Carmichael meets chebotarev

For any finite Galois extension K of ℚ and any conjugacy class C in Gal(K=ℚ), we show that there exist infinitely many Carmichael numbers composed solely of primes for which the associated class of Frobenius automorphisms is C. This result implies that for every natural number n there are infinitely many Carmichael numbers of the form a2 + nb 2 with a; b ε Z. © Canadian Mathematical Society 2012

NMR Self Diffusion and Relaxation Time Measurements for Poly (vinylidene fluoride) (PVDF) Based Polymer Gel Electrolytes Containing LiBF4 and Propylene Carbonate

Polymer gel electrolytes (PGEs) have been prepared using lithium tetrafluoroborate (LiBF4), propylene carbonate (PC) and poly (vinylidene fluoride) (PVDF). Self diffusion coefficients have been measured using pulse field gradient nuclear magnetic resonance (PFG-NMR) for the lithium cation, BF4 anion and solvent molecules using 7Li, 19F and 1H nuclei, respectively. It was found that lithium ion diffusion was slow compared to the much larger fluorinated BF4 anion, which is attributed to a large solvation shell around the lithium ions. The 7Li and 1H diffusion measurements also exhibited two unique environments for the diffusive species. The measurement of NMR transverse relaxation times has confirmed the presence of lithium ions in multiple phases as shown by the diffusion measurements

Chromosomal localization of the transcription factor YY1 in the mouse and human

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47010/1/335_2004_Article_BF00360552.pd

Assessing the uncertainties of model estimates of primary productivity in the tropical Pacific Ocean

Author Posting. © Elsevier B.V., 2009. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Journal of Marine Systems 76 (2009): 113-133, doi:10.1016/j.jmarsys.2008.05.010.Depth-integrated primary productivity (PP) estimates obtained from satellite ocean color based models (SatPPMs) and those generated from biogeochemical ocean general circulation models (BOGCMs) represent a key resource for biogeochemical and ecological studies at global as well as regional scales. Calibration and validation of these PP models are not straightforward, however, and comparative studies show large differences between model estimates. The goal of this paper is to compare PP estimates obtained from 30 different models (21 SatPPMs and 9 BOGCMs) to a tropical Pacific PP database consisting of ~1000 14C measurements spanning more than a decade (1983- 1996). Primary findings include: skill varied significantly between models, but performance was not a function of model complexity or type (i.e. SatPPM vs. BOGCM); nearly all models underestimated the observed variance of PP, specifically yielding too few low PP (< 0.2 gC m-2d-2) values; more than half of the total root-mean-squared model-data differences associated with the satellite-based PP models might be accounted for by uncertainties in the input variables and/or the PP data; and the tropical Pacific database captures a broad scale shift from low biomass-normalized productivity in the 1980s to higher biomass-normalized productivity in the 1990s, which was not successfully captured by any of the models. This latter result suggests that interdecadal and global changes will be a significant challenge for both SatPPMs and BOGCMs. Finally, average root-mean-squared differences between in situ PP data on the equator at 140°W and PP estimates from the satellite-based productivity models were 58% lower than analogous values computed in a previous PP model comparison six years ago. The success of these types of comparison exercises is illustrated by the continual modification and improvement of the participating models and the resulting increase in model skill.This research was supported by a grant from the National Aeronautics and Space Agency Ocean Biology and Biogeochemistry program (NNG06GA03G), as well as by numerous other grants to the various participating investigator

Genome-wide association study identifies two susceptibility loci for osteosarcoma

Osteosarcoma is the most common primary bone malignancy of adolescents and young adults. To better understand the genetic etiology of osteosarcoma, we performed a multistage genome-wide association study consisting of 941 individuals with osteosarcoma (cases) and 3,291 cancer-free adult controls of European ancestry. Two loci achieved genome-wide significance: a locus in the GRM4 gene at 6p21.3 (encoding glutamate receptor metabotropic 4; rs1906953; P = 8.1 × 10⁻⁹) and a locus in the gene desert at 2p25.2 (rs7591996 and rs10208273; P = 1.0 × 10⁻⁸ and 2.9 × 10⁻⁷, respectively). These two loci warrant further exploration to uncover the biological mechanisms underlying susceptibility to osteosarcoma

Female chromosome X mosaicism is age-related and preferentially affects the inactivated X chromosome

To investigate large structural clonal mosaicism of chromosome X, we analysed the SNP microarray intensity data of 38,303 women from cancer genome-wide association studies (20,878 cases and 17,425 controls) and detected 124 mosaic X events42Mb in 97 (0.25%) women. Here we show rates for X-chromosome mosaicism are four times higher than mean autosomal rates; X mosaic events more often include the entire chromosome and participants with X events more likely harbour autosomal mosaic events. X mosaicism frequency increases with age (0.11% in 50-year olds; 0.45% in 75-year olds), as reported for Y and autosomes. Methylation array analyses of 33 women with X mosaicism indicate events preferentially involve the inactive X chromosome. Our results provide further evidence that the sex chromosomes undergo mosaic events more frequently than autosomes, which could have implications for understanding the underlying mechanisms of mosaic events and their possible contribution to risk for chronic diseases