An interior point algorithm for minimum sum-of-squares clustering

Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec

Machine Learning Classification of SDSS Transient Survey Images

We show that multiple machine learning algorithms can match human performance in classifying transient imaging data from the Sloan Digital Sky Survey (SDSS) supernova survey into real objects and artefacts. This is a first step in any transient science pipeline and is currently still done by humans, but future surveys such as the Large Synoptic Survey Telescope (LSST) will necessitate fully machine-enabled solutions. Using features trained from eigenimage analysis (principal component analysis, PCA) of single-epoch g, r and i-difference images, we can reach a completeness (recall) of 96 per cent, while only incorrectly classifying at most 18 per cent of artefacts as real objects, corresponding to a precision (purity) of 84 per cent. In general, random forests performed best, followed by the k-nearest neighbour and the SkyNet artificial neural net algorithms, compared to other methods such as na\"ive Bayes and kernel support vector machine. Our results show that PCA-based machine learning can match human success levels and can naturally be extended by including multiple epochs of data, transient colours and host galaxy information which should allow for significant further improvements, especially at low signal-to-noise.Comment: 14 pages, 8 figures. In this version extremely minor adjustments to the paper were made - e.g. Figure 5 is now easier to view in greyscal

Chromosomal Gains and Losses in Uveal Melanomas Detected by Comparative Genomic Hybridization

Eleven uveal melanomas were analyzed using comparative genomic hybridization (CGH). The most abundant genetic changes were loss of chromosome 3, overrepresentation of 6p, loss of 6q, and multiplication of 8q. The smallest overrepresented regions on 6p and 8q were 6pterp21 and 8q24qter, respectively. Several additional gains and losses of chromosome segments were repeatedly observed, the most frequent one being loss of 9p (three cases). Monosomy 3 appeared to be a marker for ciliary body involvement. CGH data were compared with the results of chromosome banding. Some alterations, e.g., gains of 6p and losses of 6q, were observed with higher frequencies after CGH, while others, e.g., 9p deletions, were detected only by CGH. The data suggest some similarities of cytogenetic alterations between cutaneous and uveal melanoma. In particular, the 9p deletions are of interest due to recent reports about the location of a putative tumor-suppressor gene for cutaneous malignant melanoma in this region

Metal-Insulator-Like Behavior in Semimetallic Bismuth and Graphite

When high quality bismuth or graphite crystals are placed in a magnetic field directed along the c-axis (trigonal axis for bismuth) and the temperature is lowered, the resistance increases as it does in an insulator but then saturates. We show that the combination of unusual features specific to semimetals, i.e., low carrier density, small effective mass, high purity, and an equal number of electrons and holes (compensation), gives rise to a unique ordering and spacing of three characteristic energy scales, which not only is specific to semimetals but which concomitantly provides a wide window for the observation of apparent field induced metal-insulator behavior. Using magnetotransport and Hall measurements, the details of this unusual behavior are captured with a conventional multi-band model, thus confirming the occupation by semimetals of a unique niche between conventional metals and semiconductors.Comment: 4 pages, 4 figs, data and discussion on bismuth added, final published versio

1/m_Q Corrections to the Heavy-to-Light-Vector Transitions in the HQET

Within the HQET, the heavy to light vector meson transitions are systematically analyzed to the order of 1/m_Q. Besides the four universal functions at the leading order, there are twenty-two independent universal form factors at the order of 1/m_Q. Both the semileptonic decay B->\rho which is relevant to the |V_{ub}| extraction, and the penguin induced decay B -> K^* which is important to new physics discovering, depend on these form factors. Phenomenological implications are discussed.Comment: RevTeX, 9 pages, no figure

Stripe State in the Lowest Landau Level

The stripe state in the lowest Landau level is studied by the density matrix renormalization group (DMRG) method. The ground state energy and pair correlation functions are systematically calculated for various pseudopotentials in the lowest Landau level. We show that the stripe state in the lowest Landau level is realized only in a system whose width perpendicular to the two-dimensional electron layer is smaller than the order of magnetic length.Comment: 4 pages, 6 figures, to appear in J. Phys. Soc. Jpn. vol.73 No.1 (2004

