Statistical Mechanics of Time Domain Ensemble Learning

Conventional ensemble learning combines students in the space domain. On the other hand, in this paper we combine students in the time domain and call it time domain ensemble learning. In this paper, we analyze the generalization performance of time domain ensemble learning in the framework of online learning using a statistical mechanical method. We treat a model in which both the teacher and the student are linear perceptrons with noises. Time domain ensemble learning is twice as effective as conventional space domain ensemble learning.Comment: 10 pages, 10 figure

Statistical Mechanics of Linear and Nonlinear Time-Domain Ensemble Learning

Conventional ensemble learning combines students in the space domain. In this paper, however, we combine students in the time domain and call it time-domain ensemble learning. We analyze, compare, and discuss the generalization performances regarding time-domain ensemble learning of both a linear model and a nonlinear model. Analyzing in the framework of online learning using a statistical mechanical method, we show the qualitatively different behaviors between the two models. In a linear model, the dynamical behaviors of the generalization error are monotonic. We analytically show that time-domain ensemble learning is twice as effective as conventional ensemble learning. Furthermore, the generalization error of a nonlinear model features nonmonotonic dynamical behaviors when the learning rate is small. We numerically show that the generalization performance can be improved remarkably by using this phenomenon and the divergence of students in the time domain.Comment: 11 pages, 7 figure

Thermal and Electrical Properties of gamma-NaxCoO2 (0.70 < x < 0.78)

We have performed specific heat and electric resistivity measurements of Na$_{x}$CoO$_{2}$ ($x=0.70$-0.78). Two anomalies have been observed in the specific heat data for $x=0.78$, corresponding to magnetic transitions at $T_{c}=22$ K and $T_{k}\simeq 9$ K reported previously. In the electrical resistivity, a steep decrease at $T_{c}$ and a bending-like variation at $T_{b}$(=120K for $x=0.78$) have been observed. Moreover, we have investigated the $x$-dependence of these parameters in detail. The physical properties of this system are very sensitive to $x$, and the inconsistent results of previous reports can be explained by a small difference in $x$. Furthermore, for a higher $x$ value, a phase separation into Na-rich and Na-poor domains occurs as we previously proposed, while for a lower $x$ value, from characteristic behaviors of the specific heat and the electrical resistivity at the low-temperature region, the system is expected to be in the vicinity of the magnetic instability which virtually exists below $x=0.70$.Comment: 4 pages (3 figures included) and an extra figure (gif), to be published in J. Phys. Soc. Jpn. 73 (9) with possible minor revision

Synthesis, Characterization, and Magnetic Properties of gamma-NaxCoO2 (0.70 < x <0.84)

Powder Na$_{x}$CoO$_{2}$ ($0.70\leq x\leq 0.84$) samples were synthesized and characterized carefully by X-ray diffraction analysis, inductive-coupled plasma atomic emission spectroscopy, and redox titration. It was proved that $\gamma$-Na$_{x}$CoO$_{2}$ is formed only in the narrow range of $0.70\leq x\leq 0.78$. Nevertheless, the magnetic properties depend strongly on $x$. We found, for the first time, two characteristic features in the magnetic susceptibility of Na$_{0.78}$CoO$_{2}$, a sharp peak at $T_{p}=16$ K and an anomaly at $T_{k}=9$ K, as well as the transition at $T_{c}=22$ K and the broad maximum at $T_{m}=50$ K which had already been reported. A type of weak ferromagnetic transition seems to occur at $T_{k}$. The transition at $T_{c}$, which is believed to be caused by spin density wave formation, was observed clearly for $x\geq 0.74$ with constant $T_{c}$ and $T_{p}$ independent of $x$. On the other hand, ferromagnetic moment varies systematically depending on $x$. These facts suggest the occurrence of a phase separation at the microscopic level, such as the separation into Na-rich and Na-poor domains due to the segregation of Na ions. The magnetic phase diagram and transition mechanism proposed previously should be reconsidered.Comment: 4 pages (2 figures included) and 2 extra figures (gif), to be published in J. Phys. Soc. Jpn. 73 (8) with possible minor revision

