Random dynamics of the Morris-Lecar neural model

Determining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes. In both the transitions from excitable to oscillating regimes are associated with different bifurcation scenarios. This work examines how random perturbations affect these two bifurcation scenarios. It is first numerically shown that the Morris-Lecar model driven by white Gaussian noise current tends to have a unique stationary distribution in the phase space. Numerical evaluations also reveal quantitative and qualitative changes in this distribution in the vicinity of the bifurcations of the deterministic system. However, these changes notwithstanding, our numerical simulations show that the Lyapunov exponents of the system remain negative in these parameter regions, indicating that no dynamical stochastic bifurcations take place. Moreover, our numerical simulations confirm that, regardless of the asymptotic dynamics of the deterministic system, the random Morris-Lecar model stabilizes at a unique stationary stochastic process. In terms of random dynamical system theory, our analysis shows that additive noise destroys the above-mentioned bifurcation sequences that characterize class I and class II regimes in the Morris-Lecar model. The interpretation of this result in terms of neuronal coding is that, despite the differences in the deterministic dynamics of class I and class II membranes, their responses to noise-like stimuli present a reliable feature.     

Turbulence structures in high-speed air flow along a thin cylinder

Turbulent flow in the axial direction along a cylinder representing a monofilament yarn was reproduced for a relatively wide range of radius Reynolds numbers using direct numerical simulations. In the simulation of the thinnest cylinder, the friction coefficient agreed with a previously published formula. A pair of high- and low-speed streaks was detected around even the thinnest cylinder, whereby it was confirmed that turbulence was sustained according to the analysed turbulence statistics. Even when only a single pair of streaks around the cylinder was detected, the characteristics of the turbulence structures, such as the mean streak spacing based on the viscous length scale, were the same as those in flows over a flat plate. It was found that the friction coefficient changes in a way that maintains the structural characteristics of the flow, consistent with the view that universal characteristics of turbulence structures exist.     

Validity of retinal oxygen saturation analysis: Hyperspectral imaging in visible wavelength with fundus camera and liquid crystal wavelength tunable filter

The purpose of this paper was to investigate the feasibility of a newly developed hyperspectral fundus imaging camera with a liquid crystal tunable filter. The intensities of different wavelengths of light transmitted through an artery, vein, and the area surrounding these vessels and reflected out were measured, and the differential spectral absorptions were analyzed. Measurements were made from 16 normal eyes and from two artificial capillaries. The ratios of absorption (ROA) of arteries to veins from 500 to 580 nm (range 1) and from 600 to 720 nm (range 2) were calculated. For all eyes, the ROA_range1 was larger than ROA_range2. The ROA obtained from the artificial capillary filled with blood saturated with oxygen or nitrogen was similar to that of simulated data of oxy- and deoxyhemoglobin extinction rate. Most ROAs of human eyes were lower than those of the simulated data and the artificial capillaries. Oxygen saturation analysis by hyperspectral fundus imaging of retinal vessels were qualitatively in agreement with thein vitro analysis or simulated values. However, further improvements are necessary to evaluate the oxygen saturation quantitatively in the retinal blood vessels.     

Phase diagrams of noisy traffic states in the presence of a bottleneck

The traffic states are investigated for the noisy traffic flow in the presence of a bottleneck under the open boundary condition. The phase diagrams of the different kinds of congested traffic are presented for different values of sensitivity (the inverse of delay time). It is shown that the five different types of traffic states appear below the critical point: the free traffic with a pinned localized cluster, the weak standing shock, the moving localized cluster, the oscillatory congested traffic, and the strong standing shock. Above the critical point, the moving localized cluster and oscillatory congested traffic do not occur. Also, in the traffic flow without noise, the moving localized cluster and oscillatory congested traffic do not appear.     

Optimization of mark edge recording waveform for a phase change rewritable optical disk using a 680 nm laser diode

A high density mark edge recording method on a phase change rewritable disk is reported. A carrier-to-noise ratio of 55 dB for a mark length of 0.55,μm is obtained by using a 680 nm, NA 0.6 head and a phase change rewritable disk. In mark edge recording, it is necessary to record each mark in correct length. A new laser power modulation pattern is proposed. This pattern consists of a first-pulse, a multi-pulse chain and a last-pulse. Both positions of the first-ptilse and the last-pulse are movable. By adjusting these positions, a jitter, σ/T_w (T_w is window margin), is improved to 6.5% in high density EFM (Eight to Fourteen Modulation) recording of 0.4 μm/bit.     

Structure in the emission from pyrene evaporated films

Emission spectra and decay times of fluorescence of pyrene thin films prepared by evaporation onto substrates at liquid nitrogen temperature were measured. Structure in the emission from films warmed slowly up to higher temperature is found to the higher energy side of the excimer emission band. The decay time is about 410 ns at temperatures between 110 K and 210 K. But the emission from the film warmed up to a temperature above 210 K shows only the excimer emission. These results are discussed in relation to an amorphous structure in the pyrene evaporated thin film.     

Note on the computation of the maximal eigenvalue of a non-negative irreducible matrix

Summary We prove the convergence of Wielandt's method in the computation of the maximal eigenvalue and eigenvector of a non-negative irreducible matrix.     

Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound

The kinetic energy inequality is alternatively proved which yields Lieb's boundN < 2Z + 1 on the maximum negative ionization of an atom with nucleus chargeZ andN electrons when the kinetic energy operator is the nonrelativistic or relativistic magnetic Schrödinger operator. It is seen to follow from the free case where the vector potential vanishes. The proof applies to the Weyl quantized relativistic magnetic Schrödinger operator as well.Research partially supported by Grant-in-Aid for Scientific Research Nos. 04640141 and 05640165, Ministry of Education, Science and Culture, Japanese Government.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Development of Oxidation Sources in Preparation of High-Tc Oxide Superconductor Thin Films Using the Molecular Beam Epitaxy Method

Film preparation of oxide superconductors, mainly of the 1-2-3 (RBa₂Cu₃O_x) and Bi-containing (Bi-Sr-Ca-Cu-O) systems, by evaporation of either metals or metal compounds by low pressure is summarized, with a particular focus on the development of oxidation sources essential to the technique. Oxidizing reagents that enable the oxidation of metal evaporates to take place in high (0·1 to 10_?3 Pa) or even ultra-high (<10_?5 Pa) vacuum are summarized using the experiments of those who tried to apply the molecular beam epitaxy method to atomically controlled fabrication of thin films of the material, especially for device processing. The evaporation in various kinds of oxidizing atmosphere, including the simple method of in situ annealing of the metal layers in oxygen to the more advanced in situ preparation of the films with strong oxidizing reagents such as atomic oxygen, ozone, nitric oxide, etc. along with the thermochemistry of the oxidation of metals by low pressure with these reagents is reviewed.