Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight g/2 and genus g. When g=4, the Fourier coefficient is approximated by a certain Fourier coefficient of the central derivative of the Siegel Eisenstein series of weight 2 and genus 3, which is related to the intersection of 3 arithmetic modular correspondences. Applications include a relation between weighted averages of representation numbers of symmetric matrices

Stochastic transitions of attractors in associative memory models with correlated noise

We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient detail. Aoyagi and Aoki have shown that the state transition of a network is invoked by synchronous spikes. We introduce two types of noise to each neuron: thermal independent noise and correlated noise. Due to the effects of correlated noise, the correlation between neural inputs cannot be ignored, so the behavior of the network has sample dependence. We discuss two types of associative memory models: one with auto- and weak cross-correlation connections and one with hierarchically correlated patterns. The former is similar in structure to Aoyagi and Aoki's model. We show that stochastic transition can be presented by correlated rather than thermal noise. In the latter, we show stochastic transition from a memory state to a mixture state using correlated noise. To analyze the stochastic transitions, we derive a macroscopic dynamic description as a recurrence relation form of a probability density function when the correlated noise exists. Computer simulations agree with theoretical results.Comment: 21 page

Oscillator neural network model with distributed native frequencies

We study associative memory of an oscillator neural network with distributed native frequencies. The model is based on the use of the Hebb learning rule with random patterns ($\xi_i^{\mu}=\pm 1$), and the distribution function of native frequencies is assumed to be symmetric with respect to its average. Although the system with an extensive number of stored patterns is not allowed to get entirely synchronized, long time behaviors of the macroscopic order parameters describing partial synchronization phenomena can be obtained by discarding the contribution from the desynchronized part of the system. The oscillator network is shown to work as associative memory accompanied by synchronized oscillations. A phase diagram representing properties of memory retrieval is presented in terms of the parameters characterizing the native frequency distribution. Our analytical calculations based on the self-consistent signal-to-noise analysis are shown to be in excellent agreement with numerical simulations, confirming the validity of our theoretical treatment.Comment: 9 pages, revtex, 6 postscript figures, to be published in J. Phys.

Biocompatibility of subretinal parylene-based Ti/Pt microelectrode array in rabbit for further artificial vision studies

To evaluate the biocompatibility of subretinal implanted parylene-based Ti/Pt microelectrode arrays (MEA). Eyes were enucleated 3 months after MEAs were implanted into the subretinal space of rabbits. Morphological changes of the retinas were investigated by H&E staining. Immunohistochemical staining for glial fibrillary acidic protein and opsin were performed to evaluate changes in Muller cells and photoreceptors in the retinas. Retina tissue around the array remained intact. Photoreceptor degeneration and glial cell activation were observed in the retina overlaying the MEA implant. However, the cells in the inner retinal layers were preserved. Photoreceptor degeneration and glial cell activation at the MEA–retina interface are expected to be a normal reaction to implantation. Material used in this experiment has good biocompatibility within the subretinal environment and is expected to be promising in the further retinal prosthesis studies

Sugar metabolism in expanding husk leaves of flint corn (Zea mays L.) genotypes differing in husk leaf size

Relationships between leaf expansion and MeOH-soluble (cytosol) and cell-wall fractions, and their sugar composition prior to silking in flint corn lines were studied. A greater husk leaf area of one genotype, X-15 is mainly due to prolonged and higher rate of expansion. Prior to rapid expansion of husk leaf area, neutral sugars in the cytosol fraction accounted for most of the non-starch carbohydrates (56-62%), while hemicellulose and cellulose fractions accounted for less than 20%.0 In mature leaf parts, however, sugars in the cytosol fraction decreased but those in hemicellulose and cellulose fractions increased by 30 0x1.e499cp-891nd 42%, respectively. The predominant sugar in the cytosol fraction was glucose (Glc), while in the hemicellulose fraction xylose (Xyl) and arabinose (Ara) dominated. During rapid expansion of husk leaves, 13C was incorporated at a higher rate into hemicellulose than cellulose, and this process was more active in X-15 than in other genotypes. During an identical period, 13C atom 0.000000e+00xcess in Xyl increased markedly in the hemicellulose fraction, however it remained low in the cytosol one. The current results suggest that synthesis of Xyl and xylan plays an important role in renewal of hemicellulose, which may be required for expansion

Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast alpha-function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with alpha-function is reduced into the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.Comment: Accepted for publication in Phys. Rev.

Vibrational effect on the fragmentation dynamics of the C K-shell excited CF2CH2

Photoabsorption cross-sections of CF2CH2 were measured in the carbon K-edge region and linear time-of-flight mass spectra were acquired at some photon energies across the two π* peaks. The kinetic energy distributions of CH2+ and CF2+ with two components were deduced from the analysis of the mass spectra. The CH2+ ion with high kinetic energies increases with the extent of vibrational excitation of the CF 1s-1π* state, indicating that molecular vibrations play an important role in the photofragmentation of the inner-shell excited molecule