53,632 research outputs found
On k-Convex Polygons
We introduce a notion of -convexity and explore polygons in the plane that
have this property. Polygons which are \mbox{-convex} can be triangulated
with fast yet simple algorithms. However, recognizing them in general is a
3SUM-hard problem. We give a characterization of \mbox{-convex} polygons, a
particularly interesting class, and show how to recognize them in \mbox{} time. A description of their shape is given as well, which leads to
Erd\H{o}s-Szekeres type results regarding subconfigurations of their vertex
sets. Finally, we introduce the concept of generalized geometric permutations,
and show that their number can be exponential in the number of
\mbox{-convex} objects considered.Comment: 23 pages, 19 figure
Generalized Chaplygin gas model, supernovae and cosmic topology
In this work we study to which extent the knowledge of spatial topology may
place constraints on the parameters of the generalized Chaplygin gas (GCG)
model for unification of dark energy and dark matter. By using both the
Poincar\'e dodecahedral and binary octahedral spaces as the observable spatial
topologies, we examine the current type Ia supernovae (SNe Ia) constraints on
the GCG model parameters. We show that the knowledge of spatial topology does
provide additional constraints on the parameter of the GCG model but does
not lift the degeneracy of the parameter.Comment: Revtex 4, 8 pages, 10 figures, 1 table; version to match the
published on
Improved Algorithms for the Point-Set Embeddability problem for Plane 3-Trees
In the point set embeddability problem, we are given a plane graph with
vertices and a point set with points. Now the goal is to answer the
question whether there exists a straight-line drawing of such that each
vertex is represented as a distinct point of as well as to provide an
embedding if one does exist. Recently, in \cite{DBLP:conf/gd/NishatMR10}, a
complete characterization for this problem on a special class of graphs known
as the plane 3-trees was presented along with an efficient algorithm to solve
the problem. In this paper, we use the same characterization to devise an
improved algorithm for the same problem. Much of the efficiency we achieve
comes from clever uses of the triangular range search technique. We also study
a generalized version of the problem and present improved algorithms for this
version of the problem as well
A New family of higher-order Generalized Haantjes Tensors, Nilpotency and Integrability
We propose a new infinite class of generalized binary tensor fields, whose
first representative of is the known Fr\"olicher--Nijenhuis bracket. This new
family of tensors reduces to the generalized Nijenhuis torsions of level
recently introduced independently in \cite{KS2017} and \cite{TT2017} and
possesses many interesting algebro-geometric properties.
We prove that the vanishing of the generalized Nijenhuis torsion of level
of a nilpotent operator field over a manifold of dimension is
necessary for the existence of a local chart where the operator field takes a
an upper triangular form. Besides, the vanishing of a generalized torsion of
level provides us with a sufficient condition for the integrability of the
eigen-distributions of an operator field over an -dimensional manifold. This
condition does not require the knowledge of the spectrum and of the
eigen-distributions of the operator field. The latter result generalizes the
celebrated Haantjes theorem.Comment: 25 page
The Rényi Redundancy of Generalized Huffman Codes
Huffman's algorithm gives optimal codes, as measured by average codeword length, and the redundancy can be measured as the difference between the average codeword length and Shannon's entropy. If the objective function is replaced by an exponentially weighted average, then a simple modification of Huffman's algorithm gives optimal codes. The redundancy can now be measured as the difference between this new average and A. Renyi's (1961) generalization of Shannon's entropy. By decreasing some of the codeword lengths in a Shannon code, the upper bound on the redundancy given in the standard proof of the noiseless source coding theorem is improved. The lower bound is improved by randomizing between codeword lengths, allowing linear programming techniques to be used on an integer programming problem. These bounds are shown to be asymptotically equal. The results are generalized to the Renyi case and are related to R.G. Gallager's (1978) bound on the redundancy of Huffman codes
Signatures of rotating binaries in micro-lensing experiments
Gravitational microlensing offers a powerful method with which to probe a
variety of binary-lens systems, as the binarity of the lens introduces
deviations from the typical (single-lens) Paczy\'nski behaviour in the event
light curves. Generally, a static binary lens is considered to fit the observed
light curve and, when the orbital motion is taken into account, an
oversimplified model is usually employed. In this paper, we treat the
binary-lens motion in a realistic way and focus on simulated events that are
fitted well by a Paczy\'nski curve. We show that an accurate timing analysis of
the residuals (calculated with respect to the best-fitting Paczy\'nski model)
is usually sufficient to infer the orbital period of the binary lens. It goes
without saying that the independently estimated period may be used to further
constrain the orbital parameters obtained by the best-fitting procedure, which
often gives degenerate solutions. We also present a preliminary analysis of the
event OGLE-2011-BLG-1127 / MOA-2011-BLG-322, which has been recognized to be
the result of a binary lens. The period analysis results in a periodicity of
\simeq 12 days, which confirms the oscillation of the observed data around the
best-fitting model. The estimated periodicity is probably associated with an
intrinsic variability of the source star, and therefore there is an opportunity
to use this technique to investigate either the intrinsic variability of the
source or the effects induced by the binary-lens orbital motion.Comment: In press on MNRAS, 2014. 8 pages, 4 figures. On-line material
available on the Journal web-pag
Searchable Sky Coverage of Astronomical Observations: Footprints and Exposures
Sky coverage is one of the most important pieces of information about
astronomical observations. We discuss possible representations, and present
algorithms to create and manipulate shapes consisting of generalized spherical
polygons with arbitrary complexity and size on the celestial sphere. This shape
specification integrates well with our Hierarchical Triangular Mesh indexing
toolbox, whose performance and capabilities are enhanced by the advanced
features presented here. Our portable implementation of the relevant spherical
geometry routines comes with wrapper functions for database queries, which are
currently being used within several scientific catalog archives including the
Sloan Digital Sky Survey, the Galaxy Evolution Explorer and the Hubble Legacy
Archive projects as well as the Footprint Service of the Virtual Observatory.Comment: 11 pages, 7 figures, submitted to PAS
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