Statistical Mechanics of Nonlinear On-line Learning for Ensemble Teachers

We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using statistical mechanics in the framework of on-line learning. We treat two well-known learning rules: Hebbian learning and perceptron learning. As a result, it is proven that the nonlinear model shows qualitatively different behaviors from the linear model. Moreover, it is clarified that Hebbian learning and perceptron learning show qualitatively different behaviors from each other. In Hebbian learning, we can analytically obtain the solutions. In this case, the generalization error monotonically decreases. The steady value of the generalization error is independent of the learning rate. The larger the number of teachers is and the more variety the ensemble teachers have, the smaller the generalization error is. In perceptron learning, we have to numerically obtain the solutions. In this case, the dynamical behaviors of the generalization error are non-monotonic. The smaller the learning rate is, the larger the number of teachers is; and the more variety the ensemble teachers have, the smaller the minimum value of the generalization error is.Comment: 13 pages, 9 figure

Tribological properties of sintered polycrystalline and single crystal silicon carbide

Tribological studies and X-ray photoelectron spectroscopy analyses were conducted with sintered polycrystalline and single crystal silicon carbide surfaces in sliding contact with iron at various temperatures to 1500 C in a vacuum of 30 nPa. The results indicate that there is a significant temperature influence on both the friction properties and the surface chemistry of silicon carbide. The main contaminants on the as received sintered polycrystalline silicon carbide surfaces are adsorbed carbon, oxygen, graphite, and silicon dioxide. The surface revealed a low coefficient of friction. This is due to the presence of the graphite on the surface. At temperatures of 400 to 600 C graphite and copious amount of silicon dioxide were observed on the polycrystalline silicon carbide surface in addition to silicon carbide. At 800 C, the amount of the silicon dioxide decreased rapidly and the silicon carbide type silicon and carbon peaks were at a maximum intensity in the XPS spectra. The coefficients of friction were high in the temperature range 400 to 800 C. Small amounts of carbon and oxygen contaminants were observed on the as received single crystal silicon carbide surface below 250 C. Silicon carbide type silicon and carbon peaks were seen on the silicon carbide in addition to very small amount of graphite and silicon dioxide at temperatures of 450 to 800 C

On-line Learning of an Unlearnable True Teacher through Mobile Ensemble Teachers

On-line learning of a hierarchical learning model is studied by a method from statistical mechanics. In our model a student of a simple perceptron learns from not a true teacher directly, but ensemble teachers who learn from the true teacher with a perceptron learning rule. Since the true teacher and the ensemble teachers are expressed as non-monotonic perceptron and simple ones, respectively, the ensemble teachers go around the unlearnable true teacher with the distance between them fixed in an asymptotic steady state. The generalization performance of the student is shown to exceed that of the ensemble teachers in a transient state, as was shown in similar ensemble-teachers models. Further, it is found that moving the ensemble teachers even in the steady state, in contrast to the fixed ensemble teachers, is efficient for the performance of the student.Comment: 18 pages, 8 figure

Oscillation Phenomena in the disk around the massive black hole Sagittarius A*

We report the detection of radio QPOs with structure changes using the Very Long Baseline Array (VLBA) at 43 GHz. We found conspicuous patterned changes of the structure with P = 16.8 +- 1.4, 22.2 +- 1.4, 31.2 +- 1.5, 56.4 +- 6 min, very roughly in a 3:4:6:10 ratio. The first two periods show a rotating one-arm structure, while the P = 31.4 min shows a rotating 3-arm structure, as if viewed edge-on. At the central 50 microasec the P = 56.4 min period shows a double amplitude variation of those in its surroundings. Spatial distributions of the oscillation periods suggest that the disk of SgrA* is roughly edge-on, rotating around an axis with PA = -10 degree. Presumably, the observed VLBI images of SgrA* at 43 GHz retain several features of the black hole accretion disk of SgrA* in spite of being obscured and broadened by scattering of surrounding plasma.Comment: 24 pages, 20 figures, revised version submitted to MN main journal (2010, Jan., 12th

A Measurement of Proper Motions of SiO Maser Sources in the Galactic Center with the VLBA

We report on the high-precision astrometric observations of maser sources around the Galactic Center in the SiO J=1--0 v=1 and 2 lines with the VLBA during 2001 -- 2004. With phase-referencing interferometry referred to the radio continuum source Sgr A*, accurate positions of masers were obtained for three detected objects: IRS 10 EE (7 epochs), IRS 15NE (2 epochs), and SiO 6 (only 1 epoch). Because circumstellar masers of these objects were resolved into several components, proper motions for the maser sources were derived with several different methods. Combining our VLBA results with those of the previous VLA observations, we obtained the IRS 10EE proper motion of 76+-3 km s^{-1} (at 8 kpc) to the south relative to Sgr A*. Almost null proper motion of this star in the east--west direction results in a net transverse motion of the infrared reference frame of about 30+-9 km s^{-1} to the west relative to Sgr A*. The proper-motion data also suggests that IRS 10EE is an astrometric binary with an unseen massive companion.Comment: High-res. figures are available at ftp://ftp.nro.nao.ac.jp/nroreport/no656.pdf.gz . PASJ 60, No. 1 (2008) in pres

Magnetic and Electronic Properties of Lix_xCoO2_2 Single Crystals

Measurements of electrical resistivity ($\rho$), DC magnetization ($M$) and specific heat ($C$) have been performed on layered oxide Li$_x$CoO$_2$ (0.25$\leq$$x$$\leq$0.99) using single crystal specimens. The $\rho$ versus temperature ($T$) curve for $x$=0.90 and 0.99 is found to be insulating but a metallic behavior is observed for 0.25$\leq$$x$$\leq$0.71. At $T_{\rm S}$$\sim$155 K, a sharp anomaly is observed in the $\rho$$-$$T$, $M$$-$$T$ and $C$$/$$T$$-$$T$ curves for $x$=0.66 with thermal hysteresis, indicating the first-order charactor of the transition. The transition at $T_{\rm S}$$\sim$155 K is observed for the wide range of $x$=0.46$-$0.71. It is found that the $M$$-$$T$ curve measured after rapid cool becomes different from that after slow cool below $T_{\rm F}$, which is $\sim$130 K for $x$=0.46$-$0.71. $T_{\rm F}$ is found to agree with the temperature at which the motional narrowing in the $^7$Li NMR line width is observed, indicating that the Li ions stop diffusing and order at the regular site below $T_{\rm F}$. The ordering of Li ions below $T_{\rm F}$$\sim$130 K is likely to be triggered and stabilized by the charge ordering in CoO$_2$ layers below $T_{\rm S}$.Comment: 8 pages, 7 figure

Distance of W3(OH) by VLBI annual parallax measurement

The most powerful tool for measuring distances within our Galaxy is the annual parallax. We carried out phase-referencing VLBI observations of H$_{2}$O masers in the star forming region W3(OH) with respect to the extragalactic continuum source ICRF 0244+624 to measure their absolute proper motions. The measured annual parallax is 0.484 $\pm$ 0.004 milli-arcseconds which corresponds to a distance of 2.07^{+0.01}_{-0.02}$ kpc from the sun. This distance is consistent with photometric and kinematic distances from previous observations.Comment: Proceedings of the 7th European VLBI Network Symposium (October 12-15 2004, Toledo, Spain), eds. Bachiller, R., Colomer, F., Desmurs, J. F., & de Vicente, P., 4 pages, 4 figures, needs evn2004.cl

Origin of non-keplerian motions of masers in NGC 1068

We demonstrate that the ``sub-keplerian'' rotation curve of maser spots in NGC 1068 can be explained by the gravitational attraction of the disc orbiting the central black hole. Possible parameters matching observations are: black hole mass of 12 million solar masses, disc outer edge > 1.3 pc, aspect ratio in the range 0.003 to 0.3, surface density varying approximately as 1/R, and disc mass of about 9.4 million solar masses. The physical conditions required for the excitation of masers are fulfilled, and the outer disc would stand in a gravitationally marginally stable state.Comment: 4 pages; accepted in A&A Letter