8,025 research outputs found

    Tiling strategies for optical follow-up of gravitational wave triggers by wide field of view telescopes

    Get PDF
    Binary neutron stars are among the most promising candidates for joint gravitational-wave and electromagnetic astronomy. The goal of this work is to investigate the strategy of using gravitational wave sky-localizations for binary neutron star systems, to search for electromagnetic counterparts using wide field of view optical telescopes. We examine various strategies of scanning the gravitational wave sky-localizations on the mock 2015-16 gravitational-wave events. We propose an optimal tiling-strategy that would ensure the most economical coverage of the gravitational wave sky-localization, while keeping in mind the realistic constrains of transient optical astronomy. Our analysis reveals that the proposed tiling strategy improves the sky-localization coverage over naive contour-covering method. The improvement is more significant for observations conducted using larger field of view telescopes, or for observations conducted over smaller confidence interval of gravitational wave sky-localization probability distribution. Next, we investigate the performance of the tiling strategy for telescope arrays and compare their performance against monolithic giant field of view telescopes. We observed that distributing the field of view of the telescopes into arrays of multiple telescopes significantly improves the coverage efficiency by as much as 50% over a single large FOV telescope in 2016 localizations while scanning around 100 sq. degrees. Finally, we studied the ability of optical counterpart detection by various types of telescopes. In Our analysis for a range of wide field-of-view telescopes we found improvement in detection upon sacrificing coverage of localization in order to achieve greater observation depth for very large field-of-view - small aperture telescopes, especially if the intrinsic brightness of the optical counterparts are weak.Comment: Accepted for publication in A&A. 10 pages, 10 figure

    Structural aspects of tilings

    Get PDF
    In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in two different contexts: the first one is combinatorial and the other topological. These two approaches have independent merits and, once combined, provide somehow surprising results. The particular case where the set of produced tilings is countable is deeply investigated while we prove that the uncountable case may have a completely different structure. We introduce a pattern preorder and also make use of Cantor-Bendixson rank. Our first main result is that a tile-set that produces only periodic tilings produces only a finite number of them. Our second main result exhibits a tiling with exactly one vector of periodicity in the countable case.Comment: 11 page

    Detecting Repetitions and Periodicities in Proteins by Tiling the Structural Space

    Full text link
    The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy Landscape Theory indicates that it is much easier to find sequences that satisfy the "Principle of Minimal Frustration" when the folded structure is symmetric (Wolynes, P. G. Symmetry and the Energy Landscapes of Biomolecules. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 14249-14255). Similarly, repeats and structural mosaics may be fundamentally related to landscapes with multiple embedded funnels. Here we present analytical tools to detect and compare structural repetitions in protein molecules. By an exhaustive analysis of the distribution of structural repeats using a robust metric we define those portions of a protein molecule that best describe the overall structure as a tessellation of basic units. The patterns produced by such tessellations provide intuitive representations of the repeating regions and their association towards higher order arrangements. We find that some protein architectures can be described as nearly periodic, while in others clear separations between repetitions exist. Since the method is independent of amino acid sequence information we can identify structural units that can be encoded by a variety of distinct amino acid sequences

    The First-Order Theory of Ground Tree Rewrite Graphs

    Full text link
    We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n)). Providing a matching lower bound, we show that there is some fixed ground tree rewrite graph whose first-order theory is hard for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.Comment: accepted for Logical Methods in Computer Scienc

    The Tiling Algorithm for the 6dF Galaxy Survey

    Full text link
    The Six Degree Field Galaxy Survey (6dFGS) is a spectroscopic survey of the southern sky, which aims to provide positions and velocities of galaxies in the nearby Universe. We present here the adaptive tiling algorithm developed to place 6dFGS fields on the sky, and allocate targets to those fields. Optimal solutions to survey field placement are generally extremely difficult to find, especially in this era of large-scale galaxy surveys, as the space of available solutions is vast (2N dimensional) and false optimal solutions abound. The 6dFGS algorithm utilises the Metropolis (simulated annealing) method to overcome this problem. By design the algorithm gives uniform completeness independent of local density, so as to result in a highly complete and uniform observed sample. The adaptive tiling achieves a sampling rate of approximately 95%, a variation in the sampling uniformity of less than 5%, and an efficiency in terms of used fibres per field of greater than 90%. We have tested whether the tiling algorithm systematically biases the large-scale structure in the survey by studying the two-point correlation function of mock 6dF volumes. Our analysis shows that the constraints on fibre proximity with 6dF lead to under-estimating galaxy clustering on small scales (< 1 Mpc) by up to ~20%, but that the tiling introduces no significant sampling bias at larger scales.Comment: 11 pages, 7 figures. Full resolution version of the paper available from http://www.mso.anu.edu.au/6dFGS/ . Abridged version of abstract belo

    Smoothed Complexity Theory

    Get PDF
    Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability). Furthermore, we discuss extensions and shortcomings of our model and relate it to semi-random models.Comment: to be presented at MFCS 201
    • …
    corecore