Composition mechanisms for retrenchment

Retrenchment is a flexible model evolution formalism that arose as a reaction to the limitations imposed by refinement, and for which the proof obligations feature additional predicates for accommodating design data. Composition mechanisms for retrenchment are studied. Vertical, horizontal, dataflow, parallel and fusion compositions are described. Of particular note are the means by which the additional predicates compose. It is argued that all of the compositions introduced are associative, and that they are mutually coherent. Composition of retrenchment with refinement, so important for the smooth interworking of the two techniques, is discussed. Decomposition, allowing finer grained retrenchments to be extracted from a single large grained retrenchment, is also investigated

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

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

The efficiency of logistic regression compared to normal discriminant analysis under class-conditional classification noise

AbstractIn many real world classification problems, class-conditional classification noise (CCC-Noise) frequently deteriorates the performance of a classifier that is naively built by ignoring it. In this paper, we investigate the impact of CCC-Noise on the quality of a popular generative classifier, normal discriminant analysis (NDA), and its corresponding discriminative classifier, logistic regression (LR). We consider the problem of two multivariate normal populations having a common covariance matrix. We compare the asymptotic distribution of the misclassification error rate of these two classifiers under CCC-Noise. We show that when the noise level is low, the asymptotic error rates of both procedures are only slightly affected. We also show that LR is less deteriorated by CCC-Noise compared to NDA. Under CCC-Noise contexts, the Mahalanobis distance between the populations plays a vital role in determining the relative performance of these two procedures. In particular, when this distance is small, LR tends to be more tolerable to CCC-Noise compared to NDA

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