SDSS J075101.42+291419.1: A Super-Eddington Accreting Quasar with Extreme X-ray Variability

We report the discovery of extreme X-ray variability in a type 1 quasar: SDSS J$075101.42+291419.1$. It has a black hole mass of $1.6\times 10^7~\rm M_\odot$ measured from reverberation mapping (RM), and the black hole is accreting with a super-Eddington accretion rate. Its XMM-Newton observation in 2015 May reveals a flux drop by a factor of $\sim 22$ with respect to the Swift observation in 2013 May when it showed a typical level of X-ray emission relative to its UV/optical emission. The lack of correlated UV variability results in a steep X-ray-to-optical power-law slope ($\alpha_{\rm OX}$) of -1.97 in the low X-ray flux state, corresponding to an X-ray weakness factor of 36.2 at rest-frame 2 keV relative to its UV/optical luminosity. The mild UV/optical continuum and emission-line variability also suggest that the accretion rate did not change significantly. A single power-law model modified by Galactic absorption describes well the $0.3-10$ keV spectra of the X-ray observations in general. The spectral fitting reveals steep spectral shapes with $\Gamma\approx3$. We search for active galactic nuclei (AGNs) with such extreme X-ray variability in the literature and find that most of them are narrow-line Seyfert 1 galaxies and quasars with high accretion rates. The fraction of extremely X-ray variable objects among super-Eddington accreting AGNs is estimated to be $\approx 15-24\%$. We discuss two possible scenarios, disk reflection and partial covering absorption, to explain the extreme X-ray variability of SDSS J$075101.42+291419.1$. We propose a possible origin for the partial covering absorber, which is the thick inner accretion disk and its associated outflow in AGNs with high accretion rates.Comment: 15 pages, 9 figures, accepted for publication in Ap

Effective Mass of the Four Flux Composite Fermion at ν=1/4\nu = 1/4

We have measured the effective mass ($m^*$) of the four flux composite fermion at Landau level filling factor $\nu = 1/4$ ($^4$CF), using the activation energy gaps at the fractional quantum Hall effect (FQHE) states $\nu$ = 2/7, 3/11, and 4/15 and the temperature dependence of the Shubnikov-de Haas (SdH) oscillations around $\nu = 1/4$. We find that the energy gaps show a linear dependence on the effective magnetic field $B_{eff}$ ($\equiv B-B_{\nu=1/4}$), and from this linear dependence we obtain $m^* = 1.0 m_e$ and a disorder broadening $\Gamma \sim$ 1 K for a sample of density $n = 0.87 \times 10^{11}$ /cm$^2$. The $m^*$ deduced from the temperature dependence of the SdH effect shows large differences for $\nu > 1/4$ and $\nu < 1/4$. For $\nu > 1/4$, $m^* \sim 1.0 m_e$. It scales as $\sqrt{B_{\nu}}$ with the mass derived from the data around $\nu =1/2$ and shows an increase in $m^*$ as $\nu \to 1/4$, resembling the findings around $\nu =1/2$. For $\nu < 1/4$, $m^*$ increases rapidly with increasing $B_{eff}$ and can be described by $m^*/m_e = -3.3 + 5.7 \times B_{eff}$. This anomalous dependence on $B_{eff}$ is precursory to the formation of the insulating phase at still lower filling.Comment: 5 pages, 3 figure

Interaction of Individual Skyrmions in Nanostructured Cubic Chiral Magnet

We report the direct evidence of field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of external magnetic field the character of such long-range skyrmion interactions change from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skrymion-edge distances as function of applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. Important role of demagnetizing fields and internal symmetry of three-dimensional magnetic skyrmions are discussed in details.Comment: accepted in PR