Perception is characterized by the formation of spatiotemporal patterns of neural activity that embody mental categories of the material events provided by the senses. The patterns are constructed by modifications of the background activity, which is maintained and self-regulated at criticality, such that all frequencies and wavelengths coexist in neural activity, from the atomic level to the whole brain. Pattern formation depends on energy dissipation and occurs by phase transition upon the coincidence of two events, both endogenous. One event is the null spike in the Rayleigh noise, which is generated by mutual excitation and then band pass filtered by feedback inhibition. The frequencyspecific drop in background amplitude enhances the signal-to-noise ratio of sensory-driven activity in each sensory sample taken by an action-perception cycle under limbic control. The other event is the sensory-selected activity from a Hebbian nerve cell assembly constituting reactivation of a memory of experience from past learning that is mobilized by the limbic system. The neural mechanisms of the phase transition that mediates perception may be subject to description in terms of a renormalization group based on systematic segmentation of the temporal spectra of various measures of brain activity. 1.

IEEE Neural Networks, doi:10.1016/j.neunet.2009.06.050. Abstract — Brains interface with the world through perception. The process extracts information from microscopic sensory input and incorporates it into the mesoscopic memory store for retrieval in recognition. The process requires creation of spatiotemporal patterns of neural activity. The construction is done through phase transitions in cortical populations that condense background activity through spontaneous symmetry breaking. Large-scale interactions create fields of synaptically driven activity that is observed by measuring brain waves (electrocorticogram, ECoG) and evaluated by constructing a mesoscopic vectorial order parameter as follows. The negative feedback among excitatory and inhibitory neurons creates spatially and spectrally distributed gamma oscillations (20-80 Hz) in the background activity. Band pass filtering reveals beats in ECoG log analytic power. In some beats that recur at theta rates (3-7 Hz), the order parameter transiently approaches zero, giving a null spike in which the microscopic activity is uniformly disordered (symmetric). A phase transition that is manifested in an analytic phase discontinuity breaks the symmetry. As the null spike terminates, the resurgent order parameter imposes mesoscopic order seen in spatial patterns of ECoG amplitude modulation (AM) that actualize and update the memory of a stimulus. Readout is through a divergent/convergent projection that performs on cortical output an irreversible spatiotemporal integral transformation. The ECoG reveals a conic phase gradient that accompanies an AM pattern. The phase cone manifests a vortex, which is initiated by the null spike, and which is inferred to help stabilize and prolong its accompanying AM pattern that might otherwise be rapidly degraded by the turbulent neural noise from which it emerges.

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Copyright © 2011 M. Ebner and S. Hameroff. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Cognitive brain functions, for example, sensory perception, motor control and learning, are understood as computation by axonaldendritic chemical synapses in networks of integrate-and-fire neurons. Cognitive brain functions may occur either consciously or nonconsciously (on “autopilot”). Conscious cognition is marked by gamma synchrony EEG, mediated largely by dendriticdendritic gap junctions, sideways connections in input/integration layers. Gap-junction-connected neurons define a sub-network within a larger neural network. A theoretical model (the “conscious pilot”) suggests that as gap junctions open and close, a gammasynchronized subnetwork, or zone moves through the brain as an executive agent, converting nonconscious “auto-pilot ” cognition to consciousness, and enhancing computation by coherent processing and collective integration. In this study we implemented sideways “gap junctions ” in a single-layer artificial neural network to perform figure/ground separation. The set of neurons connected through gap junctions form a reconfigurable resistive grid or sub-network zone. In the model, outgoing spikes are temporally integrated and spatially averaged using the fixed resistive grid set up by neurons of similar function which are connected through gap-junctions. This spatial average, essentially a feedback signal from the neuron’s output, determines whether particular

We propose a new generic framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a quantum linear Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter. In this paper, we present a bidirectional quantum associative memory model for the Black–Scholes–like option price evolution, consisting of a pair of coupled NLS equations, one governing the stochastic volatility and the other governing the option price, both self-organizing in an adaptive ‘market heat potential’, trained by continuous Hebbian learning. This stiff pair of NLS equations is numerically solved using the method of lines with adaptive step-size integrator.

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