Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

The effects of winter climate on the size of the cattle egret (Bubulcus ibis L.) population in the Camargue

La population nicheuse de Hérons gardebœufs de Camargue a été suivie de 1970 à 1991. Chaque année, 60 à 70 % des oiseaux présents en fin d'été (adultes et jeunes) ont tendance à hiverner dans le delta du Rhône et ses environs. Les températures hivernales affectent la taille de la population nicheuse les années suivantes. L'afflux d'oiseaux issus de populations situées plus au Sud joue un rôle important dans le maintien de cette espèce en Camargue, particulièrement après un hiver rigoureu

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Shock-enhanced C+ emission and the detection of H2O from the Stephan’s Quintet group-wide shock using Herschel

WWe present the first Herschelspectroscopic detections of the [O i] 63 μm and [Cii] 158 μm fine-structure transitions, and a single para-H2O line from the 35 × 15 kpc2 shocked intergalactic filament in Stephan’s Quintet. The filament is believed to have been formed when a high-speed intruder to the group collided with a clumpy intergroup gas. Observations with the PACS spectrometer provide evidence for broad (>1000 km s−1) luminous [Cii] line profiles, as well as fainter [O i] 63 μm emission. SPIRE FTS observations reveal water emission from the p-H2O (111–000) transition at several positions in the filament, but no other molecular lines. The H2O line is narrow and may be associated with denser intermediate-velocity gas experiencing the strongest shock-heating. The [Cii]/PAHtot and [C ii]/FIR ratios are too large to be explained by normal photo-electric heating in photodissociation regions. H ii region excitation or X-ray/cosmic-ray heating can also be ruled out. The observations lead to the conclusion that a large fraction the molecular gas is diffuse and warm. We propose that the [Cii], [O i], and warm H2 line emission is powered by a turbulent cascade in which kinetic energy from the galaxy collision with the intergalactic medium is dissipated to small scales and low velocities, via shocks and turbulent eddies. Low-velocity magnetic shocks can help explain both the [Cii]/[O i] ratio, and the relatively high [C ii]/H2 ratios observed. The discovery that [Cii] emission can be enhanced, in large-scale turbulent regions in collisional environments, has implications for the interpretation of [C ii] emission in high-z galaxies

The XMM-Newton serendipitous ultraviolet source survey catalogue

The XMM-Newton Serendipitous Ultraviolet Source Survey (XMM-SUSS) is a catalogue of ultraviolet (UV) sources detected serendipitously by the Optical Monitor (XMM-OM) on-board the XMM-Newton observatory. The catalogue contains ultraviolet-detected sources collected from 2,417 XMM-OM observations in 1-6 broad band UV and optical filters, made between 24 February 2000 and 29 March 2007. The primary contents of the catalogue are source positions, magnitudes and fluxes in 1 to 6 passbands, and these are accompanied by profile diagnostics and variability statistics. The XMM-SUSS is populated by 753,578 UV source detections above a 3 sigma signal-to-noise threshold limit which relate to 624,049 unique objects. Taking account of substantial overlaps between observations, the net sky area covered is 29-54 square degrees, depending on UV filter. The magnitude distributions peak at 20.2, 20.9 and 21.2 in UVW2, UVM2 and UVW1 respectively. More than 10 per cent of sources have been visited more than once using the same filter during XMM-Newton operation, and > 20 per cent of sources are observed more than once per filter during an individual visit. Consequently, the scope for science based on temporal source variability on timescales of hours to years is broad. By comparison with other astrophysical catalogues we test the accuracy of the source measurements and define the nature of the serendipitous UV XMM-OM source sample. The distributions of source colours in the UV and optical filters are shown together with the expected loci of stars and galaxies, and indicate that sources which are detected in multiple UV bands are predominantly star-forming galaxies and stars of type G or earlier.Comment: Accepted for publication in MNRA

