Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm

2000 Mathematics Subject Classification: 17A50, 05C05.In this note we present the formula for the coefficients of the substitution series f(g(x)) of planar tree power series g(x) into f(x)

Effectively Closed Infinite-Genus Surfaces and the String Coupling

The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality of the maximal set of endpoints is shown to be 2^{\mit N}. The product of the coefficient of the genus-g superstring amplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is an exponential function of the genus with a base comparable in magnitude to the unified gauge coupling. The value of the string coupling is consistent with the characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.Comment: TeX, 33 page

Degenerating families of dendrograms

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist $p$-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the $p$-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are $p$-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.Comment: 13 pages, 8 figure

Technical design of the phase I Mu3e experiment

The Mu3e experiment aims to find or exclude the lepton flavour violating decay at branching fractions above . A first phase of the experiment using an existing beamline at the Paul Scherrer Institute (PSI) is designed to reach a single event sensitivity of . We present an overview of all aspects of the technical design and expected performance of the phase I Mu3e detector. The high rate of up to muon decays per second and the low momenta of the decay electrons and positrons pose a unique set of challenges, which we tackle using an ultra thin tracking detector based on high-voltage monolithic active pixel sensors combined with scintillating fibres and tiles for precise timing measurements

The Mu3e Data Acquisition

The Mu3e experiment aims to find or exclude the lepton flavor violating decay μ+→e+e−e+ with a sensitivity of one in 10 16 muon decays. The first phase of the experiment is currently under construction at the Paul Scherrer Institute (PSI, Switzerland), where beams with up to 10 8 muons per second are available. The detector will consist of an ultra-thin pixel tracker made from High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) , complemented by scintillating tiles and fibers for precise timing measurements. The experiment produces about 100Gbit/s of zero-suppressed data, which are transported to a filter farm using a network of field programmable gate arrays (FPGAs) and fast optical links. On the filter farm, tracks and three-particle vertices are reconstructed using highly parallel algorithms running on graphics processing units, leading to a reduction of the data to 100 Mbyte/s for mass storage and offline analysis. This article introduces the system design and hardware implementation of the Mu3e data acquisition and filter farm

Values of p -adic L -functions and a p -adic Poisson kernel

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46572/1/222_2005_Article_BF01231508.pd

Annual outpatient hysteroscopy and endometrial sampling (OHES) in HNPCC/Lynch syndrome (LS)

Background: LS women have a 40-60 % lifetime risk of endometrial cancer (EC). Most international guidelines recommend screening. However, data on efficacy are limited. Purpose: To assess the performance of OHES for EC screening in LS and compare it with transvaginal ultrasound (TVS) alone. Methods: A prospective observational cohort study of LS women attending a tertiary high-risk familial gynaecological cancer clinic was conducted. LS women opting for EC screening underwent annual OHES and TVS. Histopathological specimens were processed using a strict protocol. Data of women screened between October 2007 and March 2010 were analysed from a bespoke database. Histology was used as the gold standard. Diagnostic accuracy of OHES was compared with TVS using specificity, and positive (PLR) and negative (NLR) likelihood ratios. Results: Forty-one LS women underwent 69 screens (41 prevalent, 28 incident). Four (three prevalent, one incident) women were detected to have EC/atypical endometrial hyperplasia (AEH), five had endometrial polyps and two had endometrial hyperplasia (EH) on OHES. TVS detected two of four EC/AEH. OHES had similar specificity of 89.8 % (CI 79.2, 96.2 %), but higher PLR 9.8 (CI 4.6, 21) and lower NLR (zero) compared to TVS: specificity 84.75 %(CI 73, 92.8 %), PLR 3.28 (CI 1.04, 10.35) and NLR 0.59 (CI 0.22, 1.58). No interval cancers occurred over a median follow-up of 22 months. The annual incidence was 3.57 % (CI 0.09, 18.35) for EC, 10.71 % (CI 2.27, 28.23) for polyps and 21.4 % (CI 8.3, 40.1) for any endometrial pathology. Conclusions: Our findings suggest that in LS, annual OHES is acceptable and has high diagnostic accuracy for EC/AEH screening. Larger international studies are needed for confirmation, given the relatively small numbers of LS women at individual centres. It reinforces the current recommendation that endometrial sampling is crucial when screening these women. © 2012 Springer-Verlag