Consistent Digital Curved Rays and Pseudoline Arrangements

Representing a family of geometric objects in the digital world where each object is represented by a set of pixels is a basic problem in graphics and computational geometry. One important criterion is the consistency, where the intersection pattern of the objects should be consistent with axioms of the Euclidean geometry, e.g., the intersection of two lines should be a single connected component. Previously, the set of linear rays and segments has been considered. In this paper, we extended this theory to families of curved rays going through the origin. We further consider some psudoline arrangements obtained as unions of such families of rays

Street Egohood: An Alternative Perspective of Measuring Neighborhood and Spatial Patterns of Crime

Objectives: The current study proposes an approach that accounts for the importance of streets while at the same time accounting for the overlapping spatial nature of social and physical environments captured by the egohood approach. Our approach utilizes overlapping clusters of streets based on the street network distance, which we term street egohoods. Methods: We used the street segment as a base unit and employed two strategies in clustering the street segments: (1) based on the First Order Queen Contiguity; and (2) based on the street network distance considering physical barriers. We utilized our approaches for measuring ecological factors and estimated crime rates in the Los Angeles metropolitan area. Results: We found that whereas certain socio-demographics, land use, and business employee measures show stronger relationships with crime when measured at the smaller street based unit, a number of them actually exhibited stronger relationships when measured using our larger street egohoods. We compared the results for our three-sized street egohoods to street segments and two sizes of block egohoods proposed by Hipp and Boessen (Criminology 51(2):287–327, 2013) and found that two egohood strategies essentially are not different at the quarter mile egohood level but this similarity appears lower when looking at the half mile egohood level. Also, the street egohood models are a better fit for predicting violent and property crime compared to the block egohood models. Conclusions: A primary contribution of the current study is to develop and propose a new perspective of measuring neighborhood based on urban streets. We empirically demonstrated that whereas certain socio-demographic measures show the strongest relationship with crime when measured at the micro geographic unit of street segments, a number of them actually exhibited the strongest relationship when measured using our larger street egohoods. We hope future research can use egohoods to expand understanding of neighborhoods and crime

A quantitative evaluation of physical and digital approaches to centre of mass estimation

Centre of mass is a fundamental anatomical and biomechanical parameter. Knowledge of centre of mass is essential to inform studies investigating locomotion and other behaviours, through its implications for segment movements, and on whole body factors such as posture. Previous studies have estimated centre of mass position for a range of organisms, using various methodologies. However, few studies assess the accuracy of the methods that they employ, and often provide only brief details on their methodologies. As such, no rigorous, detailed comparisons of accuracy and repeatability within and between methods currently exist. This paper therefore seeks to apply three methods common in the literature (suspension, scales and digital modelling) to three 'calibration objects' in the form of bricks, as well as three birds to determine centre of mass position. Application to bricks enables conclusions to be drawn on the absolute accuracy of each method, in addition to comparing these results to assess the relative value of these methodologies. Application to birds provided insights into the logistical challenges of applying these methods to biological specimens. For bricks, we found that, provided appropriate repeats were conducted, the scales method yielded the most accurate predictions of centre of mass (within 1.49 mm), closely followed by digital modelling (within 2.39 mm), with results from suspension being the most distant (within 38.5 mm). Scales and digital methods both also displayed low variability between centre of mass estimates, suggesting they can accurately and consistently predict centre of mass position. Our suspension method resulted not only in high margins of error, but also substantial variability, highlighting problems with this method

A nonlinear detection algorithm for periodic signals in gravitational wave detectors

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Moving Difference (MDIFF) Non-adiabatic Rapid Sweep (NARS) EPR of Copper(II)

Non-adiabatic rapid sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (Kittell et al., 2011). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about four times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines

Observing Long Cosmic Strings Through Gravitational Lensing

We consider the gravitational lensing produced by long cosmic strings formed in a GUT scale phase transition. We derive a formula for the deflection of photons which pass near the strings that reduces to an integral over the light cone projection of the string configuration plus constant terms which are not important for lensing. Our strings are produced by performing numerical simulations of cosmic string networks in flat, Minkowski space ignoring the effects of cosmological expansion. These strings have more small scale structure than those from an expanding universe simulation - fractal dimension 1.3 for Minkowski versus 1.1 for expanding - but share the same qualitative features. Lensing simulations show that for both point-like and extended objects, strings produce patterns unlike more traditional lenses, and, in particluar, the kinks in strings tend to generate demagnified images which reside close to the string. Thus lensing acts as a probe of the small scale structure of a string. Estimates of lensing probablity suggest that for string energy densities consistant with string seeded structure formation, on the order of tens of string lenses should be observed in the Sloan Digital Sky Survey quasar catalog. We propose a search strategy in which string lenses would be identified in the SDSS quasar survey, and the string nature of the lens can be confirmed by the observation of nearby high redshift galaxies which are also be lensed by the string.Comment: 24 pages revtex with 12 postscript firgure