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

Algal Blooms in Arkansas Streams, Ponds, and Lakes

Did you know that algae are a natural part of ponds, lakes, streams, and rivers? These organisms grow in the water (plankton) and on rocks, plants, and other surfaces (periphyton) and sometimes periphyton slough off into the water (seston). Most of the time these algae are hardly noticeable in waterbodies; however, sometimes they can form very noticeable algal blooms

Spectral signature of short attosecond pulse trains

We report experimental measurements of high-order harmonic spectra generated in Ar using a carrier-envelope-offset (CEO) stabilized 12 fs, 800nm laser field and a fraction (less than 10%) of its second harmonic. Additional spectral peaks are observed between the harmonic peaks, which are due to interferences between multiple pulses in the train. The position of these peaks varies with the CEO and their number is directly related to the number of pulses in the train. An analytical model, as well as numerical simulations, support our interpretation

Determining the effects of cattle grazing treatments on Yosemite toads (Anaxyrus [=Bufo] canorus) in montane meadows.

Amphibians are experiencing a precipitous global decline, and population stability on public lands with multiple uses is a key concern for managers. In the Sierra Nevada Mountains (California, USA), managers have specifically identified livestock grazing as an activity that may negatively affect Yosemite toads due to the potential overlap of grazing with toad habitat. Grazing exclusion from Yosemite toad breeding and rearing areas and/or entire meadows have been proposed as possible management actions to alleviate the possible impact of cattle on this species. The primary objective of this study was to determine if different fencing treatments affect Yosemite toad populations. We specifically examined the effect of three fencing treatments on Yosemite toad breeding pool occupancy, tadpoles, and young of the year (YOY). Our hypothesis was that over the course of treatment implementation (2006 through 2010), Yosemite toad breeding pool occupancy and early life stage densities would increase within two fencing treatments relative to actively grazed meadows due to beneficial changes to habitat quality in the absence of grazing. Our results did not support our hypothesis, and showed no benefit to Yosemite toad presence or early life stages in fenced or partially fenced meadows compared to standard USDA Forest Service grazing levels. We found substantial Yosemite toad variation by both meadow and year. This variation was influenced by meadow wetness, with water table depth significant in both the tadpole and YOY models

K-Rational D-Brane Crystals

In this paper the problem of constructing spacetime from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of certain Calabi-Yau varieties. The collections of D-branes involved have algebraic base points, leading to the notion of K-arithmetic D-crystals for algebraic number fields K. This idea can be tested for D0-branes in the framework of toroidal compactifications via the conjectures of Birch and Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these conjectures can be interpreted as formulae that relate the canonical Neron-Tate height of the base points of the D-crystals to special values of the motivic L-function at the central point. In simple cases the knowledge of the D-crystals of Heegner type suffices to uniquely determine the geometry.Comment: 36 page

Recognising & responding to defendants with intellectual disability in court settings

Background To date, there is little evidence on the characteristics of defendants with intellectual disability when presenting to the criminal court system. This study was developed to recognise and examine the characteristics related to gender, ethnicity, mental health and index offences of defendants with intellectual disability and compare these to defendants without intellectual disability within Court Liaison & Diversion Services in London, England. Methods This is a retrospective data analysis of routine administrative data collected by the Liaison and Diversion services across five Magistrates courts in London, England. Data were analysed on defendants identified through screening to have an intellectual disability and compared to defendants without an intellectual disability. Results 9088 defendants were identified, of these 4%, (349) were screened as having an intellectual disability. The study found an overrepresentation of defendants of black ethnicity along with high rates of comorbid mental illness and personality disorder amongst both non-intellectual disability and intellectual disability defendants. Defendants with intellectual disability self-reported self-harm and suicidal behaviour at higher rates. For neurodevelopmental disorders (NDD), those with intellectual disability were over 4 times more likely to have comorbid ADHD and over 14 times more likely to have ASD. Index offences were mostly similar although defendants with intellectual disability had elevated rates of being charged with sexual offences and breach of the peace. Conclusion The findings confirm the presence of a small but significant number of defendants with intellectual disability presenting to the Court Liaison & Diversion services who have significant needs in terms of comorbidity and risk for suicide and self-harm behaviour. Further research is needed to understand the experiences of defendants with intellectual disability presenting to the Court including how best to deliver service models to improve recognition and respond to their high rates of health needs

Structural basis for membrane attack complex inhibition by CD59

CD59 is an abundant immuno-regulatory receptor that protects human cells from damage during complement activation. Here we show how the receptor binds complement proteins C8 and C9 at the membrane to prevent insertion and polymerization of membrane attack complex (MAC) pores. We present cryo-electron microscopy structures of two inhibited MAC precursors known as C5b8 and C5b9. We discover that in both complexes, CD59 binds the pore-forming β-hairpins of C8 to form an intermolecular β-sheet that prevents membrane perforation. While bound to C8, CD59 deflects the cascading C9 β-hairpins, rerouting their trajectory into the membrane. Preventing insertion of C9 restricts structural transitions of subsequent monomers and indirectly halts MAC polymerization. We combine our structural data with cellular assays and molecular dynamics simulations to explain how the membrane environment impacts the dual roles of CD59 in controlling pore formation of MAC, and as a target of bacterial virulence factors which hijack CD59 to lyse human cells