Hirohito Kiwata

We consider inference in the inverse Ising problem using full data, which means incorporating sets of spin configurations. We approximate the Boltzmann distribution of the system to generate a frequency distribution derived from the given data. Then, the ratio between two Boltzmann distributions with different spin configurations eliminates the partition function and we obtain linear equations which can be solved to yield statistical parameters. Our method is applicable to cases where the absolute values of the coupling parameters and external fields are large. Compared to pseudolikelihood maximization, the accuracy of the inference obtained from our method is similar, although our approach is less labor intensive. (C) 2015 Elsevier B.V. All rights reserved.

We consider a method for the accurate estimation of quenched random fields in the inverse Ising problem. Approximations such as the mean-field or Bethe methods are applied to estimate quenched random coupling parameters and external fields. A diagonal matching method is introduced to ensure consistency of the diagonal part of the susceptibility, and the method yields an accurate estimation of the external fields. We introduce the diagonal matching method into the mean-field, Thouless-Anderson-Palmer, and Bethe approximations, and we investigate the effect of the diagonal matching method on the accuracy of estimation of the external fields.

We consider image restoration by Bayes' formula and investigate the relationship between an image and a prior probability from the following two viewpoints: hyperparameter estimation and the accuracy of a restored image. The Q-Ising model is adopted as a prior probability in Bayes' formula. Not the Q-Ising energy, but the Potts energy plays an important role in the hyperparameter estimation. From the viewpoint of the hyperparameter estimation, the relationship between a natural image and a prior probability is characterized through the Potts energy and magnetization of an image. The Potts energy and magnetization of an image are defined by a set of pixels' state of an image. The closer to the average Potts energy and magnetization over a prior probability the Potts energy and magnetization of a natural image is, the closer to the true value of a hyperparameter the estimated value of a hyperparameter from a degraded image is. For the accuracy of a restored image, the image which has a smaller Q-Ising energy is better restored by Bayes' formula composed of the Q-Ising prior. The consideration for the relationship between an image and a prior probability is expected to be valid for a more complicated prior probability. (C) 2011 Elsevier B.V. All rights reserved.

We consider using a Wiener filter for denoising a set of input signals that is degraded by additive white Gaussian noise. The Wiener filter is designed to minimize the mean square error, and it requires the knowledge of covariance of input signals and variance of the noise. The mean square error is defined as a distance between input signals and input signals estimated by the Wiener filter from noisy output signals. Although we have to infer input signals fromonly noisy output signals, the input signals are required for the evaluation of the mean square error. We reformulate the mean square error using noisy output signals and the covariance of the input signals. The covariance of the input signals is estimated by minimizing the mean square error. We apply our method to the case when an input signal is not generated by the assumed prior probability. In particular, we apply our method to image restoration and obtain good estimation results. © 2012 IOP Publishing Ltd.

We investigate stability of a cylindrical domain in a phase-separating binary fluid under a Poiseuille flow. Linearization for a couple of the Navier-Stokes and Cahn-Hilliard equations around stationary solutions leads to an eigenvalue problem, a solution of which yields a stability eigenvalue. The stability eigenvalue is composed of a term originated from the hydrodynamic Rayleigh instability and that from the diffusive instability. Concerning the stability eigenvalue of the hydrodynamic instability, a set of equations is obtained from boundary conditions at an interface and a solution of the equations yields the stability eigenvalue. In case of equal viscosity, the analytic formula of the solution is obtained without an external flow. The Tomotika's stability eigenvalue with the equal viscosity [Proc. R. Soc. London, Ser. A 150 (1935) 322] is shown to agree with the Stone and Brenner's result [J. Fluid Mech. 318 (1996) 373] explicitly. The Poiseuille flow has an effect of mixing an unstable axisymmetric mode with stable nonaxisymmetric modes, so that the two instability are suppressed. A radius of a stable cylindrical domain depends on a distance from the center of the Poiseuille flow. We estimate a Reynolds number under an external flow. Validity of the Stokes' approximation for the Navier-Stokes equation is confirmed.

We investigate effect of external flow on domains in two-dimensional phase-separating binary fluid. By use of the coupled Cahn-Hillard and Navier-Stokes equations, we study stability of a lamellar domain under two-dimensional Poiseuille flow within a linear stability analysis. We derive stability eigenvalues for long wavelength fluctuations. The two-dimensional Poiseuille now has the effect if mixing a stable zigzag mode and an unstable varicose mode so that they both become Stable. The width of the stable lamellar domain depends on a distance from wall.

We study the magnetic properties of the one-dimensional Hubbard model under fixed chemical potential. By using derivatives of the Lieb-Wu equation, the magnetization curve at zero temperature is obtained for various fixed band fillings and/or chemical potentials. As a well known result, in the case of the fixed band filling, there is only one second-order phase transition at magnetic saturation. On the other hand, when the chemical potential is fixed instead of the electron density, it is found that there is an additional phase transition in the magnetization curve.

It has been shown that there exists an additional magnetic phase transition of the magnetization curve for the S=1 SU(3) antiferromagnetic spin chain at zero temperature. As a the magnetic field decreases from the saturation field, there is a phase change at a critical field hc, where the magnetization curve versus the magnetic field has a cusp. The critical field is a boundary between two states, one of which contains the particles with the spin +1 and 0 and the other with the spin +1, 0 and -1. In this paper we estimate the critical field hc of the phase transition by examining the stability of these states.

We study the integrable SU(M) and SUq(M) quantum spin chains in the high-magnetic-field region at zero temperature. For M=4 we found second-order phase transitions at two different fields, H-1 and H-2. At both transition points, the magnetization curve versus magnetic field has cusps with discontinuities in the magnetic susceptibility. We clarify the mechanism of the phase transitions, from which we conclude that the SU(M) and SUq(M) quantum spin chains undergo (M-2) times field-induced phase transitions at zero temperature.

We introduce an approximation scheme where the Bethe ansatz is applied to non-integrable systems: the many-body S matrix is approximated by a product of two-body S matrices. We call this method Bethe-ansatz approximation (BAA). We apply the BAA to the S = 1 antiferromagnetic bilinear-biquadratic quantum spin chain. The model contains a parameter beta, the ratio of the biquadratic coupling to the bilinear coupling. Except for beta = - infinity, +/- 1, the system is non-integrable. Varying beta, we performed BAA calculation of the ground-state energy as a function of the total magnetization. Comparison with the numerical diagonalization shows a considerable efficiency of the BAA up to medium or more particle density.

For the integrable long-range SU(M) spin chain, the exact ground-state wave function is constructed for arbitrary irreducible representation of the permutation group.

We present an exactly solvable quantum SU(M) (M: arbitrary integer greater-than-or-equal-to 2) spin chain with long-range (approximately inverse-square) interactions. The model generalizes the so-called Haldane-Shastry system which corresponds to M = 2. We find the Lax pair for the system which guarantees the integrability of the system. An exact many-body ground-state wave function with particular symmetry is explicitly constructed.