33-dimensional Continued Fraction Algorithms Cheat Sheets

Multidimensional Continued Fraction Algorithms are generalizations of the Euclid algorithm and find iteratively the gcd of two or more numbers. They are defined as linear applications on some subcone of $\mathbb{R}^d$. We consider multidimensional continued fraction algorithms that acts symmetrically on the positive cone $\mathbb{R}^d_+$ for $d=3$. We include well-known and old ones (Poincar\'e, Brun, Selmer, Fully Subtractive) and new ones (Arnoux-Rauzy-Poincar\'e, Reverse, Cassaigne). For each algorithm, one page (called cheat sheet) gathers a handful of informations most of them generated with the open source software Sage with the optional Sage package \texttt{slabbe-0.2.spkg}. The information includes the $n$-cylinders, density function of an absolutely continuous invariant measure, domain of the natural extension, lyapunov exponents as well as data regarding combinatorics on words, symbolic dynamics and digital geometry, that is, associated substitutions, generated $S$-adic systems, factor complexity, discrepancy, dual substitutions and generation of digital planes. The document ends with a table of comparison of Lyapunov exponents and gives the code allowing to reproduce any of the results or figures appearing in these cheat sheets.Comment: 9 pages, 66 figures, landscape orientatio

A Multi-wavelength Survey of AGN in Massive Clusters: AGN Detection and Cluster AGN Fraction

We aim to study the effect of environment on the presence and fuelling of Active Galactic Nuclei (AGN) in massive galaxy clusters. We explore the use of different AGN detection techniques with the goal of selecting AGN across a broad range of luminosities, AGN/host galaxy flux ratios, and obscuration levels. From a sample of 12 galaxy clusters at redshifts 0.5 < z < 0.9, we identify AGN candidates using optical variability from multi-epoch HST imaging, X-ray point sources in Chandra images, and mid-IR SED power-law fits through the Spitzer IRAC channels. We find 178 optical variables, 74 X-ray point sources, and 64 IR power law sources, resulting in an average of ~25 AGN per cluster. We find no significant difference between the fraction of AGN among galaxies in clusters and the percentage of similarly-detected AGN in field galaxy studies (~2.5%). This result provides evidence that galaxies are still able to fuel accretion onto their supermassive black holes, even in dense environments. We also investigate correlations between the percentage of AGN and cluster physical properties such as mass, X-ray luminosity, size, morphology class and redshift. We find no significant correlations among cluster properties and the percentage of AGN detected.Comment: 68 pages, 22 figures, 15 table

Binary Properties from Cepheid Radial Velocities (CRaV)

We have examined high accuracy radial velocities of Cepheids to determine the binary frequency. The data are largely from the CORAVEL spectrophotometer and the Moscow version, with a typical uncertainty of $\leq1$~km~s$^{-1}$, and a time span from 1 to 20 years. A systemic velocity was obtained by removing the pulsation component using a high order Fourier series. From this data we have developed a list of stars showing no orbital velocity larger than $\pm1$~km~s$^{-1}$. The binary fraction was analyzed as a function of magnitude, and yields an apparent decrease in this fraction for fainter stars. We interpret this as incompleteness at fainter magnitudes, and derive the preferred binary fraction of $29\pm8$\% ( $20\pm6$\% per decade of orbital period) from the brightest 40 stars. Comparison of this fraction in this period range (1-20 years) implies a large fraction for the full period range. This is reasonable in that the high accuracy velocities are sensitive to the longer periods and smaller orbital velocity amplitudes in the period range sampled here. Thus the Cepheid velocity sample provides a sensitive detection in the period range between short period spectroscopic binaries and resolved companions. The recent identification of $\delta$ Cep as a binary with very low amplitude and high eccentricity underscores the fact that the binary fractions we derive are lower limits, to which other low amplitude systems will probably be added. The mass ratio (q) distribution derived from ultraviolet observations of the secondary is consistent with a flat distribution for the applicable period range (1 to 20 years).Comment: accepted for publication in A

Transport, shot noise, and topology in AC-driven dimer arrays

We analyze an AC-driven dimer chain connected to a strongly biased electron source and drain. It turns out that the resulting transport exhibits fingerprints of topology. They are particularly visible in the driving-induced current suppression and the Fano factor. Thus, shot noise measurements provide a topological phase diagram as a function of the driving parameters. The observed phenomena can be explained physically by a mapping to an effective time-independent Hamiltonian and the emergence of edge states. Moreover, by considering quantum dissipation, we determine the requirements for the coherence properties in a possible experimental realization. For the computation of the zero-frequency noise, we develop an efficient method based on matrix-continued fractions.Comment: 8 pages, 6 figure

Interventions for the treatment of oral cavity and oropharyngeal cancer:chemotherapy

