Evi Kopelowitz

Public-channel cryptography based on mutual chaos pass filters

We study the mutual coupling of chaotic lasers and observe both experimentally and in numeric simulations that there exists a regime of parameters for which two mutually coupled chaotic lasers establish isochronal synchronization, while a third laser coupled unidirectionally to one of the pair does not synchronize. We then propose a cryptographic scheme, based on the advantage of mutual coupling over unidirectional coupling, where all the parameters of the system are public knowledge. We numerically demonstrate that in such a scheme the two communicating lasers can add a message signal (compressed binary message) to the transmitted coupling signal and recover the message in both directions with high fidelity by using a mutual chaos pass filter procedure. An attacker, however, fails to recover an errorless message even if he amplifies the coupling signal.

Nonlocal mechanism for cluster synchronization in neural circuits

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.

Synthetic reverberating activity patterns embedded in networks of cortical neurons

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 a 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.

Spiking optical patterns and synchronization.

We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period, which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks.

Synchronization of mutually coupled chaotic lasers in the presence of a shutter

Two mutually coupled chaotic diode lasers exhibit stable isochronal synchronization in the presence of self-feedback. When the mutual communication between the lasers is discontinued by a shutter and the two uncoupled lasers are subject to self-feedback only, the desynchronization time is found to scale as Adtau, where Ad>1 and tau corresponds to the optical distance between the lasers. Prior to synchronization, when the two lasers are uncorrelated and the shutter between them is opened, the synchronization time is found to be much shorter, though still proportional to tau. As a consequence of these results, the synchronization is not significantly altered if the shutter is opened or closed faster than the desynchronization time. Experiments in which the coupling between two chaotic-synchronized diode lasers is modulated with an electro-optic shutter are found to be consistent with the results of numerical simulations.

Chaos synchronization with dynamic filters: Two-way is better than one-way

Two chaotic systems which interact by mutually exchanging a signal built from their delayed internal variables, can synchronize. A third unit may be able to record and to manipulate the exchanged signal. Can the third unit synchronize to the common chaotic trajectory, as well? If all parameters of the system are public, a proof is given that the recording system can synchronize as well. However, if the two interacting systems use private commutative filters to generate the exchanged signal, a driven system cannot synchronize. It is shown that with dynamic private filters the chaotic trajectory even cannot be calculated. Hence two-way (interaction) is better than one-way (drive). The implication of this general result to secret communication with chaos synchronization is discussed.

Quantification of pairwise neuronal interactions: Going beyond the significance lines

BACKGROUND Normal brain function depends on intact interactions between multiple neuronal ensembles. Interactions within and between local networks comprising multiple neuronal types may occur on a range of time scales thus affecting the estimation of interaction strength. A common technique to investigate functional interactions within neuronal ensembles is pairwise cross-correlation analysis. However, conventional cross-correlation methods address the question of whether an observed peak in the cross-correlation is statistically significant relative to the null hypothesis which assumes a lack of correlation. Ultimately, these methods were not designed to evaluate the strength of the observed interactions. NEW METHOD We devised four complementary measures - Triplets, Bin crossing, Bin height and Entropy - for assessing the strength of neuronal interactions; each is sensitive to different features of the cross-correlogram peak such as height, width and smoothness. RESULTS First, a comparison of five prevalent methods for evaluating whether an observed peak in neuronal cross-correlogram is significant allowed their ranking from the most conservative to the more sensitive for purposes of selecting the appropriate method based on the data structure and preferred strategy. Second, the performance of the four measures we derived improved with interaction strength and the number of spikes in the cross-correlogram. The four measures also enabled the reconstruction of interaction parameters of simulated networks including the detection of time-dependent alterations. CONCLUSIONS We suggest that the combination of several measures of peak characteristics helps rectify the individual shortcomings of specific measures and can yield a broad coverage of interaction strengths and widths.

Synchronized optical spiking

Diode laser with optical feedback can show chaotic intensity fluctuations in the form of short intensity spikes. Two such lasers can be synchronized to give identical isochronal spiking patterns.