L2L_2 boosting in kernel regression

In this paper, we investigate the theoretical and empirical properties of $L_2$ boosting with kernel regression estimates as weak learners. We show that each step of $L_2$ boosting reduces the bias of the estimate by two orders of magnitude, while it does not deteriorate the order of the variance. We illustrate the theoretical findings by some simulated examples. Also, we demonstrate that $L_2$ boosting is superior to the use of higher-order kernels, which is a well-known method of reducing the bias of the kernel estimate.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ160 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Exact Ground-State Energy of the Ising Spin Glass on Strips

We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for complex values of the probability describing quenched randomness. We study the $\pm J$ and the site-random models using this method for strips of various sizes up to $5\times\infty$. The ground-state energy of these models is found to have singular points in the complex-probability plane, reminiscent of Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The $\pm J$ Ising model has a series of singularities which may approach a limiting point around $p \sim 0.9$ on the real axis in the limit of infinite width.Comment: 10 pages, 12 Postscript figures, LaTeX, uses subeqn.sty, minor changes in tex-fil

Cosmic String Spacetime in Dilaton Gravity and Flat Rotation Curves

In dilaton gravity theories, we consider a string-like topological defect formed during U(1) gauge symmetry-breaking phase transition in the early Universe, and far from the cosmic string we have vacuum solutions of the generalized Einstein equation. We discuss how they can be related to the flatness of galactic rotation curves.Comment: 9 pages, RevTeX4 fil

Novel Synthesis and High Pressure Behavior of Na0.3CoO2 x 1.3 H2O and Related Phases

We have prepared powder samples of NaxCoO2 x yH2O using a new synthesis route. Superconductivity was observed in Na0.3CoO2 x 1.3H2O between 4 and 5K as indicated by the magnetic susceptibility. The bulk compressibilities of Na0.3CoO2 x 1.3H2O, Na0.3CoO2 x 0.6H2O and Na0.3CoO2 were determined using a diamond anvil cell and synchrotron powder diffraction. Chemical changes occurring under pressure when using different pressure transmitting media are discussed and further transport measurements are advocated.Comment: 7 pages, 4 figures, PRrapid submitte