Covering and Separation for Permutations and Graphs

This is a thesis of two parts, focusing on covering and separation topics of extremal combinatorics and graph theory, two major themes in this area. They entail the existence and properties of collections of combinatorial objects which together either represent all objects (covering) or can be used to distinguish all objects from each other (separation). We will consider a range of problems which come under these areas. The first part will focus on shattering k-sets with permutations. A family of permutations is said to shatter a given k-set if the permutations cover all possible orderings of the k elements. In particular, we investigate the size of permutation families which cover t orders for every possible k-set as well as study the problem of determining the largest number of k-sets that can be shattered by a family with given size. We provide a construction for a small permutation family which shatters every k-set. We also consider constructions of large families which do not shatter any triple. The second part will be concerned with the problem of separating path systems. A separating path system for a graph is a family of paths where, for any two edges, there is a path containing one edge but not the other. The aim is to find the size of the smallest such family. We will study the size of the smallest separating path system for a range of graphs, including complete graphs, complete bipartite graphs, and lattice-type graphs. A key technique we introduce is the use of generator paths - constructed to utilise the symmetric nature of Kn. We continue this symmetric approach for bipartite graphs and study the limitations of the method. We consider lattice-type graphs as an example of the most efficient possible separating systems for any graph

A Determination of the Centre-of-Mass Energy at LEP2 using Radiative 2-fermion Events

Using e+e- -> mu+mu-(gamma) and e+e- -> qqbar(gamma) events radiative to the Z pole, DELPHI has determined the centre-of-mass energy, sqrt{s}, using energy and momentum constraint methods. The results are expressed as deviations from the nominal LEP centre-of-mass energy, measured using other techniques. The results are found to be compatible with the LEP Energy Working Group estimates for a combination of the 1997 to 2000 data sets.Comment: 20 pages, 6 figures, Accepted by Eur. Phys. J.

Genomic Analysis of the Basal Lineage Fungus Rhizopus oryzae Reveals a Whole-Genome Duplication

Rhizopus oryzae is the primary cause of mucormycosis, an emerging, life-threatening infection characterized by rapid angioinvasive growth with an overall mortality rate that exceeds 50%. As a representative of the paraphyletic basal group of the fungal kingdom called “zygomycetes,” R. oryzae is also used as a model to study fungal evolution. Here we report the genome sequence of R. oryzae strain 99–880, isolated from a fatal case of mucormycosis. The highly repetitive 45.3 Mb genome assembly contains abundant transposable elements (TEs), comprising approximately 20% of the genome. We predicted 13,895 protein-coding genes not overlapping TEs, many of which are paralogous gene pairs. The order and genomic arrangement of the duplicated gene pairs and their common phylogenetic origin provide evidence for an ancestral whole-genome duplication (WGD) event. The WGD resulted in the duplication of nearly all subunits of the protein complexes associated with respiratory electron transport chains, the V-ATPase, and the ubiquitin–proteasome systems. The WGD, together with recent gene duplications, resulted in the expansion of multiple gene families related to cell growth and signal transduction, as well as secreted aspartic protease and subtilase protein families, which are known fungal virulence factors. The duplication of the ergosterol biosynthetic pathway, especially the major azole target, lanosterol 14α-demethylase (ERG11), could contribute to the variable responses of R. oryzae to different azole drugs, including voriconazole and posaconazole. Expanded families of cell-wall synthesis enzymes, essential for fungal cell integrity but absent in mammalian hosts, reveal potential targets for novel and R. oryzae-specific diagnostic and therapeutic treatments

The Mating Type Locus (MAT) and Sexual Reproduction of Cryptococcus heveanensis: Insights into the Evolution of Sex and Sex-Determining Chromosomal Regions in Fungi

