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 nonchaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the sign amplitude of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneous with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the size of the network. Results are exemplified by a network of modified Duffing oscillators with infinite range pseudoinverse delayed interactions.

Coexistence of exponentially many chaotic spin-glass attractors

A chaotic network of size N with delayed interactions which resembles a pseudoinverse 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.

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 behavior of networks of semiconductor lasers.

Zero lag synchronization of chaotic systems with time delayed couplings

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 chaotic semiconductor lasers. The mechanism is based on two mutual coupling delay times with certain allowed integer ratios, whereas for a single mutual delay time ZLS cannot be achieved. This mechanism is also found numerically for mutually coupled chaotic maps where its stability is analyzed using the Schur-Cohn theorem for the roots of polynomials. The symmetry of the polynomials allows only specific integer ratios for ZLS. In addition, we present a general argument for ZLS when several mutual coupling delay times are present.

On chaos synchronization and secure communication

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems.

Synchronization of networks of chaotic units with time-delayed couplings

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

Phase synchronization in mutually coupled chaotic diode lasers

Semiconductor lasers with optical feedback have chaotically pulsating output behavior. When two similar chaotic lasers are optically coupled, they can become synchronized in their optical fluctuations. Here we show that the synchronization is not only in the amplitude and in the timing of the pulses but that the short pulses are also phase coherent with each other. This is true even when the lasers are separated by distances much larger than their coherence length.

Simulation of self-assembled nanopatterns in strained 2D alloys on the face centered cubic (111) surface

We investigate the formation of nanostructures in 2D strained alloys on face centered cubic (111) surfaces by means of equilibrium Monte Carlo simulations. In the framework of an off-lattice model, we consider one monolayer of two bulk-immiscible adsorbates A and B with negative and positive misfit relative to the substrate, respectively. Simulations show that the adsorbates partly self-organize into island or stripe-like patterns. We show how these structures depend on the relative misfits, interaction, and concentration of components. The morphology is quite different for phase separation and intermixing regimes.

Secure key-exchange protocol with an absence of injective functions

The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and synchronize to a time dependent secret key. The weights of the networks have integer values between +/-L. Recently an algorithm for an eavesdropper which could break the key was introduced by [A. Shamir, A. Mityagin, and A. Klimov, Ramp Session (Eurocrypt, Amsterdam, 2002)]. We show that the synchronization time increases with L2 while the probability to find a successful attacker decreases exponentially with L. Hence for large L we find a secure key-exchange protocol which depends neither on number theory nor on injective trapdoor functions used in conventional cryptography.

Multichoice minority game

The generalization of the problem of adaptive competition, known as the minority game, to the case of K possible choices for each player, is addressed, and applied to a system of interacting perceptrons with input and output units of a type of K-state Potts spins. An optimal solution of this minority game, as well as the dynamic evolution of the adaptive strategies of the players, are solved analytically for a general K and compared with numerical simulations.

Generation of unpredictable time series by a neural network

A perceptron that "learns" the opposite of its own output is used to generate a time series. We analyze properties of the weight vector and the generated sequence, such as the cycle length and the probability distribution of generated sequences. A remarkable suppression of the autocorrelation function is explained, and connections to the Bernasconi model are discussed. If a continuous transfer function is used, the system displays chaotic and intermittent behavior, with the product of the learning rate and amplification as a control parameter.

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 neighbor. 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 the Minority Game. In this game, a set of agents who have to make a binary decision is considered.); 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.

Receiver operating characteristics of perceptrons: influence of sample size and prevalence

In many practical classification problems it is important to distinguish false positive from false negative results when evaluating the performance of the classifier. This is of particular importance for medical diagnostic tests. In this context, receiver operating characteristic (ROC) curves have become a standard tool. Here we apply this concept to characterize the performance of a simple neural network. Investigating the binary classification of a perceptron we calculate analytically the shape of the corresponding ROC curves. The influence of the size of the training set and the prevalence of the quality considered are studied by means of a statistical-mechanics analysis.

Antipredictable sequences: harder to predict than random sequences

For any discrete-state sequence prediction algorithm A, it is always possible, using an algorithm B no more complicated than A, to generate a sequence for which A's prediction is always wrong. For any prediction algorithm A and sequence x, there exists a sequence y no more complicated than x, such that if A performs better than random on x, then it will perform worse than random on y by the same margin. An example of a simple neural network predicting a bit sequence is used to illustrate this very general but not widely recognized phenomenon. This implies that any predictor with good performance must rely on some (usually implicitly) assumed prior distributions of the problem.

