Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k

Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a sign that both the mathematics and physics communities do not yet completely understand the field. Here, we assemble results for Euler/Zagier sums (also known as multidimensional zeta/harmonic sums) of arbitrary depth, including sign alternations. Many of our results were obtained empirically and are apparently new. By carefully compiling and examining a huge data base of high precision numerical evaluations, we can claim with some confidence that certain classes of results are exhaustive. While many proofs are lacking, we have sketched derivations of all results that have so far been proved.Comment: 19 pages, LaTe

Collector Failures on 350 MHz, 1.2 MW CW Klystrons at the Low Energy Demonstration Accelerator (LEDA)

We are currently operating the front end of the accelerator production of tritium (APT) accelerator, a 7 MeV radio frequency quadrapole (RFQ) using three, 1.2 MW CW klystrons. These klystrons are required and designed to dissipate the full beam power in the collector. The klystrons have less than 1500 operational hours. One collector has failed and all collectors are damaged. This paper will discuss the damage and the difficulties in diagnosing the cause. The collector did not critically fail. Tube operation was still possible and the klystron operated up to 70% of full beam power with excellent vacuum. The indication that finally led us to the collector failure was variable emission. This information will be discussed. A hydrophonic system was implemented to diagnose collector heating. The collectors are designed to allow for mixed-phase cooling and with the hydrophonic test equipment we are able to observe: normal, single-phase cooling, mixed-phase cooling, and a hard boil. These data will be presented. The worst case beam profile from a collector heating standpoint is presented. The paper will also discuss the steps taken to halt the collector damage on the remaining 350 MHz klystrons and design changes that are being implemented to correct the problem.Comment: LINAC2000 conference paper THE1

A systematic review of arthropod community diversity in association with invasive plants

Invasive plants represent a significant financial burden for land managers and also have the potential to severely degrade ecosystems. Arthropods interact strongly with plants, relying on them for food, shelter, and as nurseries for their young. For these reasons, the impacts of plant invasions are likely strongly reflected by arthropod community dynamics including diversity and abundances. A systematic review was conducted to ascertain the state of the literature with respect to plant invaders and their associated arthropod communities. We found that the majority of studies did not biogeographically contrast arthropod community dynamics from both the home and away ranges and that studies were typically narrow in scope, focusing only on the herbivore feeding guild, rather than assessing two or more trophic levels. Importantly, relative arthropod richness was significantly reduced on invasive plant species. Phylogenetic differences between the invasive and local plant community as well as the plant functional group impact arthropod diversity patterns. A framework highlighting some interaction mechanisms between multiple arthropod trophic levels and native and invasive plants is discussed and future research directions relating to these interactions and the findings herein are proposed

The Kavirondo Escarpment: a previously unrecognized site of high conservation value in Western Kenya

In western Kenya, extant woodland habitats and their representative bird species are increasingly scarce outside of protected areas. With the assistance of satellite imagery we located several minimally impacted ecosystems on the Kavirondo Escarpment (0°1.7’ S, 34°56.5’ E), which we then visited to examine the vegetation communities and investigate the avifauna. Despite only a limited effort there, we report several new atlas square occurrences, presence of the local and poorly known Rock Cisticola Cisticola emini and a significant range extension for the Stone Partridge Ptilopachus petrosus. Our short visits indicate high avian species richness is associated with the escarpment and we suggest comprehensive biodiversity surveys here are warranted

Keplerian Motion of Broad-Line Region Gas as Evidence for Supermassive Black Holes in Active Galactic Nuclei

Emission-line variability data on NGC 5548 argue strongly for the existence of a mass of order 7 x 10^7 solar masses within the inner few light days of the nucleus in the Seyfert 1 galaxy NGC 5548. The time-delayed response of the emission lines to continuum variations is used to infer the size of the line-emitting region, and these determinations are combined with measurements of the Doppler widths of the variable line components to estimate a virial mass. The data for several different emission lines spanning an order of magnitude in distance from the central source show the expected V proportional to r^{-1/2} correlation and are consistent with a single value for the mass.Comment: 9 pages, 2 Figures. accepted by ApJ Letter

Electricity load profile classification using Fuzzy C-Means method

This paper presents the Fuzzy C-Means (FCM) clustering method. The FCM technique assigns a degree of membership for each data set to several clusters, thus offering the opportunity to deal with load profiles that could belong to more than one group at the same time. The FCM algorithm is based on minimising a c-means objective function to determine an optimal classification. The simulation of FCM was carried out using actual sample data from Indonesia and the results are presented. Some validity index measurements was carried out to estimate the compactness of the resulting clusters or to find the optimal number of clusters for a data set

Matrix Adhesion Polarizes Heart Progenitor Induction In The Invertebrate Chordate Ciona Intestinalis

Cell-matrix adhesion strongly influences developmental signaling. Resulting impacts on cell migration and tissue morphogenesis are well characterized. However, the in vivo impact of adhesion on fate induction remains ambiguous. Here, we employ the invertebrate chordate Ciona intestinalis to delineate an essential in vivo role for matrix adhesion in heart progenitor induction. In Ciona pre-cardiac founder cells, invasion of the underlying epidermis promotes localized induction of the heart progenitor lineage. We found that these epidermal invasions are associated with matrix adhesion along the pre-cardiac cell/epidermal boundary. Through targeted manipulations of RAP GTPase activity, we were able to manipulate pre-cardiac cell-matrix adhesion. Targeted disruption of pre-cardiac cell-matrix adhesion blocked heart progenitor induction. Conversely, increased matrix adhesion generated expanded induction. We were also able to selectively restore cell-matrix adhesion and heart progenitor induction through targeted expression of Ci-Integrin β2. These results indicate that matrix adhesion functions as a necessary and sufficient extrinsic cue for regional heart progenitor induction. Furthermore, time-lapse imaging suggests that cytokinesis acts as an intrinsic temporal regulator of heart progenitor adhesion and induction. Our findings highlight a potentially conserved role for matrix adhesion in early steps of vertebrate heart progenitor specification

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

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