Strong CH+ J=1-0 emission and absorption in DR21

We report the first detection of the ground-state rotational transition of the methylidyne cation CH+ towards the massive star-forming region DR21 with the HIFI instrument onboard the Herschel satellite. The line profile exhibits a broad emission line, in addition to two deep and broad absorption features associated with the DR21 molecular ridge and foreground gas. These observations allow us to determine a CH+ J=1-0 line frequency of 835137 +/- 3 MHz, in good agreement with a recent experimental determination. We estimate the CH+ column density to be a few 1e13 cm^-2 in the gas seen in emission, and > 1e14 cm^-2 in the components responsible for the absorption, which is indicative of a high line of sight average abundance [CH+]/[H] > 1.2x10^-8. We show that the CH+ column densities agree well with the predictions of state-of-the-art C-shock models in dense UV-illuminated gas for the emission line, and with those of turbulent dissipation models in diffuse gas for the absorption lines.Comment: Accepted for publication in A&

OC6 project Phase IV: Validation of numerical models for novel floating offshore wind support structures

\ua9 Copyright: This paper provides a summary of the work done within Phase IV of the Offshore Code Comparison Collaboration, Continued with Correlation and unCertainty (OC6) project, under International Energy Agency Wind Technology Collaboration Programme Task 30. This phase focused on validating the loading on and motion of a novel floating offshore wind system. Numerical models of a 3.6MW horizontal-axis wind turbine atop the TetraSpar floating support structure were compared using measurement data from a 1:43-Froude-scale test performed in the University of Maine\u27s Alfond Wind-Wave (W2) Ocean Engineering Laboratory. Participants in the project ran a series of simulations, including system equilibrium, surge offsets, free-decay tests, wind-only conditions, wave-only conditions, and a combination of wind and wave conditions. Validation of the models was performed by comparing the aerodynamic loading, floating support structure motion, tower base loading, mooring line tensions, and keel line tensions. The results show a relatively good estimation of the aerodynamic loading and a reasonable estimation of the platform motion and tower base fore-aft bending moment. However, there is a significant dispersion in the dynamic loading for the upwind mooring line. Very good agreement was observed between most of the numerical models and the experiment for the keel line tensions

<i>Gaia</i> Data Release 1. Summary of the astrometric, photometric, and survey properties

Context. At about 1000 days after the launch of Gaia we present the first Gaia data release, Gaia DR1, consisting of astrometry and photometry for over 1 billion sources brighter than magnitude 20.7. Aims. A summary of Gaia DR1 is presented along with illustrations of the scientific quality of the data, followed by a discussion of the limitations due to the preliminary nature of this release. Methods. The raw data collected by Gaia during the first 14 months of the mission have been processed by the Gaia Data Processing and Analysis Consortium (DPAC) and turned into an astrometric and photometric catalogue. Results. Gaia DR1 consists of three components: a primary astrometric data set which contains the positions, parallaxes, and mean proper motions for about 2 million of the brightest stars in common with the HIPPARCOS and Tycho-2 catalogues – a realisation of the Tycho-Gaia Astrometric Solution (TGAS) – and a secondary astrometric data set containing the positions for an additional 1.1 billion sources. The second component is the photometric data set, consisting of mean G-band magnitudes for all sources. The G-band light curves and the characteristics of ∼3000 Cepheid and RR-Lyrae stars, observed at high cadence around the south ecliptic pole, form the third component. For the primary astrometric data set the typical uncertainty is about 0.3 mas for the positions and parallaxes, and about 1 mas yr−1 for the proper motions. A systematic component of ∼0.3 mas should be added to the parallax uncertainties. For the subset of ∼94 000 HIPPARCOS stars in the primary data set, the proper motions are much more precise at about 0.06 mas yr−1. For the secondary astrometric data set, the typical uncertainty of the positions is ∼10 mas. The median uncertainties on the mean G-band magnitudes range from the mmag level to ∼0.03 mag over the magnitude range 5 to 20.7. Conclusions. Gaia DR1 is an important milestone ahead of the next Gaia data release, which will feature five-parameter astrometry for all sources. Extensive validation shows that Gaia DR1 represents a major advance in the mapping of the heavens and the availability of basic stellar data that underpin observational astrophysics. Nevertheless, the very preliminary nature of this first Gaia data release does lead to a number of important limitations to the data quality which should be carefully considered before drawing conclusions from the data

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page