The interplay between the topology of cortical circuits and synchronized activity modes in distinct cortical areas is a key enigma in neuroscience. We present a new nonlocal mechanism governing the periodic activity mode: the greatest common divisor (GCD) of network loops. For a stimulus to one node, the network splits into GCD-clusters in which cluster neurons are in zero-lag synchronization. For complex external stimuli, the number of clusters can be any common divisor. The synchronized mode and the transients to synchronization pinpoint the type of external stimuli. The findings, supported by an information mixing argument and simulations of Hodgkin Huxley population dynamic networks with unidirectional connectivity and synaptic noise, call for reexamining sources of correlated activity in cortex and shorter information processing time scales. I. INRODUCTIONThe spiking activity of neurons within a local cortical population is typically correlated [1][2][3][4]. As a result, local cortical signals are robust to noise, which is a prerequisite for reliable signal processing in cortex. Under special conditions, coherent activity in a local cortical population is an inevitable consequence of shared presynaptic input [5-9]. Nevertheless, the mechanism for the emergence of correlation, synchronization or even nearly zero-lag synchronization (ZLS) among two or more cortical areas which do not share the same input is one of the main enigmas in neuroscience [7][8][9]. It has been argued that nonlocal synchronization is a marker of binding activities in different cortical areas into one perceptual entity [8,[10][11][12]. This prompted the hypothesis that synchronization may hold key information about higher and complex functionalities of the network. To investigate the synchronization of complex neural circuits we studied the activity modes of networks in which the properties of solitary neurons, population dynamics, delays, connectivity and background noise mimic the inter-columnar connectivity of the neocortex. II. NEURONAL CIRCUITWe start with a description of the neuronal circuits and define the properties of a neuronal cell, the structure of a node in a network representing one cortical patch, and the connection between nodes. Each neural cell was simulated using the well known Hodgkin Huxley model [13] (see Appendix for details). Each node in the network was comprised of a balanced population of 30 neurons, 80/20 percent of which were excitatory/inhibitory (Fig. 1a). The lawful reciprocal connections within each node were only between pairs of excitatory and inhibitory neurons and were selected at random with probability p in . In terms of biological properties it was assumed that distant cortico-cortical connections are (almost) exclusively excitatory whereas local connections are both excitatory and inhibitory [14,15]. In this framework, cortical areas are connected reciprocally across the two hemispheres and within a single hemisphere [16], where small functional cortical units (patches) connect to other cortical...

We propose a new experimentally corroborated paradigm in which the functionality of the brain's logicgates depends on the history of their activity, e.g. an OR-gate that turns into a XOR-gate over time. Our results are based on an experimental procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. The underlying biological mechanism is the unavoidable increase of neuronal response latency to ongoing stimulations, which imposes a non-uniform gradual stretching of network delays. . The long-lasting rejection of this simplified neuronal framework left the fundamental concept of the computational abilities of the nervous system unclear [6]. In the present study, we propose a new experimentally corroborated paradigm in which the logical operations of the brain differ from the logic of computers. Unlike a burned gate on a designed chip that consistently follows the same truth-table, here the functionality of the brain's logic-gates depends on the history of their activity, i.e. the truth tables are time-dependent. Our results are based on an experimental procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro [7,8]. We demonstrate that the underlying biological mechanism is an unavoidable increase of neuronal response latency [9-11] to ongoing stimulations, which imposes a non-uniform gradual stretching of delays associated with the neuronal circuit [12]. We anticipate our results will lead to a better understanding of the suitability of this computational paradigm to account for the brain's functionalities. In addition, this paradigm will require the development of new systematic methods and practical tools beyond traditional Boolean algebra methods [13]. Elastic response latency-single neuron: At the single neuron level, one of the most significant timedependent features is the neuronal response latency that measures the elapsed time between stimulation and evoked spike. The latency is typically on the order of several milliseconds [10,12] which reflects the neuronal internal dynamics [14]. To exemplify this neuronal feature, experiments with a stimulation rate of 10 Hz [ Fig. 1(a)] were conducted on cultured cortical neurons that were functionally isolated from their network using a cocktail of synaptic blockers (Methods in [15]). The stimulated neuron typically responded to each and every stimulus with high reliability and the latency increased by a few ms over a few hundreds of repeated stimulations [ Fig. 1(a)]. The results indicate a stretching of a few s per evoked spike, which introduces a finer time scale, s, of cortical dynamics [12]. Specifically, for the first several stimulations the stretching per spike is typically a few dozen s followed by a fast decay to a roughly linear stretching of only several s per spike until the neuron enters an intermittent phase, characterized by relatively large fluctuations of the latency around ...

Neurons are the computational elements that compose the brain and their fundamental principles of activity are known for decades. According to the long-lasting computational scheme, each neuron sums the incoming electrical signals via its dendrites and when the membrane potential reaches a certain threshold the neuron typically generates a spike to its axon. Here we present three types of experiments, using neuronal cultures, indicating that each neuron functions as a collection of independent threshold units. The neuron is anisotropically activated following the origin of the arriving signals to the membrane, via its dendritic trees. The first type of experiments demonstrates that a single neuron’s spike waveform typically varies as a function of the stimulation location. The second type reveals that spatial summation is absent for extracellular stimulations from different directions. The third type indicates that spatial summation and subtraction are not achieved when combining intra- and extra- cellular stimulations, as well as for nonlocal time interference, where the precise timings of the stimulations are irrelevant. Results call to re-examine neuronal functionalities beyond the traditional framework, and the advanced computational capabilities and dynamical properties of such complex systems.

Realizations of low firing rates in neural networks usually require globally balanced distributions among excitatory and inhibitory links, while feasibility of temporal coding is limited by neuronal millisecond precision. We show that cooperation, governing global network features, emerges through nodal properties, as opposed to link distributions. Using in vitro and in vivo experiments we demonstrate microsecond precision of neuronal response timings under low stimulation frequencies, whereas moderate frequencies result in a chaotic neuronal phase characterized by degraded precision. Above a critical stimulation frequency, which varies among neurons, response failures were found to emerge stochastically such that the neuron functions as a low pass filter, saturating the average inter-spike-interval. This intrinsic neuronal response impedance mechanism leads to cooperation on a network level, such that firing rates are suppressed toward the lowest neuronal critical frequency simultaneously with neuronal microsecond precision. Our findings open up opportunities of controlling global features of network dynamics through few nodes with extreme properties.

Synthetic reverberating activity patterns are experimentally generated by stimulation of a subset of neurons embedded in a spontaneously active network of cortical cells in-vitro. The neurons are artificially connected by means of conditional stimulation matrix, forming a synthetic local circuit with a predefined programmable connectivity and time-delays. Possible uses of this experimental design are demonstrated, analyzing the sensitivity of these deterministic activity patterns to transmission delays and to the nature of ongoing network dynamics.