A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Aggregation and Representation in the European Parliament Party Groups

While members of the European Parliament are elected in national constituencies, their votes are determined by the aggregation of MEPs in multinational party groups. The uncoordinated aggregation of national party programmes in multinational EP party groups challenges theories of representation based on national parties and parliaments. This article provides a theoretical means of understanding representation by linking the aggregation of dozens of national party programmes in different EP party groups to the aggregation of groups to produce the parliamentary majority needed to enact policies. Drawing on an original data source of national party programmes, the EU Profiler, the article shows that the EP majorities created by aggregating MEP votes in party groups are best explained by cartel theories. These give priority to strengthening the EP’s collective capacity to enact policies rather than voting in accord with the programmes they were nationally elected to represent

Decoding 3D search coil signals in a non-homogeneous magnetic field

We present a method for recording eye-head movements with the magnetic search coil technique in a small external magnetic field. Since magnetic fields are typically non-linear, except in a relative small region in the center small field frames have not been used for head-unrestrained experiments in oculomotor studies. Here we present a method for recording 3D eye movements by accounting for the magnetic non-linearities using the Biot-Savart law. We show that the recording errors can be significantly reduced by monitoring current head position and thereby taking the location of the eye in the external magnetic field into account

Attentive Learning of Sequential Handwriting Movements: A Neural Network Model

Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409, N00014-92-J-1309); National Science Foundation (IRI-97-20333); National Institutes of Health (I-R29-DC02952-01)

The {Mondshein} Sequence

Canonical orderings [STOC'88, FOCS'92] have been used as a key tool in graph drawing, graph encoding and visibility representations for the last decades. We study a far-reaching generalization of canonical orderings to non-planar graphs that was published by Lee Mondshein in a PhD-thesis at M.I.T.\ as early as 1971. Mondshein proposed to order the vertices of a graph in a sequence such that, for any $i$, the vertices from $1$ to $i$ induce essentially a $2$-connected graph while the remaining vertices from $i+1$ to $n$ induce a connected graph. Mondshein's sequence generalizes canonical orderings and became later and independently known under the name \emph{non-separating ear decomposition}. Currently, the best known algorithm for computing this sequence achieves a running time of $O(nm)$; the main open problem in Mondshein's and follow-up work is to improve this running time to a subquadratic time. In this paper, we present the first algorithm that computes a Mondshein sequence in time and space $O(m)$, improving the previous best running time by a factor of $n$. In addition, we illustrate the impact of this result by deducing linear-time algorithms for several other problems, for which the previous best running times have been quadratic. In particular, we show how to compute three independent spanning trees in a $3$-connected graph in linear time, improving a result of Cheriyan and Maheshwari [J. Algorithms 9(4)]. Secondly, we improve the preprocessing time for the output-sensitive data structure by Di Battista, Tamassia and Vismara [Algorithmica 23(4)] that reports three internally disjoint paths between any given vertex pair from $O(n^2)$ to $O(m)$. Finally, we show how a very simple linear-time planarity test can be derived once a Mondshein sequence is computed

Association of germline variation with the survival of women with BRCA1/2 pathogenic variants and breast cancer

Germline genetic variation has been suggested to influence the survival of breast cancer patients independently of tumor pathology. We have studied survival associations of genetic variants in two etiologically unique groups of breast cancer patients, the carriers of germline pathogenic variants in BRCA1 or BRCA2 genes. We found that rs57025206 was significantly associated with the overall survival, predicting higher mortality of BRCA1 carrier patients with estrogen receptor-negative breast cancer, with a hazard ratio 4.37 (95% confidence interval 3.03-6.30, P = 3.1 × 10-9). Multivariable analysis adjusted for tumor characteristics suggested that rs57025206 was an independent survival marker. In addition, our exploratory analyses suggest that the associations between genetic variants and breast cancer patient survival may depend on tumor biological subgroup and clinical patient characteristics

Refined histopathological predictors of BRCA1 and BRCA2 mutation status: A large-scale analysis of breast cancer characteristics from the BCAC, CIMBA, and ENIGMA consortia

Introduction: The distribution of histopathological features of invasive breast tumors in BRCA1 or BRCA2 germline mutation carriers differs from that of individuals with no known mutation. Histopathological features thus have utility for mutation prediction, including statistical modeling to assess pathogenicity of BRCA1 or BRCA2 variants of uncertain clinical significance. We analyzed large pathology datasets accrued by the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA) and the Breast Cancer Association Consortium (BCAC) to reassess histopathological predictors of BRCA1 and BRCA2 mutation status, and provide robust likelihood ratio (LR) estimates for statistical modeling. Methods: Selection criteria for study/center inclusion were estrogen receptor (ER) status or grade data available for invasive breast cancer diagnosed younger than 70 years. The dataset included 4,477 BRCA1 mutation carriers, 2,565 BRCA2 mutation carriers, and 47,565 BCAC breast cancer cases. Country-stratified estimates of the

Identification of independent association signals and putative functional variants for breast cancer risk through fine-scale mapping of the 12p11 locus.

BACKGROUND: Multiple recent genome-wide association studies (GWAS) have identified a single nucleotide polymorphism (SNP), rs10771399, at 12p11 that is associated with breast cancer risk. METHOD: We performed a fine-scale mapping study of a 700 kb region including 441 genotyped and more than 1300 imputed genetic variants in 48,155 cases and 43,612 controls of European descent, 6269 cases and 6624 controls of East Asian descent and 1116 cases and 932 controls of African descent in the Breast Cancer Association Consortium (BCAC; http://bcac.ccge.medschl.cam.ac.uk/ ), and in 15,252 BRCA1 mutation carriers in the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA). Stepwise regression analyses were performed to identify independent association signals. Data from the Encyclopedia of DNA Elements project (ENCODE) and the Cancer Genome Atlas (TCGA) were used for functional annotation. RESULTS: Analysis of data from European descendants found evidence for four independent association signals at 12p11, represented by rs7297051 (odds ratio (OR) = 1.09, 95 % confidence interval (CI) = 1.06-1.12; P = 3 × 10(-9)), rs805510 (OR = 1.08, 95 % CI = 1.04-1.12, P = 2 × 10(-5)), and rs1871152 (OR = 1.04, 95 % CI = 1.02-1.06; P = 2 × 10(-4)) identified in the general populations, and rs113824616 (P = 7 × 10(-5)) identified in the meta-analysis of BCAC ER-negative cases and BRCA1 mutation carriers. SNPs rs7297051, rs805510 and rs113824616 were also associated with breast cancer risk at P < 0.05 in East Asians, but none of the associations were statistically significant in African descendants. Multiple candidate functional variants are located in putative enhancer sequences. Chromatin interaction data suggested that PTHLH was the likely target gene of these enhancers. Of the six variants with the strongest evidence of potential functionality, rs11049453 was statistically significantly associated with the expression of PTHLH and its nearby gene CCDC91 at P < 0.05. CONCLUSION: This study identified four independent association signals at 12p11 and revealed potentially functional variants, providing additional insights into the underlying biological mechanism(s) for the association observed between variants at 12p11 and breast cancer risk.UK funding includes Cancer Research UK and NIH.This is the final version of the article. It first appeared from BioMed Central via http://dx.doi.org/10.1186/s13058-016-0718-