Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Seal Formation in Silicon Planar Patch-Clamp Microstructures

This paper presents a microfabricated planar patch-clamp electrode design and looks at the impact of several physical characteristics on seal formation. The device consists of a patch aperture, 1.5-2.5 mum in diameter and 7-12 mum in depth, with a reverse-side deep-etched 80-mum well. The patch aperture was coated with either thermal oxide or plasma-enhanced chemical vapor deposited (PECVD) SiO2. Some of the thermal oxide devices were converted into protruding nozzle structures, and some were boron-doped. Seal formation was tested with cultured N2a neuroblastoma cells. The PECVD oxide devices produced an average seal resistance of 34 MOmega(n = 24), and the thermal oxide devices produced an average seal resistance of 96 MOmega(n = 59). Seal resistance was found to positively correlate with patch aperture depth. Whole-cell recordings were obtained from 14% of cells tested with the thermal oxide devices, including a single recording where a gigaohm seal was obtained.

Chemistry and structure by design: ordered CuNi(CN)4 sheets with copper(II) in a square-planar environment

Layered copper–nickel cyanide, CuNi(CN)4, a 2-D negative thermal expansion material, is one of a series of copper(II)-containing cyanides derived from Ni(CN)2. In CuNi(CN)4, unlike in Ni(CN)2, the cyanide groups are ordered generating square-planar Ni(CN)4 and Cu(NC)4 units. The adoption of square-planar geometry by Cu(II) in an extended solid is very unusual.

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

Proton flux induced by free fatty acids across phospholipid bilayers: New evidences based on short-circuit measurements in planar lipid membranes

Free fatty acids (FFA) are important mediators of proton transport across membranes. However, information concerning the influence of the Structural features of both FFA and the membrane environment on the proton translocation mechanisms across phospholipid membranes is relatively scant. The effects of FFA chain length, unsaturation and membrane composition on proton transport have been addressed in this study by means of electrical measurements in planar lipid bilayers. Proton conductance (G(H)(+)) was calculated from open-circuit voltage and short-circuit current density measurements. We found that cis-unsaturated FFA caused a more pronounced effect on proton transport as compared to Saturated and trans-unsaturated FFA. Cholesterol and cardiolipin decreased membrane leak conductance. Cardiolipin also decreased proton conductance. These effects indicate a dual modulation of protein-independent proton transport by FFA: through a flip-flop mechanism and by modifying a proton diffusional pathway. Moreover the membrane phospholipid composition was shown to importantly affect both processes. (C) 2009 Elsevier Inc. All rights reserved.

Effects of the cationic antimicrobial peptide eumenitin from the venom of solitary wasp Eumenes rubronotatus in planar lipid bilayers: Surface charge and pore formation activity

Eumenitin, a novel cationic antimicrobial peptide from the venom of solitary wasp Eumenes rubronotatus, was characterized by its effects on black lipid membranes of negatively charged (azolectin) and zwitterionic (1,2-diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) or DPhPC-cholesterol) phospholipids: surface potential changes, single-channel activity, ion selectivity, and pore size were studied. We found that eumenitin binds preferentially to charged lipid membranes as compared with zwitterionic ones. Eumenitin is able to form pores in azolectin (G(1) = 118.00 +/- 3.67 pS or G(2) = 160.00 +/- 7.07 pS) and DPhPC membranes (G = 61.13 +/- 7.57 pS). Moreover, cholesterol addition to zwitterionic DPhPC membranes inhibits pore formation activity but does not interfere with the binding of peptide. Open pores presented higher cation (K (+)) over anion (Cl-) selectivity. The pore diameter was estimated at between 8.5and 9.8 angstrom in azolectin membranes and about 4.3 angstrom in DPhPC membranes. The results are discussed based on the toroidal pore model for membrane pore-forming activity and ion selectivity. (c) 2007 Elsevier Ltd. All rights reserved.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Searching for planar signatures in WMAP

