Dynamical and Statistical Criticality in a Model of Neural Tissue

For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongly stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian' behavior: {\sl all} degrees of freedom achieve a close balance of excitation and inhibition and become "critical" in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex "breakout" dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense

Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

A search for x-ray counterparts of gamma-ray bursts with the ROSAT PSPC

We search for faint X-ray bursts with duration 10--300 seconds in the ROSAT PSPC pointed observations with a total exposure of 1.6e7 seconds. We do not detect any events shorter than ~100s, i.e. those that could be related to the classic gamma-ray bursts. At the same time, we detect a number of long flares with durations of several hundred seconds. Most, but not all, of the long flares are associated with stars. If even a small number of those long flares, that cannot identified with stars, are X-ray afterglows of GRB, the number of X-ray afterglows greatly exceeds the number of BATSE GRB. This would imply that the beaming factor of gamma-rays from the burst should be >100. The non-detection of any short bursts in our data constrains the GRB counts at the fluences 1--2.5 orders of magnitude below the BATSE limit. The constrained burst counts are consistent with the extrapolation of the BATSE log N - log S relation. Finally, our results do not confirm a reality of short X-ray flashes found in the Einstein IPC data by Gotthelf, Hamilton and Helfand.Comment: Accepted to ApJ Letters. 4 pages with 3 figures, LaTeX2

Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which rotation dominates over shear, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of impurities subject not only to drag but also to fluctuating forces modelled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation

Redshift determination in the X-ray band of gamma-ray bursts

If gamma-ray bursts originate in dense stellar forming regions, the interstellar material can imprint detectable absorption features on the observed X-ray spectrum. Such features can be detected by existing and planned X-ray satellites, as long as the X-ray afterglow is observed after a few minutes from the burst. If the column density of the interstellar material exceeds ~10^{23} cm^{-2} there exists the possibility to detect the K_alpha fluorescent iron line, which should be visible for more than one year, long after the X-ray afterglow continuum has faded away. Detection of these X-ray features will make possible the determination of the redshift of gamma-ray bursts even when their optical afterglow is severely dimmed by extinction.Comment: 15 pages with 5 figures. Submitted to Ap

Emission Spectra from Internal Shocks in Gamma-Ray-Burst Sources

Unsteady activity of gamma-ray burst sources leads to internal shocks in their emergent relativistic wind. We study the emission spectra from such shocks, assuming that they produce a power-law distribution of relativistic electrons and posses strong magnetic fields. The synchrotron radiation emitted by the accelerated electrons is Compton up-scattered multiple times by the same electrons. A substantial component of the scattered photons acquires high energies and produces e+e- pairs. The pairs transfer back their kinetic energy to the radiation through Compton scattering. The generic spectral signature from pair creation and multiple Compton scattering is highly sensitive to the radius at which the shock dissipation takes place and to the Lorentz factor of the wind. The entire emission spectrum extends over a wide range of photon energies, from the optical regime up to TeV energies. For reasonable values of the wind parameters, the calculated spectrum is found to be in good agreement with the burst spectra observed by BATSE.Comment: 12 pages, latex, 2 figures, submitted to ApJ

BeppoSAX observations of Mrk 841 and Mrk335

We present and discuss BeppoSAX observations of Mrk841 and Mrk335, two Seyfert 1 galaxies in which previous observations have established the presence of soft excesses. We confirm the soft excess in both sources, even if for Mrk~841 a warm absorber provides a fit almost as good as the one with a true excess. As far as the hard X-ray continuum is concerned, a Comptonization model provides a fit as good as a power law and a physically sound solution for Mrk841. For Mrk335, the Comptonization model gives a result which is somewhat better on statistical ground, but rather problematic on physical ground. The most interesting results regard the reprocessing components. For Mrk841 we find a very large reflection continuum but an almost normal iron line equivalent width even if, within the errors, a solution in which both components are a factor ~2 larger than expected for an accretion disc is still marginally acceptable. If this is the case, an anisotropy of the primary emission seems the best explanation. On the contrary, in Mrk335 we find a very large iron line EW but a reflection component not accordingly large. In this case, the best solution seems to be in terms of reflection from an ionized disc.Comment: Accepted for publication in A&

A self-consistent test of Comptonization models using a long BeppoSAX observation of NGC 5548

We test accurate models of Comptonization spectra over the high quality data of the BeppoSAX long look at NGC 5548. The data are well represented by a plane parallel corona with an inclination angle of 30$^{\circ}$, a soft photon temperature of 5 eV and a hot plasma temperature and optical depth of $kT_{\rm e}\simeq$ 360 keV and $\tau\simeq$ 0.1, respectively. If energy balance applies, such values suggest that a more ``photon-starved'' geometry (e.g. a hemispheric region) is necessary. The spectral softening detected during a flare, appears to be associated to a decrease of the heating-to-cooling ratio, indicating a geometric and/or energetic modification of the disk plus corona system. The hot plasma temperature derived with the models above is significantly higher than that obtained fitting the same data with a power law plus high energy cut off model for the continuum. This is due to the fact that in anisotropic geometries Comptonization spectra show "intrinsic" curvature which moves the fitted high energy cut-off to higher energies.Comment: 4 pages, 2 figures, to appear in the proceedings of the conference "X-ray Astronomy '99", Bologna, Italy, September 199

Three-frequency resonances in dynamical systems

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental device (an electronic oscillator). We compare the hierarchies of three-frequency resonances we find in each of these systems. All three show similar qualitative behaviour, suggesting the existence of generic features in the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya

Interactions between Hair Cells Shape Spontaneous Otoacoustic Emissions in a Model of the Tokay Gecko's Cochlea

Background The hearing of tetrapods including humans is enhanced by an active process that amplifies the mechanical inputs associated with sound, sharpens frequency selectivity, and compresses the range of responsiveness. The most striking manifestation of the active process is spontaneous otoacoustic emission, the unprovoked emergence of sound from an ear. Hair cells, the sensory receptors of the inner ear, are known to provide the energy for such emissions; it is unclear, though, how ensembles of such cells collude to power observable emissions. Methodology and Principal Findings We have measured and modeled spontaneous otoacoustic emissions from the ear of the tokay gecko, a convenient experimental subject that produces robust emissions. Using a van der Pol formulation to represent each cluster of hair cells within a tonotopic array, we have examined the factors that influence the cooperative interaction between oscillators. Conclusions and Significance A model that includes viscous interactions between adjacent hair cells fails to produce emissions similar to those observed experimentally. In contrast, elastic coupling yields realistic results, especially if the oscillators near the ends of the array are weakened so as to minimize boundary effects. Introducing stochastic irregularity in the strength of oscillators stabilizes peaks in the spectrum of modeled emissions, further increasing the similarity to the responses of actual ears. Finally, and again in agreement with experimental findings, the inclusion of a pure-tone external stimulus repels the spectral peaks of spontaneous emissions. Our results suggest that elastic coupling between oscillators of slightly differing strength explains several properties of the spontaneous otoacoustic emissions in the gecko.This investigation was supported by grants DC000241, DC007294, and GM07739 from the National Institutes of Health, by the Spanish Ministerio de Educacion y Ciencias, and by Consejo Superior de Investigaciones Cientificas (CSIC) project HIELOCRIS. A.J.H. is an Investigator of Howard Hughes Medical Institute. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscriptPeer reviewe