89 research outputs found
A Note on the Complexity of One-Sided Crossing Minimization of Trees
In 2011, Harrigan and Healy published a polynomial-time algorithm for
one-sided crossing minimization for trees. We point out a counterexample to
that algorithm, and show that one-sided crossing minimization is NP-hard for
trees.Comment: 3 pages, 2 figure
Turbocharging Heuristics for Weak Coloring Numbers
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which generalize the well-known graph invariant degeneracy (also called k-core number). Being NP-hard, weak-coloring numbers were previously computed on real-world graphs mainly via incremental heuristics. We study whether it is feasible to augment such heuristics with exponential-time subprocedures that kick in when a desired upper bound on the weak coloring number is breached. We provide hardness and tractability results on the corresponding computational subproblems. We implemented several of the resulting algorithms and show them to be competitive with previous approaches on a previously studied set of benchmark instances containing 86 graphs with up to 183831 edges. We obtain improved weak coloring numbers for over half of the instances
LinSets.zip: Compressing Linear Set Diagrams
Linear diagrams are used to visualize set systems by depicting set
memberships as horizontal line segments in a matrix, where each set is
represented as a row and each element as a column. Each such line segment of a
set is shown in a contiguous horizontal range of cells of the matrix indicating
that the corresponding elements in the columns belong to the set. As each set
occupies its own row in the matrix, the total height of the resulting
visualization is as large as the number of sets in the instance. Such a linear
diagram can be visually sparse and intersecting sets containing the same
element might be represented by distant rows. To alleviate such undesirable
effects, we present LinSets.zip, a new approach that achieves a more
space-efficient representation of linear diagrams. First, we minimize the total
number of gaps in the horizontal segments by reordering columns, a criterion
that has been shown to increase readability in linear diagrams. The main
difference of LinSets.zip to linear diagrams is that multiple non-intersecting
sets can be positioned in the same row of the matrix. Furthermore, we present
several different rendering variations for a matrix-based representation that
utilize the proposed row compression. We implemented the different steps of our
approach in a visualization pipeline using integer-linear programming, and
suitable heuristics aiming at sufficiently fast computations in practice. We
conducted both a quantitative evaluation and a small-scale user experiment to
compare the effects of compressing linear diagrams.Comment: To be presented at PacificVis 202
The Complexity of Cluster Vertex Splitting and Company
Clustering a graph when the clusters can overlap can be seen from three
different angles: We may look for cliques that cover the edges of the graph, we
may look to add or delete few edges to uncover the cluster structure, or we may
split vertices to separate the clusters from each other. Splitting a vertex
means to remove it and to add two new copies of and to make each previous
neighbor of adjacent with at least one of the copies. In this work, we
study the underlying computational problems regarding the three angles to
overlapping clusterings, in particular when the overlap is small. We show that
the above-mentioned covering problem, which also has been independently studied
in different contexts,is NP-complete. Based on a previous so-called
critical-clique lemma, we leverage our hardness result to show that Cluster
Editing with Vertex Splitting is also NP-complete, resolving an open question
by Abu-Khzam et al. [ISCO 2018]. We notice, however, that the proof of the
critical-clique lemma is flawed and we give a counterexample. Our hardness
result also holds under a version of the critical-clique lemma to which we
currently do not have a counterexample. On the positive side, we show that
Cluster Vertex Splitting admits a vertex-linear problem kernel with respect to
the number of splits.Comment: 30 pages, 9 figure
Fermi Bubbles in the Milky Way: the closest AGN feedback laboratory courtesy of Sgr A*?
Deposition of a massive ( to 10^5 \msun) giant molecular cloud (GMC)
into the inner parsec of the Galaxy is widely believed to explain the origin of
over a hundred unusually massive young stars born there Myr ago. An
unknown fraction of that gas could have been accreted by Sgr A*, the
supermassive black hole (SMBH) of the Milky Way. It has been recently suggested
that two observed -ray-emitting bubbles emanating from the very center
of our Galaxy were inflated by this putative activity of Sgr A*. We run a suite
of numerical simulations to test whether the observed morphology of the bubbles
could be due to the collimation of a wide angle outflow from Sgr A* by the
disc-like Central Molecular Zone (CMZ), a well known massive repository of
molecular gas in the central pc. We find that an Eddington-limited
outburst of Sgr A* lasting Myr is required to reproduce the
morphology of the {\it Fermi} bubbles, suggesting that the GMC mass was \sim
10^5 \msun and it was mainly accreted by Sgr A* rather than used to make
stars. We also find that the outflow from Sgr A* enforces strong angular
momentum mixing in the CMZ disc, robustly sculpting it into a much narrower
structure -- a ring -- perhaps synonymous with the recently reported "Herschel
ring". In addition, we find that Sgr A* outflow is likely to have induced
formation of massive star-forming GMCs in the CMZ. In this scenario, the Arches
and Quintuplet clusters, the two observed young star clusters in the central
tens of parsecs of the Galaxy, and also GMCs such as Sgr B2, owe their
existence to the recent Sgr A* activity.Comment: 18 pages, 10 figures, submitted to MNRA
Turbulence induced collisional velocities and density enhancements: large inertial range results from shell models
To understand the earliest stages of planet formation, it is crucial to be
able to predict the rate and the outcome of dust grains collisions, be it
sticking and growth, bouncing, or fragmentation. The outcome of such collisions
depends on the collision speed, so we need a solid understanding of the rate
and velocity distribution of turbulence-induced dust grain collisions. The rate
of the collisions depends both on the speed of the collisions and the degree of
clustering experienced by the dust grains, which is a known outcome of
turbulence. We evolve the motion of dust grains in simulated turbulence, an
approach that allows a large turbulent inertial range making it possible to
investigate the effect of turbulence on meso-scale grains (millimeter and
centimeter). We find three populations of dust grains: one highly clustered,
cold and collisionless; one warm; and the third "hot". Our results can be fit
by a simple formula, and predict both significantly slower typical collisional
velocities for a given turbulent strength than previously considered, and
modest effective clustering of the collisional populations, easing difficulties
associated with bouncing and fragmentation barriers to dust grain growth.