We search for planar deviations of statistical isotropy in the Wilkinson Microwave Anisotropy Probe (WMAP) data by applying a recently introduced angular-planar statistics both to full-sky and to masked temperature maps, including in our analysis the effect of the residual foreground contamination and systematics in the foreground removing process as sources of error. We confirm earlier findings that full-sky maps exhibit anomalies at the planar (l) and angular (l) scales (l; l) = (2; 5); (4; 7); and (6; 8), which seem to be due to unremoved foregrounds since this features are present in the full-sky map but not in the masked maps. On the other hand, our test detects slightly anomalous results at the scales (l; l) = (10; 8) and (2; 9) in the masked maps but not in the full-sky one, indicating that the foreground cleaning procedure (used to generate the full-sky map) could not only be creating false anomalies but also hiding existing ones. We also find a significant trace of an anomaly in the full-sky map at the scale (l; l) = (10; 5), which is still present when we consider galactic cuts of 18.3% and 28.4%. As regards the quadrupole (l = 2), we find a coherent over-modulation over the whole celestial sphere, for all full-sky and cut-sky maps. Overall, our results seem to indicate that current CMB maps derived from WMAP data do not show significant signs of anisotropies, as measured by our angular-planar estimator. However, we have detected a curious coherence of planar modulations at angular scales of the order of the galaxy`s plane, which may be an indication of residual contaminations in the full-and cut-sky maps.

Elaboration and optimization of (Y,Er)Al(3)(BO(3))(4) glassy planar waveguides through the sol-gel process

In this work, a sol-gel route was used to prepare Y(0.9)Er(0.1)Al(3)(BO(3))(4) glassy thin films by spin-coating technique looking for the preparation and optimization of planar waveguides for integrated optics. The films were deposited on silica and silicon substrates using stable sols synthesized by the sol-gel process. Deposits with thicknesses ranging between 520 and 720 nm were prepared by a multi-layer process involving heat treatments at different temperatures from glass transition to the film crystallization and using heating rates of 2 degrees C/min. The structural characterization of the layers was performed by using grazing incidence X-ray diffraction and Raman spectroscopy as a function of the heat treatment. Microstructural evolution in terms of annealing temperatures was followed by high resolution scanning electron microscopy and atomic force microscopy. Optical transmission spectra were used to determine the refractive index and the film thicknesses through the envelope method. The optical and guiding properties of the films were studied by m-line spectroscopy. The best films were monomode with 620 nm thickness and a refractive index around 1.664 at 980 nm wavelength. They showed good waveguiding properties with high light-coupling efficiency and low propagation loss at 632.8 and 1550 nm of about 0.88 dB/cm. (C) 2009 Elsevier B.V. All rights reserved.

Er:YAl(3)(BO(3))(4) glassy thin films from polymeric precursor and sol-gel methods: Waveguides for integrated optics

This paper presents the characterization of single-mode waveguides for 980 and 1550 nm wavelengths. High quality planar waveguide structure was fabricated from Y(1-x)Er(x)Al(3)(BO(3))(4) multilayer thin films with x = 0.02, 0.05, 0.1, 0.3, and 0.5, prepared through the polymeric precursor and sol-gel methods using spin-coating. The propagation losses of the planar waveguides varying from 0.63 to 0.88 dB/cm were measured at 632.8 and 1550 nm. The photoluminescence spectra and radiative lifetimes of the Er(3+) (4)I(13/2) energy level were measured in waveguiding geometry. For most samples the photoluminescence decay was single exponential with lifetimes in between 640 mu s and 200 mu s, depending on the erbium concentration and synthesis method. These results indicate that Er doped YAl(3)(BO(3))(4) compounds are promising for low loss waveguides. (C) 2009 Elsevier B.V. All fights reserved.

Erbium and Ytterbium Codoped Titanoniobophosphate Glasses for Ion-Exchange-Based Planar Waveguides

This work presents the optical properties of erbium-doped and erbium/ytterbium codoped Na(2)O-Al(2)O(3)-TiO(2)-Nb(2)O(5)-P(2)O(5) glass systems and also the characterization of planar waveguides obtained by typical thermally assisted Ag+<-> Na+ ion-exchange process. The glass systems allow the preparation of single mode and multimode planar waveguides presenting a strong and relatively broad emission at 1536 nm. The emission signal in the infrared region is intensified for silver-containing samples when compared with free-silver samples. The emission signal intensification may be attributed to a nonplasmonic energy transfer from silver species to Er3+ ions as no bands related to surface plasmon resonance (SPR) of silver nanoparticles were observed.

Improving the Detectability of Sequential Injection Chromatography (SIC): Determination of Triazines by Exploiting Liquid Core Waveguide (LCW) Detection

Coupling a liquid core waveguide cell to a sequential injection chromatograph improved the detection limits for determination of triazine herbicides without compromising peak resolution. Separation of simazine, atrazine, and propazine was achieved in water samples by a 25mm long C18 monolithic column. Detection was made at 238nm using a type II LCW (silica capillary coated with Teflon (R) AF2400) cell with 100cm of optical path length. Detection limits for simazine, atrazine, and propazine were 2.3, 1.9, and 4.5 mu g L-1, respectively. Reduced analysis time and low solvent consumption are other remarkable features of the proposed method.