Clustering Scatter Plots Using Data Depth Measures.

Clustering is rapidly becoming a powerful data mining technique, and has been broadly applied to many domains such as bioinformatics and text mining. However, the existing methods can only deal with a data matrix of scalars. In this paper, we introduce a hierarchical clustering procedure that can handle a data matrix of scatter plots. To more accurately reflect the nature of data, we introduce a dissimilarity statistic based on "data depth" to measure the discrepancy between two bivariate distributions without oversimplifying the nature of the underlying pattern. We then combine hypothesis testing with hierarchical clustering to simultaneously cluster the rows and columns of the data matrix of scatter plots. We also propose novel painting metrics and construct heat maps to allow visualization of the clusters. We demonstrate the utility and power of our new clustering method through simulation studies and application to a microbe-host-interaction study

Kinematic properties of the helicopter in coordinated turns

A study on the kinematic relationship of the variables of helicopter motion in steady, coordinated turns involving inherent sideslip is described. A set of exact kinematic equations which govern a steady coordinated helical turn about an Earth referenced vertical axis is developed. A precise definition for the load factor parameter that best characterizes a coordinated turn is proposed. Formulas are developed which relate the aircraft angular rates and pitch and roll attitudes to the turn parameters, angle of attack, and inherent sideslip. A steep, coordinated helical turn at extreme angles of attack with inherent sideslip is of primary interest. The bank angle of the aircraft can differ markedly from the tilt angle of the normal load factor. The normal load factor can also differ substantially from the accelerometer reading along the vertical body axis of the aircraft. Sideslip has a strong influence on the pitch attitude and roll rate of the helicopter. Pitch rate is independent of angle of attack in a coordinated turn and in the absence of sideslip, angular rates about the stability axes are independent of the aerodynamic characteristics of the aircraft

Breaking the degeneracy between anisotropy and mass: The dark halo of the E0 galaxy NGC 6703

(abridged) We have measured line-of-sight velocity profiles (VPs) in the E0 galaxy NGC 6703 out to 2.6 R_e. From these data we constrain the mass distribution and the anisotropy of the stellar orbits in this galaxy. We have developed a non-parametric technique to determine the DF f(E,L^2) directly from the kinematic data. From Monte Carlo tests using the spatial extent, sampling, and error bars of the NGC 6703 data we find that smooth underlying DFs can be recovered to an rms accuracy of 12%, and the anisotropy parameter beta(r) to an accuracy of 0.1, in a given potential. An asymptotically constant halo circular velocity v_0 can be determined with an accuracy of +- \lta 50km/s. For NGC 6703 we determine the true circular velocity at 2.6 R_e to be 250 +- 40km/s at 95% c.l., corresponding to a total mass in NGC 6703 inside 78'' (13.5 h_50^-1 kpc), of 1.6-2.6 x 10^11 h_50^-1 Msun. No model without dark matter will fit the data; however, a maximum stellar mass model in which the luminous component provides nearly all the mass in the centre does. In such a model, the total luminous mass inside 78'' is 9 x 10^10 Msun and the integrated M/L_B=5.3-10, corresponding to a rise from the center by at least a factor of 1.6. The anisotropy of the stellar distribution function in NGC 6703 changes from near-isotropic at the centre to slightly radially anisotropic (beta=0.3-0.4 at 30'', beta=0.2-0.4 at 60'') and is not well-constrained at the outer edge of the data. Our results suggest that also elliptical galaxies begin to be dominated by dark matter at radii of \sim 10kpc.Comment: 19 pages LaTex, 18 figures. MNRAS, in press. Also available at http://www.astro.unibas.ch/~gerhard/papers/dm6703.ps.g

Breaking the degeneracy between anisotropy and mass: the dark halo of the E0 galaxy NGC 6703

