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.

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.

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.

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.

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.

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.