Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.Comment: 11 page

Approximation of corner polyhedra with families of intersection cuts

We study the problem of approximating the corner polyhedron using intersection cuts derived from families of lattice-free sets in $\mathbb{R}^n$. In particular, we look at the problem of characterizing families that approximate the corner polyhedron up to a constant factor, which depends only on $n$ and not the data or dimension of the corner polyhedron. The literature already contains several results in this direction. In this paper, we use the maximum number of facets of lattice-free sets in a family as a measure of its complexity and precisely characterize the level of complexity of a family required for constant factor approximations. As one of the main results, we show that, for each natural number $n$, a corner polyhedron with $n$ basic integer variables and an arbitrary number of continuous non-basic variables is approximated up to a constant factor by intersection cuts from lattice-free sets with at most $i$ facets if $i> 2^{n-1}$ and that no such approximation is possible if $i \leq 2^{n-1}$. When the approximation factor is allowed to depend on the denominator of the fractional vertex of the linear relaxation of the corner polyhedron, we show that the threshold is $i > n$ versus $i \leq n$. The tools introduced for proving such results are of independent interest for studying intersection cuts

Colour reconnections in Herwig++

We describe the implementation details of the colour reconnection model in the event generator Herwig++. We study the impact on final-state observables in detail and confirm the model idea from colour preconfinement on the basis of studies within the cluster hadronization model. Moreover, we show that the description of minimum bias and underlying event data at the LHC is improved with this model and present results of a tune to available data.Comment: 19 pages, 21 figures, 2 tables. Matches with published versio

The landscape of viral associations in human cancers

Here, as part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, for which whole-genome and—for a subset—whole-transcriptome sequencing data from 2,658 cancers across 38 tumor types was aggregated, we systematically investigated potential viral pathogens using a consensus approach that integrated three independent pipelines. Viruses were detected in 382 genome and 68 transcriptome datasets. We found a high prevalence of known tumor-associated viruses such as Epstein–Barr virus (EBV), hepatitis B virus (HBV) and human papilloma virus (HPV; for example, HPV16 or HPV18). The study revealed significant exclusivity of HPV and driver mutations in head-and-neck cancer and the association of HPV with APOBEC mutational signatures, which suggests that impaired antiviral defense is a driving force in cervical, bladder and head-and-neck carcinoma. For HBV, HPV16, HPV18 and adeno-associated virus-2 (AAV2), viral integration was associated with local variations in genomic copy numbers. Integrations at the TERT promoter were associated with high telomerase expression evidently activating this tumor-driving process. High levels of endogenous retrovirus (ERV1) expression were linked to a worse survival outcome in patients with kidney cancer

Multiple Interactions and the Structure of Beam Remnants

Recent experimental data have established some of the basic features of multiple interactions in hadron-hadron collisions. The emphasis is therefore now shifting, to one of exploring more detailed aspects. Starting from a brief review of the current situation, a next-generation model is developed, wherein a detailed account is given of correlated flavour, colour, longitudinal and transverse momentum distributions, encompassing both the partons initiating perturbative interactions and the partons left in the beam remnants. Some of the main features are illustrated for the Tevatron and the LHC.Comment: 69pp, 33 figure

Increasing consistency of disease biomarker prediction across datasets

Microarray studies with human subjects often have limited sample sizes which hampers the ability to detect reliable biomarkers associated with disease and motivates the need to aggregate data across studies. However, human gene expression measurements may be influenced by many non-random factors such as genetics, sample preparations, and tissue heterogeneity. These factors can contribute to a lack of agreement among related studies, limiting the utility of their aggregation. We show that it is feasible to carry out an automatic correction of individual datasets to reduce the effect of such 'latent variables' (without prior knowledge of the variables) in such a way that datasets addressing the same condition show better agreement once each is corrected. We build our approach on the method of surrogate variable analysis but we demonstrate that the original algorithm is unsuitable for the analysis of human tissue samples that are mixtures of different cell types. We propose a modification to SVA that is crucial to obtaining the improvement in agreement that we observe. We develop our method on a compendium of multiple sclerosis data and verify it on an independent compendium of Parkinson's disease datasets. In both cases, we show that our method is able to improve agreement across varying study designs, platforms, and tissues. This approach has the potential for wide applicability to any field where lack of inter-study agreement has been a concern. © 2014 Chikina, Sealfon

Author Correction: The landscape of viral associations in human cancers

Correction to: Nature Genetics https://doi.org/10.1038/s41588-019-0558-9, published online 05 February 2020