Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density

STUDYING THE ROLE OF SYNCHRONIZED AND CHAOTIC SPIKING NEURAL ENSEMBLES IN NEURAL INFORMATION PROCESSING

The brain is characterized by performing many diverse processing tasks ranging from elaborate processes such as pattern recognition, memory or decision making to more simple functionalities such as linear filtering in image processing. Understanding the mechanisms by which the brain is able to produce such a different range of cortical operations remains a fundamental problem in neuroscience. Here we show a study about which processes are related to chaotic and synchronized states based on the study of in-silico implementation of Stochastic Spiking Neural Networks (SSNN). The measurements obtained reveal that chaotic neural ensembles are excellent transmission and convolution systems since mutual information between signals is minimized. At the same time, synchronized cells (that can be understood as ordered states of the brain) can be associated to more complex nonlinear computations. In this sense, we experimentally show that complex and quick pattern recognition processes arise when both synchronized and chaotic states are mixed. These measurements are in accordance with in vivo observations related to the role of neural synchrony in pattern recognition and to the speed of the real biological process. We also suggest that the high-level adaptive mechanisms of the brain that are the Hebbian and non-Hebbian learning rules can be understood as processes devoted to generate the appropriate clustering of both synchronized and chaotic ensembles. The measurements obtained from the hardware implementation of different types of neural systems suggest that the brain processing can be governed by the superposition of these two complementary states with complementary functionalities (nonlinear processing for synchronized states and information convolution and parallelization for chaotic).

Firing statistics of inhibitory neuron with delayed feedback. II: Non-Markovian behavior

The instantaneous state of a neural network consists of both the degree of excitation of each neuron the network is composed of and positions of impulses in communication lines between the neurons. In neurophysiological experiments, the neuronal firing moments are registered, but not the state of communication lines. But future spiking moments depend essentially on the past positions of impulses in the lines. This suggests, that the sequence of intervals between firing moments (inter-spike intervals, ISIs) in the network could be non-Markovian. In this paper, we address this question for a simplest possible neural "net", namely, a single inhibitory neuron with delayed feedback. The neuron receives excitatory input from the driving Poisson stream and inhibitory impulses from its own output through the feedback line. We obtain analytic expressions for conditional probability density P(tn+1|tn, …, t1, t0), which gives the probability to get an output ISI of duration tn+1 provided the previous (n+1) output ISIs had durations tn, …, t1, t0. It is proven exactly, that P(tn+1|tn, …, t1, t0) does not reduce to P(tn+1|tn, …, t1) for any n≥0. This means that the output ISIs stream cannot be represented as a Markov chain of any finite order.