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 $1/2$ 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 $\pi \lambda/3$ as $\lambda\to0.$ 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 $N^2$ operations (if the size of the data set is $N$) 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 $C_\ell$ 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