Low energy high angular resolution neutral atom detection by means of micro-shuttering techniques: the BepiColombo SERENA/ELENA sensor

The neutral sensor ELENA (Emitted Low-Energy Neutral Atoms) for the ESA cornerstone BepiColombo mission to Mercury (in the SERENA instrument package) is a new kind of low energetic neutral atoms instrument, mostly devoted to sputtering emission from planetary surfaces, from E ~20 eV up to E~5 keV, within 1-D (2x76 deg). ELENA is a Time-of-Flight (TOF) system, based on oscillating shutter (operated at frequencies up to a 100 kHz) and mechanical gratings: the incoming neutral particles directly impinge upon the entrance with a definite timing (START) and arrive to a STOP detector after a flight path. After a brief dissertation on the achievable scientific objectives, this paper describes the instrument, with the new design techniques approached for the neutral particles identification and the nano-techniques used for designing and manufacturing the nano-structure shuttering core of the ELENA sensor. The expected count-rates, based on the Hermean environment features, are shortly presented and discussed. Such design technologies could be fruitfully exported to different applications for planetary exploration.Comment: 11 page

An alpha theory of time-dependent warped accretion discs

The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is here extended to take proper account of thermal and radiative effects by solving an energy equation that includes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momentum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal-viscous stability of such a disc is also investigated.Comment: 16 pages, 3 figures, to be published in MNRA

Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences

Stimulated by the methods applied for the observational determination of masses in the central regions of the AGNs, we examine the conditions under which, in the interior of a gravitating perfect fluid source, the geodesic motions and the general relativistic hydrodynamic flows are dynamically equivalent to each other. Dynamical equivalence rests on the functional similarity between the corresponding (covariantly expressed) differential equations of motion and is obtained by conformal transformations. In this case, the spaces of the solutions of these two kinds of motion are isomorphic. In other words, given a solution to the problem "hydrodynamic flow in a perfect fluid", one can always construct a solution formally equivalent to the problem "geodesic motion of a fluid element" and vice versa. Accordingly, we show that, the observationally determined nuclear mass of the AGNs is being overestimated with respect to the real, physical one. We evaluate the corresponding mass-excess and show that it is not always negligible with respect to the mass ofthe central dark object, while, under circumstances, can be even larger than the rest-mass of the circumnuclear gas involved.Comment: LaTeX file, 22 page

Meridional Distribution of Middle-Energy Protons and Pressure-Driven Currents in the Nightside Inner Magnetosphere: Arase Observations

We examined the average meridional distribution of middle‐energy protons (10–180 keV) and pressure‐driven currents in the nightside (20–04 hr magnetic local time) ring current region during moderately disturbed times using the Arase satellite\u27s data. Because the Arase satellite has a large inclination orbit of 31°, it covers the magnetic latitude (MLAT) in the range of −40° to 40° and a radial distance of <6RE. We found that the plasma pressure decreased significantly with increasing MLAT. The plasma pressure on the same L* shell at 30° < MLAT < 40° was ∼10–60% of that at 0° < 4 MLAT < 10°, and the rate of decrease was larger on lower L* shells. The pressure anisotropy, derived as the perpendicular pressure divided by the parallel pressure minus 1, decreased with radial distance and showed a weak dependence on MLAT. The magnitude of the plasma beta at 30°<MLAT<40° was 1 or 2 orders smaller than that at 0°<MLAT<10°. The plasma pressure normalized by the value at 0°<MLAT<10° estimated from the magnetic strength and anisotropy was roughly consistent with the observed plasma pressure for L*=3.5–5.5. The azimuthal pressure‐gradient current derived from the plasma pressure was distributed over MLAT∼0–20°, while the curvature current was limited within MLAT∼0–10°. We suggest that the latitudinal dependence should be taken into account in interpretations of plasma parameters in successive orbits during magnetic storms