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

Cow, farm, and herd management factors in the dry period associated with raised somatic cell counts in early lactation

This study investigated cow characteristics, farm facilities, and herd management strategies during the dry period to examine their joint influence on somatic cell counts (SCC) in early lactation. Data from 52 commercial dairy farms throughout England and Wales were collected over a 2-yr period. For the purpose of analysis, cows were separated into those housed for the dry period (6,419 cow-dry periods) and those at pasture (7,425 cow-dry periods). Bayesian multilevel models were specified with 2 response variables: ln SCC (continuous) and SCC >199,000 cells/mL (binary), both within 30 d of calving. Cow factors associated with an increased SCC after calving were parity, an SCC >199,000 cells/mL in the 60 d before drying off, increasing milk yield 0 to 30 d before drying off, and reduced DIM after calving at the time of SCC estimation. Herd management factors associated with an increased SCC after calving included procedures at drying off, aspects of bedding management, stocking density, and method of pasture grazing. Posterior predictions were used for model assessment, and these indicated that model fit was generally good. The research demonstrated that specific dry-period management strategies have an important influence on SCC in early lactation

Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

Shuttle flight pressure instrumentation: Experience and lessons for the future

Flight data obtained from the Space Transportation System orbiter entries are processed and analyzed to assess the accuracy and performance of the Development Flight Instrumentation (DFI) pressure measurement system. Selected pressure measurements are compared with available wind tunnel and computational data and are further used to perform air data analyses using the Shuttle Entry Air Data System (SEADS) computation technique. The results are compared to air data from other sources. These comparisons isolate and demonstrate the effects of the various limitations of the DFI pressure measurement system. The effects of these limitations on orbiter performance analyses are addressed, and instrumentation modifications are recommended to improve the accuracy of similar fight data systems in the future

Widely wavelength-selective Al2O3:Er3+ ring laser

Integrated Al2O3:Er3+ channel waveguide ring lasers were realized on thermally oxidized silicon substrates. High pump power coupling into- and low output power coupling from the ring is achieved in a straightforward design. Wavelength\ud selection in the range 1532 to 1557 nm was demonstrated by\ud varying the length of the output coupler from the ring

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

What Fraction of the Young Clusters in the Antennae Galaxies are "Missing"?

A reexamination of the correspondence between 6 cm radio continuum sources and young star clusters in the Antennae galaxies indicates that 85 % of the strong thermal sources have optical counterparts, once the optical image is shifted 1.2 arcsec to the southwest. A sample of 37 radio-optical matches are studied in detail showing correlations between radio properties and a variety of optical characteristics. There is a strong correlation between the radio flux and the intrinsic optical brightness. In particular, the brightest radio source is also the intrinsically brightest optical cluster (WS80). It is also the most extincted cluster in the sample, the strongest CO source and the strongest 15 micron source . Furthermore, the brightest ten radio sources are all amongst the youngest clusters with ages in the range 0 - 4 Myr and extinctions from A_V = 0.5 to 7.6 mag (with a median value of 2.6 mag). Only a few of the very red clusters originally discovered by Whitmore & Schweizer are radio sources, contrary to earlier suggestions. Finally, a new hybrid method of determining cluster ages has been developed using both UBVI colors and H_alpha equivalent widths to break the age-reddening degeneracy.Comment: 51 pages, 13 postscript figures, LaTex. To appear in the Astronomical Journal, 124, 2002, Septembe