A probabilistic approach to Zhang's sandpile model

The current literature on sandpile models mainly deals with the abelian sandpile model (ASM) and its variants. We treat a less known - but equally interesting - model, namely Zhang's sandpile. This model differs in two aspects from the ASM. First, additions are not discrete, but random amounts with a uniform distribution on an interval $[a,b]$. Second, if a site topples - which happens if the amount at that site is larger than a threshold value $E_c$ (which is a model parameter), then it divides its entire content in equal amounts among its neighbors. Zhang conjectured that in the infinite volume limit, this model tends to behave like the ASM in the sense that the stationary measure for the system in large volumes tends to be peaked narrowly around a finite set. This belief is supported by simulations, but so far not by analytical investigations. We study the stationary distribution of this model in one dimension, for several values of $a$ and $b$. When there is only one site, exact computations are possible. Our main result concerns the limit as the number of sites tends to infinity, in the one-dimensional case. We find that the stationary distribution, in the case $a \geq E_c/2$, indeed tends to that of the ASM (up to a scaling factor), in agreement with Zhang's conjecture. For the case $a=0$, $b=1$ we provide strong evidence that the stationary expectation tends to $\sqrt{1/2}$.Comment: 47 pages, 3 figure

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 page

Public health impact of achieving 80% colorectal cancer screening rates in the United States by 2018

BACKGROUND: The National Colorectal Cancer Roundtable, a national coalition of public, private, and voluntary organizations, has recently announced an initiative to increase colorectal cancer (CRC) screening rates in the United States to 80% by 2018. The authors evaluated the potential public health benefits of achieving this goal. METHODS: The authors simulated the 1980 through 2030 United States population of individuals aged 50 to 100 years using microsimulation modeling. Test-specific historical screening rates were based on National Health Interview Survey data for 1987 through 2013. The effects of increasing screening rates from approximately 58% in 2013 to 80% in 2018 were compared to a scenario in which the screening rate remained approximately constant. The outcomes were cancer incidence and mortality rates and numbers of CRC cases and deaths during short-term follow-up (2013-2020) and extended follow-up (2013-2030). RESULTS: Increasing CRC screening rates to 80% by 2018 would reduce CRC incidence rates by 17% and mortality rates by 19% during short-term follow-up and by 22% and 33%, respectively, during extended follow-up. These reductions would amount to a total of 277,000 averted new cancers and 203,000 averted CRC deaths from 2013 through 2030. CONCLUSIONS: Achieving the goal of increasing the uptake of CRC screening in the United States to 80% by 2018 may have a considerable public health impact by averting approximately 280,000 new cancer cases and 200,000 cancer deaths within <20 years

Strict inequalities of critical values in continuum percolation

We consider the supercritical finite-range random connection model where the points $x,y$ of a homogeneous planar Poisson process are connected with probability $f(|y-x|)$ for a given $f$. Performing percolation on the resulting graph, we show that the critical probabilities for site and bond percolation satisfy the strict inequality $p_c^{\rm site} > p_c^{\rm bond}$. We also show that reducing the connection function $f$ strictly increases the critical Poisson intensity. Finally, we deduce that performing a spreading transformation on $f$ (thereby allowing connections over greater distances but with lower probabilities, leaving average degrees unchanged) {\em strictly} reduces the critical Poisson intensity. This is of practical relevance, indicating that in many real networks it is in principle possible to exploit the presence of spread-out, long range connections, to achieve connectivity at a strictly lower density value.Comment: 38 pages, 8 figure

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

The detached dust shells of AQ And, U Ant, and TT Cyg

Detached circumstellar dust shells are detected around three carbon variables using Herschel-PACS. Two of them are already known on the basis of their thermal CO emission and two are visible as extensions in IRAS imaging data. By model fits to the new data sets, physical sizes, expansion timescales, dust temperatures, and more are deduced. A comparison with existing molecular CO material shows a high degree of correlation for TT Cyg and U Ant but a few distinct differences with other observables are also found.Comment: Letter accepted for publication on the A&A Herschel Special Issu

The inflammatory potential of diet is associated with the risk of age-related eye diseases

Background &amp; aims: Inflammation is involved in the pathogenesis of cataract, age-related macular degeneration (AMD), and possibly open-angle glaucoma (OAG). We assessed whether the inflammatory potential of diet (quantified using the dietary inflammatory index; DII) affects the incidence of these common blinding age-related eye diseases. Serum inflammation markers were investigated as possible mediators.Methods: Participants aged &gt;45 years were selected from the prospective, population-based Rotterdam Study. From 1991 onwards, every 4–5 years, participants underwent extensive eye examinations. At baseline, blood samples and dietary data (using food frequency questionnaires) were collected. The DII was adapted based on the data available. Of the 7436 participants free of eye diseases at baseline, 4036 developed incident eye diseases during follow-up (cataract = 2895, early-intermediate AMD = 891, late AMD = 81, OAG = 169). Results: The adapted DII (aDII) ranged from −4.26 (i.e., anti-inflammatory) to 4.53 (i.e., pro-inflammatory). A higher aDII was significantly associated with increased inflammation. A higher neutrophil-lymphocyte ratio (NLR) was associated with an increased risk of cataract and AMD. Additionally, complement component 3c (C3c) and systemic immune-inflammation index (SII) were associated with increased risks of cataract and late AMD, respectively. Every point increase in the aDII was associated with a 9% increased risk of cataract (Odds ratio [95% confidence interval]: 1.09 [1.04–1.14]). The NLR and C3c partly mediated this association. We also identified associations of the aDII with risk of AMD (early-intermediate AMD, OR [95% CI]: 1.11 [1.03–1.19]; late AMD, OR [95% CI]: 1.24 [1.02–1.53]). The NLR partly mediated these associations. The aDII was not associated with OAG. Conclusions: A pro-inflammatory diet was associated with increased risks of cataract and AMD. Particularly the NLR, a marker of subclinical inflammation, appears to be implicated. These findings are relevant for patients with AMD and substantiate the current recommendations to strive for a healthy lifestyle to prevent blindness.</p

Towards ensemble asteroseismology of the young open clusters Chi Persei and NGC 6910

As a result of the variability survey in Chi Persei and NGC6910, the number of Beta Cep stars that are members of these two open clusters is increased to twenty stars, nine in NGC6910 and eleven in Chi Persei. We compare pulsational properties, in particular the frequency spectra, of Beta Cep stars in both clusters and explain the differences in terms of the global parameters of the clusters. We also indicate that the more complicated pattern of the variability among B type stars in Chi Persei is very likely caused by higher rotational velocities of stars in this cluster. We conclude that the sample of pulsating stars in the two open clusters constitutes a very good starting point for the ensemble asteroseismology of Beta Cep-type stars and maybe also for other B-type pulsators.Comment: 4 pages, Astronomische Nachrichten, HELAS IV Conference, Arecife, Lanzarote, Feb 2010, submitte

The Naming Game in Social Networks: Community Formation and Consensus Engineering

We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. We find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.Comment: The original publication is available at http://www.springerlink.com/content/70370l311m1u0ng3