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

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

Adhesion, friction, and wear of plasma-deposited thin silicon nitride films at temperatures to 700 C

The adhesion, friction, and wear behavior of silicon nitride films deposited by low- and high-frequency plasmas (30 kHz and 13.56 MHz) at various temperatures to 700 C in vacuum were examined. The results of the investigation indicated that the Si/N ratios were much greater for the films deposited at 13.56 MHz than for those deposited at 30 kHz. Amorphous silicon was present in both low- and high-frequency plasma-deposited silicon nitride films. However, more amorphous silicon occurred in the films deposited at 13.56 MHz than in those deposited at 30 kHz. Temperature significantly influenced adhesion, friction, and wear of the silicon nitride films. Wear occurred in the contact area at high temperature. The wear correlated with the increase in adhesion and friction for the low- and high-frequency plasma-deposited films above 600 and 500 C, respectively. The low- and high-frequency plasma-deposited thin silicon nitride films exhibited a capability for lubrication (low adhesion and friction) in vacuum at temperatures to 500 and 400 C, respectively

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

Analysis of ensemble learning using simple perceptrons based on online learning theory

Ensemble learning of $K$ nonlinear perceptrons, which determine their outputs by sign functions, is discussed within the framework of online learning and statistical mechanics. One purpose of statistical learning theory is to theoretically obtain the generalization error. This paper shows that ensemble generalization error can be calculated by using two order parameters, that is, the similarity between a teacher and a student, and the similarity among students. The differential equations that describe the dynamical behaviors of these order parameters are derived in the case of general learning rules. The concrete forms of these differential equations are derived analytically in the cases of three well-known rules: Hebbian learning, perceptron learning and AdaTron learning. Ensemble generalization errors of these three rules are calculated by using the results determined by solving their differential equations. As a result, these three rules show different characteristics in their affinity for ensemble learning, that is ``maintaining variety among students." Results show that AdaTron learning is superior to the other two rules with respect to that affinity.Comment: 30 pages, 17 figure

Fluctuation theorem applied to Dictyostelium discoideum system

In this paper, we analyze the electrotactic movement of Dictyostelium discoideum from the viewpoint of non-equilibrium statistical mechanics. Because we can observe fluctuating behavior of cellular trajectories, we analyze the probability distribution of the trajectories with the aid of the fluctuation theorem. Recently, the validity of the fluctuation theorem was verified in a colloidal system, and it has also been applied to granular systems, turbulent systems and chemical oscillatory waves to investigate some of their statistical properties that are not yet completely understood. Noting that the fluctuation theorem is potentially applicable to cellular electrotaxis, here we employ it to help us obtain a phenomenological model of this biological system.Comment: 2 pages, to appear in J. Phys. Soc. Jp

Electron Power-Law Spectra in Solar and Space Plasmas

Particles are accelerated to very high, non-thermal energies in solar and space plasma environments. While energy spectra of accelerated electrons often exhibit a power law, it remains unclear how electrons are accelerated to high energies and what processes determine the power-law index $\delta$. Here, we review previous observations of the power-law index $\delta$ in a variety of different plasma environments with a particular focus on sub-relativistic electrons. It appears that in regions more closely related to magnetic reconnection (such as the `above-the-looptop' solar hard X-ray source and the plasma sheet in Earth's magnetotail), the spectra are typically soft ($\delta \gtrsim$ 4). This is in contrast to the typically hard spectra ($\delta \lesssim$ 4) that are observed in coincidence with shocks. The difference implies that shocks are more efficient in producing a larger non-thermal fraction of electron energies when compared to magnetic reconnection. A caveat is that during active times in Earth's magnetotail, $\delta$ values seem spatially uniform in the plasma sheet, while power-law distributions still exist even in quiet times. The role of magnetotail reconnection in the electron power-law formation could therefore be confounded with these background conditions. Because different regions have been studied with different instrumentations and methodologies, we point out a need for more systematic and coordinated studies of power-law distributions for a better understanding of possible scaling laws in particle acceleration as well as their universality.Comment: 67 pages, 15 figures; submitted to Space Science Reviews; comments welcom

A 4% Geometric Distance to the Galaxy NGC4258 from Orbital Motions in a Nuclear Gas Disk

The water maser in the mildly active nucleus in the nearby galaxy NGC4258 traces a thin, nearly edge-on, subparsec-scale Keplerian disk. Using the technique of very long baseline interferometry, we have detected the proper motions of these masers as they sweep in front of the central black hole at an orbital velocity of about 1100 km/s. The average maser proper motion of 31.5 microarcseconds per year is used in conjunction with the observed acceleration of the masers to derive a purely geometric distance to the galaxy of 7.2 +- 0.3 Mpc. This is the most precise extragalactic distance measured to date, and, being independent of all other distance indicators, is likely to play an important role in calibrating the extragalactic distance scale.Comment: 11 pages, 3 figures. Accepted for publication in Natur

Asymmetry in the Spectrum of High-Velocity H2O Maser Emission Features in Active Galactic Nuclei

We suggest a mechanism for the amplification of high-velocity water-vapor maser emission features from the central regions of active galactic nuclei. The model of an emitting accretion disk is considered. The high-velocity emission features originate in the right and left wings of the Keplerian disk. The hyperfine splitting of the signal levels leads to an asymmetry in the spectral profile of the water vapor maser line at a frequency of 22.235 GHz. We show that the gain profile asymmetry must lead to an enhanced brightness of the blueshifted high-velocity emission features compared to the redshifted ones. Such a situation is observed in the source UGC 3789.Comment: 11 pages 3 figure

Athena: A New Code for Astrophysical MHD

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume-averages for mass, momentum, and energy, and face-centered area-averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally-split time advance, and (3) the extension to MHD of two different dimensionally-unsplit integration methods. Implementation of the algorithm in both C and Fortran95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.Comment: 61 pages, 36 figures. accepted by ApJ