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

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

Prediction of crude fat content of longissimus muscle of beef using the ratio of fat area calculated from computer image analysis: Comparison of regression equations for prediction using different input devices at different stations

Crude fat content of longissimus (ribeye) muscle of beef cattle was predicted from a ratio of fat area (RFA) to area of ribeye muscle calculated from computer image analysis (CIA). Cross sections of 64 ribeyes taken from the 6–7th rib from cattle at experiment station A and cross sections of 94 ribeyes taken from the 6–7th rib from cattle at Experiment Station B were used in this study. Slices (1 to 1.5 cm in thickness) of just the Longissimus dorsi were homogenized and sampled for chemical estimation of crude fat content using petroleum ether. Crude fat content as determined from chemical analysis was used as the true estimate of fat content. A CCD (charge-coupled device) camera was used as the input device at Experiment Station A, and a single-lens reflex camera was used at Experiment Station B to photograph ribeyes for CIA. The contour comparison method, which assigns a threshold value for each marbling particle, was used to obtain accurate binarization in this study. Minimum and maximum of chemical measurements of crude fat were 2.1 and 39.8%, and for CIA calculation of the RFA were 6.1 and 56.8%, respectively. This range covered almost the complete range of the beef marbling standard used in carcass grading in Japan. The equation for the regression of the crude fat content (Y) on RFA (X) calculated from CIA for all of the data was Y = .793X − 3.04 with r2 = .96. Regression equations for prediction of crude fat percentage from RFA taking into consideration the effect of experiment station were Y = .741X − 2.22 with r2 = .91 for Experiment Station A, and Y = .782X − 2.54 with r2 = .91 for Experiment Station B. Analysis of covariance showed that the effects of experiment stations on intercepts and slopes were not significant (P \u3e .10). The ranges of differences between actual and predicted crude fat content from the prediction equation that was calculated without consideration of the effect of station were − 6.4 to 4.0%. CIA of cross sections of the ribeye muscle seems to have potential for prediction of crude fat content

Prediction of crude fat content of longissimus muscle of beef using the ratio of fat area calculated from computer image analysis: Comparison of regression equations for prediction using different input devices at different stations

Crude fat content of longissimus (ribeye) muscle of beef cattle was predicted from a ratio of fat area (RFA) to area of ribeye muscle calculated from computer image analysis (CIA). Cross sections of 64 ribeyes taken from the 6–7th rib from cattle at experiment station A and cross sections of 94 ribeyes taken from the 6–7th rib from cattle at Experiment Station B were used in this study. Slices (1 to 1.5 cm in thickness) of just the Longissimus dorsi were homogenized and sampled for chemical estimation of crude fat content using petroleum ether. Crude fat content as determined from chemical analysis was used as the true estimate of fat content. A CCD (charge-coupled device) camera was used as the input device at Experiment Station A, and a single-lens reflex camera was used at Experiment Station B to photograph ribeyes for CIA. The contour comparison method, which assigns a threshold value for each marbling particle, was used to obtain accurate binarization in this study. Minimum and maximum of chemical measurements of crude fat were 2.1 and 39.8%, and for CIA calculation of the RFA were 6.1 and 56.8%, respectively. This range covered almost the complete range of the beef marbling standard used in carcass grading in Japan. The equation for the regression of the crude fat content (Y) on RFA (X) calculated from CIA for all of the data was Y = .793X − 3.04 with r2 = .96. Regression equations for prediction of crude fat percentage from RFA taking into consideration the effect of experiment station were Y = .741X − 2.22 with r2 = .91 for Experiment Station A, and Y = .782X − 2.54 with r2 = .91 for Experiment Station B. Analysis of covariance showed that the effects of experiment stations on intercepts and slopes were not significant (P \u3e .10). The ranges of differences between actual and predicted crude fat content from the prediction equation that was calculated without consideration of the effect of station were − 6.4 to 4.0%. CIA of cross sections of the ribeye muscle seems to have potential for prediction of crude fat content

Data assimilation insights on selecting the most valuable atmospheric measurements

We discuss how objective guidance on selecting the most valuable atmospheric measurements on future Mars spacecraft missions can be provided through already developed Martian atmospheric data assimilation systems, and in particular through Observing System Simulation Experiments (OSSEs) which are widely used to design instruments for the Earth’s atmosphere

Primordial fractal density perturbations and structure formation in the Universe: 1-Dimensional collisionless sheet model

Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze the time evolution of fractal density perturbations in Einstein-de Sitter universe, and study how the perturbation evolves and what kind of nonlinear structure will come out. We assume a one-dimensional collisionless sheet model with initial Cantor-type fractal perturbations. The nonlinear structure seems to approach some attractor with a unique fractal dimension, which is independent of the fractal dimensions of initial perturbations. A discrete self-similarity in the phase space is also found when the universal nonlinear fractal structure is reached.Comment: 17 pages, 19 jpeg figures. Accepted for publication in ApJ. Figures are also available from http://www.phys.waseda.ac.jp/gravity/~tatekawa/0003124/figs.tar.g

Erosion Coatings Developed to Increase the Life and Durability of Composites

Both the NASA Glenn Research Center and the Allison Advanced Development Company (AADC) have worked to develop and demonstrate erosion-resistant coatings that would increase the life and durability of composite materials used in commercial aircraft engines. These composite materials reduce component weight by 20 to 30 percent and result in less fuel burn and emissions and more fuel savings. Previously, however, their use was limited because of poor erosion resistance, which causes concerns about safety and leads to high maintenance costs. The coatings were tested by the University of Cincinnati, and the composites were manufactured by Texas Composites and coated by Engelhard and NASA Glenn. Rolls-Royce Corporation uses composite materials, which are stronger and less dense than steel or titanium, to make bypass vanes for their AE3007 engines. These engines are widely used in regional jet aircraft (Embraer) and unmanned air vehicles such as the Northrop Grumman Global Hawk. Coatings developed by NASA/Rolls-Royce can reduce erosion from abrasive materials and from impurities in the air that pass over these vanes, allowing Rolls-Royce to take advantage of the benefits of composite materials over titanium without the added costs of increased maintenance and/or engine failure. The Higher Operating Temperature Propulsion Components (HOTPC) Project developed cost-effective, durable coatings as part of NASA's goal to increase aviation system capacity growth. These erosion coatings will reduce the number of special inspections or instances of discontinued service due to erosion, allowing aircraft capacity to be maintained without inconveniencing the traveling public. A specific example of extending component life showed that these coatings increased the life of graphite fiber and polymer composite bypass vanes up to 8 times over that of the uncoated vanes. This increased durability allows components to operate to full design life without the fear of wear or failure. Recently, Rolls-Royce completed over 2000 hr of engine testing with the coated fan exit bypass vanes. There was no loss of coating after nearly 5000 typical engine cycles. Midway through the engine tests, the coated vanes were removed from the engine during a scheduled maintenance and inspection period. The vanes were shipped back to Glenn, where they underwent further stress testing in the Structural Dynamics Lab, mimicking more extreme conditions than those typical of the AE3007 engine cycle. These vanes were then replaced in the AE3007 and subjected to another 1000 hr of engine tests. Once again, there was no loss of coating and only a minimal appearance of cracking

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

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