52,719 research outputs found
Labeled Interleaving Distance for Reeb Graphs
Merge trees, contour trees, and Reeb graphs are graph-based topological
descriptors that capture topological changes of (sub)level sets of scalar
fields. Comparing scalar fields using their topological descriptors has many
applications in topological data analysis and visualization of scientific data.
Recently, Munch and Stefanou introduced a labeled interleaving distance for
comparing two labeled merge trees, which enjoys a number of theoretical and
algorithmic properties. In particular, the labeled interleaving distance
between merge trees can be computed in polynomial time. In this work, we define
the labeled interleaving distance for labeled Reeb graphs. We then prove that
the (ordinary) interleaving distance between Reeb graphs equals the minimum of
the labeled interleaving distance over all labelings. We also provide an
efficient algorithm for computing the labeled interleaving distance between two
labeled contour trees (which are special types of Reeb graphs that arise from
simply-connected domains). In the case of merge trees, the notion of the
labeled interleaving distance was used by Gasparovic et al. to prove that the
(ordinary) interleaving distance on the set of (unlabeled) merge trees is
intrinsic. As our final contribution, we present counterexamples showing that,
on the contrary, the (ordinary) interleaving distance on (unlabeled) Reeb
graphs (and contour trees) is not intrinsic. It turns out that, under mild
conditions on the labelings, the labeled interleaving distance is a metric on
isomorphism classes of Reeb graphs, analogous to the ordinary interleaving
distance. This provides new metrics on large classes of Reeb graphs
An edit distance for Reeb graphs
We consider the problem of assessing the similarity of 3D shapes
using Reeb graphs from the standpoint of robustness under
perturbations. For this purpose, 3D objects are viewed as spaces
endowed with real-valued functions, while the similarity between
the resulting Reeb graphs is addressed through a graph edit
distance. The cases of smooth functions on manifolds and piecewise
linear functions on polyhedra stand out as the most interesting
ones. The main contribution of this paper is the introduction of a
general edit distance suitable for comparing Reeb graphs in these
settings. This edit distance promises to be useful for
applications in 3D object retrieval because of its stability
properties in the presence of noise
Gravitational Waves from Supermassive Black Hole Coalescence in a Hierarchical Galaxy Formation Model
We investigate the expected gravitational wave emission from coalescing
supermassive black hole (SMBH) binaries resulting from mergers of their host
galaxies. When galaxies merge, the SMBHs in the host galaxies sink to the
center of the new merged galaxy and form a binary system. We employ a
semi-analytic model of galaxy and quasar formation based on the hierarchical
clustering scenario to estimate the amplitude of the expected stochastic
gravitational wave background owing to inspiraling SMBH binaries and bursts
owing to the SMBH binary coalescence events. We find that the characteristic
strain amplitude of the background radiation is for just below the detection
limit from measurements of the pulsar timing provided that SMBHs coalesce
simultaneously when host galaxies merge. The main contribution to the total
strain amplitude of the background radiation comes from SMBH coalescence events
at . We also find that a future space-based gravitational wave
interferometer such as the planned \textit{Laser Interferometer Space Antenna}
({\sl LISA}) might detect intense gravitational wave bursts associated with
coalescence of SMBH binaries with total mass at
at a rate . Our model predicts that
burst signals with a larger amplitude correspond
to coalescence events of massive SMBH binary with total mass at low redshift at a rate whereas those with a smaller amplitude
correspond to coalescence events of less massive SMBH binary with total mass
at high redshift .Comment: Accepted for publication in ApJ. 11 pages, 7 figure
Plasmon tunability in metallodielectric metamaterials
The dielectric properties of metamaterials consisting of periodically
arranged metallic nanoparticles of spherical shape are calculated by rigorously
solving Maxwell's equations. Effective dielectric functions are obtained by
comparing the reflectivity of planar surfaces limiting these materials with
Fresnel's formulas for equivalent homogeneous media, showing mixing and
splitting of individual-particle modes due to inter-particle interaction.
Detailed results for simple cubic and fcc crystals of aluminum spheres in
vacuum, silver spheres in vacuum, and silver spheres in a silicon matrix are
presented. The filling fraction of the metal f is shown to determine the
position of the plasmon modes of these metamaterials. Significant deviations
are observed with respect to Maxwell-Garnett effective medium theory for large
f, and multiple plasmons are predicted to exist in contrast to Maxwell-Garnett
theory.Comment: 6 pages, 4 figure
Gravitational Radiation From Globular Clusters
Space-based gravitational wave detectors will have the ability to observe
continuous low frequency gravitational radiation from binary star systems. They
can determine the direction to continuous sources with an angular resolution
approaching tens of arcminutes. This resolution should be sufficient to
identify binary sources as members of some nearby globular clusters. Thus,
gravitational radiation can be used to determine the population of hard
binaries in globular clusters. For particularly hard binaries, the orbital
period may change as a result of gravitational wave emission. If one of these
binaries can be identified with a globular cluster, then the distance to that
cluster can be determined. Thus, gravitational radiation may provide
reddening-independent distance measurements to globular clusters.Comment: 26 pages, 1 figure, LaTeX, uses aasms4.sty, submitted to Ap.
Arabic parsing using grammar transforms
We investigate Arabic Context Free Grammar parsing with dependency annotation comparing lexicalised and unlexicalised parsers. We study how morphosyntactic as well as function tag information percolation in the form of grammar transforms (Johnson, 1998, Kulick et al., 2006) affects the performance of a parser and helps dependency assignment. We focus on the three most frequent functional
tags in the Arabic Penn Treebank: subjects, direct objects and predicates . We merge these functional tags with their phrasal categories and (where appropriate) percolate case information to the non-terminal (POS) category to train the parsers. We then automatically enrich the output of these parsers with full dependency information in order to annotate trees with Lexical Functional Grammar (LFG)
f-structure equations with produce f-structures, i.e. attribute-value matrices approximating to basic predicate-argument-adjunct structure representations. We present a series of experiments evaluating how well lexicalized, history-based, generative (Bikel) as well as latent
variable PCFG (Berkeley) parsers cope with the enriched Arabic data. We measure quality and coverage of both the output trees and the generated LFG f-structures. We show that joint functional and morphological information percolation improves both the recovery of trees as well as dependency results in the form of LFG f-structures
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