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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.
A powerful experimental approach for investigating computation in networks of biological neurons is the use of cultured dissociated cortical cells grown into networks on a multi-electrode array. Such preparations allow investigation of network develo
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We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individ
Neurostimulation using weak electric fields has generated excitement in recent years due to its potential as a medical intervention. However, study of this stimulation modality has been hampered by inconsistent results and large variability within an