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

Ensemble learning of linear perceptron; Online learning theory

Within the framework of on-line learning, we study the generalization error of an ensemble learning machine learning from a linear teacher perceptron. The generalization error achieved by an ensemble of linear perceptrons having homogeneous or inhomogeneous initial weight vectors is precisely calculated at the thermodynamic limit of a large number of input elements and shows rich behavior. Our main findings are as follows. For learning with homogeneous initial weight vectors, the generalization error using an infinite number of linear student perceptrons is equal to only half that of a single linear perceptron, and converges with that of the infinite case with O(1/K) for a finite number of K linear perceptrons. For learning with inhomogeneous initial weight vectors, it is advantageous to use an approach of weighted averaging over the output of the linear perceptrons, and we show the conditions under which the optimal weights are constant during the learning process. The optimal weights depend on only correlation of the initial weight vectors.Comment: 14 pages, 3 figures, submitted to Physical Review

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package

Elastic Instabilities within Antiferromagnetically Ordered Phase in the Orbitally-Frustrated Spinel GeCo2_2O4_4

Ultrasound velocity measurements of the orbitally-frustrated GeCo$_2$O$_4$ reveal unusual elastic instabilities due to the phonon-spin coupling within the antiferromagnetic phase. Shear moduli exhibit anomalies arising from the coupling to short-range ferromagnetic excitations. Diplike anomalies in the magnetic-field dependence of elastic moduli reveal magnetic-field-induced orbital order-order transitions. These results strongly suggest the presence of geometrical orbital frustration which causes novel orbital phenomena within the antiferromagnetic phase.Comment: 5 pages, 3 figure

The Economic Footprint of the Rosen College of Hospitality Management in the Metro Orlando Area

The report documents the economic value of the Rosen College of Hospitality Management (RCHM) to the Metro Orlando area. The purpose of estimating the economic value of the program is to calculate the increased economic activities in the Metro Orlando area as generated by college degree attainment through the RCHM. The report is the result of an assignment commissioned by the Dean of the RCHM. The report assessed the economic impact of the alumni of the College during the period from 2000 to 2012. In that period, more than 5,000 students earned a degree either at the undergraduate or graduate level. The College was able to steadily increase the graduation growth rate, albeit at a slower pace since 2010. The report is premised on a broad focus of the potential economic impact of alumni from the RCHM, i.e., the earned wage when integrated in the labor market. The report did not consider the productivity that college degree holders could spawn in the economy; nor did the report contemplate the social return of higher education. The report follows an economic based approach by only considering the direct and indirect economic effects that the expenditures associated with the wage differentials infuse into the Metro Orlando area\u27s economy. It treats the RCHM like any other firm sans consideration for any spillover effects that higher education may have on a region. The total economic contribution of the College alumni surpassed $531 million. This amount was triggered by the graduate wage totaling$322 million over the period reviewed, which generated spillover effects in terms of $96 million in business transactions of goods and services and$113 million in increased households\u27 income. Additionally, the RCHM also supplies an economically valuable source of labor to the market in the form of interns. Based on the available data, the total economic value of RCHM interns in 2012 was estimated at $17,189,647. The total economic contribution of the RCHM in 2012 (graduates and interns taken together) amounted to$69,263,647. This amount includes $52,074,000 that stems from 789 graduates and 2,676 RCHM internship students that work on average 25.1 labor hours per week as interns. The value of the RCHM is clearly manifested in the sizeable amount of graduates, interns supplying the labor market, the high number of degree attainment and the commensurate economic contribution of the alumni to the Metro Orlando area (Orange, Osceola and Seminole counties)

Hinode EUV Imaging Spectrometer Observations of Solar Active Region Dynamics

The EUV Imaging Spectrometer (EIS) on the Hinode satellite is capable of measuring emission line center positions for Gaussian line profiles to a fraction of a spectral pixel, resulting in relative solar Doppler-shift measurements with an accuracy of less than a km/s for strong lines. We show an example of the application of that capability to an active region sit-and-stare observation in which the EIS slit is placed at one location on the Sun and many exposures are taken while the spacecraft tracking keeps the same solar location within the slit. For the active region examined (NOAA 10930), we find that significant intensity and Doppler-shift fluctuations as a function of time are present at a number of locations. These fluctuations appear to be similar to those observed in high-temperature emission lines with other space-borne spectroscopic instruments. With its increased sensitivity over earlier spectrometers and its ability to image many emission lines simultaneously, EIS should provide significant new constraints on Doppler-shift oscillations in the corona.Comment: 7 Pages, 7 figure

Transition region features observed with Hinode/EIS

Two types of active region feature prominent at transition region temperatures are identified in Hinode/EIS data of AR 10938 taken on 2007 January 20. The footpoints of 1 MK TRACE loops are shown to emit strongly in emission lines formed at log T=5.4-5.8, allowing the temperature increase along the footpoints to be clearly seen. A density diagnostic of Mg VII yields the density in the footpoints, with one loop showing a decrease from 3x10^9 cm^-3 at the base to 1.5x10^9 cm^-3 at a projected height of 20 Mm. The second feature is a compact active region transition region brightening which is particularly intense in O V emission (log T=5.4) but also has a signature at temperatures up to log T=6.3. The Mg VII diagnostic gives a density of 4x10^10 cm^-3, and emission lines of Mg VI and Mg VII show line profiles broadened by 50 km/s and wings extending beyond 200 km/s. Continuum emission in the short wavelength band is also found to be enhanced, and is suggested to be free-bound emission from recombination onto He^+.Comment: 11 pages, 9 figures, submitted to PASJ Hinode first results issu

Observation and Modeling of Coronal "Moss" With the EUV Imaging Spectrometer on Hinode

Observations of transition region emission in solar active regions represent a powerful tool for determining the properties of hot coronal loops. In this Letter we present the analysis of new observations of active region moss taken with the Extreme Ultraviolet Imaging Spectrometer (EIS) on the \textit{Hinode} mission. We find that the intensities predicted by steady, uniformly heated loop models are too intense relative to the observations, consistent with previous work. To bring the model into agreement with the observations a filling factor of about 16% is required. Furthermore, our analysis indicates that the filling factor in the moss is nonuniform and varies inversely with the loop pressure

Theoretical study of the (3x2) reconstruction of beta-SiC(001)

By means of ab initio molecular dynamics and band structure calculations, as well as using calculated STM images, we have singled out one structural model for the (3x2) reconstruction of the Si-terminated (001) surface of cubic SiC, amongst several proposed in the literature. This is an alternate dimer-row model, with an excess Si coverage of 1/3, yielding STM images in good accord with recent measurements [F.Semond et al. Phys. Rev. Lett. 77, 2013 (1996)].Comment: To be published in PRB Rapid. Com