The pagenumber of k-trees is O(k)

AbstractA k-tree is a graph defined inductively in the following way: the complete graph Kk is a k-tree, and if G is a k-tree, then the graph resulting from adding a new vertex adjacent to k vertices inducing a Kk in G is also a k-tree. This paper examines the book-embedding problem for k-trees. A book embedding of a graph maps the vertices onto a line along the spine of the book and assigns the edges to pages of the book such that no two edges on the same page cross. The pagenumber of a graph is the minimum number of pages in a valid book embedding. In this paper, it is proven that the pagenumber of a k-tree is at most k+1. Furthermore, it is shown that there exist k-trees that require k pages. The upper bound leads to bounds on the pagenumber of a variety of classes of graphs for which no bounds were previously known

Across the Digital Divide: A Cross-Country Multi-Technology Analysis of the Determinants of IT Penetration

This paper studies the country-level digital divide across successive generations of IT, providing detailed insights into the magnitude and changing nature of the divide. We examine a panel of 40 countries from 1985-2001, based on data from three distinct generations of IT: mainframes, personal computers, and the Internet. Using two measures of IT penetration, we conduct an empirical investigation of socio-economic factors driving the digital divide. We find that IT penetration is positively associated with national income for all three technology generations, and the association between penetration and income is stronger for countries with higher levels of IT penetration. We also examine other demographic and economic factors, going beyond income, and find significant differences in the nature of their effects across countries at different stages of IT adoption. Importantly, factors that previously may have been expanding the divide with earlier technologies are narrowing the gap as the Internet becomes the defining technology of the Information Age

MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Pharmacological inhibition of ULK1 kinase blocks mammalian target of rapamycin (mTOR)-dependent autophagy

Autophagy is a cell-protective and degradative process that recycles damaged and long-lived cellular components. Cancer cells are thought to take advantage of autophagy to help them to cope with the stress of tumorigenesis; thus targeting autophagy is an attractive therapeutic approach. However, there are currently no specific inhibitors of autophagy. ULK1, a serine/threonine protein kinase, is essential for the initial stages of autophagy, and here we report that two compounds, MRT67307 and MRT68921, potently inhibit ULK1 and ULK2 in vitro and block autophagy in cells. Using a drug-resistant ULK1 mutant, we show that the autophagy-inhibiting capacity of the compounds is specifically through ULK1. ULK1 inhibition results in accumulation of stalled early autophagosomal structures, indicating a role for ULK1 in the maturation of autophagosomes as well as initiation

Genome sequences of six Phytophthora species associated with forests in New Zealand

In New Zealand there has been a long association of Phytophthora diseases in forests, nurseries, remnant plantings and horticultural crops. However, new Phytophthora diseases of trees have recently emerged. Genome sequencing has been performed for 12 Phytophthora isolates, from six species: Phytophthora pluvialis, Phytophthora kernoviae, Phytophthora cinnamomi, Phytophthora agathidicida, Phytophthora multivora and Phytophthora taxon Totara. These sequences will enable comparative analyses to identify potential virulence strategies and ultimately facilitate better control strategies. This Whole Genome Shotgun data have been deposited in DDBJ/ENA/GenBank under the accession numbers LGTT00000000, LGTU00000000, JPWV00000000, JPWU00000000, LGSK00000000, LGSJ00000000, LGTR00000000, LGTS00000000, LGSM00000000, LGSL00000000, LGSO00000000, and LGSN0000000

Prevalence and dynamics of ribosomal DNA micro-heterogeneity are linked to population history in two contrasting yeast species

Despite the considerable number and taxonomic breadth of past and current genome sequencing projects, many of which necessarily encompass the ribosomal DNA, detailed information on the prevalence and evolutionary significance of sequence variation in this ubiquitous genomic region are severely lacking. Here, we attempt to address this issue in two closely related yet contrasting yeast species, the baker's yeast Saccharomyces cerevisiae and the wild yeast Saccharomyces paradoxus. By drawing on existing datasets from the Saccharomyces Genome Resequencing Project, we identify a rich seam of ribosomal DNA sequence variation, characterising 1,068 and 970 polymorphisms in 34 S. cerevisiae and 26 S. paradoxus strains respectively. We discover the two species sets exhibit distinct mutational profiles. Furthermore, we show for the first time that unresolved rDNA sequence variation resulting from imperfect concerted evolution of the ribosomal DNA region follows a U-shaped allele frequency distribution in each species, similar to loci that evolve under non-concerted mechanisms but arising through rather different evolutionary processes. Finally, we link differences between the shapes of these allele frequency distributions to the two species' contrasting population histories

Repeat Elements Organise 3D Genome Structure and Mediate Transcription in the Filamentous Fungus \u3cem\u3eEpichloë festucae\u3c/em\u3e

Structural features of genomes, including the three-dimensional arrangement of DNA in the nucleus, are increasingly seen as key contributors to the regulation of gene expression. However, studies on how genome structure and nuclear organisation influence transcription have so far been limited to a handful of model species. This narrow focus limits our ability to draw general conclusions about the ways in which three-dimensional structures are encoded, and to integrate information from three-dimensional data to address a broader gamut of biological questions. Here, we generate a complete and gapless genome sequence for the filamentous fungus, Epichloë festucae. We use Hi-C data to examine the three-dimensional organisation of the genome, and RNA-seq data to investigate how Epichloë genome structure contributes to the suite of transcriptional changes needed to maintain symbiotic relationships with the grass host. Our results reveal a genome in which very repeat-rich blocks of DNA with discrete boundaries are interspersed by gene-rich sequences that are almost repeat-free. In contrast to other species reported to date, the three-dimensional structure of the genome is anchored by these repeat blocks, which act to isolate transcription in neighbouring gene-rich regions. Genes that are differentially expressed in planta are enriched near the boundaries of these repeat-rich blocks, suggesting that their three-dimensional orientation partly encodes and regulates the symbiotic relationship formed by this organism

DNA replication stress restricts ribosomal DNA copy number

Ribosomal RNAs (rRNAs) in budding yeast are encoded by ~100–200 repeats of a 9.1kb sequence arranged in tandem on chromosome XII, the ribosomal DNA (rDNA) locus. Copy number of rDNA repeat units in eukaryotic cells is maintained far in excess of the requirement for ribosome biogenesis. Despite the importance of the repeats for both ribosomal and non-ribosomal functions, it is currently not known how “normal” copy number is determined or maintained. To identify essential genes involved in the maintenance of rDNA copy number, we developed a droplet digital PCR based assay to measure rDNA copy number in yeast and used it to screen a yeast conditional temperature-sensitive mutant collection of essential genes. Our screen revealed that low rDNA copy number is associated with compromised DNA replication. Further, subculturing yeast under two separate conditions of DNA replication stress selected for a contraction of the rDNA array independent of the replication fork blocking protein, Fob1. Interestingly, cells with a contracted array grew better than their counterparts with normal copy number under conditions of DNA replication stress. Our data indicate that DNA replication stresses select for a smaller rDNA array. We speculate that this liberates scarce replication factors for use by the rest of the genome, which in turn helps cells complete DNA replication and continue to propagate. Interestingly, tumors from mini chromosome maintenance 2 (MCM2)-deficient mice also show a loss of rDNA repeats. Our data suggest that a reduction in rDNA copy number may indicate a history of DNA replication stress, and that rDNA array size could serve as a diagnostic marker for replication stress. Taken together, these data begin to suggest the selective pressures that combine to yield a “normal” rDNA copy number