equilibrium may be introduced through dimensionless numbers: the Nusselt numbers, accounting for both the nature of the boundaries and the size of the system. From an analysis based on fluctuating hydrodynamics, we conclude that the mean-square fluctuations satisfy scaling laws, since they depend only on the dimensionless numbers in addition to reduced variables. We focus on the case of diffusion modes and describe some physical situations in which finite-size effects may be relevant.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Cherenkov mesons as in-medium quark energy loss

We recently showed that a heavy quark moving su ciently fast through a quark-gluon plasma may lose energy by Cherenkov-radiating mesons [1]. Here we review our previous holographic calculation of the energy loss in N = 4 Super Yang-Mills and extend it to longitudinal vector mesons and scalar mesons. We also discuss phenomenological implications for heavy-ion collision experiments. Although the Cherenkov energy loss is an O(1=Nc) effect, a ballpark estimate yields a value of dE/dx for Nc = 3 which is comparable to that of other mechanisms.