Length statistics of random multicurves on closed hyperbolic surfaces

In this note, we determine the length distribution of components of a random multicurve on a fixed hyperbolic surface using Mirzakhani's equidistribution theorem for horospheres and Margulis' thickening technique. We obtain an explicit formula for the resulting lengths statistics and prove, in particular, that it depends only on the topological type of the multicurve and does not depend on the hyperbolic metric. This result generalizes prior result of M. Mirzakhani, providing the length statistics for multicurves decomposing the surface into pairs of pants. Results very close to ours are obtained independently and simultaneously by F. Arana-Herrera

Low-lying geodesics on the modular surface and necklaces

The m-thick part of the modular surface X is the smallest compact subsurface of X with horocycle boundary containing all the closed geodesics which wind around the cusp at most m times. The m-thick parts form a compact exhaustion of X. We are interested in the geodesics that lie in the m-thick part (so called m low-lying geodesics). We produce a complete asymptotic expansion for the number of m low-lying geodesics of length equal to 2n in the modular surface. In particular, we obtain the asymptotic growth rate of the m low-lying geodesics in terms of their word length using the natural generators of the modular group. After establishing a correspondence between this counting problem and the problem of counting necklaces with n beads, we perform a careful singularity analysis on the associated generating function of the sequence

Evaluation of translocation impacts on genetic patterns in farmed and naturalized populations of Mytilus galloprovincialis along the China coast: clues from mitochondrial cytochrome c oxidase I sequences

As an introduced species, Mytilus galloprovincialis has developed into self-sustaining naturalized populations and has been widely cultivated in northern China. The M. galloprovincialis aquaculture industry wholly depends on the movement of naturalized juveniles onto farms. It is, therefore, necessary to understand the genetic effect of continuous spats’ translocation. This study divided 12 localities of M. galloprovincialis along the China coast into three types of populations—farmed, naturalized adjacent farmed, and isolated—to investigate the genetic variation and differentiation. The genetic variability is reflected by haplotype diversity, nucleotide diversity, and the mean number of pairwise differences expressed as farmed populations > naturalized adjacent farmed populations > isolated populations. The Hierarchical analyses and Mantel-test indicated slight divergence between farmed and naturalized populations, northern and southern populations. The farmed and naturalized populations clustered into two separate categories in the neighbor-joining tree except two anthropogenically intervened localities. The present results suggest that the translocation practice positively affected genetic variability and played a vital role in shaping genetic composition. The information obtained in this study provides new insights into the impacts of the translocation culture model of marine mollusks

Inter-calibration of HY-1B/COCTS thermal infrared channels with MetOp-A/IASI

The Chinese Ocean Color and Temperature Scanner (COCTS) on board the Haiyang-1B (HY-1B) satellite has two thermal infrared channels (9 and 10) centred near 11 μm and 12 μm respectively which are intended for sea surface temperature (SST) observations. In order to improve the accuracy of COCTS SSTs, the inter-calibration of COCTS thermal infrared radiance is carried out. The Infrared Atmospheric Sounding Interferometer (IASI) on board MetOp-A satellite is used as inter-calibration reference owing to its hyperspectral nature and high-quality measurements. The inter-calibration of HY-1B COCTS thermal infrared radiances with IASI is undertaken for data from the period 2009 to 2011 located in the northwest Pacific. Collocations of COCTS radiance with IASI are identified within a temporal window of 30 minutes, a spatial window of 0.12° and an atmospheric path tolerance of 3%. Matched IASI spectra are convolved with the COCTS spectral response functions, while COCTS pixels within the footprint of each IASI pixel are spatially averaged, thus creating matched IASI-COCTS radiance pairs that should agree well in the absence of satellite biases. The radiances of COCTS 11 and 12 μm channel are lower than IASI with relatively large biases, and a strong dependence of difference on radiance in the case of 11 μm channel. We use linear robust regression for different four detectors of COCTS separately to obtain the inter-calibration coefficients to correct the COCTS radiance. After correction, the mean values of COCTS 11 and 12 μm channel minus IASI radiance are -0.02 mW m-2 cm sr-1 and -0.01 mW m-2 cm sr-1 respectively, with corresponding standard deviations of 0.51 mW m-2 cm sr-1 and 0.57 mW m-2 cm sr-1. Striped noise is present in COCTS original radiance imagery associated with inconsistency between four detectors, and inter-calibration is shown to reduce, although not eliminate, the striping. The calibration accuracy of COCTS is improved after inter-calibration, that is potentially useful for improving COCTS SST accuracy in the future