8,025 research outputs found
Tiling strategies for optical follow-up of gravitational wave triggers by wide field of view telescopes
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
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
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
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
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
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
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