438 research outputs found
Constructing Intrinsic Delaunay Triangulations of Submanifolds
We describe an algorithm to construct an intrinsic Delaunay triangulation of
a smooth closed submanifold of Euclidean space. Using results established in a
companion paper on the stability of Delaunay triangulations on -generic
point sets, we establish sampling criteria which ensure that the intrinsic
Delaunay complex coincides with the restricted Delaunay complex and also with
the recently introduced tangential Delaunay complex. The algorithm generates a
point set that meets the required criteria while the tangential complex is
being constructed. In this way the computation of geodesic distances is
avoided, the runtime is only linearly dependent on the ambient dimension, and
the Delaunay complexes are guaranteed to be triangulations of the manifold
A probabilistic approach to reducing the algebraic complexity of computing Delaunay triangulations
Computing Delaunay triangulations in involves evaluating the
so-called in\_sphere predicate that determines if a point lies inside, on
or outside the sphere circumscribing points . This
predicate reduces to evaluating the sign of a multivariate polynomial of degree
in the coordinates of the points . Despite
much progress on exact geometric computing, the fact that the degree of the
polynomial increases with makes the evaluation of the sign of such a
polynomial problematic except in very low dimensions. In this paper, we propose
a new approach that is based on the witness complex, a weak form of the
Delaunay complex introduced by Carlsson and de Silva. The witness complex
is defined from two sets and in some metric space
: a finite set of points on which the complex is built, and a set of
witnesses that serves as an approximation of . A fundamental result of de
Silva states that if .
In this paper, we give conditions on that ensure that the witness complex
and the Delaunay triangulation coincide when is a finite set, and we
introduce a new perturbation scheme to compute a perturbed set close to
such that . Our perturbation
algorithm is a geometric application of the Moser-Tardos constructive proof of
the Lov\'asz local lemma. The only numerical operations we use are (squared)
distance comparisons (i.e., predicates of degree 2). The time-complexity of the
algorithm is sublinear in . Interestingly, although the algorithm does not
compute any measure of simplex quality, a lower bound on the thickness of the
output simplices can be guaranteed.Comment: 24 page
An obstruction to Delaunay triangulations in Riemannian manifolds
Delaunay has shown that the Delaunay complex of a finite set of points of
Euclidean space triangulates the convex hull of , provided
that satisfies a mild genericity property. Voronoi diagrams and Delaunay
complexes can be defined for arbitrary Riemannian manifolds. However,
Delaunay's genericity assumption no longer guarantees that the Delaunay complex
will yield a triangulation; stronger assumptions on are required. A natural
one is to assume that is sufficiently dense. Although results in this
direction have been claimed, we show that sample density alone is insufficient
to ensure that the Delaunay complex triangulates a manifold of dimension
greater than 2.Comment: This is a revision and extension of a note that appeared as an
appendix in the (otherwise unpublished) report arXiv:1303.649
Only distances are required to reconstruct submanifolds
In this paper, we give the first algorithm that outputs a faithful
reconstruction of a submanifold of Euclidean space without maintaining or even
constructing complicated data structures such as Voronoi diagrams or Delaunay
complexes. Our algorithm uses the witness complex and relies on the stability
of power protection, a notion introduced in this paper. The complexity of the
algorithm depends exponentially on the intrinsic dimension of the manifold,
rather than the dimension of ambient space, and linearly on the dimension of
the ambient space. Another interesting feature of this work is that no explicit
coordinates of the points in the point sample is needed. The algorithm only
needs the distance matrix as input, i.e., only distance between points in the
point sample as input.Comment: Major revision, 16 figures, 47 page
Should health professionals screen women for domestic violence? : systematic review
Objective To assess the evidence for the acceptability
and effectiveness of screening women for domestic
violence in healthcare settings.
Design Systematic review of published quantitative
studies.
Search strategy Three electronic databases (Medline,
Embase, and CINAHL) were searched for articles
published in the English language up to February
2001.
Included studies Surveys that elicited the attitudes of
women and health professionals on the screening of
women in health settings; comparative studies
conducted in healthcare settings that measured rates
of identification of domestic violence in the presence
and absence of screening; studies measuring
outcomes of interventions for women identified in
health settings who experience abuse from a male
partner or expartner compared with abused women
not receiving an intervention.
Results 20 papers met the inclusion criteria. In four
surveys, 4385% of women respondents found
screening in healthcare settings acceptable. Two
surveys of health professionals' views found that two
thirds of physicians and almost half of emergency
department nurses were not in favour of screening. In
nine studies of screening compared with no
screening, most detected a greater proportion of
abused women identified by healthcare professionals.
Six studies of interventions used weak study designs
and gave inconsistent results. Other than increased
referral to outside agencies, little evidence exists for
changes in important outcomes such as decreased
exposure to violence. No studies measured quality of
life, mental health outcomes, or potential harm to
women from screening programmes.
Conclusion Although domestic violence is a common
problem with major health consequences for women,
implementation of screening programmes in
healthcare settings cannot be justified. Evidence of the
benefit of specific interventions and lack of harm from
screening is needed
Local Criteria for Triangulation of Manifolds
We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use
Performance of LED-Based Fluorescence Microscopy to Diagnose Tuberculosis in a Peripheral Health Centre in Nairobi.
Sputum microscopy is the only tuberculosis (TB) diagnostic available at peripheral levels of care in resource limited countries. Its sensitivity is low, particularly in high HIV prevalence settings. Fluorescence microscopy (FM) can improve performance of microscopy and with the new light emitting diode (LED) technologies could be appropriate for peripheral settings. The study aimed to compare the performance of LED-FM versus Ziehl-Neelsen (ZN) microscopy and to assess feasibility of LED-FM at a low level of care in a high HIV prevalence country
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