Maximizing the Total Resolution of Graphs

A major factor affecting the readability of a graph drawing is its resolution. In the graph drawing literature, the resolution of a drawing is either measured based on the angles formed by consecutive edges incident to a common node (angular resolution) or by the angles formed at edge crossings (crossing resolution). In this paper, we evaluate both by introducing the notion of "total resolution", that is, the minimum of the angular and crossing resolution. To the best of our knowledge, this is the first time where the problem of maximizing the total resolution of a drawing is studied. The main contribution of the paper consists of drawings of asymptotically optimal total resolution for complete graphs (circular drawings) and for complete bipartite graphs (2-layered drawings). In addition, we present and experimentally evaluate a force-directed based algorithm that constructs drawings of large total resolution

The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

Effects of Particulate Air Pollution on Cardiovascular Health: A Population Health Risk Assessment

Particulate matter (PM) air pollution is increasingly recognized as an important and modifiable risk factor for adverse health outcomes including cardiovascular disease (CVD). However, there are still gaps regarding large population risk assessment. Results from the nationwide Behavioral Risk Factor Surveillance System (BRFSS) were used along with air quality monitoring measurements to implement a systematic evaluation of PM-related CVD risks at the national and regional scales. CVD status and individual-level risk factors were collected from more than 500,000 BRFSS respondents across 2,231 contiguous U.S. counties for 2007 and 2009. Chronic exposures to PM pollutants were estimated with spatial modeling from measurement data. CVD outcomes attributable to PM pollutants were assessed by mixed-effects logistic regression and latent class regression (LCR), with adjustment for multicausality. There were positive associations between CVD and PM after accounting for competing risk factors: the multivariable-adjusted odds for the multiplicity of CVD outcomes increased by 1.32 (95% confidence interval: 1.23–1.43) and 1.15 (1.07–1.22) times per 10 µg/m3 increase in PM2.5 and PM10 respectively in the LCR analyses. After controlling for spatial confounding, there were moderate estimated effects of PM exposure on multiple cardiovascular manifestations. These results suggest that chronic exposures to ambient particulates are important environmental risk factors for cardiovascular morbidity

Hui and Walter's latent-class model extended to estimate diagnostic test properties from surveillance data: a latent model for latent data

Diagnostic test sensitivity and specificity are probabilistic estimates with far reaching implications for disease control, management and genetic studies. In the absence of ‘gold standard’ tests, traditional Bayesian latent class models may be used to assess diagnostic test accuracies through the comparison of two or more tests performed on the same groups of individuals. The aim of this study was to extend such models to estimate diagnostic test parameters and true cohort-specific prevalence, using disease surveillance data. The traditional Hui-Walter latent class methodology was extended to allow for features seen in such data, including (i) unrecorded data (i.e. data for a second test available only on a subset of the sampled population) and (ii) cohort-specific sensitivities and specificities. The model was applied with and without the modelling of conditional dependence between tests. The utility of the extended model was demonstrated through application to bovine tuberculosis surveillance data from Northern and the Republic of Ireland. Simulation coupled with re-sampling techniques, demonstrated that the extended model has good predictive power to estimate the diagnostic parameters and true herd-level prevalence from surveillance data. Our methodology can aid in the interpretation of disease surveillance data, and the results can potentially refine disease control strategies

Improving Angular Resolution in Visualizations of Geographic Networks

In visualizations of large-scale transportation and communications networks, node coordinates are usually fixed to preserve the underlying geography, while links are represented as geodesics for simplicity. This often lead

The impact of positive peritoneal washings and serosal and adnexal involvement on survival in patients with stage IIIA uterine cancer

Objective. The aim of this study was to determine the prognostic significance of serosal involvement (SER), adnexal involvement (ADN), and positive peritoneal washings (PPW) in patients with Stage IIIA uterine cancer. We also sought to determine patterns of recurrence in patients with this disease. Methods. The records of 136 patients with Stage IIIA uterine cancer treated at the Queensland Centre for Gynecological Cancer between March 1983 and August 2001 were reviewed. One hundred thirty-six patients underwent surgery and 58 (42.6%) had full surgical staging. Seventy-five patients (55.2%) had external beam radiotherapy and/or brachytherapy postoperatively. Overall survival was the primary statistical endpoint. Statistical analysis included univariate and multivariate Cox models. Results. Forty-six patients (33.8%) had adnexal involvement, 23 (16.9%) had serosal involvement, and 40 (29.4%) had positive peritoneal washings. Median follow-up was 55.1 months (95% confidence interval, 36.9 to 73.4 months) after which time 71 patients (52.2%) remained alive. For patients with endometrioid adenocarcinoma, ADN and SER were associated with impaired survival on multivariate analysis (odds ratio 2.8 and 3.2, respectively). In the subgroup of patients with high-risk tumors (including papillary serous carcinomas, clear cell carcinomas, and uterine sarcomas), neither ADN, nor SER, nor PPW influenced survival. Conclusion. Patients with Stage IIIA uterine cancer constitute a heterogeneous group. For patients with endometrioid adenocarcinoma, both ADN and SER, but not PPW, were associated with impaired prognosis. For patients with high-risk histological types, prognosis is poor for all three factors. (C) 2002 Elsevier Science (USA)