Correspondence between phase oscillator network and classical XY model with the same random and frustrated interactions.

We study correspondence between a phase oscillator network with distributed natural frequencies and a classical XY model at finite temperatures with the same random and frustrated interactions used in the Sherrington-Kirkpatrick model. We perform numerical calculations of the spin glass order parameter q and the distributions of the local fields P(R), where R is the amplitude of the local field. As a result, we find that the parameter dependences of P(R) in both models agree fairly well in all ranges of parameters in the spin glass phase and those of q agree at least for lower values of parameters in the spin glass phase, if parameters are normalized by using the previously obtained correspondence relation between two models with the same other types of interactions. Furthermore, we numerically calculate the time evolution of quantities such as the instantaneous local field in the phase oscillator network in order to study the roles of synchronous and asynchronous oscillators. We also study the self-consistent equation of the local fields in the oscillator network and XY model derived by the mean-field approximation.

Statistical mechanical evaluation of a 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 two-dimensional (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.

Analysis of a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction.

We study a phase oscillator network on a circle with an infinite-range interaction. First, we treat the Mexican-hat interaction with the zeroth and first Fourier components. We give detailed derivations of the auxiliary equations for the phases and self-consistent equations for the amplitudes. We solve these equations and characterize the nontrivial solutions in terms of order parameters and the rotation number. Furthermore, we derive the boundaries of the bistable regions and study the bifurcation structures in detail. Expressions for location-dependent resultant frequencies and entrained phases are also derived. Secondly, we treat a different interaction that is composed of mth and nth Fourier components, where m

Novel features of computer-simulated clonal life of Paramecium caudatum.

The clone of the ciliated protozoan Paramecium caudatum has the immaturity period of about 60 fissions and the lifespan of about 600 fissions. These life cycle figures have been depicted through laboratory experiments that allow continuous cell divisions for hundreds, which never occur in nature. We here constructed the nature-mimicking model culture that alternated the log- and stationary phases to allow conjugation, and computer-simulated the age structure modifying parameters such as cell distributions to start the culture, fission rates, death rates, immaturity periods, probabilities of conjugation, proportions of transplantation and so on. The average and maximum ages in the culture after thousands of alternations were converged to 43+/-2 and 140+/-5 fissions, respectively, when parameters for the immaturity period and the maximum clonal lifespan were set at 60 and 600 fissions. This result explains why cells collected in nature are usually young and vigorous. The average and maximum ages proportionally prolonged as the immaturity period was prolonged, as reported true for species of the ciliate. These results indicate the validity of our simulation. The average and maximum ages remained unchanged when the initial condition for starting the culture was changed from two complementary mating-type cells to a population with a quadratic-function distribution, and when the fission rate at the log-phase and the death rate at the stationary phase were modified for older ages. The average and maximum ages changed slightly when either the conjugation rate or the proportion of transplantation was somewhat lowered. Although they changed considerably when such parameters as the immaturity period, conjugation rate and death rate were extremely modified, no clones with the age over 230 fissions appeared in any simulations. These results indicate the robustness of the model, which provides us with fresh insight into the structural system of the clonal lifespan of P. caudatum in nature.

Mean field and cavity analysis for coupled oscillator networks.

We study coupled oscillator spin systems on sparse, random graphs. In particular, we examine the recent conjecture of Ichinomiya on the equivalence of a sparsely connected oscillator network with ferromagnetic interactions to a fully connected network with disordered (i.e., randomly quenched) interactions. By restricting our investigation to a Hamiltonian case we can use the techniques of equilibrium statistical mechanics to compare these two models analytically including phase diagrams and the calculation of order parameters in the ordered phase. We complete our investigation by performing some Monte Carlo simulations to compare our theoretical predictions against.

Realization of immune response features by dynamical system models.

Among the features of real immune responses that occur when antigens invade a body are two remarkable features. One is that the number of antibodies produced in the secondary invasion by identical antigens is more than 10 times larger than in the primary invasion. The other is that more effective antibodies, which are produced by somatic hypermutation during the immune response, can neutralize the antigens more quickly. This phenomenon is called "affinity maturation". In this paper, we try to reproduce these features by dynamical system models and present possible factors to realize them. Further, we present a model in which the memory of the antigen invasion is realized without immune memory cells.