Self-sustained irregular activity in an ensemble of neural oscillators

An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The "synchronised phase", which emerges upon increasing the coupling strength, is characterized by highly-irregular fluctuations: a time-series analysis reveals that the dynamics of the order parameter is indeed high-dimensional. The complex dynamics appears to be the result of the non-perturbative action of a suitably shaped phase-response curve. Such mechanism differs from the often invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the inter-spike intervals.Comment: 11 pages, 10 figure

Parallel Machines for Computer Graphics

Computer graphics provides some ideal applications for the kind of highly parallel implementations made possible by advances in integrated circuit technology. Specifically, hidden line and hidden surface algorithms, while easily defined and simple in concept, entail a substantial amount of computation. This requirement fits the characteristics of integrated circuit technology, where modular designs involving regular communication between many concurrent operations are rewarded with high performance at an acceptable cost. Ray tracing is a very flexible technique that can be used to produce some of the most realistic of all computer generated images by simulating the interactions of light rays with surfaces in a modeled scene. Because light rays are mutually independent, many may be processed simultaneously, and the potential for concurrency is great. One architecture for expediting a ray tracing algorithm consists of a conventional computer equipped with a special purpose peripheral device for locating the intersections of ray8 and surfaces. This intersection computation is the most time consuming aspect of a ray tracing algorithm. Although the attached processor configuration can produce images more quickly than an unaided computer, its per- formance is limited. Alternatively, a pipeline of surface processors can replace the peripheral device. Each processor computes the intersections of its stored surface with rays that flow through the pipe. Such a machine machine can be quite fast, and its performance can be increased by lengthening the pipeline, but the component processors are not very effectively utilized. A third approach combines the advantages of the prior two machines by using an array of processors, each simulating a distinct subvolume of the modeled world by treating light rays traveling through space as messages flowing between processors. Local communication is sufficient because light rays travel continuously through space. In real time computer graphics, successive images must be produced in times that are imperceptible to a viewer. Although the ray tracing machines fall short of this performance, it is possible to compromise image quality in order to produce a highly parallel machine capable of real time operation. The processors in such a machine are organized to form a binary tree. Leaf processors scan-convert surfaces, producing a sequence of segments, where a segment is the portion of a surface that appears on a single scan line of the display. Processors towards the root of the tree accept two such segment sequences and produce a third in which all segment overlap has been resolved. The final image is available at the root of the tree. The communication bottleneck that would otherwise occur at the root can be eliminated by breaking out parallel roots, and the resulting tree may be extended to scenes of almost arbitrary complexity merely by increasing the supply of available processors. Massive parallelism can also be applied to the problem of removing hidden edges from line drawings. A suitable architecture takes the form of a pipeline in which each processor is dedicated to the handling of a single polygon edge. These processors successively clip line segments passing through the pipeline to eliminate portions hidden behind surfaces. Each edge processor can be constructed out of little more than three serial multipliers. The machines described here are varied in organization, and each functions differently, but their treatment of sorting is one ingredient common to all. Sorting is a key component of hidden surface algorithms running on conventional computers, but its extensive communication requirements make it costly for use in a highly integrated design. Consequently, the highly parallel machines described here operate largely without sorting. Instead, they maintain information in sorted order or make use of already sorted information to limit communication requirements

Theoretical basis of the community effect in development

Peer reviewedPublisher PD

Chaotic macroscopic phases in one-dimensional oscillators

APo and EU wish to acknowledge the Advanced Study Group activity at the Max Planck Institute for the Physics of Complex Systems in Dresden “From Microscopic to Collective Dynamics in Neural Circuits” for the opportunity to develop part of the project.Peer reviewedPublisher PD

The Electrostatic Persistence Length Calculated from Monte Carlo, Variational and Perturbation Methods

Monte Carlo simulations and variational calculations using a Gaussian ansatz are applied to a model consisting of a flexible linear polyelectrolyte chain as well as to an intrinsically stiff chain with up to 1000 charged monomers. Addition of salt is treated implicitly through a screened Coulomb potential for the electrostatic interactions. For the flexible model the electrostatic persistence length shows roughly three regimes in its dependence on the Debye-H\"{u}ckel screening length, $\kappa^{-1}$.As long as the salt content is low and $\kappa^{-1}$ is longer than the end-to-end distance, the electrostatic persistence length varies only slowly with $\kappa^{-1}$. Decreasing the screening length, a controversial region is entered. We find that the electrostatic persistence length scales as $sqrt{\xi_p}/\kappa$, in agreement with experiment on flexible polyelectrolytes, where $\xi_p$ is a strength parameter measuring the electrostatic interactions within the polyelectrolyte. For screening lengths much shorter than the bond length, the $\kappa^{-1}$ dependence becomes quadratic in the variational calculation. The simulations suffer from numerical problems in this regime, but seem to give a relationship half-way between linear and quadratic. A low temperature expansion only reproduces the first regime and a high temperature expansion, which treats the electrostatic interactions as a perturbation to a Gaussian chain, gives a quadratic dependence on the Debye length. For a sufficiently stiff chain, the persistence length varies quadratically with $\kappa^{-1}$ in agreement with earlier theories.Comment: 20 pages LaTeX, 9 postscript figure

Filtering high quality text for display on raster scan devices

Recently several investigators have studied the problem of displaying text characters on grey level raster scan displays. Despite arguments suggesting that grey level displays are equivalent to very high resolution bitmaps, the performance of grey level displays has been disappointing. this paper will show that much of the problem can be traced to inappropriate antialiasing procedures. Instead of the classical (sin x)/x filter, the situation calls for a filter with characteristics matched both to the nature of display on CRTs and to the human visual system. We give examples to illustrate the problems of the existing methods and the advantages of the new methods. Although the techniques are described in terms of text, the results have application to the general antialiasing problem--at least in theory if not practice

Cortical Spike Synchrony as a Measure of Input Familiarity

J.G.O. was supported by the Ministerio de Economia y Competividad and FEDER (Spain, project FIS2015-66503-C3-1-P) and the ICREA Academia programme. E.U. acknowledges support from the Scottish Universities Life Sciences Alliance (SULSA) and HPC-Europa2.Peer reviewedPostprin

Mammalian Brain As a Network of Networks

Acknowledgements AZ, SG and AL acknowledge support from the Russian Science Foundation (16-12-00077). Authors thank T. Kuznetsova for Fig. 6.Peer reviewedPublisher PD

Titrating Polyelectrolytes - Variational Calculations and Monte Carlo Simulations

Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being used as variational parameters to minimize the free energy. For the titrating charges, a mean field approach is used. The accuracy is tested against Monte Carlo data for up to 1000 monomers. For an unscreened chain, excellent agreement is obtained for the end-to-end distance and the apparent dissociation constant. With screening, the thermodynamical properties are invariably well described, although the structural agreement deteriorates. A very simple rigid-rod approximation is also considered, giving surprisingly good results for certain properties.Comment: 22 pages, PostScript, 9 figure

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