Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Model calculations have been performed on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by recurrent excitatory-excitatory couplings with time delay. The coupled, excitable HH neurons are assumed to receive the two kinds of spike-train inputs: the transient input consisting of $M$ impulses for the finite duration ($M$: integer) and the sequential input with the constant interspike interval (ISI). The distribution of the output ISI $T_{\rm o}$ shows a rich of variety depending on the coupling strength and the time delay. The comparison is made between the dependence of the output ISI for the transient inputs and that for the sequential inputs.Comment: 19 pages, 4 figure

Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist novel hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.Comment: 4 pages, 4 figure

Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure $M_s$ by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$ is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of $M_s$, we quantitatively characterize the stochastic spiking coherence, and find that $M_s$ reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure $M_s$ may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc

Long gamma-ray bursts and core-collapse supernovae have different environments

When massive stars exhaust their fuel they collapse and often produce the extraordinarily bright explosions known as core-collapse supernovae. On occasion, this stellar collapse also powers an even more brilliant relativistic explosion known as a long-duration gamma-ray burst. One would then expect that long gamma-ray bursts and core-collapse supernovae should be found in similar galactic environments. Here we show that this expectation is wrong. We find that the long gamma-ray bursts are far more concentrated on the very brightest regions of their host galaxies than are the core-collapse supernovae. Furthermore, the host galaxies of the long gamma-ray bursts are significantly fainter and more irregular than the hosts of the core-collapse supernovae. Together these results suggest that long-duration gamma-ray bursts are associated with the most massive stars and may be restricted to galaxies of limited chemical evolution. Our results directly imply that long gamma-ray bursts are relatively rare in galaxies such as our own Milky Way.Comment: 27 pages, 4 figures, submitted to Nature on 22 August 2005, revised 9 February 2006, online publication 10 May 2006. Supplementary material referred to in the text can be found at http://www.stsci.edu/~fruchter/GRB/locations/supplement.pdf . This new version contains minor changes to match the final published versio

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.

Discovery of the optical counterpart and early optical observations of GRB990712

We present the discovery observations of the optical counterpart of the gamma-ray burster GRB990712 taken 4.16 hours after the outburst and discuss its light curve observed in the V, R and I bands during the first ~35 days after the outburst. The observed light curves were fitted with a power-law decay for the optical transient (OT), plus an additional component which was treated in two different ways. First, the additional component was assumed to be an underlying galaxy of constant brightness. The resulting slope of the decay is 0.97+/-0.05 and the magnitudes of the underlying galaxy are: V = 22.3 +/- 0.05, R = 21.75 +/- 0.05 and I = 21.35 +/- 0.05. Second, the additional component was assumed to be a galaxy plus an underlying supernova with a time-variable brightness identical to that of GRB980425, appropriately scaled to the redshift of GRB990712. The resulting slope of the decay is similar, but the goodness-of-fit is worse which would imply that either this GRB is not associated with an underlying supernova or the underlying supernova is much fainter than the supernova associated with GRB980425. The galaxy in this case is fainter: V = 22.7 +/- 0.05, R = 22.25 +/- 0.05 and I = 22.15 +/- 0.05; and the OT plus the underlying supernova at a given time is brighter. Measurements of the brightnesses of the OT and the galaxy by late-time HST observation and ground-based observations can thus assess the presence of an underlying supernova.Comment: To appear in Ap

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced in $ep$ interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function of \xpom, the momentum fraction lost by the proton, of $\beta$, the momentum fraction of the struck quark with respect to \xpom, and of $Q^2$. The \xpom dependence is consistent with the form \xpoma where $a~=~1.30~\pm~0.08~(stat)~^{+~0.08}_{-~0.14}~(sys)$ in all bins of $\beta$ and $Q^2$. In the measured $Q^2$ range, the diffractive structure function approximately scales with $Q^2$ at fixed $\beta$. In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.Comment: 36 pages, latex, 11 figures appended as uuencoded fil

A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.Comment: Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

Measurement of Jet Shapes in Photoproduction at HERA

The shape of jets produced in quasi-real photon-proton collisions at centre-of-mass energies in the range $134-277$ GeV has been measured using the hadronic energy flow. The measurement was done with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the $\eta - \phi$ plane with a cone radius of one unit. Measured jet shapes both in inclusive jet and dijet production with transverse energies $E^{jet}_T>14$ GeV are presented. The jet shape broadens as the jet pseudorapidity ($\eta^{jet}$) increases and narrows as $E^{jet}_T$ increases. In dijet photoproduction, the jet shapes have been measured separately for samples dominated by resolved and by direct processes. Leading-logarithm parton-shower Monte Carlo calculations of resolved and direct processes describe well the measured jet shapes except for the inclusive production of jets with high $\eta^{jet}$ and low $E^{jet}_T$. The observed broadening of the jet shape as $\eta^{jet}$ increases is consistent with the predicted increase in the fraction of final state gluon jets.Comment: 29 pages including 9 figure