75 research outputs found
Vertex labeling and routing in expanded Apollonian networks
We present a family of networks, expanded deterministic Apollonian networks,
which are a generalization of the Apollonian networks and are simultaneously
scale-free, small-world, and highly clustered. We introduce a labeling of their
vertices that allows to determine a shortest path routing between any two
vertices of the network based only on the labels.Comment: 16 pages, 2 figure
Minimal chordal sense of direction and circulant graphs
A sense of direction is an edge labeling on graphs that follows a globally
consistent scheme and is known to considerably reduce the complexity of several
distributed problems. In this paper, we study a particular instance of sense of
direction, called a chordal sense of direction (CSD). In special, we identify
the class of k-regular graphs that admit a CSD with exactly k labels (a minimal
CSD). We prove that connected graphs in this class are Hamiltonian and that the
class is equivalent to that of circulant graphs, presenting an efficient
(polynomial-time) way of recognizing it when the graphs' degree k is fixed
Recursive graphs with small-world scale-free properties
We discuss a category of graphs, recursive clique trees, which have
small-world and scale-free properties and allow a fine tuning of the clustering
and the power-law exponent of their discrete degree distribution. We determine
relevant characteristics of those graphs: the diameter, degree distribution,
and clustering parameter. The graphs have also an interesting recursive
property, and generalize recent constructions with fixed degree distributions.Comment: 4 pages, 2 figure
High Dimensional Apollonian Networks
We propose a simple algorithm which produces high dimensional Apollonian
networks with both small-world and scale-free characteristics. We derive
analytical expressions for the degree distribution, the clustering coefficient
and the diameter of the networks, which are determined by their dimension
Upward Three-Dimensional Grid Drawings of Graphs
A \emph{three-dimensional grid drawing} of a graph is a placement of the
vertices at distinct points with integer coordinates, such that the straight
line segments representing the edges do not cross. Our aim is to produce
three-dimensional grid drawings with small bounding box volume. We prove that
every -vertex graph with bounded degeneracy has a three-dimensional grid
drawing with volume. This is the broadest class of graphs admiting
such drawings. A three-dimensional grid drawing of a directed graph is
\emph{upward} if every arc points up in the z-direction. We prove that every
directed acyclic graph has an upward three-dimensional grid drawing with
volume, which is tight for the complete dag. The previous best upper
bound was . Our main result is that every -colourable directed
acyclic graph ( constant) has an upward three-dimensional grid drawing with
volume. This result matches the bound in the undirected case, and
improves the best known bound from for many classes of directed
acyclic graphs, including planar, series parallel, and outerplanar
Nonrepetitive Colouring via Entropy Compression
A vertex colouring of a graph is \emph{nonrepetitive} if there is no path
whose first half receives the same sequence of colours as the second half. A
graph is nonrepetitively -choosable if given lists of at least colours
at each vertex, there is a nonrepetitive colouring such that each vertex is
coloured from its own list. It is known that every graph with maximum degree
is -choosable, for some constant . We prove this result
with (ignoring lower order terms). We then prove that every subdivision
of a graph with sufficiently many division vertices per edge is nonrepetitively
5-choosable. The proofs of both these results are based on the Moser-Tardos
entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek
for the nonrepetitive choosability of paths. Finally, we prove that every graph
with pathwidth is nonrepetitively -colourable.Comment: v4: Minor changes made following helpful comments by the referee
Sex- and age-related differences in the management and outcomes of chronic heart failure: an analysis of patients from the ESC HFA EORP Heart Failure Long-Term Registry
Aims: This study aimed to assess age- and sex-related differences in management and 1-year risk for all-cause mortality and hospitalization in chronic heart failure (HF) patients. Methods and results: Of 16 354 patients included in the European Society of Cardiology Heart Failure Long-Term Registry, 9428 chronic HF patients were analysed [median age: 66 years; 28.5% women; mean left ventricular ejection fraction (LVEF) 37%]. Rates of use of guideline-directed medical therapy (GDMT) were high (angiotensin-converting enzyme inhibitors/angiotensin receptor blockers, beta-blockers and mineralocorticoid receptor antagonists: 85.7%, 88.7% and 58.8%, respectively). Crude GDMT utilization rates were lower in women than in men (all differences: P\ua0 64 0.001), and GDMT use became lower with ageing in both sexes, at baseline and at 1-year follow-up. Sex was not an independent predictor of GDMT prescription; however, age >75 years was a significant predictor of GDMT underutilization. Rates of all-cause mortality were lower in women than in men (7.1% vs. 8.7%; P\ua0=\ua00.015), as were rates of all-cause hospitalization (21.9% vs. 27.3%; P\ua075 years. Conclusions: There was a decline in GDMT use with advanced age in both sexes. Sex was not an independent predictor of GDMT or adverse outcomes. However, age >75 years independently predicted lower GDMT use and higher all-cause mortality in patients with LVEF 6445%
ADENOSINE DEAMINASE ACTIVITY AND SERUM C-REACTIVE PROTEIN AS PROGNOSTIC MARKERS OF CHAGAS DISEASE SEVERITY
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