954 research outputs found
Drawing Planar Graphs with Few Geometric Primitives
We define the \emph{visual complexity} of a plane graph drawing to be the
number of basic geometric objects needed to represent all its edges. In
particular, one object may represent multiple edges (e.g., one needs only one
line segment to draw a path with an arbitrary number of edges). Let denote
the number of vertices of a graph. We show that trees can be drawn with
straight-line segments on a polynomial grid, and with straight-line
segments on a quasi-polynomial grid. Further, we present an algorithm for
drawing planar 3-trees with segments on an
grid. This algorithm can also be used with a small modification to draw maximal
outerplanar graphs with edges on an grid. We also
study the problem of drawing maximal planar graphs with circular arcs and
provide an algorithm to draw such graphs using only arcs. This is
significantly smaller than the lower bound of for line segments for a
nontrivial graph class.Comment: Appeared at Proc. 43rd International Workshop on Graph-Theoretic
Concepts in Computer Science (WG 2017
Impact of boundaries on fully connected random geometric networks
Many complex networks exhibit a percolation transition involving a
macroscopic connected component, with universal features largely independent of
the microscopic model and the macroscopic domain geometry. In contrast, we show
that the transition to full connectivity is strongly influenced by details of
the boundary, but observe an alternative form of universality. Our approach
correctly distinguishes connectivity properties of networks in domains with
equal bulk contributions. It also facilitates system design to promote or avoid
full connectivity for diverse geometries in arbitrary dimension.Comment: 6 pages, 3 figure
Embedding Four-directional Paths on Convex Point Sets
A directed path whose edges are assigned labels "up", "down", "right", or
"left" is called \emph{four-directional}, and \emph{three-directional} if at
most three out of the four labels are used. A \emph{direction-consistent
embedding} of an \mbox{-vertex} four-directional path on a set of
points in the plane is a straight-line drawing of where each vertex of
is mapped to a distinct point of and every edge points to the direction
specified by its label. We study planar direction-consistent embeddings of
three- and four-directional paths and provide a complete picture of the problem
for convex point sets.Comment: 11 pages, full conference version including all proof
Dynamic Range Majority Data Structures
Given a set of coloured points on the real line, we study the problem of
answering range -majority (or "heavy hitter") queries on . More
specifically, for a query range , we want to return each colour that is
assigned to more than an -fraction of the points contained in . We
present a new data structure for answering range -majority queries on a
dynamic set of points, where . Our data structure uses O(n)
space, supports queries in time, and updates in amortized time. If the coordinates of the points are integers,
then the query time can be improved to . For constant values of , this improved query
time matches an existing lower bound, for any data structure with
polylogarithmic update time. We also generalize our data structure to handle
sets of points in d-dimensions, for , as well as dynamic arrays, in
which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201
Invasive pulmonary aspergillosis in chronic obstructive pulmonary disease: an emerging fungal pathogen
ABSTRACTAcute invasive pulmonary aspergillosis occurs predominantly in immunocompromised hosts, with increasing numbers of cases of invasive aspergillosis among patients with chronic obstructive pulmonary disease (COPD) being reported. Among 13 cases of invasive aspergillosis diagnosed in COPD patients admitted to the intensive care unit with acute respiratory distress, the only risk factor for invasive fungal infection was corticosteroid treatment. Invasive aspergillosis should be suspected in COPD patients receiving steroid treatment who have extensive pulmonary infiltrates. Survival depends on rapid diagnosis and early appropriate treatment. A decrease or interruption of steroid treatment should be considered as part of the overall therapeutic strategy
The Complexity of Drawing Graphs on Few Lines and Few Planes
It is well known that any graph admits a crossing-free straight-line drawing
in and that any planar graph admits the same even in
. For a graph and , let denote
the minimum number of lines in that together can cover all edges
of a drawing of . For , must be planar. We investigate the
complexity of computing these parameters and obtain the following hardness and
algorithmic results.
- For , we prove that deciding whether for a
given graph and integer is -complete.
- Since , deciding is NP-hard for . On the positive side, we show that the problem
is fixed-parameter tractable with respect to .
- Since , both and
are computable in polynomial space. On the negative side, we show
that drawings that are optimal with respect to or
sometimes require irrational coordinates.
- Let be the minimum number of planes in needed
to cover a straight-line drawing of a graph . We prove that deciding whether
is NP-hard for any fixed . Hence, the problem is
not fixed-parameter tractable with respect to unless
Community-level respiration of prokaryotic microbes may rise with global warming
Understanding how the metabolic rates of prokaryotes respond to temperature is fun-damental to our understanding of how ecosystem functioning will be altered by climatechange, as these micro-organisms are major contributors to global carbon efflux. Ecologicalmetabolic theory suggests that species living at higher temperatures evolve higher growthrates than those in cooler niches due to thermodynamic constraints. Here, using a globalprokaryotic dataset, we find that maximal growth rate at thermal optimum increases withtemperature for mesophiles (temperature optima.45◦C), but not thermophiles (&45◦C).Furthermore, short-term (within-day) thermal responses of prokaryotic metabolic rates aretypically more sensitive to warming than those of eukaryotes. Because climatic warmingwill mostly impact ecosystems in the mesophilic temperature range, we conclude that asmicrobial communities adapt to higher temperatures, their metabolic rates and therefore,biomass-specific CO2production, will inevitably rise. Using a mathematical model, weillustrate the potential global impacts of these findings
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