Mean Row Values in (u,v)(u,v)-Calkin-Wilf Trees

We fix integers $u,v \geq 1$, and consider an infinite binary tree $\mathcal{T}^{(u,v)}(z)$ with a root node whose value is a positive rational number $z$. For every vertex $a/b$, we label the left child as $a/(ua+b)$ and right child as $(a+vb)/b$. The resulting tree is known as the $(u,v)$-Calkin-Wilf tree. As $z$ runs over $[1/u,v]\cap \mathbb{Q}$, the vertex sets of $\mathcal{T}^{(u,v)}(z)$ form a partition of $\mathbb{Q}^+$. When $u=v=1$, the mean row value converges to $3/2$ as the row depth increases. Our goal is to extend this result for any $u,v\geq 1$. We show that, when $z\in [1/u,v]\cap \mathbb{Q}$, the mean row value in $\mathcal{T}^{(u,v)}(z)$ converges to a value close to $v+\log 2/u$ uniformly on $z$

Charge distribution in two-dimensional electrostatics

We examine the stability of ringlike configurations of N charges on a plane interacting through the potential $V(z_1,...,z_N)=\sum_i |z_i|^2-\sum_{i<j} ln|z_i-z_j|^2$. We interpret the equilibrium distributions in terms of a shell model and compare predictions of the model with the results of numerical simulations for systems with up to 100 particles.Comment: LaTe

Elliptic curves, modular forms, and sums of Hurwitz class numbers

Let H(N) denote the Hurwitz class number. It is known that if $p$ is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the behavior of this sum with the additional condition $r\equiv c\pmod m$. Three different methods will be explored for determining the values of such sums. First, we will count isomorphism classes of elliptic curves over finite fields. Second, we will express the sums as coefficients of modular forms. Third, we will manipulate the Eichler-Selberg trace for ula for Hecke operators to obtain Hurwitz class number relations. The cases $m=2,3$ and 4 are treated in full. Partial results, as well as several conjectures, are given for $m=5$ and 7.Comment: Preprint of an old pape

Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy

MiR-155 has a protective role in the development of non-alcoholic hepatosteatosis in mice

Hepatic steatosis is a global epidemic that is thought to contribute to the pathogenesis of type 2 diabetes. MicroRNAs (miRs) are regulators that can functionally integrate a range of metabolic and inflammatory pathways in liver. We aimed to investigate the functional role of miR-155 in hepatic steatosis. Male C57BL/6 wild-type (WT) and miR-155−/− mice were fed either normal chow or high fat diet (HFD) for 6 months then lipid levels, metabolic and inflammatory parameters were assessed in livers and serum of the mice. Mice lacking endogenous miR-155 that were fed HFD for 6 months developed increased hepatic steatosis compared to WT controls. This was associated with increased liver weight and serum VLDL/LDL cholesterol and alanine transaminase (ALT) levels, as well as increased hepatic expression of genes involved in glucose regulation (Pck1, Cebpa), fatty acid uptake (Cd36) and lipid metabolism (Fasn, Fabp4, Lpl, Abcd2, Pla2g7). Using miRNA target prediction algorithms and the microarray transcriptomic profile of miR-155−/− livers, we identified and validated that Nr1h3 (LXRα) as a direct miR-155 target gene that is potentially responsible for the liver phenotype of miR-155−/− mice. Together these data indicate that miR-155 plays a pivotal role regulating lipid metabolism in liver and that its deregulation may lead to hepatic steatosis in patients with diabetes

Annotating Relationships between Multiple Mixed-media Digital Objects by Extending Annotea

