Elliptic curves of large rank and small conductor

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.Comment: 16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page break

Direct Measurement of the Pseudoscalar Decay Constant fD+

The absolute branching fraction of $D^+ \to \mu^+ \nu$ has been directly measured by an analysis of a data sample of about 33 ${\rm pb^{-1}}$ collected around $\sqrt{s}=3.773$ GeV with the BES-II at the BEPC. At these energies, $D^-$ meson is produced in pair as $e^+e^-\to D^{+} D^{-}$. A total of $5321 \pm 149 \pm 160$ $D^-$ mesons are reconstructed from this data set. In the recoil side of the tagged $D^-$ mesons, $2.67\pm1.74$ purely leptonic decay events of $D^+ \to \mu^+ \nu$ are observed. This yields a branching fraction of $BF(D^+ \to \mu^+ \nu_{\mu}) = (0.122^{+0.111}_{-0.053}\pm 0.010)$, and a corresponding pseudoscalar decay constant $f_{D^+}=(371^{+129}_{-119}\pm 25)$ MeV.Comment: 7 pages, 8 figures, Submitted to Physics Letters B in October, 200

Detectable clonal mosaicism and its relationship to aging and cancer

In an analysis of 31,717 cancer cases and 26,136 cancer-free controls from 13 genome-wide association studies, we observed large chromosomal abnormalities in a subset of clones in DNA obtained from blood or buccal samples. We observed mosaic abnormalities, either aneuploidy or copy-neutral loss of heterozygosity, of >2 Mb in size in autosomes of 517 individuals (0.89%), with abnormal cell proportions of between 7% and 95%. In cancer-free individuals, frequency increased with age, from 0.23% under 50 years to 1.91% between 75 and 79 years (P = 4.8 × 10(-8)). Mosaic abnormalities were more frequent in individuals with solid tumors (0.97% versus 0.74% in cancer-free individuals; odds ratio (OR) = 1.25; P = 0.016), with stronger association with cases who had DNA collected before diagnosis or treatment (OR = 1.45; P = 0.0005). Detectable mosaicism was also more common in individuals for whom DNA was collected at least 1 year before diagnosis with leukemia compared to cancer-free individuals (OR = 35.4; P = 3.8 × 10(-11)). These findings underscore the time-dependent nature of somatic events in the etiology of cancer and potentially other late-onset diseases

Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with Subtype and Stage Inference

The heterogeneity of neurodegenerative diseases is a key confound to disease understanding and treatment development, as study cohorts typically include multiple phenotypes on distinct disease trajectories. Here we introduce a machine-learning technique\u2014Subtype and Stage Inference (SuStaIn)\u2014able to uncover data-driven disease phenotypes with distinct temporal progression patterns, from widely available cross-sectional patient studies. Results from imaging studies in two neurodegenerative diseases reveal subgroups and their distinct trajectories of regional neurodegeneration. In genetic frontotemporal dementia, SuStaIn identifies genotypes from imaging alone, validating its ability to identify subtypes; further the technique reveals within-genotype heterogeneity. In Alzheimer\u2019s disease, SuStaIn uncovers three subtypes, uniquely characterising their temporal complexity. SuStaIn provides fine-grained patient stratification, which substantially enhances the ability to predict conversion between diagnostic categories over standard models that ignore subtype (p = 7.18 7 10 124 ) or temporal stage (p = 3.96 7 10 125 ). SuStaIn offers new promise for enabling disease subtype discovery and precision medicine