416 research outputs found
A cost function for similarity-based hierarchical clustering
The development of algorithms for hierarchical clustering has been hampered
by a shortage of precise objective functions. To help address this situation,
we introduce a simple cost function on hierarchies over a set of points, given
pairwise similarities between those points. We show that this criterion behaves
sensibly in canonical instances and that it admits a top-down construction
procedure with a provably good approximation ratio
k-Trails: Recognition, Complexity, and Approximations
The notion of degree-constrained spanning hierarchies, also called k-trails,
was recently introduced in the context of network routing problems. They
describe graphs that are homomorphic images of connected graphs of degree at
most k. First results highlight several interesting advantages of k-trails
compared to previous routing approaches. However, so far, only little is known
regarding computational aspects of k-trails.
In this work we aim to fill this gap by presenting how k-trails can be
analyzed using techniques from algorithmic matroid theory. Exploiting this
connection, we resolve several open questions about k-trails. In particular, we
show that one can recognize efficiently whether a graph is a k-trail.
Furthermore, we show that deciding whether a graph contains a k-trail is
NP-complete; however, every graph that contains a k-trail is a (k+1)-trail.
Moreover, further leveraging the connection to matroids, we consider the
problem of finding a minimum weight k-trail contained in a graph G. We show
that one can efficiently find a (2k-1)-trail contained in G whose weight is no
more than the cheapest k-trail contained in G, even when allowing negative
weights.
The above results settle several open questions raised by Molnar, Newman, and
Sebo
Counting Hamilton cycles in sparse random directed graphs
Let D(n,p) be the random directed graph on n vertices where each of the
n(n-1) possible arcs is present independently with probability p. A celebrated
result of Frieze shows that if then D(n,p) typically
has a directed Hamilton cycle, and this is best possible. In this paper, we
obtain a strengthening of this result, showing that under the same condition,
the number of directed Hamilton cycles in D(n,p) is typically
. We also prove a hitting-time version of this statement,
showing that in the random directed graph process, as soon as every vertex has
in-/out-degrees at least 1, there are typically
directed Hamilton cycles
Effects of oral, smoked, and vaporized cannabis on endocrine pathways related to appetite and metabolism: a randomized, double-blind, placebo-controlled, human laboratory study.
As perspectives on cannabis continue to shift, understanding the physiological and behavioral effects of cannabis use is of paramount importance. Previous data suggest that cannabis use influences food intake, appetite, and metabolism, yet human research in this regard remains scant. The present study investigated the effects of cannabis administration, via different routes, on peripheral concentrations of appetitive and metabolic hormones in a sample of cannabis users. This was a randomized, crossover, double-blind, placebo-controlled study. Twenty participants underwent four experimental sessions during which oral cannabis, smoked cannabis, vaporized cannabis, or placebo was administered. Active compounds contained 6.9 ± 0.95% (~50.6 mg) ∆9-tetrahydrocannabinol (THC). Repeated blood samples were obtained, and the following endocrine markers were measured: total ghrelin, acyl-ghrelin, leptin, glucagon-like peptide-1 (GLP-1), and insulin. Results showed a significant drug main effect (p = 0.001), as well as a significant drug × time-point interaction effect (p = 0.01) on insulin. The spike in blood insulin concentrations observed under the placebo condition (probably due to the intake of brownie) was blunted by cannabis administration. A significant drug main effect (p = 0.001), as well as a trend-level drug × time-point interaction effect (p = 0.08) was also detected for GLP-1, suggesting that GLP-1 concentrations were lower under cannabis, compared to the placebo condition. Finally, a significant drug main effect (p = 0.01) was found for total ghrelin, suggesting that total ghrelin concentrations during the oral cannabis session were higher than the smoked and vaporized cannabis sessions. In conclusion, cannabis administration in this study modulated blood concentrations of some appetitive and metabolic hormones, chiefly insulin, in cannabis users. Understanding the mechanisms underpinning these effects may provide additional information on the cross-talk between cannabinoids and physiological pathways related to appetite and metabolism
Identifying and exploring factors influencing career choice, recruitment and retention of anaesthesia trainees in the UK
Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/Peer reviewedPostprin
Time-limited excitation of damped field-line resonances: Implications for satellite observations
Clustering and the hyperbolic geometry of complex networks
Clustering is a fundamental property of complex networks and it is the
mathematical expression of a ubiquitous phenomenon that arises in various types
of self-organized networks such as biological networks, computer networks or
social networks. In this paper, we consider what is called the global
clustering coefficient of random graphs on the hyperbolic plane. This model of
random graphs was proposed recently by Krioukov et al. as a mathematical model
of complex networks, under the fundamental assumption that hyperbolic geometry
underlies the structure of these networks. We give a rigorous analysis of
clustering and characterize the global clustering coefficient in terms of the
parameters of the model. We show how the global clustering coefficient can be
tuned by these parameters and we give an explicit formula for this function.Comment: 51 pages, 1 figur
Optimality program in segment and string graphs
Planar graphs are known to allow subexponential algorithms running in time
or for most of the paradigmatic
problems, while the brute-force time is very likely to be
asymptotically best on general graphs. Intrigued by an algorithm packing curves
in by Fox and Pach [SODA'11], we investigate which
problems have subexponential algorithms on the intersection graphs of curves
(string graphs) or segments (segment intersection graphs) and which problems
have no such algorithms under the ETH (Exponential Time Hypothesis). Among our
results, we show that, quite surprisingly, 3-Coloring can also be solved in
time on string graphs while an algorithm running
in time for 4-Coloring even on axis-parallel segments (of unbounded
length) would disprove the ETH. For 4-Coloring of unit segments, we show a
weaker ETH lower bound of which exploits the celebrated
Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over
to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent
Dominating Set.Comment: 19 pages, 15 figure
Exploiting dietary fibre and the gut microbiota in pelvic radiotherapy patients
ACKNOWLEDGEMENTS We thank Mrs Pat Bain for her assistance in creating Fig. 1. Funding Information: AEK’s salary is funded by Friends of ANCHOR and the University of Aberdeen Development Trust. CKT’s DPhil was funded by the Clarendon Fund, Balliol College, Oxford and Cancer Research UK. JK’s summer research project was funded by a Royal College of Radiologists’ Summer Undergraduate Research Fellowship. The authors received no specific funding for this work.Peer reviewedPublisher PD
Teaching Advocacy to Health Professional Students: Advancing Global and Population Health by Training the Next Generation of Health Professionals
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