16,014 research outputs found
Methods for Rapidly Processing Angular Masks of Next-Generation Galaxy Surveys
As galaxy surveys become larger and more complex, keeping track of the
completeness, magnitude limit, and other survey parameters as a function of
direction on the sky becomes an increasingly challenging computational task.
For example, typical angular masks of the Sloan Digital Sky Survey contain
about N=300,000 distinct spherical polygons. Managing masks with such large
numbers of polygons becomes intractably slow, particularly for tasks that run
in time O(N^2) with a naive algorithm, such as finding which polygons overlap
each other. Here we present a "divide-and-conquer" solution to this challenge:
we first split the angular mask into predefined regions called "pixels," such
that each polygon is in only one pixel, and then perform further computations,
such as checking for overlap, on the polygons within each pixel separately.
This reduces O(N^2) tasks to O(N), and also reduces the important task of
determining in which polygon(s) a point on the sky lies from O(N) to O(1),
resulting in significant computational speedup. Additionally, we present a
method to efficiently convert any angular mask to and from the popular HEALPix
format. This method can be generically applied to convert to and from any
desired spherical pixelization. We have implemented these techniques in a new
version of the mangle software package, which is freely available at
http://space.mit.edu/home/tegmark/mangle/, along with complete documentation
and example applications. These new methods should prove quite useful to the
astronomical community, and since mangle is a generic tool for managing angular
masks on a sphere, it has the potential to benefit terrestrial mapmaking
applications as well.Comment: New version 2.1 of the mangle software now available at
http://space.mit.edu/home/tegmark/mangle/ - includes galaxy survey masks and
galaxy lists for the latest SDSS data release and the 2dFGRS final data
release as well as extensive documentation and examples. 14 pages, 9 figures,
matches version accepted by MNRA
Multiple-sensor integration for efficient reverse engineering of geometry
This paper describes a multi-sensor measuring system for reverse engineering applications. A sphere-plate artefact is developed for data unification of the hybrid system. With the coordinate data acquired using the optical system, intelligent feature recognition and segmentation algorithms can be applied to extract the global surface information of the object. The coordinate measuring machine (CMM) is used to re-measure the geometric features with a small amount of sampling points and the obtained information can be subsequently used to compensate the point data patches which are measured by optical system. Then the optimized point data can be exploited for accurate reverse engineering of CAD model. The limitations of each measurement system are compensated by the other. Experimental results validate the accuracy and effectiveness of this data optimization approach
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
Tactics for Reasoning modulo AC in Coq
We present a set of tools for rewriting modulo associativity and
commutativity (AC) in Coq, solving a long-standing practical problem. We use
two building blocks: first, an extensible reflexive decision procedure for
equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We
handle associative only operations, neutral elements, uninterpreted function
symbols, and user-defined equivalence relations. By relying on type-classes for
the reification phase, we can infer these properties automatically, so that
end-users do not need to specify which operation is A or AC, or which constant
is a neutral element.Comment: 16
- …