Significance analysis and statistical mechanics: an application to clustering

This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.Comment: to appear in Phys. Rev. Let

A New Approach to Time Domain Classification of Broadband Noise in Gravitational Wave Data

Broadband noise in gravitational wave (GW) detectors, also known as triggers, can often be a deterrant to the efficiency with which astrophysical search pipelines detect sources. It is important to understand their instrumental or environmental origin so that they could be eliminated or accounted for in the data. Since the number of triggers is large, data mining approaches such as clustering and classification are useful tools for this task. Classification of triggers based on a handful of discrete properties has been done in the past. A rich information content is available in the waveform or 'shape' of the triggers that has had a rather restricted exploration so far. This paper presents a new way to classify triggers deriving information from both trigger waveforms as well as their discrete physical properties using a sequential combination of the Longest Common Sub-Sequence (LCSS) and LCSS coupled with Fast Time Series Evaluation (FTSE) for waveform classification and the multidimensional hierarchical classification (MHC) analysis for the grouping based on physical properties. A generalized k-means algorithm is used with the LCSS (and LCSS+FTSE) for clustering the triggers using a validity measure to determine the correct number of clusters in absence of any prior knowledge. The results have been demonstrated by simulations and by application to a segment of real LIGO data from the sixth science run.Comment: 16 pages, 16 figure

Kepler-424 b: A "lonely" hot Jupiter that found a companion

Peer reviewe

Population genetics of the highly polymorphic RPP8 gene family

Plant nucleotide-binding domain and leucine-rich repeat containing (NLR) genes provide some of the most extreme examples of polymorphism in eukaryotic genomes, rivalling even the vertebrate major histocompatibility complex. Surprisingly, this is also true in Arabidopsis thaliana, a predominantly selfing species with low heterozygosity. Here, we investigate how gene duplication and intergenic exchange contribute to this extraordinary variation. RPP8 is a three-locus system that is configured chromosomally as either a direct-repeat tandem duplication or as a single copy locus, plus a locus 2 Mb distant. We sequenced 48 RPP8 alleles from 37 accessions of A. thaliana and 12 RPP8 alleles from Arabidopsis lyrata to investigate the patterns of interlocus shared variation. The tandem duplicates display fixed differences and share less variation with each other than either shares with the distant paralog. A high level of shared polymorphism among alleles at one of the tandem duplicates, the single-copy locus and the distal locus, must involve both classical crossing over and intergenic gene conversion. Despite these polymorphism-enhancing mechanisms, the observed nucleotide diversity could not be replicated under neutral forward-in-time simulations. Only by adding balancing selection to the simulations do they approach the level of polymorphism observed at RPP8. In this NLR gene triad, genetic architecture, gene function and selection all combine to generate diversity

Long-lived, long-period radial velocity variations in Aldebaran: A planetary companion and stellar activity

We investigate the nature of the long-period radial velocity variations in Alpha Tau first reported over 20 years ago. We analyzed precise stellar radial velocity measurements for Alpha Tau spanning over 30 years. An examination of the Halpha and Ca II 8662 spectral lines, and Hipparcos photometry was also done to help discern the nature of the long-period radial velocity variations. Our radial velocity data show that the long-period, low amplitude radial velocity variations are long-lived and coherent. Furthermore, Halpha equivalent width measurements and Hipparcos photometry show no significant variations with this period. Another investigation of this star established that there was no variability in the spectral line shapes with the radial velocity period. An orbital solution results in a period of P = 628.96 +/- 0.90 d, eccentricity, e = 0.10 +/- 0.05, and a radial velocity amplitude, K = 142.1 +/- 7.2 m/s. Evolutionary tracks yield a stellar mass of 1.13 +/- 0.11 M_sun, which corresponds to a minimum companion mass of 6.47 +/- 0.53 M_Jup with an orbital semi-major axis of a = 1.46 +/- 0.27 AU. After removing the orbital motion of the companion, an additional period of ~ 520 d is found in the radial velocity data, but only in some time spans. A similar period is found in the variations in the equivalent width of Halpha and Ca II. Variations at one-third of this period are also found in the spectral line bisector measurements. The 520 d period is interpreted as the rotation modulation by stellar surface structure. Its presence, however, may not be long-lived, and it only appears in epochs of the radial velocity data separated by $\sim$ 10 years. This might be due to an activity cycle. The data presented here provide further evidence of a planetary companion to Alpha Tau, as well as activity-related radial velocity variations.Comment: 18 pages, 14 figures. Accepted for publication in Astronomy and Astrophysic

The Kepler Follow-up Observation Program

The Kepler Mission was launched on March 6, 2009 to perform a photometric survey of more than 100,000 dwarf stars to search for terrestrial-size planets with the transit technique. Follow-up observations of planetary candidates identified by detection of transit-like events are needed both for identification of astrophysical phenomena that mimic planetary transits and for characterization of the true planets and planetary systems found by Kepler. We have developed techniques and protocols for detection of false planetary transits and are currently conducting observations on 177 Kepler targets that have been selected for follow-up. A preliminary estimate indicates that between 24% and 62% of planetary candidates selected for follow-up will turn out to be true planets.Comment: 12 pages, submitted to the Astrophysical Journal Letter

Exploring The Frequency Of Close-In Jovian Planets Around M Dwarfs

We discuss our high precision radial velocity results of a sample of 90 M dwarfs observed with the Hobby-Eberly Telescope and the Harlan J. Smith 2.7 m Telescope at McDonald Observatory, as well as the ESO VLT and the Keck I telescopes, within the context of the overall frequency of Jupiter-mass planetary companions to main sequence stars. None of the stars in our sample show variability indicative of a giant planet in a short period orbit, with a 3.8 M_Jup and a 3.5 M_Jup and a < 0.7 AU. Our results point toward a generally lower frequency of close-in Jovian planets for M dwarfs as compared to FGK-type stars. This is an important piece of information for our understanding of the process of planet formation as a function of stellar mass

Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided

Autonomous clustering using rough set theory

This paper proposes a clustering technique that minimises the need for subjective human intervention and is based on elements of rough set theory. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency

Propagation of an Earth-directed coronal mass ejection in three dimensions

Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather at Earth, but the physics governing their propagation through the heliosphere is not well understood. While stereoscopic imaging of CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear due to difficulties in reconstructing their true 3D structure. Here we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its deflected trajectory from high latitudes along the ecliptic, and measure its increasing angular width and propagation from 2-46 solar radii (approximately 0.2 AU). Beyond 7 solar radii, we show that its motion is determined by an aerodynamic drag in the solar wind and, using our reconstruction as input for a 3D magnetohydrodynamic simulation, we determine an accurate arrival time at the Lagrangian L1 point near Earth.Comment: 5 figures, 2 supplementary movie