13,709 research outputs found
Triaxial projected shell model approach
The projected shell model analysis is carried out using the triaxial
Nilsson+BCS basis. It is demonstrated that, for an accurate description of the
moments of inertia in the transitional region, it is necessary to take the
triaxiality into account and perform the three-dimensional angular-momentum
projection from the triaxial Nilsson+BCS intrinsic wavefunction.Comment: 9 pages, 2 figure
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
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
Dual-camera system for high-speed imaging in particle image velocimetry
Particle image velocimetry is an important technique in experimental fluid
mechanics, for which it has been essential to use a specialized high-speed
camera. However, the high speed is at the expense of other performances of the
camera, i.e., sensitivity and image resolution. Here, we demonstrate that the
high-speed imaging is also possible with a pair of still cameras.Comment: 4 pages, accepted by Journal of Visualization (see
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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
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