A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination

By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks

Pentaquark baryons in SU(3) quark model

We study the SU(3) group structure of pentaquark baryons which are made of four quarks and one antiquark. The pentaquark baryons form {1}, {8}, {10}, {10}-bar, {27}, and {35} multiplets in SU(3) quark model. First, the flavor wave functions of all the pentaquark baryons are constructed in SU(3) quark model and then the flavor SU(3) symmetry relations for the interactions of the pentaquarks with three-quark baryons and pentaquark baryons are obtained.Comment: REVTeX, 36 pages, 8 figures, references added, section for mass sum rules is added, to appear in Phys. Rev.

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-

OGLE-2013-BLG-0102LA,B: Microlensing binary with components at star/brown-dwarf and brown-dwarf/planet boundaries

We present the analysis of the gravitational microlensing event OGLE-2013-BLG-0102. The light curve of the event is characterized by a strong short-term anomaly superposed on a smoothly varying lensing curve with a moderate magnification $A_{\rm max}\sim 1.5$. It is found that the event was produced by a binary lens with a mass ratio between the components of $q = 0.13$ and the anomaly was caused by the passage of the source trajectory over a caustic located away from the barycenter of the binary. From the analysis of the effects on the light curve due to the finite size of the source and the parallactic motion of the Earth, the physical parameters of the lens system are determined. The measured masses of the lens components are $M_{1} = 0.096 \pm 0.013~M_{\odot}$ and $M_{2} = 0.012 \pm 0.002~M_{\odot}$, which correspond to near the hydrogen-burning and deuterium-burning mass limits, respectively. The distance to the lens is $3.04 \pm 0.31~{\rm kpc}$ and the projected separation between the lens components is $0.80 \pm 0.08~{\rm AU}$.Comment: 6 figures, 2 tables, ApJ submitte

Study of B -> \rho \pi decays at Belle

This paper describes a study of B meson decays to the pseudoscalar-vector final state \rho\pi using 31.9\times 10^6 B\bar{B} events collected with the Belle detector at KEKB. The branching fractions B(B^+ \to \rho^0\pi^+) = (8.0^{+2.3+0.7}_{-2.0-0.7}) \times 10^{-6} and B(B^0 -> \rho^{+-} \pi^{-+}) = (20.8^{+6.0+2.8}_{-6.3-3.1}) \times 10^{-6} are obtained. In addition, a 90% confidence level upper limit of B(B^0 \to \rho^0\pi^0) < 5.3 \times 10^{-6}is reported.Comment: 14 pages, 3 figures, to be submitted to Phys. Lett.

Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices

We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W=X^T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value =N/c decreases for large N as $\sim \exp[-\frac{\beta}{2}N^2 \Phi_{-}(\frac{2}{\sqrt{c}}+1;c)]$, where \beta=1,2 correspond respectively to real and complex Wishart matrices, c=N/M < 1 and \Phi_{-}(x;c) is a large deviation function that we compute explicitly. The result for the Anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of constrained Wishart matrices whose eigenvalues are forced to be smaller than a fixed barrier. The numerical simulations are in excellent agreement with the analytical predictions.Comment: Published version. References and appendix adde

Search for the Lepton-Flavor-Violating Decay τ−→μ−η\tau^- \to \mu^- \eta at Belle

We have searched for the Lepton Flavor Violating decay $\tau^- \to \mu^- \eta$ using a data sample of 84.3 fb$^{-1}$ accumulated with the Belle detector at KEK. The $\eta$-meson was detected through the decay modes: $\eta \to \gamma\gamma$ and $\pi^+\pi^-\pi^0$. No signal candidates are found, and we obtain an upper limit for the branching fraction ${\cal B}(\tau^- \to \mu^- \eta)<3.4\times 10^{-7}$ at the 90% confidence level.Comment: Submitted to Phys.Rev.Let