&lt;b&gt;Background:&lt;/b&gt; Oral cavity and oropharyngeal cancers are frequently described as part of a group of oral cancers or head and neck cancer. Treatment of oral cavity cancer is generally surgery followed by radiotherapy, whereas oropharyngeal cancers, which are more likely to be advanced at the time of diagnosis, are managed with radiotherapy or chemoradiation. Surgery for oral cancers can be disfiguring and both surgery and radiotherapy have significant functional side effects, notably impaired ability to eat, drink and talk. The development of new chemotherapy agents, new combinations of agents and changes in the relative timing of surgery, radiotherapy, and chemotherapy treatments may potentially bring about increases in both survival and quality of life for this group of patients.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Objectives:&lt;/b&gt; To determine whether chemotherapy, in addition to radiotherapy and/or surgery for oral cavity and oropharyngeal cancer results in improved survival, disease free survival, progression free survival, locoregional control and reduced recurrence of disease. To determine which regimen and time of administration (induction, concomitant or adjuvant) is associated with better outcomes.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Search strategy:&lt;/b&gt; Electronic searches of the Cochrane Oral Health Group's Trials Register, CENTRAL, MEDLINE, EMBASE, AMED were undertaken on 28th July 2010. Reference lists of recent reviews and included studies were also searched to identify further trials.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Selection criteria:&lt;/b&gt; Randomised controlled trials where more than 50% of participants had primary tumours in the oral cavity or oropharynx, and which compared the addition of chemotherapy to other treatments such as radiotherapy and/or surgery, or compared two or more chemotherapy regimens or modes of administration, were included.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Data collection and analysis:&lt;/b&gt; Trials which met the inclusion criteria were assessed for risk of bias using six domains: sequence generation, allocation concealment, blinding, completeness of outcome data, selective reporting and other possible sources of bias. Data were extracted using a specially designed form and entered into the characteristics of included studies table and the analysis sections of the review. The proportion of participants in each trial with oral cavity and oropharyngeal cancers are recorded in Additional Table 1.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Main results:&lt;/b&gt; There was no statistically significant improvement in overall survival associated with induction chemotherapy compared to locoregional treatment alone in 25 trials (hazard ratio (HR) of mortality 0.92, 95% confidence interval (CI) 0.84 to 1.00). Post-surgery adjuvant chemotherapy was associated with improved overall survival compared to surgery +/- radiotherapy alone in 10 trials (HR of mortality 0.88, 95% CI 0.79 to 0.99), and there was an additional benefit of adjuvant concomitant chemoradiotherapy compared to radiotherapy in 4 of these trials (HR of mortality 0.84, 95% CI 0.72 to 0.98). Concomitant chemoradiotherapy resulted in improved survival compared to radiotherapy alone in patients whose tumours were considered unresectable in 25 trials (HR of mortality 0.79, 95% CI 0.74 to 0.84). However, the additional toxicity attributable to chemotherapy in the combined regimens remains unquantified.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Authors' conclusions:&lt;/b&gt; Chemotherapy, in addition to radiotherapy and surgery, is associated with improved overall survival in patients with oral cavity and oropharyngeal cancers. Induction chemotherapy is associated with a 9% increase in survival and adjuvant concomitant chemoradiotherapy is associated with a 16% increase in overall survival following surgery. In patients with unresectable tumours, concomitant chemoradiotherapy showed a 22% benefit in overall survival compared with radiotherapy alone.&lt;p&gt;&lt;/p&gt

Star formation in Perseus: III. Outflows

We present a search for outflows towards 51 submillimetre cores in Perseus. With consistently derived outflow properties from a large homogeneous dataset within one molecular cloud we can investigate further the mass dependence and time evolution of protostellar mass loss. Of the 51 cores, 37 show broad linewings indicative of molecular outflows. In 13 cases, the linewings could be due to confusion with neighbouring flows but 9 of those sources also have near-infrared detections confirming their protostellar nature. The total fraction of protostars in our sample is 65%. All but four outflow detections are confirmed as protostellar by Spitzer IR detections and only one Spitzer source has no outflow, showing that outflow maps at this sensitivity are equally good at identifying protostars as Spitzer. Outflow momentum flux correlates both with source luminosity and with core mass but there is considerable scatter even within this one cloud despite the homogeneous dataset. We fail to confirm the result of Bontemps et al. (1996) that Class I sources show lower momentum fluxes on average than Class 0 sources, with a KS test showing a significant probability that the momentum fluxes for both Class 0s and Class Is are drawn from the same distribution. We find that outflow power may not show a simple decline between the Class 0 to Class I stages. Our sample includes low momentum flux, low-luminosity Class 0 sources, possibly at a very early evolutionary stage. If the only mass loss from the core were due to outflows, cores would last for 10^5-10^8 years, longer than current estimates of 1.5-4 x 10^5 years for the mean lifetime for the embedded phase. Additional mechanisms for removing mass from protostellar cores may be necessary.Comment: 26 pages, 21 figures. Version with full colour figures from http://www.astro.ex.ac.uk/people/hatchell/RecentPapers/hatchell07_outflows.pd

Abell 2111: An Optical and Radio Study of the Richest Butcher-Oemler Cluster

We present an in-depth analysis of the Butcher-Oemler cluster A2111, including new optical spectroscopy plus a deep Very Large Array (VLA) radio continuum observation. These are combined with optical imaging from the Sloan Digital Sky Survey (SDSS) to assess the activity and properties of member galaxies. Prior X-ray studies have suggested A2111 is a head-on cluster merger, a dynamical state which might be connected to the high level of activity inferred from its blue fraction. We are able to directly assess this claim, using our spectroscopic data to identify 95 cluster members among 196 total galaxy spectra. These galaxy velocities do not themselves provide significant evidence for the merger interpretation, however they are consistent with it provided the system is viewed near the time of core passage and at a viewing angle >~30 degrees different from the merger axis. The SDSS data allow us to confirm the high blue fraction for A2111, f_b = 0.15 +/- 0.03 based on photometry alone and f_b = 0.23 +/- 0.03 using spectroscopic data to remove background galaxies. We are able to detect 175 optical sources from the SDSS in our VLA radio data, of which 35 have redshift information. We use the SDSS photometry to determine photometric redshifts for the remaining 140 radio-optical sources. In total we identify up to 26 cluster radio galaxies, 14 of which have spectroscopic redshifts. The optical spectroscopy and radio data reveal a substantial population of dusty starbursts within the cluster. The high blue fraction and prevalence of star formation is consistent with the hypothesis that dynamically-active clusters are associated with more active member galaxies than relaxed clusters.Comment: To appear in AJ; 53 pages including 10 figures and several long table