We have measured line-of-sight velocity profiles (VPs) in the E0 galaxy NGC 6703 out to 2.6Re. Comparing these with the VPs predicted from spherical distribution functions (DFs), we constrain the mass distribution and the anisotropy of the stellar orbits in this galaxy. We have developed a non-parametric technique to determine the DF f(E, L2) directly from the kinematic data. We test this technique on Monte Carlo simulated data with the spatial extent, sampling, and error bars of the NGC 6703 data. We find that smooth underlying DFs can be recovered to an rms accuracy of 12 per cent inside three times the radius of the last kinematic data point, and the anisotropy parameter β(r) can be recovered to an accuracy of 0.1, in a known potential. These uncertainties can be reduced with improved data. By comparing such best-estimate, regularized models in different potentials, we can derive constraints on the mass distribution and anisotropy. Tests show that, with presently available data, an asymptotically constant halo circular velocity υ0 can be determined with an accuracy of ±≲50 km s−1. This formal range often includes high-υ0 models with implausibly large gradients across the data boundary. However, even with extremely high quality data some uncertainty on the detailed shape of the underlying circular velocity curve remains. In the case of NGC 6703, we thus determine the true circular velocity at 2.6Re to be 250±40 km s−1 at 95 per cent confidence, corresponding to a total mass in NGC 6703 inside 78 arcsec (13.5 h−150 kpc, where h50≡H0/50 km s−1 Mpc−1) of 1.6-2.6×1011h−150 M⊙. No model without dark matter will fit the data; however, a maximum stellar mass model in which the luminous component provides nearly all the mass in the centre will. In such a model, the total luminous mass inside 78 arcsec is 9Å-1010 M⊙ and the integrated B-band mass-to-light ratio out to this radius is ΥB=5.3-10, corresponding to a rise from the centre by at least a factor of 1.6. The anisotropy of the stellar distribution function in NGC 6703 changes from near-isotropic at the centre to slightly radially anisotropic (β=0.3-0.4 at 30 arcsec, β=0.2-0.4 at 60 arcsec) and is not well-constrained at the outer edge of the data, where β=−0.5 to +0.4, depending on variations of the potential in the allowed range. Our results suggest that also elliptical galaxies begin to be dominated by dark matter at radii of ∼10 kp

A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies

We have measured differential cross sections for \pp elastic scattering with internal fiber targets in the recirculating beam of the proton synchrotron COSY. Measurements were made continuously during acceleration for projectile kinetic energies between 0.23 and 2.59 GeV in the angular range $30 \leq \theta_{c.m.} \leq 90$ deg. Details of the apparatus and the data analysis are given and the resulting excitation functions and angular distributions presented. The precision of each data point is typically better than 4%, and a relative normalization uncertainty of only 2.5% within an excitation function has been reached. The impact on phase shift analysis as well as upper bounds on possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure

Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Stellar disks of Collisional Ring Galaxies I. New multiband images, Radial intensity and color profiles, and confrontation with N-body simulations

We present new multi-band imaging data in the optical (BVRI and Halpha) and near infrared bands (JHK) of 15 candidate ring galaxies from the sample of Appleton & Marston (1997). We use these data to obtain color composite images, global magnitudes and colors of both the ring galaxy and its companion(s), and radial profiles of intensity and colors. We find that only nine of the observed galaxies have multi-band morphologies expected for the classical collisional scenario of ring formation, indicating the high degree of contamination of the ring galaxy sample by galaxies without a clear ring morphology. The radial intensity profiles, obtained by masking the off-centered nucleus, peak at the position of the ring, with the profiles in the continuum bands broader than that in the Halpha line. The images as well as the radial intensity and color profiles clearly demonstrate the existence of the pre-collisional stellar disk outside the star-forming ring, which is in general bluer than the disk internal to the ring. The stellar disk seems to have retained its size, with the disk outside the ring having a shorter exponential scale length as compared to the values expected in normal spiral galaxies of comparable masses. The rings in our sample of galaxies are found to be located preferentially at around half-way through the stellar disk. The most likely reason for this preference is bias against detecting rings when they are close to the center (they would be confused with the resonant rings), and at the edge of the disk the gas surface density may be below the critical density required for star formation. Most of the observed characteristics point to relatively recent collisions (<80 Myr ago) according to the N-body simulations of Gerber et al. (1996).Comment: To appear in AJ issue of September 2008. High resolution color image of Figure 2 and other supplementary images are available at http://www.inaoep.mx/~ydm/rings