Percolation Is Odd.

We prove a remarkable combinatorial symmetry in the number of spanning configurations in site percolation: for a large class of lattices, the number of spanning configurations with an odd or even number of occupied sites differs by ±1. In particular, this symmetry implies that the total number of spanning configurations is always odd, independent of the size or shape of the lattice. The class of lattices that share this symmetry includes the square lattice and the hypercubic lattice in any dimension, with a wide variety of boundary conditions.

SANRA-a scale for the quality assessment of narrative review articles.

BACKGROUND: Narrative reviews are the commonest type of articles in the medical literature. However, unlike systematic reviews and randomized controlled trials (RCT) articles, for which formal instruments exist to evaluate quality, there is currently no instrument available to assess the quality of narrative reviews. In response to this gap, we developed SANRA, the Scale for the Assessment of Narrative Review Articles. METHODS: A team of three experienced journal editors modified or deleted items in an earlier SANRA version based on face validity, item-total correlations, and reliability scores from previous tests. We deleted an item which addressed a manuscript's writing and accessibility due to poor inter-rater reliability. The six items which form the revised scale are rated from 0 (low standard) to 2 (high standard) and cover the following topics: explanation of (1) the importance and (2) the aims of the review, (3) literature search and (4) referencing and presentation of (5) evidence level and (6) relevant endpoint data. For all items, we developed anchor definitions and examples to guide users in filling out the form. The revised scale was tested by the same editors (blinded to each other's ratings) in a group of 30 consecutive non-systematic review manuscripts submitted to a general medical journal. RESULTS: Raters confirmed that completing the scale is feasible in everyday editorial work. The mean sum score across all 30 manuscripts was 6.0 out of 12 possible points (SD 2.6, range 1-12). Corrected item-total correlations ranged from 0.33 (item 3) to 0.58 (item 6), and Cronbach's alpha was 0.68 (internal consistency). The intra-class correlation coefficient (average measure) was 0.77 [95% CI 0.57, 0.88] (inter-rater reliability). Raters often disagreed on items 1 and 4. CONCLUSIONS: SANRA's feasibility, inter-rater reliability, homogeneity of items, and internal consistency are sufficient for a scale of six items. Further field testing, particularly of validity, is desirable. We recommend rater training based on the "explanations and instructions" document provided with SANRA. In editorial decision-making, SANRA may complement journal-specific evaluation of manuscripts-pertaining to, e.g., audience, originality or difficulty-and may contribute to improving the standard of non-systematic reviews.

Percolation thresholds and Fisher exponents in hypercubic lattices.

We use invasion percolation to compute highly accurate numerical values for bond and site percolation thresholds p_{c} on the hypercubic lattice Z^{d} for d=4,...,13. We also compute the Fisher exponent τ governing the cluster size distribution at criticality. Our results support the claim that the mean-field value τ=5/2 holds for d≥6, with logarithmic corrections to power-law scaling at d=6.

Percolation thresholds in hyperbolic lattices.

We use invasion percolation to compute numerical values for bond and site percolation thresholds p_{c} (existence of an infinite cluster) and p_{u} (uniqueness of the infinite cluster) of tesselations {P,Q} of the hyperbolic plane, where Q faces meet at each vertex and each face is a P-gon. Our values are accurate to six or seven decimal places, allowing us to explore their functional dependency on P and Q and to numerically compute critical exponents. We also prove rigorous upper and lower bounds for p_{c} and p_{u} that can be used to find the scaling of both thresholds as a function of P and Q.

Universal features of cluster numbers in percolation.

The number of clusters per site n(p) in percolation at the critical point p=p_{c} is not itself a universal quantity; it depends upon the lattice and percolation type (site or bond). However, many of its properties, including finite-size corrections, scaling behavior with p, and amplitude ratios, show various degrees of universal behavior. Some of these are universal in the sense that the behavior depends upon the shape of the system, but not lattice type. Here, we elucidate the various levels of universality for elements of n(p) both theoretically and by carrying out extensive studies on several two- and three-dimensional systems, by high-order series analysis, Monte Carlo simulation, and exact enumeration. We find many results, including precise values for n(p_{c}) for several systems, a clear demonstration of the singularity in n^{''}(p), and metric scale factors. We make use of the matching polynomial of Sykes and Essam to find exact relations between properties for lattices and matching lattices. We propose a criterion for an absolute metric factor b based upon the singular behavior of the scaling function, rather than a relative definition of the metric that has previously been used.

