Approximation Algorithms for Partially Colorable Graphs

Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For alpha = alpha |V| such that the graph induced on S is k-colorable. Partial k-colorability is a more robust structural property of a graph than k-colorability. For graphs that arise in practice, partial k-colorability might be a better notion to use than k-colorability, since data arising in practice often contains various forms of noise. We give a polynomial time algorithm that takes as input a (1 - epsilon)-partially 3-colorable graph G and a constant gamma in [epsilon, 1/10], and colors a (1 - epsilon/gamma) fraction of the vertices using O~(n^{0.25 + O(gamma^{1/2})}) colors. We also study natural semi-random families of instances of partially 3-colorable graphs and partially 2-colorable graphs, and give stronger bi-criteria approximation guarantees for these family of instances

Robust mixtures in the presence of measurement errors

We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to errors, aiming to retrieve potentially interesting peculiar objects. Since exact inference is not possible in this model, we develop a tree-structured variational EM solution. This compares favorably against a fully factorial approximation scheme, approaching the accuracy of a Markov-Chain-EM, while maintaining computational simplicity. We demonstrate the benefits of including measurement errors in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. We then use this approach in detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.Comment: (Refereed) Proceedings of the 24-th Annual International Conference on Machine Learning 2007 (ICML07), (Ed.) Z. Ghahramani. June 20-24, 2007, Oregon State University, Corvallis, OR, USA, pp. 847-854; Omnipress. ISBN 978-1-59593-793-3; 8 pages, 6 figure

Origin of Ferromagnetism and its pressure and doping dependence in Tl2_{2}Mn2_{2}O7_{7}

Using NMTO-{\it downfolding} technique, we explore and establish the origin of ferromagnetism in the pyrochlore system, Tl$_{2}$Mn$_{2}$O$_{7}$. It is found to be driven by hybridization induced spin-polarization of the delocalized charge carriers derived from Tl-$s$ and O-$p$ states. The mean-field estimate of the ferromagnetic transition temperature, T$_c$, estimated using computed exchange integrals are found to be in good agreement with the measurements. We find an enhancement of T$_{c}$ for moderate doping with nonmagnetic Sb and a suppression of T$_{c}$ upon application of pressure, both in agreement with experimental findings.Comment: Accepted for publication in PR

A Lens Mapping Algorithm for Weak Lensing

We develop an algorithm for the reconstruction of the two-dimensional mass distribution of a gravitational lens from the observable distortion of background galaxies. From the measured reduced shear, the lens mapping is obtained, from which a mass distribution is derived. This is unlike other methods where the convergence ("kappa") is directly obtained. We show that this method works best for sub-critical lenses, but can be applied to a critical lens away from the critical lines. For finite fields the usual mass-sheet degeneracy is shown to exist in this method as well. We show that the algorithm reproduces the mass distribution within acceptable limits when applied to simulated noisy data.Comment: 4 pages, 6 figures, uses emulateapj5.sty (included); substantially revised; a slightly shorter version (fewer figures) will appear in Ap.J.Letter

Finding Young Stellar Populations in Elliptical Galaxies from Independent Components of Optical Spectra

Elliptical galaxies are believed to consist of a single population of old stars formed together at an early epoch in the Universe, yet recent analyses of galaxy spectra seem to indicate the presence of significant younger populations of stars in them. The detailed physical modelling of such populations is computationally expensive, inhibiting the detailed analysis of the several million galaxy spectra becoming available over the next few years. Here we present a data mining application aimed at decomposing the spectra of elliptical galaxies into several coeval stellar populations, without the use of detailed physical models. This is achieved by performing a linear independent basis transformation that essentially decouples the initial problem of joint processing of a set of correlated spectral measurements into that of the independent processing of a small set of prototypical spectra. Two methods are investigated: (1) A fast projection approach is derived by exploiting the correlation structure of neighboring wavelength bins within the spectral data. (2) A factorisation method that takes advantage of the positivity of the spectra is also investigated. The preliminary results show that typical features observed in stellar population spectra of different evolutionary histories can be convincingly disentangled by these methods, despite the absence of input physics. The success of this basis transformation analysis in recovering physically interpretable representations indicates that this technique is a potentially powerful tool for astronomical data mining.Comment: 12 Pages, 7 figures; accepted in SIAM 2005 International Conference on Data Mining, Newport Beach, CA, April 200

Star formation in galaxies along the Pisces-Cetus Supercluster filaments

We investigate the variation of current star formation in galaxies as a function of distance along three supercluster filaments, each joining pairs of rich clusters, in the Pisces-Cetus supercluster, which is part of the 2dFGRS. We find that even though there is a steady decline in the rate of star formation, as well as in the fraction of star forming galaxies, as one approaches the core of a cluster at an extremity of such a filament, there is an increased activity of star formation in a narrow distance range between 3-4/h_70 Mpc, which is 1.5-2 times the virial radius of the clusters involved. This peak in star formation is seen to be entirely due to the dwarf galaxies (-20<M_B<-17.5). The position of the peak does not seem to depend on the velocity dispersion of the nearest cluster, undermining the importance of the gravitational effect of the clusters involved. We find that this enhancement in star formation occurs at the same place for galaxies which belong to groups within these filaments, while group members elsewhere in the 2dFGRS do not show this effect. We conclude that the most likely mechanism for this enhanced star formation is galaxy-galaxy harassment, in the crowded infall region of rich clusters at the extremities of filaments, which induces a burst of star formation in galaxies, before they have been stripped of their gas in the denser cores of clusters. The effects of strangulation in the cores of clusters, as well as excess star formation in the infall regions along the filaments, are more pronounced in dwarfs since they more vulnerable to the effects of strangulation and harassment than giant galaxies.Comment: 10 pages, 9 figures; accepted for publication in MNRA