A neural network model which is capable of recalling time sequences and cycles patterns introduced. In this model, some the synaptic connections, ${J}_{\mathrm{ij}}$, between pairs neurons are asymmetric (${J}_{\mathrm{ij}}\ensuremath{\ne}{J}_{\mathrm{ji}}$) have slow dynamic response. The effects thermal noise on generated discussed. Simulation results demonstrating performance presented. may be also useful in understanding generation rhythmic biological motor systems.

The fluctuating intensity of a chaotic semiconductor laser is used for generating random sequences at rates up to 12.5 Gbits/s. conversion the bit sequence can be implemented in either software or hardware and overall rate generation much faster than any previously reported number generator based on physical mechanism. generator's simplicity, robustness, insensitivity control parameters should enable its application tasks secure communication calculation procedures requiring ultrahigh-speed...

Randomly interacting p-state Potts spins may freeze into a Potts-glass phase in which the symmetry is unbroken, on average. The mean-field theory of this transition presented. Unlike spin-glass case, there exist two distinct phases that differ nature correlations among many degenerate ground states system. For p>4, from disordered unusual: freezing occurs discontinuously but without latent heat. Similar results hold for quadrupolar-glass models.

The mean-field theory of dilute spin-glasses is studied in the limit where average coordination number finite. zero-temperature phase diagram calculated and relationship between spin-glass percolation transition discussed. present formalism applicable also to graph optimization problems.

We study chaotic synchronization in networks with time-delayed coupling. introduce the notion of strong and weak chaos, distinguished by scaling properties maximum Lyapunov exponent within manifold for large delay times, relate this to condition stable or unstable synchronization, respectively. In simulations laser models experiments electronic circuits, we identify transitions from back chaos upon monotonically increasing coupling strength.

The paper is concerned in the main with a Maxwell material, which corresponds to model having spring and dashpot series. equation for longitudinal wave propagation rods shown be equivalent telegraph equation, solutions of transient problems are treated briefly Appendix using Laplace transform technique. Impact on semi-infinite rod considered detail report. A method superposition images discussed use this solution solve boundary value finite rods. resulting stress distributions contrasted...

The theory of neural networks is extended to include discrete neurons with more than two states. dynamics such systems are studied. maximum number storage patterns found be proportional Nq(q-1), where q the Potts states and N size network. properties network compared Ising case, similarity between a diluted multineuron interacting Hopfield model discussed.

The learing time of a simple neural-network model is obtained through an analytic computation the eigenvalue spectrum for Hessian matrix, which describes second-order properties objective function in space coupling coefficients. results are generic symmetric matrices by summing outer products random vectors. form distribution suggests new techniques accelerating learning process, and provides theoretical justification choice centered versus biased state variables.

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

The dynamics of two mutually coupled chaotic diode lasers are investigated experimentally and numerically. By adding self feedback to each laser, stable isochronal synchronization is established. This stability, which can be achieved for symmetric operation, essential constructing an optical public-channel cryptographic system. experimental results on well described by rate equations single mode lasers.

A network of chaotic units is investigated where the are coupled by signals with a transmission delay. Any arbitrary finite considered trajectories uncoupled solution dynamic equations network. It shown that cannot be synchronized if delay larger than time scales individual units. For several models master stability function calculated which determines maximal for synchronization possible.

Synchronization in large laser networks with both homogeneous and heterogeneous coupling delay times is examined. The number of synchronized clusters lasers established to equal the greatest common divisor network loops. We experimentally demonstrate up 16 multicluster phase synchronization scenarios within unidirectional coupled networks, whereby deduced by mapping an equivalent network. controlled means tunable self-coupling.

Neurons are the computational elements that compose brain and their fundamental principles of activity known for decades. According to long-lasting scheme, each neuron sums incoming electrical signals via its dendrites when membrane potential reaches a certain threshold typically generates spike axon. Here we present three types experiments, using neuronal cultures, indicating functions as collection independent units. The is anisotropically activated following origin arriving membrane,...

An all-electronic physical random number generator at rates up to 80 Gbit/s is presented, based on weakly coupled GaAs/Ga0.55Al0.45As superlattices operated room temperature. It large-amplitude, chaotic current oscillations characterized by a bandwidth of several hundred MHz and do not require external feedback or conversion an electronic signal prior digitization. The method robust insensitive perturbations its fully implementation suggests scalability minimal postprocessing in comparison...

Synaptic plasticity is a long-lasting core hypothesis of brain learning that suggests local adaptation between two connecting neurons and forms the foundation machine learning. The main complexity synaptic synapses dendrites connect in series existing experiments cannot pinpoint significant imprinted location. We showed efficient backpropagation Hebbian on dendritic trees, inspired by experimental-based evidence, for sub-dendritic its nonlinear amplification. It has proven to achieve success...

Abstract In neural network's literature, Hebbian learning traditionally refers to the procedure by which Hopfield model and its generalizations store archetypes ( i.e. , definite patterns that are experienced just once form synaptic matrix). However, term in machine ability of extract features from supplied dataset e.g. made blurred examples these archetypes), order make own representation unavailable archetypes. Here, given a sample examples, we define supervised protocol based on Hebb's...

It is shown that a 2-parameter random Markov process constructed with $N$ states and biased transitions gives rise to stationary distribution where the probabilities of occurrence states, $P(k),k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,\dots{},N$, exhibit following three universal behaviors which characterize biological sequences texts in natural languages: (a) rank-ordered frequencies words are given by Zipf's law $P(k)\ensuremath{\propto}1/{k}^{\ensuremath{\rho}}$,...

Zero-lag synchronization (ZLS) between chaotic units, which do not have self-feedback or a relay unit connecting them, is experimentally demonstrated for two mutually coupled semiconductor lasers. The mechanism based on mutual coupling delay times with certain allowed integer ratios, whereas single time ZLS cannot be achieved. This also found numerically maps where its stability analyzed using the Schur-Cohn theorem roots of polynomials. symmetry polynomials allows only specific ratios ZLS....

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish fundamental rules that govern their state synchronization. identified a specific substructure imposes its synchronization on entire network show for any configuration forms at most two synchronized clusters. Our results indicate is nonlocal phenomenon cannot be deduced by decomposing into smaller substructures, each individual state.

The realization of complex classification tasks requires training deep learning (DL) architectures consisting tens or even hundreds convolutional and fully connected hidden layers, which is far from the reality human brain. According to DL rationale, first layer reveals localized patterns in input large-scale following until it reliably characterizes a class inputs. Here, we demonstrate that with fixed ratio between depths second error rates generalized shallow LeNet architecture, only five...