Nonrepetitive Colouring via Entropy Compression

A vertex colouring of a graph is \emph{nonrepetitive} if there is no path whose first half receives the same sequence of colours as the second half. A graph is nonrepetitively $k$-choosable if given lists of at least $k$ colours at each vertex, there is a nonrepetitive colouring such that each vertex is coloured from its own list. It is known that every graph with maximum degree $\Delta$ is $c\Delta^2$-choosable, for some constant $c$. We prove this result with $c=1$ (ignoring lower order terms). We then prove that every subdivision of a graph with sufficiently many division vertices per edge is nonrepetitively 5-choosable. The proofs of both these results are based on the Moser-Tardos entropy-compression method, and a recent extension by Grytczuk, Kozik and Micek for the nonrepetitive choosability of paths. Finally, we prove that every graph with pathwidth $k$ is nonrepetitively $O(k^{2})$-colourable.Comment: v4: Minor changes made following helpful comments by the referee

Genetic Variation in DNA Repair Pathways and Risk of Non-Hodgkin's Lymphoma

Molecular and genetic evidence suggests that DNA repair pathways may contribute to lymphoma susceptibility. Several studies have examined the association of DNA repair genes with lymphoma risk, but the findings from these reports have been inconsistent. Here we provide the results of a focused analysis of genetic variation in DNA repair genes and their association with the risk of non-Hodgkin's lymphoma (NHL). With a population of 1,297 NHL cases and 1,946 controls, we have performed a two-stage case/control association analysis of 446 single nucleotide polymorphisms (SNPs) tagging the genetic variation in 81 DNA repair genes. We found the most significant association with NHL risk in the ATM locus for rs227060 (OR = 1.27, 95% CI: 1.13–1.43, p = 6.77×10−5), which remained significant after adjustment for multiple testing. In a subtype-specific analysis, associations were also observed for the ATM locus among both diffuse large B-cell lymphomas (DLBCL) and small lymphocytic lymphomas (SLL), however there was no association observed among follicular lymphomas (FL). In addition, our study provides suggestive evidence of an interaction between SNPs in MRE11A and NBS1 associated with NHL risk (OR = 0.51, 95% CI: 0.34–0.77, p = 0.0002). Finally, an imputation analysis using the 1,000 Genomes Project data combined with a functional prediction analysis revealed the presence of biologically relevant variants that correlate with the observed association signals. While the findings generated here warrant independent validation, the results of our large study suggest that ATM may be a novel locus associated with the risk of multiple subtypes of NHL

Induction of Epithelial Mesenchimal Transition and Vasculogenesis in the Lenses of Dbl Oncogene Transgenic Mice

BACKGROUND: The Dbl family of proteins represents a large group of proto-oncogenes involved in cell growth regulation. The numerous domains that are present in many Dbl family proteins suggest that they act to integrate multiple inputs in complicated signaling networks involving the Rho GTPases. Alterations of the normal function of these proteins lead to pathological processes such as developmental disorders and neoplastic transformation. We generated transgenic mice introducing the cDNA of Dbl oncogene linked to the metallothionein promoter into the germ line of FVB mice and found that onco-Dbl expression in mouse lenses affected proliferation, migration and differentiation of lens epithelial cells. RESULTS: We used high density oligonucleotide microarray to define the transcriptional profile induced by Dbl in the lenses of 2 days, 2 weeks, and 6 weeks old transgenic mice. We observed modulation of genes encoding proteins promoting epithelial-mesenchymal transition (EMT), such as down-regulation of epithelial cell markers and up-regulation of fibroblast markers. Genes encoding proteins involved in the positive regulation of apoptosis were markedly down regulated while anti-apoptotic genes were strongly up-regulated. Finally, several genes encoding proteins involved in the process of angiogenesis were up-regulated. These observations were validated by histological and immunohistochemical examination of the transgenic lenses where vascularization can be readily observed. CONCLUSION: Onco-Dbl expression in mouse lens correlated with modulation of genes involved in the regulation of EMT, apoptosis and vasculogenesis leading to disruption of the lens architecture, epithelial cell proliferation, and aberrant angiogenesis. We conclude that onco-Dbl has a potentially important, previously unreported, capacity to dramatically alter epithelial cell migration, replication, polarization and differentiation and to induce vascularization of an epithelial tissue

The early-life environment and individual plasticity in life-history traits

We tested whether the early-life environment can influence the extent of individual plasticity in a life-history trait. We asked: can the early-life environment explain why, in response to the same adult environmental cue, some individuals invest more than others in current reproduction? Moreover, can it additionally explain why investment in current reproduction trades off against survival in some individuals, but is positively correlated with survival in others? We addressed these questions using the burying beetle, which breeds on small carcasses and sometimes carries phoretic mites. These mites breed alongside the beetle, on the same resource, and are a key component of the beetle's early-life environment. We exposed female beetles to mites twice during their lives: during their development as larvae and again as adults during their first reproductive event. We measured investment in current reproduction by quantifying average larval mass and recorded the female's life span after breeding to quantify survival. We found no effect of either developing or breeding alongside mites on female reproductive investment, nor on her life span, nor did developing alongside mites influence her size. In post hoc analyses, where we considered the effect of mite number (rather than their mere presence/absence) during the female's adult breeding event, we found that females invested more in current reproduction when exposed to greater mite densities during reproduction, but only if they had been exposed to mites during development as well. Otherwise, they invested less in larvae at greater mite densities. Furthermore, females that had developed with mites exhibited a trade-off between investment in current reproduction and future survival, whereas these traits were positively correlated in females that had developed without mites. The early-life environment thus generates individual variation in life-history plasticity. We discuss whether this is because mites influence the resources available to developing young or serve as important environmental cues

Climatic effects on breeding and morphology: evidence for phenotypic plasticity

1. A trend towards increasing average spring temperatures has been observed in Europe over the past 25 years. This climatic variation has been attributed to a natural, large-scale atmospheric phenomenon, the North Atlantic Oscillation (NAO). A number of studies have reported associations between the winter NAO-index and both breeding phenology and cohort-specific morphology. These studies have been cross-sectional rather than longitudinal and therefore have not been able to determine whether the changes result from phenotypic plasticity or microevolutionary processes. 2. We analysed (i) cross-sectional correlations between the winter NAO-index and breeding performance (laying date, clutch size, fledging success and number of recruits produced) and morphological traits (tarsus and wing length), and (ii) within-individual variation in the same traits for individuals experiencing different values of the NAO-index in a population of collared flycatchers (Ficedula albicollis) breeding on Gotland, Sweden, over a period of 16 years (1980-95). 3. None of the four measures of breeding performance changed consistently over the study period, while tarsus length of males (and marginally females) decreased over time. Of the six traits investigated using cross-sectional data, only laying date was related to variation in the NAO-index. 4. All characters investigated showed significant repeatability within individuals among years, revealing the importance of factors specific to individuals in determining their value. However, within individuals the NAO-index significantly affected laying date and clutch size such that females laid earlier and produced larger clutches after warmer, moister winters. 5. Our data show a high degree of concordance between cross-sectional and longitudinal analyses of the effect of NAO on laying date and clutch size. The similarity of responses across and within individuals suggests that the population-level response to the NAO-index can be explained entirely as the result of phenotypic plasticity