Nonetheless, the rate of high velocity collisions falls off merely
exponentially with relative velocity so some mid- or high-velocity collisions
will still occur, promising some fragmentation.Comment: 14 pages, 8 figures, 4 tables, Accepted, MNRA
LIGHT-RAILS MODEL IN TEMPE, ARIZONA: STRATEGIES TO REDUCE AIR POLLUTION
To rethink growth is important to keep up with an increase demand of transport in order to decrease greenhouse gas emissions. It is clear that transportation generates a loss in vegetation then leads to an increase of carbon dioxide, a prime contributor to global warming, in the atmosphere. However, new alternatives are available to show an attempt to solve congestion that ultimately promotes a further increase of pollutants in the atmosphere. From this insight, we find solutions to resolve traffic problem in the megalopolis Phoenix, in particular the city of Tempe. Although this research we highlight the factors that make up a good ridership of the Phoenix light rail looking at similar low density cities like Phoenix, we searched for solutions that would prevent low ridership in future light rail extensions. It was found that a more pedestrian friendly environment was created with businesses and residential buildings close together, especially in Tempe City around the Arizona State University (ASU), extremely benefited by the project
The Chang-Refsdal Lens Revisited
This paper provides a complete theoretical treatment of the point-mass lens
perturbed by constant external shear, often called the Chang-Refsdal lens. We
show that simple invariants exist for the products of the (complex) positions
of the four images, as well as moment sums of their signed magnifications. The
image topographies and equations of the caustics and critical curves are also
studied. We derive the fully analytic expressions for precaustics, which are
the loci of non-critical points that map to the caustics under the lens
mapping. They constitute boundaries of the region in the image domain that maps
onto the interior of the caustics. The areas under the critical curves,
caustics and precaustics are all evaluated, which enables us to calculate the
mean magnification of the source within the caustics. Additionally, the exact
analytic expression for the magnification distribution for the source in the
triangular caustics is derived, as well as a useful approximate expression.
Finally, we find that the Chang-Refsdal lens with the convergence greater than
unity can exhibit third-order critical behaviour, if the reduced shear is
exactly equal to \sqrt{3}/2, and that the number of images for N-point masses
with non-zero constant shear cannot be greater than 5N-1.Comment: to appear in MNRAS (including 6 figures, 3 appendices; v2 - minor
update with corrected typos etc.
From Lab to Pilot Scale: Commissioning of an Integrated Device for the Generation of Crystals
Fast time-to-market, increased efficiency, and flexibility of production processes are major motivators for the development of integrated, continuous apparatuses with short changeover times. Following this trend, the modular belt crystallizer was developed and characterized in lab scale with the model system sucrose-water. Based on the promising results, the plant concept was upscaled and commissioned in industrial environment. The results are presented within the scope of this work. Starting from small seed crystals in solution, it was possible to grow, separate, and dry product particles. Further, the conducted experiments demonstrated that it is feasible to transfer the results from laboratory to pilot scale, which in turn enables accelerated process design as well as development
High accretion rates in magnetised Keplerian discs mediated by a Parker instability driven dynamo
Hydromagnetic stresses in accretion discs have been the subject of intense
theoretical research over the past one and a half decades. Most of the disc
simulations have assumed a small initial magnetic field and studied the
turbulence that arises from the magnetorotational instability. However, gaseous
discs in galactic nuclei and in some binary systems are likely to have
significant initial magnetisation. Motivated by this, we performed ideal
magnetohydrodynamic simulations of strongly magnetised, vertically stratified
discs in a Keplerian potential. Our initial equilibrium configuration, which
has an azimuthal magnetic field in equipartion with thermal pressure, is
unstable to the Parker instability. This leads to the expelling of magnetic
field arcs, anchored in the midplane of the disc, to around five scale heights
from the midplane. Transition to turbulence happens primarily through
magnetorotational instability in the resulting vertical fields, although
magnetorotational shear instability in the unperturbed azimuthal field plays a
significant role as well, especially in the midplane where buoyancy is weak.
High magnetic and hydrodynamical stresses arise, yielding an effective
-value of around 0.1 in our highest resolution run. Azimuthal magnetic
field expelled by magnetic buoyancy from the disc is continuously replenished
by the stretching of a radial field created as gas parcels slide in the linear
gravity field along inclined magnetic field lines. This dynamo process, where
the bending of field lines by the Parker instability leads to re-creation of
the azimuthal field, implies that highly magnetised discs are astrophysically
viable and that they have high accretion rates.Comment: 14 pages, 14 figures, accepted for publication in A&
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