63,292 research outputs found
Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model
Given a 3D binary digital image I, we define and compute
an edge-weighted tree, called Homological Region Tree (or Hom-Tree,
for short). It coincides, as unweighted graph, with the classical Region
Adjacency Tree of black 6-connected components (CCs) and white 26-
connected components of I. In addition, we define the weight of an edge
(R, S) as the number of tunnels that the CCs R and S “share”. The
Hom-Tree structure is still an isotopic invariant of I. Thus, it provides
information about how the different homology groups interact between
them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different
shapes and different complexity of connected component nesting is performed
for numerically validating the method.Ministerio de EconomĂa y Competitividad MTM2016-81030-
Designing Gapped Soft Functions for Jet Production
Distributions in jet production often depend on a soft function, S, which
describes hadronic radiation between the jets. Near kinematic thresholds S
encodes nonperturbative information, while far from thresholds S can be
computed with an operator product expansion (OPE). We design soft functions for
jets that serve this dual purpose, reducing to the perturbative result in the
OPE region and to a consistent model in the nonperturbative region. We use the
MSbar scheme, and in both regions S displays the appropriate renormalization
group scale dependence. We point out that viable soft function models should
have a gap associated with the minimum hadronic energy deposit. This gap is
connected to the leading O(Lambda_QCD) renormalon ambiguity in jet event
shapes. By defining the gap in a suitable scheme we demonstrate that the
leading renormalon can be eliminated. This improves the convergence of
perturbative results, and also the stability by which non-perturbative
parameters encode the underlying soft physics.Comment: 17 pages, 5 figure
The linewidth-size relationship in the dense ISM of the Central Molecular Zone
The linewidth (sigma) - size (R) relationship has been extensively measured
and analysed, in both the local ISM and in nearby normal galaxies. Generally, a
power-law describes the relationship well with an index ranging from 0.2-0.6,
now referred to as one of "Larson's Relationships." The nature of turbulence
and star formation is considered to be intimately related to these
relationships, so evaluating the sigma-R correlations in various environments
is important for developing a comprehensive understanding of the ISM. We
measure the sigma-R relationship in the Central Molecular Zone (CMZ) of the
Galactic Centre using spectral line observations of the high density tracers
N2H+, HCN, H13CN, and HCO+. We use dendrograms, which map the hierarchical
nature of the position-position-velocity (PPV) data, to compute sigma and R of
contiguous structures. The dispersions range from ~2-30 km/s in structures
spanning sizes 2-40 pc, respectively. By performing Bayesian inference, we show
that a power-law with exponent 0.3-1.1 can reasonably describe the sigma-R
trend. We demonstrate that the derived sigma-R relationship is independent of
the locations in the PPV dataset where sigma and R are measured. The uniformity
in the sigma-R relationship suggests turbulence in the CMZ is driven on the
large scales beyond >30 pc. We compare the CMZ sigma-R relationship to that
measured in the Galactic molecular cloud Perseus. The exponents between the two
systems are similar, suggestive of a connection between the turbulent
properties within a cloud to its ambient medium. Yet, the velocity dispersion
in the CMZ is systematically higher, resulting in a coefficient that is nearly
five times larger. The systematic enhancement of turbulent velocities may be
due to the combined effects of increased star formation activity, larger
densities, and higher pressures relative to the local ISM.Comment: 11 pages, 8 figures, Accepted for publication in MNRA
Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions
A greedily routable region (GRR) is a closed subset of , in
which each destination point can be reached from each starting point by
choosing the direction with maximum reduction of the distance to the
destination in each point of the path.
Recently, Tan and Kermarrec proposed a geographic routing protocol for dense
wireless sensor networks based on decomposing the network area into a small
number of interior-disjoint GRRs. They showed that minimum decomposition is
NP-hard for polygons with holes.
We consider minimum GRR decomposition for plane straight-line drawings of
graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing
style which has become a popular research topic in graph drawing. We show that
minimum decomposition is still NP-hard for graphs with cycles, but can be
solved optimally for trees in polynomial time. Additionally, we give a
2-approximation for simple polygons, if a given triangulation has to be
respected.Comment: full version of a paper appearing in ISAAC 201
New Geometric Algorithms for Fully Connected Staged Self-Assembly
We consider staged self-assembly systems, in which square-shaped tiles can be
added to bins in several stages. Within these bins, the tiles may connect to
each other, depending on the glue types of their edges. Previous work by
Demaine et al. showed that a relatively small number of tile types suffices to
produce arbitrary shapes in this model. However, these constructions were only
based on a spanning tree of the geometric shape, so they did not produce full
connectivity of the underlying grid graph in the case of shapes with holes;
designing fully connected assemblies with a polylogarithmic number of stages
was left as a major open problem. We resolve this challenge by presenting new
systems for staged assembly that produce fully connected polyominoes in O(log^2
n) stages, for various scale factors and temperature {\tau} = 2 as well as
{\tau} = 1. Our constructions work even for shapes with holes and uses only a
constant number of glues and tiles. Moreover, the underlying approach is more
geometric in nature, implying that it promised to be more feasible for shapes
with compact geometric description.Comment: 21 pages, 14 figures; full version of conference paper in DNA2
Triaxial Black-Hole Nuclei
We demonstrate that the nuclei of galaxies containing supermassive black
holes can be triaxial in shape. Schwarzschild's method was first used to
construct self-consistent orbital superpositions representing nuclei with axis
ratios of 1:0.79:0.5 and containing a central point mass representing a black
hole. Two different density laws were considered, with power-law slopes of -1
and -2. We constructed two solutions for each power law: one containing only
regular orbits and the other containing both regular and chaotic orbits.
Monte-Carlo realizations of the models were then advanced in time using an
N-body code to verify their stability. All four models were found to retain
their triaxial shapes for many crossing times. The possibility that galactic
nuclei may be triaxial complicates the interpretation of stellar-kinematical
data from the centers of galaxies and may alter the inferred interaction rates
between stars and supermassive black holes.Comment: 4 pages, 4 postscript figures, uses emulateapj.st
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