Annotea provides an annotation protocol to support collaborative Semantic Web-based annotation of digital resources accessible through the Web. It provides a model whereby a user may attach supplementary information to a resource or part of a resource in the form of: either a simple textual comment; a hyperlink to another web page; a local file; or a semantic tag extracted from a formal ontology and controlled vocabulary. Hence, annotations can be used to attach subjective notes, comments, rankings, queries or tags to enable semantic reasoning across web resources. More recently tabbed Browsers and specific annotation tools, allow users to view several resources (e.g., images, video, audio, text, HTML, PDF) simultaneously in order to carry out side-by-side comparisons. In such scenarios, users frequently want to be able to create and annotate a link or relationship between two or more objects or between segments within those objects. For example, a user might want to create a link between a scene in an original film and the corresponding scene in a remake and attach an annotation to that link. Based on past experiences gained from implementing Annotea within different communities in order to enable knowledge capture, this paper describes and compares alternative ways in which the Annotea Schema may be extended for the purpose of annotating links between multiple resources (or segments of resources). It concludes by identifying and recommending an optimum approach which will enhance the power, flexibility and applicability of Annotea in many domains

Transverse-spin dependence of the p-p total cross section ΔσT from 0.8 to 2.5 GeV/c

The difference ΔσT=σ(↓↑)-σ(↑↑) between the proton-proton total cross sections for protons in pure transverse-spin states, was measured at incident momenta 0.8 to 2.5 GeV/c in experiments performed at the Los Alamos Clinton P. Anderson Meson Physics Facility and the Argonne Zero Gradient Synchrotron. In agreement with other data, peaks were observed at center-of-mass energies of 2.14 and 2.43 GeV/c2, where 1D2 and 1G4 dibaryon resonances have been proposed

Sequential cavity method for computing free energy and surface pressure

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of $\Z^d$. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of $\Z^3$ belongs to the interval $[0.78595,0.78599]$, improving best previously known estimate of (approximately) $[0.7850,0.7862]$ obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}. Moreover, we show that given a target additive error $\epsilon>0$, the computational effort of our method for these two models is $(1/\epsilon)^{O(1)}$ \emph{both} for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require $\exp\big((1/\epsilon)^{O(1)}\big)$ computation effort.Comment: 33 pages, 4 figure

Holocene pollen records from the central Arctic Foothills, northern Alaska: testing the role of substrate in the response of tundra to climate change

1   To explore the role of edaphic controls in the response of arctic tundra to climate change, we analysed Holocene pollen records from lakes in northern Alaska located on glaciated surfaces with contrasting soil texture, topography and tundra communities. Using indicator taxa, pollen accumulation rates (PARs) and multivariate comparison of fossil and modern pollen assemblages, we reconstructed the vegetational changes at Upper Capsule Lake (Sagavanirktok surface) and Red Green Lake (Itkillik II surface) in response to increased effective moisture between the early and middle Holocene. 2   In the Red Green record, low PARs and the continuous presence of taxa indicative of prostrate-shrub tundra (PST; Equisetum , Polypodiaceae, Thalictrum and Rosaceae) indicate that the vegetation resembled PST throughout the Holocene. During the warm, dry early Holocene (11 300–10 000 cal years BP), PST also occurred on Sagavanirktok surfaces, as evidenced by PST indicators (Bryidae, Polypodiaceae, Equisetum and Rosaceae) in this interval of the Upper Capsule record. However, PARs increased, suggesting increased vegetation cover, PST taxa declined and taxa indicative of dwarf-shrub tundra (DST; Rubus chamaemorus and Lycopodium annotinum ) increased between 10 000 and 7500 cal years BP. 3   We hypothesize that between the early and middle Holocene the fine-textured soils and smooth topography of Sagavanirktok surfaces led to increased soil moisture, greater vegetation cover, permafrost aggradation, anoxic and acidic soil conditions, slower decomposition and the development of a thick organic layer. In contrast, soil moisture remained low on the better-drained Itkillik II surface, and vegetational changes were minor. 4   Landscape-scale substrate variations have an effect on how tundra responds to climate change, suggesting that the response of arctic ecosystems to future variability may be spatially heterogeneous. Journal of Ecology (2003) 91 , 1034–1048Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73204/1/j.1365-2745.2003.00833.x.pd