5,130 research outputs found
The critical probability for Voronoi percolation in the hyperbolic plane tends to 1/2
We consider percolation on the Voronoi tessellation generated by a
homogeneous Poisson point process on the hyperbolic plane. We show that the
critical probability for the existence of an infinite cluster tends to as
the intensity of the Poisson process tends to infinity. This confirms a
conjecture of Benjamini and Schramm.Comment: 15 pages, 6 figures, to be published in Random Structures and
Algorithms, very minor corrections since the last versio
Poisson-Voronoi percolation in the hyperbolic plane with small intensities
We consider percolation on the Voronoi tessellation generated by a
homogeneous Poisson point process on the hyperbolic plane. We show that the
critical probability for the existence of an infinite cluster is asymptotically
equal to as This answers a question of Benjamini
and Schramm.Comment: 70 pages, 11 figures, various corrections made compared to the last
versio
Dynamics of genotype-specific HPV clearance and reinfection in rural Ghana may compromise HPV screening approaches
Persistent Human Papillomavirus (HPV) infection is a prerequisite for cervical cancer development. Few studies investigated clearance of high-risk HPV in low-and-middle-income countries. Our study investigated HPV clearance and persistence over four years in women from North Tongu District, Ghana. In 2010/2011, cervical swabs of 500 patients were collected and HPV genotyped (nested multiplex PCR) in Accra, Ghana. In 2014, 104 women who previously tested positive for high-risk HPV and remained untreated were re-tested for HPV. Cytobrush samples were genotyped (GP5+/6+ PCR & Luminex-MPG readout) in Berlin, Germany. Positively tested patients underwent colposcopy and treatment if indicated. Of 104 women, who tested high-risk HPV+ in 2010/2011, seven (6,7%; 95%CI: 2.7-13.4%) had ≥1 persistent high-risk-infection after ~4 years (mean age 39 years). Ninety-seven (93,3%; 95%CI: 86.6-97.3%) had cleared the original infection, while 22 (21.2%; 95%CI: 13.8-30.3%) had acquired new high-risk infections with other genotypes. Persistent types found were HPV 16, 18, 35, 39, 51, 52, 58, and 68. Among those patients, one case of CIN2 (HPV 68) and one micro-invasive cervical cancer (HPV 16) were detected. This longitudinal observational data suggest that single HPV screening rounds may lead to over-referral. Including type-specific HPV re-testing or additional triage methods could help reduce follow-up rates
Fast, exact CMB power spectrum estimation for a certain class of observational strategies
We describe a class of observational strategies for probing the anisotropies
in the cosmic microwave background (CMB) where the instrument scans on rings
which can be combined into an n-torus, the {\em ring torus}. This class has the
remarkable property that it allows exact maximum likelihood power spectrum
estimation in of order operations (if the size of the data set is )
under circumstances which would previously have made this analysis intractable:
correlated receiver noise, arbitrary asymmetric beam shapes and far side lobes,
non-uniform distribution of integration time on the sky and partial sky
coverage. This ease of computation gives us an important theoretical tool for
understanding the impact of instrumental effects on CMB observables and hence
for the design and analysis of the CMB observations of the future. There are
members of this class which closely approximate the MAP and Planck satellite
missions. We present a numerical example where we apply our ring torus methods
to a simulated data set from a CMB mission covering a 20 degree patch on the
sky to compute the maximum likelihood estimate of the power spectrum
with unprecedented efficiency.Comment: RevTeX, 14 pages, 5 figures. A full resolution version of Figure 1
and additional materials are at http://feynman.princeton.edu/~bwandelt/RT
Diminishing Effectiveness of Long-Term Maintenance Topical Steroid Therapy in PPI Non-Responsive Eosinophilic Esophagitis
While topical corticosteroids are first-line therapy for eosinophilic esophagitis (EoE), the data regarding long-term effectiveness are lacking. We aimed to determine long-term histologic and endoscopic outcomes of maintenance therapy in EoE steroid responders
Cosmological Constraints from Galaxy Clustering and the Mass-to-Number Ratio of Galaxy Clusters
We place constraints on the average density (Omega_m) and clustering
amplitude (sigma_8) of matter using a combination of two measurements from the
Sloan Digital Sky Survey: the galaxy two-point correlation function, w_p, and
the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to
cluster M/L ratios. Our w_p measurements are obtained from DR7 while the sample
of clusters is the maxBCG sample, with cluster masses derived from weak
gravitational lensing. We construct non-linear galaxy bias models using the
Halo Occupation Distribution (HOD) to fit both w_p and M/N for different
cosmological parameters. HOD models that match the same two-point clustering
predict different numbers of galaxies in massive halos when Omega_m or sigma_8
is varied, thereby breaking the degeneracy between cosmology and bias. We
demonstrate that this technique yields constraints that are consistent and
competitive with current results from cluster abundance studies, even though
this technique does not use abundance information. Using w_p and M/N alone, we
find Omega_m^0.5*sigma_8=0.465+/-0.026, with individual constraints of
Omega_m=0.29+/-0.03 and sigma_8=0.85+/-0.06. Combined with current CMB data,
these constraints are Omega_m=0.290+/-0.016 and sigma_8=0.826+/-0.020. All
errors are 1-sigma. The systematic uncertainties that the M/N technique are
most sensitive to are the amplitude of the bias function of dark matter halos
and the possibility of redshift evolution between the SDSS Main sample and the
maxBCG sample. Our derived constraints are insensitive to the current level of
uncertainties in the halo mass function and in the mass-richness relation of
clusters and its scatter, making the M/N technique complementary to cluster
abundances as a method for constraining cosmology with future galaxy surveys.Comment: 23 pages, submitted to Ap
Amplitude equations and pattern selection in Faraday waves
We present a systematic nonlinear theory of pattern selection for parametric
surface waves (Faraday waves), not restricted to fluids of low viscosity. A
standing wave amplitude equation is derived from the Navier-Stokes equations
that is of gradient form. The associated Lyapunov function is calculated for
different regular patterns to determine the selected pattern near threshold.
For fluids of large viscosity, the selected wave pattern consists of parallel
stripes. At lower viscosity, patterns of square symmetry are obtained in the
capillary regime (large frequencies). At lower frequencies (the mixed
gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold, ...
patterns are predicted. The regions of stability of the various patterns are in
quantitative agreement with recent experiments conducted in large aspect ratio
systems.Comment: 12 pages, 1 figure, Revte
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