Quasi-ordinary singularities and Newton trees

In this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinary hypersurface singularities among nu-quasi-ordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasi-ordinary Weierstrass polynomial in terms of the decorations of its Newton tree is given. This allows to compute the discriminant avoiding the use of determinants and even for non Weierstrass prepared polynomials. This is important for applications like algorithmic resolutions. We compare the Newton tree of a quasi-ordinary singularity and those of its curve transversal sections. We show that the Newton trees of the transversal sections do not give the tree of the quasi-ordinary singularity in general. It does if we know that the Newton tree of the quasi-ordinary singularity has only one arrow.Comment: 32 page

Non-Destructive Method for Estimating Log Volume for Melia Azedarach L. Trees in Erbil-Iraqi Kurdistan Region

The accuracy of four traditional formulas (Smalian, Huber, Bruce and Newton) to calculate log volumes was compared and tested against volumes determined by the water-displacement technique (xylometer). 150 standing trees were measured in a Sami Abd-Alrahman Plantation Park in Erbil governorate on 1 May, 2012. The accuracy of these four procedures was analyzed considering merchantable outside bark volumes of logs of large, mid-and small diameter. The results showed that Newton’s formula was superior for all volumes and log lengths considered. Thus, Newton’s formula could be used in the majority of circumstances for log lengths of Melia azedarach trees. Applying the Newton formula to the tree volumes, DBH and height presented the best fit regression equation which for use in predicting the log volume of Melia azedarach trees in Erbil Governorate

Walks on SPR Neighborhoods

A nearest-neighbor-interchange (NNI) walk is a sequence of unrooted phylogenetic trees, T_0, T_1, T_2,... where each consecutive pair of trees differ by a single NNI move. We give tight bounds on the length of the shortest NNI-walks that visit all trees in an subtree-prune-and-regraft (SPR) neighborhood of a given tree. For any unrooted, binary tree, T, on n leaves, the shortest walk takes {\theta}(n^2) additional steps than the number of trees in the SPR neighborhood. This answers Bryant's Second Combinatorial Conjecture from the Phylogenetics Challenges List, the Isaac Newton Institute, 2011, and the Penny Ante Problem List, 2009

XMMPZCAT: A catalogue of photometric redshifts for X-ray sources

The third version of the XMM-Newton serendipitous catalogue (3XMM), containing almost half million sources, is now the largest X-ray catalogue. However, its full scientific potential remains untapped due to the lack of distance information (i.e. redshifts) for the majority of its sources. Here we present XMMPZCAT, a catalogue of photometric redshifts (photo-z) for 3XMM sources. We searched for optical counterparts of 3XMM-DR6 sources outside the Galactic plane in the SDSS and Pan-STARRS surveys, with the addition of near- (NIR) and mid-infrared (MIR) data whenever possible (2MASS, UKIDSS, VISTA-VHS, and AllWISE). We used this photometry data set in combination with a training sample of 5157 X-ray selected sources and the MLZ-TPZ package, a supervised machine learning algorithm based on decision trees and random forests for the calculation of photo-z. We have estimated photo-z for 100,178 X-ray sources, about 50% of the total number of 3XMM sources (205,380) in the XMM-Newton fields selected to build this catalogue (4208 out of 9159). The accuracy of our results highly depends on the available photometric data, with a rate of outliers ranging from 4% for sources with data in the optical+NIR+MIR, up to $\sim$40% for sources with only optical data. We also addressed the reliability level of our results by studying the shape of the photo-z probability density distributions.Comment: 16 pages, 14 figures, A&A accepte

A classification of postcritically finite Newton maps

The dynamical classification of rational maps is a central concern of holomorphic dynamics. Much progress has been made, especially on the classification of polynomials and some approachable one-parameter families of rational maps; the goal of finding a classification of general rational maps is so far elusive. Newton maps (rational maps that arise when applying Newton's method to a polynomial) form a most natural family to be studied from the dynamical perspective. Using Thurston's characterization and rigidity theorem, a complete combinatorial classification of postcritically finite Newton maps is given in terms of a finite connected graph satisfying certain explicit conditions

Stochastic B-series analysis of iterated Taylor methods

For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor and the number of iterations, for It\^o and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments