An analysis of chaos via contact transformation

Transition from chaotic to quasi-periodic phase in modified Lorenz model is analyzed by performing the contact transformation such that the trajectory in {\Vec R}^3 is projected on {\Vec R}^2. The relative torsion number and the characteristics of the template are measured using the eigenvector of the Jacobian instead of vectors on moving frame along the closed trajectory. Application to the circulation of a fluid in a convection loop and oscillation of the electric field in single-mode laser system are performed. The time series of the eigenvalues of the Jacobian and the scatter plot of the trajectory in the transformed coordinate plane $X-Z$ in the former and $|X|-|Z|$ in the latter, allow to visualize characteristic pattern change at the transition from quasi-periodic to chaotic. In the case of single mode laser, we observe the correlation between the critical movement of the eigenvalues of the Jacobian in the complex plane and intermittency.Comment: 20 pages, 24 eps figures, 2 gif figures, use elsart.cls, accepted for publication in Chaos,Solitons & Fractals(2003

On the conditions for the existence of Perfect Learning and power law in learning from stochastic examples by Ising perceptrons

In a previous letter, we studied learning from stochastic examples by perceptrons with Ising weights in the framework of statistical mechanics. Under the one-step replica symmetry breaking ansatz, the behaviours of learning curves were classified according to some local property of the rules by which examples were drawn. Further, the conditions for the existence of the Perfect Learning together with other behaviors of the learning curves were given. In this paper, we give the detailed derivation about these results and further argument about the Perfect Learning together with extensive numerical calculations.Comment: 28 pages, 43 figures. Submitted to J. Phys.

Statistical mechanical evaluation of spread spectrum watermarking model with image restoration

In cases in which an original image is blind, a decoding method where both the image and the messages can be estimated simultaneously is desirable. We propose a spread spectrum watermarking model with image restoration based on Bayes estimation. We therefore need to assume some prior probabilities. The probability for estimating the messages is given by the uniform distribution, and the ones for the image are given by the infinite range model and 2D Ising model. Any attacks from unauthorized users can be represented by channel models. We can obtain the estimated messages and image by maximizing the posterior probability. We analyzed the performance of the proposed method by the replica method in the case of the infinite range model. We first calculated the theoretical values of the bit error rate from obtained saddle point equations and then verified them by computer simulations. For this purpose, we assumed that the image is binary and is generated from a given prior probability. We also assume that attacks can be represented by the Gaussian channel. The computer simulation retults agreed with the theoretical values. In the case of prior probability given by the 2D Ising model, in which each pixel is statically connected with four-neighbors, we evaluated the decoding performance by computer simulations, since the replica theory could not be applied. Results using the 2D Ising model showed that the proposed method with image restoration is as effective as the infinite range model for decoding messages. We compared the performances in a case in which the image was blind and one in which it was informed. The difference between these cases was small as long as the embedding and attack rates were small. This demonstrates that the proposed method with simultaneous estimation is effective as a watermarking decoder

Spindle-like activity appearing during paradoxical sleep in rats with iron-induced cortical focus.

Under barbiturate anesthesia, male Wistar rats weighing 250-300 g were injected with 2.5 microliters of 0.2 M FeCl3 solution into the left sensori-motor cortex to induce an epileptic focus with minimal abnormal activities. Polygraphy started 1 week after the surgery, showed a spindle-like hypersynchronous activity that appeared not only in the slow wave sleep period but also during paradoxical sleep (PS). This activity had a frequency of 8-14 Hz. The amplitude was more than 200 mu v in the right (non-injected side) cortex but very small in the left cortex (injected side). Isolated spike discharges were observed in an ECoG of slow wave sleep. Apart from this activity there was nothing resembling the usual sleep spindles.</p

Response to Invasion by Antigen and Effects of Threshold in an Immune Network Dynamical System Model with a Small Number of Degrees of Freedom

We study a dynamical system model of an idiotypic immune network with a small number of degrees of freedom, mainly focusing on the effect of a threshold above which antibodies can recognise antibodies. The response of the system to invasions by antigens is investigated in the both models with and without the threshold and it turns out that the system changes in a desirable direction for moderate magnitude of perturbation. direction for moderate magnitude of perturbation. Also, the propagation of disturbance by an antigen is investigated in the system of one-dimensionally connected basic units taking the closed 3-clone system as a unit, and it is clarified that the threshold of the system has effects to enhance the stability of the network and to localise the immune response.Comment: 6 pages, 6 figures. Submitted to Prog. Theor. Phy