Percolation in finite matching lattices.

We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and Essam, and it can be used to find exact or very accurate approximations of the critical density. The criterion that follows is related to the criterion used by Scullard and Jacobsen to find precise approximate thresholds, and our work provides a different perspective on their approach.

Substantial agreement of referee recommendations at a general medical journal--a peer review evaluation at Deutsches Ärzteblatt International.

BACKGROUND: Peer review is the mainstay of editorial decision making for medical journals. There is a dearth of evaluations of journal peer review with regard to reliability and validity, particularly in the light of the wide variety of medical journals. Studies carried out so far indicate low agreement among reviewers. We present an analysis of the peer review process at a general medical journal, Deutsches Ärzteblatt International. METHODOLOGY/PRINCIPAL FINDINGS: 554 reviewer recommendations on 206 manuscripts submitted between 7/2008 and 12/2009 were analyzed: 7% recommended acceptance, 74% revision and 19% rejection. Concerning acceptance (with or without revision) versus rejection, there was a substantial agreement among reviewers (74.3% of pairs of recommendations) that was not reflected by Fleiss' or Cohen's kappa (<0.2). The agreement rate amounted to 84% for acceptance, but was only 31% for rejection. An alternative kappa-statistic, however, Gwet's kappa (AC1), indicated substantial agreement (0.63). Concordance between reviewer recommendation and editorial decision was almost perfect when reviewer recommendations were unanimous. The correlation of reviewer recommendations and citations as counted by Web of Science was low (partial correlation adjusted for year of publication: -0.03, n.s.). CONCLUSIONS/SIGNIFICANCE: Although our figures are similar to those reported in the literature our conclusion differs from the widely held view that reviewer agreement is low: Based on overall agreement we consider the concordance among reviewers sufficient for the purposes of editorial decision making. We believe that various measures, such as positive and negative agreement or alternative Kappa values are superior to the application of Cohen's or Fleiss' Kappa in the analysis of nominal or ordinal level data regarding reviewer agreement. Also, reviewer recommendations seem to be a poor proxy for citations because, for example, manuscripts will be changed considerably during the revision process.

Continuum percolation thresholds in two dimensions.

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the connected clusters, and (in two dimensions) using exact values from conformal field theory for the probability, at the phase transition, that various kinds of wrapping clusters exist on the torus. We apply this approach to percolation in continuum models, finding overlaps between objects with real-valued positions and orientations. In particular, we find precise values of the percolation transition for disks, squares, rotated squares, and rotated sticks in two dimensions and confirm that these transitions behave as conformal field theory predicts. The running time and memory use of our algorithm are essentially linear as a function of the number of objects at criticality.

Random numbers for large-scale distributed Monte Carlo simulations.

Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue of generating random numbers in a parallel, distributed environment. In this contribution we demonstrate that multiple linear recurrences in finite fields are an ideal method to produce high quality pseudorandom numbers in sequential and parallel algorithms. Their known weakness (failure of sampling points in high dimensions) can be overcome by an appropriate delinearization that preserves all desirable properties of the underlying linear sequence.

Universality in the level statistics of disordered systems.

Energy spectra of disordered systems share a common feature: If the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between energy and configuration is lost. We demonstrate this effect for the Edwards-Anderson model, but we also discuss its universality.

Entropy of pseudo-random-number generators.

Since the work of Phys. Rev. Lett. 69, 3382 (1992)]] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number x(i) from preceding values, x(i) =f( x(i-1), x(i-2), ..., x(i-q) ). Failure of these generators in cluster Monte Carlo simulations and related experiments can be attributed to the low entropy of the production rule f() conditioned on the statistics of the input values x(i-1), ..., x(i-q). Being a measure only of the arithmetic operations in the generator rule, the conditional entropy is independent of the lag in the recurrence or the period of the sequence. In that sense it measures a more profound quality of a random-number generator than empirical tests with their limited horizon.

Phase transition in multiprocessor scheduling.

An "easy-hard" phase transition is shown to characterize the multiprocessor scheduling problem in which one has to distribute the workload on a parallel computer such as to minimize the overall run time. The transition can be analyzed in detail by mapping it on a mean-field antiferromagnetic Potts model. The static phase transition, characterized by a vanishing ground state entropy, corresponds to a transition in the performance of practical scheduling algorithms.