NARX-based nonlinear system identification using orthogonal least squares basis hunting

An orthogonal least squares technique for basis hunting (OLS-BH) is proposed to construct sparse radial basis function (RBF) models for NARX-type nonlinear systems. Unlike most of the existing RBF or kernel modelling methods, whichplaces the RBF or kernel centers at the training input data points and use a fixed common variance for all the regressors, the proposed OLS-BH technique tunes the RBF center and diagonal covariance matrix of individual regressor by minimizing the training mean square error. An efficient optimization method isadopted for this basis hunting to select regressors in an orthogonal forward selection procedure. Experimental results obtained using this OLS-BH technique demonstrate that it offers a state-of-the-art method for constructing parsimonious RBF models with excellent generalization performance

Normalized Ricci flow on Riemann surfaces and determinants of Laplacian

In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under the action of the normalized Ricci flow the smooth metric tends asymptotically to metric of constant curvature for $g\geq 1$, this leads to a simple proof of Osgood-Phillips-Sarnak theorem stating that that within the class of smooth metrics with fixed conformal class and fixed volume the determinant of Laplace operator is maximal on metric of constant curvatute.Comment: a reference to paper math.DG/9904048 by W.Mueller and K.Wendland where the main theorem of this paper was proved a few years earlier is adde

Uniqueness and examples of compact toric Sasaki-Einstein metrics

In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.Comment: Statements of the results are modifie

Properties and Performance of Two Wide Field of View Cherenkov/Fluorescence Telescope Array Prototypes

A wide field of view Cherenkov/fluorescence telescope array is one of the main components of the Large High Altitude Air Shower Observatory project. To serve as Cherenkov and fluorescence detectors, a flexible and mobile design is adopted for easy reconfiguring of the telescope array. Two prototype telescopes have been constructed and successfully run at the site of the ARGO-YBJ experiment in Tibet. The features and performance of the telescopes are presented

Charge ordering in charge-compensated Na0.41CoO2Na_{0.41}CoO_2 by oxonium ions

Charge ordering behavior is observed in the crystal prepared through the immersion of the $Na_{0.41}CoO_2$ crystal in distilled water. Discovery of the charge ordering in the crystal with Na content less than 0.5 indicates that the immersion in water brings about the reduction of the $Na_{0.41}CoO_2$. The formal valence of Co changes from +3.59 estimated from the Na content to +3.5, the same as that in $Na_{0.5}CoO_2$. The charge compensation is confirmed to arise from the intercalation of the oxonium ions as occurred in the superconducting sodium cobalt oxide bilayer-hydrate.\cite{takada1} The charge ordering is the same as that observed in $Na_{0.5}CoO_2$. It suggests that the Co valence of +3.5 is necessary for the charge ordering.Comment: 5 pages, 4 figure

The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension

The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has been the subject of intensive study over the last few decades, following Yau's solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton has become one of the most powerful tools in geometric analysis. We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical is a generalized K\"ahler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for K\"aher surfaces with a numerical effective canonical line bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding canonical metrics on canonical models of projective varieties of positive Kodaira dimension

Surface structure and solidification morphology of aluminum nanoclusters

Classical molecular dynamics simulation with embedded atom method potential had been performed to investigate the surface structure and solidification morphology of aluminum nanoclusters Aln (n = 256, 604, 1220 and 2048). It is found that Al cluster surfaces are comprised of (111) and (001) crystal planes. (110) crystal plane is not found on Al cluster surfaces in our simulation. On the surfaces of smaller Al clusters (n = 256 and 604), (111) crystal planes are dominant. On larger Al clusters (n = 1220 and 2048), (111) planes are still dominant but (001) planes can not be neglected. Atomic density on cluster (111)/(001) surface is smaller/larger than the corresponding value on bulk surface. Computational analysis on total surface area and surface energies indicates that the total surface energy of an ideal Al nanocluster has the minimum value when (001) planes occupy 25% of the total surface area. We predict that a melted Al cluster will be a truncated octahedron after equilibrium solidification.Comment: 22 pages, 6 figures, 34 reference