[Testing with the computer--the Diamed System]

The Diamed System has been developed to reduce the time-consuming testing routines involved in psychopathometric studies of disease course in the field of medicine. Test administration was to be relieved of those activities, in particular in repeat testing, examiners experienced as weary, unpleasant, repetitive, and uncreative. An important aim had been to permit data collection by as independent a dialogue as possible between the patient and the micro-computer, and extremely simple operations and instructions were considered of great importance. The opportunity has, however, also been utilized to implement promising performance testing procedures for measuring basic parameters of mental capability. Beside mental-amnestic capacity, the procedures cover subjective complaints because these, too, frequently are relevant in measuring the course of psychic disorders. The procedures incorporated in the Diamed System permit reliability verifications as to whether self-assessment and independent computerized testing might not be asking too much of the patients intellectually. Most of the procedures will be used for studying disease course in acute Organic Psychosyndromes and in all disorders that are associated with changes in mood and/or with subjective complaints. Diagnostic assistance moreover is offered for determining the presence of acute Organic Psychosyndromes. Under the name of "brain jogging", an economical programme is introduced for mental training, aimed at maintaining and improving basic central information processing capacities. Its effect on intelligence and memory has been demonstrated on in-patient populations, both with and without brain-organic disorders. Notably in the case of acute Organic Psychosyndromes, it has turned out to be an effective supplement to drug treatment.

Cross-sectional epidemiological study on neurotoxicity of solvents in paints and lacquers

In a multi-disciplinary retrospective study we examined 105 house painters employed for at least ten years (median 27 years, range 10-36 years). Fifty-three workers from various professions (non-painters), who were matched with regard to age, occupational training and socio-economic status served as the control group. In both groups no cases of a clinically manifest polyneuropathy or encephalopathy were found. The neurophysiological examinations (EEG and NCV-measurement) showed no differences in painters and controls that would indicate adverse effects of organic solvents. There were no cases with neuroradiological findings of a diffuse cerebral atrophy. Furthermore the evaluation of certain brain structures (ventricular diameter, cella media index) of the CAT films did not reveal any significant differences. In the neurobehavioral tests significant differences in the results were only found in the subtests "change of personality" and "short term memory capacity" in a subgroup of painters with repeated prenarcotic symptoms at the workplace. Ambient air monitoring measurements at 30 representative workplaces showed that the concentrations of the main components of the solvent-mixtures were well below the MAK-values. The results of the "Erlangen Painter Study" does not confirm former epidemiologic findings from other countries, mainly Denmark. However, there are some aspects, such as minor solvent exposure in German house painters, insufficient diagnostic and etiological procedures as well as misclassifications which may explain the different experiences.

[Short forms of a short psychopathological intelligence test (author's transl)]

Even short tests can still be materially shortened when they are intended to provide rough information. An example of a short intelligence test shows that considerable reductions are permissible when the procedure is intended to classify subjects into IQ groups of roughly "under 100" or "over 100". Also division into three as below average, average and above average level of intelligence is possible, and also division into four grades. If about 85% accuracy is satisfactory, a three-problem test is sufficient. For grading into three and four parts, six and nine problems, respectively may be adequate.

[Disturbances of orientation with functional psychoses (author's transl)]

It was supposed by clinical impressions that disturbances of orientation do not appear only in severe degrees of a transit-syndrome, but also in the light stadium of such a physically founded psychosis. In order to verify these impressions, a questionnaire was developed which permitted an objective scoring. This Q-Test consists of 37 questions (items), which measure the orientations of time, space, situation, and person. On the base of this questionnaire two samples were tested, the one consisting of 50 patients with functional psychoses (reversible physically founded psychoses), the other consisting of 50 patients with only neurological disturbances. The degree of the functional psychoses was determined by the "Syndrome-Test" (F. Bocker, 1959). The range of the scores corresponded with the clinical categories from a low degree of the transit-syndrome to a medium degree of disturbances of consciousness. The scoring was based on an standard system derived from the results of the control group (patients with only neurological disturbances). The clinical impressions could be verified by empirical and statistical methods. According to the test results, disturbances of orientation already appear during the light stadium of the transit-syndrome. Furthermore there is a high significant correlation (p. less than 001) between the degree of the functional psychoses and the degree of the disturbances of orientation. This applies to all categories of orientation. The orientation concerning time, space and situation proved to be more susceptible to disturbances than the orientation concerning the person. The very close correlation between the degrees of the functional psychoses and the degrees of the disturbances of orientation make it possible to determine the stadium of the functional psychoses promptly. The complete and very handy "short-time-test" will be published in a special paper.