Optimal Algorithms for Some Intersection Radius Problems

Abstract --Zusammenfassung Optimal Algorithms for Some Intersection Radius Problems. The intersection radius of a set of n geometrical objects in a d-dimensional Euclidean space, E d, is the radius of the smallest closed hypersphere that intersects all the objects of the set. In this paper, we describe optimal algorithms for some intersection radius problems. We first present a linear-time algorithm to determine the smallest closed hypcrsphere that intersects a set of hyperplanes in E ~, assuming d to be a fixed parameter. This is done by reducing the problem to a linear programming problem in a (d + 1)-dimensional space, involving 2n linear constraints. We also show how the prune-and-search technique, coupled with the strategy of replacing a ray by a point or a line can be used to solve, in linear time, the intersection radius problem for a set of n line segments in the plane. Currently, no algorithms are known that solve these intersection radius problems within the same time bounds. AM

The exchangeability of shape

<p>Abstract</p> <p>Background</p> <p>Landmark based geometric morphometrics (GM) allows the quantitative comparison of organismal shapes. When applied to systematics, it is able to score shape changes which often are undetectable by traditional morphological studies and even by classical morphometric approaches. It has thus become a fast and low cost candidate to identify cryptic species. Due to inherent mathematical properties, shape variables derived from one set of coordinates cannot be compared with shape variables derived from another set. Raw coordinates which produce these shape variables could be used for data exchange, however they contain measurement error. The latter may represent a significant obstacle when the objective is to distinguish very similar species.</p> <p>Results</p> <p>We show here that a single user derived dataset produces much less classification error than a multiple one. The question then becomes how to circumvent the lack of exchangeability of shape variables while preserving a single user dataset. A solution to this question could lead to the creation of a relatively fast and inexpensive systematic tool adapted for the recognition of cryptic species.</p> <p>Conclusions</p> <p>To preserve both exchangeability of shape and a single user derived dataset, our suggestion is to create a free access bank of reference images from which one can produce raw coordinates and use them for comparison with external specimens. Thus, we propose an alternative geometric descriptive system that separates 2-D data gathering and analyzes.</p

Polarized parton distributions measured at the HERMES experiment

The HERMES experiment at DESY, Germany was designed to carry out precision measurements of the proton spin structure using polarized deep-inelastic scattering. The experiment utilizes the 27.5 GeV electron or positron beam of the HERA accelerator which is longitudinally polarized at HERMES, in combination with a polarized internal gas target. For this work, data on longitudinally polarized hydrogen and deuterium targets were used to determine cross section asymmetries with respect to the alignment of the target and beam polarizations. Inclusive asymmetries on the proton and the deuteron, where only the scattered electron/positron is detected, were measured with high precision. In semi-inclusive deep-inelastic scattering, at least one final-state hadron is detected in coincidence. Semi-inclusive asymmetries of pions on the proton and pion and kaon asymmetries on the deuteron were measured for the first time by the HERMES collaboration. The measured asymmetries include detector effects and effects of higher-order processes in quantum electrodynamics. A new unfolding procedure that takes into account the correlations between kinematic bins was implemented to correct for these effects. The polarized parton densities of the up, down, and sea flavours were obtained from the unfolded inclusive and semi-inclusive asymmetries in a probabilistic analysis based on leading-order quantum chromodynamics. In the case of the up quark and the down quark, the polarized densities were determined to be positive and negative, respectively. The polarized densities of the sea flavours, decomposed for the first time into the densities of the anti-up, anti-down, and strange quarks, were found to be compatible with zero. Moments of the polarized parton densities were computed. The Bjoerken sum rule was verified and the total spin carried by the quark spins was determined to be (38.0 #+-# 8.0)%. This latter result is larger than earlier measurements but still smaller than #propor to# 60% predicted in relativistic models of the proton. (orig.)Available from TIB Hannover: RA 8919(2003-032) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman