Three possibilities for completing triangles in the time-directed network of ECJ case law.

<p>Given two citations between three cases, <i>A</i> being more recent than <i>B</i>, which in turn is more recent than <i>C</i>, we can complete triangles in three different situations. Panel A: If a new case <i>A</i> cites two older cases <i>B</i> and <i>C</i>, but <i>B</i> does not cite <i>C</i>, we can make <i>B</i> cite <i>C</i>. Panel B: If a new case <i>A</i> cites <i>B</i>, and <i>B</i> cites <i>C</i> but <i>A</i> does not cite <i>C</i>, we can make <i>A</i> cite <i>C</i>. Panel C: If two new cases <i>A</i> and <i>B</i> both cite an old case <i>C</i> and the newest case <i>A</i> does not cite <i>B</i>, we can make <i>A</i> cite <i>B</i>.</p

The success of triangle completion depends on the module mixing.

<p>Similarity between the community structure of the original network and the perturbed networks for three different average degrees as a function of the module mixing parameter . In panel A the similarity is quantified in terms of the normalized mutual information (NMI) and in panel B the similarity is quantified in terms of the module size ratio. Filled lines and circles correspond to triangle completion and dashed lines and open circles correspond to random link addition. No links were removed prior link addition and the number of links were doubled in all networks by link addition. Each point corresponds to an average over 100 networks.</p

Test of triangle completion on unweighted undirected benchmark networks.

<p>The panels show the similarity between the community structure of the original and the perturbed networks as a function of relative link perturbation, in A and B for low module mixing and in C and D for high module mixing. Panels A and C quantifies the similarity in terms of the normalized mutual information (NMI) and panels B and D quantifies the similarity in terms of the module size ratio. Filled circles correspond to the similarity after link removal. Open symbols correspond to the similarity after subsequently adding links by triangle completion (colored circles) and random link addition (gray squares). Link addition starts at 0, 30, and 60 percent link removal. Each point corresponds to an average over 100 networks.</p

Completing triangles followed by clustering aggregate shattered communities.

<p>Dashed lines show different possibilities for completing triangles.</p

Map of ECJ case law.

<p>We partitioned 8,200 court case documents with 32,000 citations. Afterwards, we generated 100 resampled networks using the triangle completion method. By clustering these resampled networks and comparing them to the clustering of the raw network, we can estimate how much support the data provide in partitioning the raw network. The map represents the 40 top modules. Insignificant clusters and their mutually insignificant friends are shaded with blue areas.</p

Completing triangles in the court case network generates non-destroyed resample networks.

<p>Panel A: Normalized mutual information (NMI) between the original network and the link-added networks as a function of the relative link perturbation. Panel B: Module size ratio between the original network and the link-added networks as a function of the relative link perturbation. Each point corresponds to an average over 100 runs.</p

Triangle completion aggregates shattered modules.

<p>Original network with 4 communities in A, removing links leads to small shattered communities in B, and completing triangles in the shattered network integrates small communities in C.</p

15th Sport&EU Conference Book of Proceedings

Book of abstracts of the 15th Annual Conference of the Association for the Study of Sport and the European Union (Sport&EU)

Comparisons of differences in gene expression levels within primary/secondary cancer samples and primary/benign samples.

<p>The same definition of sample measurements as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0109610#s2" target="_blank">Materials and Methods</a> section is used here. The expression levels of three genes were measured as the delta Ct values (i.e. Ct value of gene-Ct value of GAPDH). The differences in gene expression levels between different samples originating from the same patient are presented as Diff (delta Ct),  =  max (delta Ct value)-min (delta Ct value). We estimated the similarity of gene expression levels in tumor biopsies by comparing the three genes' Diff (delta Ct) values in primary and secondary cancer samples from 43 patients (Panels A, B and C) and presenting results in the form of frequency histograms. Among these patients, 30 patients were also measured for gene expression in their accompanying benign prostate tissue samples, and results are presented in the right panels (Panels D, E and F), as frequency histograms of Diff (delta Ct) values between the primary cancer samples and benign samples. The frequency counts for delta Ct value differences within 0–1.0 or 1.0–2.0 interval were dramatically higher than those with differences larger than 2.0 for IGFBP3 and F3 as shown in the left panels of comparison. Compared to the left panels, the Diff (delta Ct) values in the right panels showed higher frequency in the larger Diff (delta Ct) value intervals for all three genes, but particularly for VGLL3.</p

Delta Ct values distribution graphs of IGFBP3 and F3 according to Gleason score and clinical stage.

<p>Upper panels (A) and (C), are box plots of Delta Ct values for IGFBP3 and F3 for subcategories of Gleason score value. Each patient is represented as a blue circle. The box covers the two center quartiles, and the median value is represented as a horizontal line in the box. The same data of delta Ct values for the two genes were plotted for each clinical stage subcategory (Lower panels: (B) and (C)). Delta Ct for IGFBP3 decreased with increasing Gleason Score and Delta Ct for F3 increased slightly with increasing Gleason score. The significances of expression level differences between subgroups were analyzed by TTEST, differences between subgroups marked with stars meaning P<0.05.</p