21,333 research outputs found
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 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
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