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 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

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 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

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

An extracellular serine protease produced by Vibrio vulnificus NCIMB 2137, a metalloprotease-gene negative strain isolated from a diseased eel

Vibrio vulnificus is a ubiquitous estuarine microorganism but causes fatal systemic infections in immunocompromised humans, cultured eels or shrimps. An extracellular metalloprotease VVP/VvpE has been reported to be a potential virulence factor of the bacterium; however, a few strains isolated from a diseased eel or shrimp were recently found to produce a serine protease termed VvsA, but not VVP/VvpE. In the present study, we found that these strains had lost the 80 kb genomic region including the gene encoding VVP/VvpE. We also purified VvsA from the culture supernatant through ammonium sulfate fractionation, gel filtration and ion-exchange column chromatography, and the enzyme was demonstrated to be a chymotrypsin-like protease, as well as those from some vibrios. The gene vvsA was shown to constitute an operon with a downstream gene vvsB, and several Vibrio species were found to have orthologues of vvsAB. These findings indicate that the genes vvp/vvpE and vvsAB might be mobile genetic elements

Optimization of the Asymptotic Property of Mutual Learning Involving an Integration Mechanism of Ensemble Learning

We propose an optimization method of mutual learning which converges into the identical state of optimum ensemble learning within the framework of on-line learning, and have analyzed its asymptotic property through the statistical mechanics method.The proposed model consists of two learning steps: two students independently learn from a teacher, and then the students learn from each other through the mutual learning. In mutual learning, students learn from each other and the generalization error is improved even if the teacher has not taken part in the mutual learning. However, in the case of different initial overlaps(direction cosine) between teacher and students, a student with a larger initial overlap tends to have a larger generalization error than that of before the mutual learning. To overcome this problem, our proposed optimization method of mutual learning optimizes the step sizes of two students to minimize the asymptotic property of the generalization error. Consequently, the optimized mutual learning converges to a generalization error identical to that of the optimal ensemble learning. In addition, we show the relationship between the optimum step size of the mutual learning and the integration mechanism of the ensemble learning.Comment: 13 pages, 3 figures, submitted to Journal of Physical Society of Japa

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

Southward propagating auroral structure in meso-micro scale obtained from ground-based multiple observations at Poker Flat Research Range

第3回極域科学シンポジウム/第36回極域宙空圏シンポジウム 11月26日（月）、27日（火） 国立極地研究所 2階ラウン

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