Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

The response of Anabaena-free Azolla and the symbiotic Azolla to temperature

The performance of Anabaena-free (algae free) and symbiotic types of three speeies of Azolla (A. filiculoides, A. pinnata and A. microphylla) were studied in a phytotron at two average temperatures (22 and 33 oC). The growth of both the Anabaena-free and symbiotic types were depressed at a high temperature (33 DC) to varying degrees for all species of Azolla tested. There was a marked reduction of both growth and nitrogen-fixing ability (pereent N) of the symbiotie Azalia compared to its Anabaena-free counterpart suggesting that the low tolerance of A. jiliculoides No.1 0 I to high temperature was probably dictated by the symbiont Anabaena azollae. A. azollae of both A, microphylla No. 418 and A, pinnata No.2 appeared more tolerant to high temperature than that of A. filiculaides No. 101

Spontaneous breaking of continuous translational invariance

Unbroken continuous translational invariance is often taken as a basic assumption in discussions of spontaneous symmetry breaking (SSB), which singles out SSB of translational invariance itself as an exceptional case. We present a framework which allows us to treat translational invariance on the same footing as other symmetries. It is shown that existing theorems on SSB can be straightforwardly extended to this general case. As a concrete application, we analyze the Nambu-Goldstone modes in a (ferromagnetic) supersolid. We prove on the ground of the general theorems that the Bogoliubov mode stemming from a spontaneously broken internal U(1) symmetry and the longitudinal phonon due to a crystalline order are distinct physical modes.Comment: 14 pages, 4 pdf/jpg figures, REVTeX 4.1; v2: section IV expanded, new appendix and references added, numerous other minor modifications throughout the tex

Muon-spin-relaxation and magnetic-susceptibility studies of effects of the magnetic impurity Ni on the Cu-spin dynamics and superconductivity in La_2-x_Sr_x_Cu_1-y_Ni_y_O_4_ with x = 0.13

Effects of the magnetic impurity Ni on the Cu-spin dynamics and superconductivity have been studied in La_2-x_Sr_x_Cu_1-y_Ni_y_O_4_ with x = 0.13 changing y finely up to 0.10. Compared with the case of the nonmagnetic impurity Zn, it has been found from the muon-spin-relaxation measurements that a large amount of Ni is required to stabilize a magnetic order of Cu spins. However, the evolution toward the stabilization of the magnetic order with increasing impurity concentration is qualitatively similar to each other. The area of the non-superconducting and slowly fluctuating or static region of Cu spins around Ni has been found to be smaller than that around Zn, suggesting that the pinning of rather long-ranged dynamical spin correlation such as the so-called dynamical stripe by Ni is weaker than that by Zn. This may be the reason why Zn destroys the superconductivity in the hole-doped high-T_c_ cuprates more markedly than Ni.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev.

1D Modeling for Temperature-Dependent Upflow in the Dimming Region Observed by Hinode/EIS

We have previously found a temperature-dependent upflow in the dimming region following a coronal mass ejection (CME) observed by the {\it Hinode} EUV Imaging Spectrometer (EIS). In this paper, we reanalyzed the observations along with previous work on this event, and provided boundary conditions for modeling. We found that the intensity in the dimming region dramatically drops within 30 minutes from the flare onset, and the dimming region reaches the equilibrium stage after $\sim$1 hour later. The temperature-dependent upflows were observed during the equilibrium stage by EIS. The cross sectional area of the fluxtube in the dimming region does not appear to expand significantly. From the observational constraints, we reconstructed the temperature-dependent upflow by using a new method which considers the mass and momentum conservation law, and demonstrated the height variation of plasma conditions in the dimming region. We found that a super radial expansion of the cross sectional area is required to satisfy the mass conservation and momentum equations. There is a steep temperature and velocity gradient of around 7 Mm from the solar surface. This result may suggest that the strong heating occurred above 7 Mm from the solar surface in the dimming region. We also showed that the ionization equilibrium assumption in the dimming region is violated especially in the higher temperature range.Comment: accepted for publication in The Astrophysical Journa