arXiv subjects

I. Kanter

Publications and source records attributed to I. Kanter.

At least 19 recordsLinked to original sources

arXiv2013

Time delayed laser networks: phase versus chaos synchronization

The synchronization of chaotic lasers and the optical phase synchronization of light originating in multiple coupled lasers have both been extensively studied, however, the interplay between these two phenomena, especially at the network level is unexplored. Here we experimentally compare chaos synchronization of laser networks with heterogeneous coupling delay times to phase synchronization of similar networks. While chaotic lasers exhibit deterioration in synchronization as the network time delay heterogeneity increases, phase synchronization is found to be independent of heterogeneity. The experimental results are found to be in agreement with numerical simulations for semiconductor lasers.

physics.optics↗

arXiv2012

Transient to Zero-Lag Synchronization in Excitable Networks

The scaling of transient times to zero-lag synchronization in networks composed of excitable units is shown to be governed by three features of the graph representing the network: the longest path between pairs of neurons (diameter), the largest loop (circumference) and the loop with the maximal average out degree. The upper bound of transient times can vary between O(1) and O(N2), where N is the size of the network, and its scaling can be predicted in many scenarios from finite time accumulated information of the transient. Results challenge the assumption that functionality of neural networks might depend solely upon the synchronized repeated activation such as zero-lag synchronization.

q-bio.NC↗

arXiv2012

Random Symmetry Breaking and Freezing in Chaotic Networks

Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the amplitude sign of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneously with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the ize of the network. Results are exemplified by a network of modified Duffing oscillators with infinite ange pseudo-inverse delayed interactions.

nlin.CD↗

arXiv2011

Time-delayed coupled chaotic semiconductor lasers show new types of synchronization: Experiment and theory

Topologies of two, three and four time-delay-coupled chaotic semiconductor lasers are experimentally and theoretically found to show new types of synchronization. Shifted zero-lag synchronization is observed for two lasers separated by long distances even when their self-feedback delays are not equal. Shifted sub-lattice synchronization is observed for quadrilateral geometries while the equilateral triangle is zero-lag synchronized. Generalized zero-lag synchronization, without the limitation of precisely matched delays, opens possibilities for advanced multi-user communication protocols.

nlin.CD↗

arXiv2011

Coexistence of exponentially many chaotic spin-glass attractors

A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $α=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with $α$. At finite $α$, a chaotic spin glass phase exists, where the number of distinct chaotic attractors scales exponentially with $N$. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the $N$ chaotic units or freezing with respect to the $P$ patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.

nlin.CD↗

arXiv2011

Synchronization of unidirectional time delay chaotic networks and the greatest common divisor

We present the interplay between synchronization of unidirectional coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented graph. In the weak chaos region and for GCD=1 the network is in chaotic zero-lag synchronization, whereas for GCD=m>1 synchronization of m-sublattices emerges. Complete synchronization can be achieved when all chaotic nodes are influenced by an identical set of delays and in particular for the limiting case of homogeneous delays. Results are supported by simulations of chaotic systems, self-consistent and mixing arguments, as well as analytical solutions of Bernoulli maps.

nlin.CD↗

arXiv2011

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.

nlin.CD↗

arXiv2011

Synchronization of chaotic networks with time-delayed couplings: An analytic study

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations which imitate the behaviour of networks of semiconductor lasers.

nlin.CD↗

arXiv2005

The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in epsilon. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series.

cs.IT↗

arXiv2003

Cooperating Attackers in Neural Cryptography

A new and successful attack strategy in neural cryptography is presented. The neural cryptosystem, based on synchronization of neural networks by mutual learning, has been recently shown to be secure under different attack strategies. The advanced attacker presented here, named the ``Majority-Flipping Attacker'', is the first whose success does not decay with the parameters of the model. This new attacker's outstanding success is due to its using a group of attackers which cooperate throughout the synchronization process, unlike any other attack strategy known. An analytical description of this attack is also presented, and fits the results of simulations.

cond-mat.dis-nn↗

arXiv2002

Parallel versus sequential updating for Belief Propagation decoding

sequential updating scheme (SUS) for the belief propagation algorithm is proposed, and is compared with the parallel (regular) updating scheme (PUS). Simulation results on various codes indicate that the number of iterations of the belief algorithm for the SUS is about one half of the required iterations for the PUS, where both decoding algorithms have the same error correction properties. The complexity per iteration for both schemes is similar, resulting in a lower total complexity for the SUS. The explanation of this effect is related to the inter-iteration information sharing, which is a property of only the SUS, and which increases the "correction gain" per iteration

cond-mat.stat-mech↗

arXiv2002

Secure exchange of information by synchronization of neural networks

A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks is leading to a new method of exchange of secret messages. Numerical simulations show that two artificial networks being trained by Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for a secure transmission of secret data. It is shown that an opponent who knows the protocol and all details of any transmission of the data has no chance to decrypt the secret message, since tracking the weights is a hard problem compared to synchronization. The complexity of the generation of the secure channel is linear with the size of the network.

cond-mat.stat-mech↗

arXiv2001

Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.

cond-mat.soft↗

arXiv2000

Secure and linear cryptosystems using error-correcting codes

A public-key cryptosystem, digital signature and authentication procedures based on a Gallager-type parity-check error-correcting code are presented. The complexity of the encryption and the decryption processes scale linearly with the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted by Bob, whereas a private-noise added by Alice to a given fraction of the ciphertext of each encrypted plaintext serves to increase the secure channel and is the cornerstone for digital signatures and authentication. Various scenarios are discussed including the possible actions of the opponent Oscar as an eavesdropper or as a disruptor.

cond-mat.dis-nn↗

arXiv2000

On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system size, whereas the time scale for relaxation to equilibrium depends on microscopic dynamics. To illustrate this, we also look at deterministic and stochastic versions of the Ehrenfest model with a distribution of microscopic relaxation times.

cond-mat.stat-mech↗

arXiv2000

Learning and generation of long-range correlated sequences

We study the capability to learn and to generate long-range, power-law correlated sequences by a fully connected asymmetric network. The focus is set on the ability of neural networks to extract statistical features from a sequence. We demonstrate that the average power-law behavior is learnable, namely, the sequence generated by the trained network obeys the same statistical behavior. The interplay between a correlated weight matrix and the sequence generated by such a network is explored. A weight matrix with a power-law correlation function along the vertical direction, gives rise to a sequence with a similar statistical behavior.

cond-mat.dis-nn↗

arXiv2000

Robust chaos generation by a perceptron

The properties of time series generated by a perceptron with monotonic and non-monotonic transfer function, where the next input vector is determined from past output values, are examined. Analysis of the parameter space reveals the following main finding: a perceptron with a monotonic function can produce fragile chaos only whereas a non-monotonic function can generate robust chaos as well. For non-monotonic functions, the dimension of the attractor can be controlled monotonically by tuning a natural parameter in the model.

cond-mat.dis-nn↗

arXiv2000

Interacting Neural Networks

Several scenarios of interacting neural networks which are trained either in an identical or in a competitive way are solved analytically. In the case of identical training each perceptron receives the output of its neighbour. The symmetry of the stationary state as well as the sensitivity to the used training algorithm are investigated. Two competitive perceptrons trained on mutually exclusive learning aims and a perceptron which is trained on the opposite of its own output are examined analytically. An ensemble of competitive perceptrons is used as decision-making algorithms in a model of a closed market (El Farol Bar problem or Minority Game); each network is trained on the history of minority decisions. This ensemble of perceptrons relaxes to a stationary state whose performance can be better than random.

cond-mat.dis-nn↗