Mating in basidiomycetous fungi is often controlled by two unlinked, multiallelic loci encoding homeodomain transcription factors or pheromones/pheromone receptors. In contrast to this tetrapolar organization, Cryptococcus neoformans/Cryptococcus gattii have a bipolar mating system, and a single biallelic locus governs sexual reproduction. The C. neoformans MAT locus is unusually large (>100 kb), contains >20 genes, and enhances virulence. Previous comparative genomic studies provided insights into how this unusual MAT locus might have evolved involving gene acquisitions into two unlinked loci and fusion into one contiguous locus, converting an ancestral tetrapolar system to a bipolar one. Here we tested this model by studying Cryptococcus heveanensis, a sister species to the pathogenic Cryptococcus species complex. An extant sexual cycle was discovered; co-incubating fertile isolates results in the teleomorph (Kwoniella heveanensis) with dikaryotic hyphae, clamp connections, septate basidia, and basidiospores. To characterize the C. heveanensis MAT locus, a fosmid library was screened with C. neoformans/C. gattii MAT genes. Positive fosmids were sequenced and assembled to generate two large probably unlinked MAT gene clusters: one corresponding to the homeodomain locus and the other to the pheromone/receptor locus. Strikingly, two divergent homeodomain genes (SXI1, SXI2) are present, similar to the bE/bW Ustilago maydis paradigm, suggesting one or the other homeodomain gene was recently lost in C. neoformans/C. gattii. Sequencing MAT genes from other C. heveanensis isolates revealed a multiallelic homeodomain locus and at least a biallelic pheromone/receptor locus, similar to known tetrapolar species. Taken together, these studies reveal an extant C. heveanensis sexual cycle, define the structure of its MAT locus consistent with tetrapolar mating, and support the proposed evolutionary model for the bipolar Cryptococcus MAT locus revealing transitions in sexuality concomitant with emergence of a pathogenic clade. These studies provide insight into convergent processes that independently punctuated evolution of sex-determining loci and sex chromosomes in fungi, plants, and animals

Discovery of a Modified Tetrapolar Sexual Cycle in Cryptococcus amylolentus and the Evolution of MAT in the Cryptococcus Species Complex

Sexual reproduction in fungi is governed by a specialized genomic region called the mating-type locus (MAT). The human fungal pathogenic and basidiomycetous yeast Cryptococcus neoformans has evolved a bipolar mating system (a, α) in which the MAT locus is unusually large (>100 kb) and encodes >20 genes including homeodomain (HD) and pheromone/receptor (P/R) genes. To understand how this unique bipolar mating system evolved, we investigated MAT in the closely related species Tsuchiyaea wingfieldii and Cryptococcus amylolentus and discovered two physically unlinked loci encoding the HD and P/R genes. Interestingly, the HD (B) locus sex-specific region is restricted (∼2 kb) and encodes two linked and divergently oriented homeodomain genes in contrast to the solo HD genes (SXI1α, SXI2a) of C. neoformans and Cryptococcus gattii. The P/R (A) locus contains the pheromone and pheromone receptor genes but has expanded considerably compared to other outgroup species (Cryptococcus heveanensis) and is linked to many of the genes also found in the MAT locus of the pathogenic Cryptococcus species. Our discovery of a heterothallic sexual cycle for C. amylolentus allowed us to establish the biological roles of the sex-determining regions. Matings between two strains of opposite mating-types (A1B1×A2B2) produced dikaryotic hyphae with fused clamp connections, basidia, and basidiospores. Genotyping progeny using markers linked and unlinked to MAT revealed that meiosis and uniparental mitochondrial inheritance occur during the sexual cycle of C. amylolentus. The sexual cycle is tetrapolar and produces fertile progeny of four mating-types (A1B1, A1B2, A2B1, and A2B2), but a high proportion of progeny are infertile, and fertility is biased towards one parental mating-type (A1B1). Our studies reveal insights into the plasticity and transitions in both mechanisms of sex determination (bipolar versus tetrapolar) and sexual reproduction (outcrossing versus inbreeding) with implications for similar evolutionary transitions and processes in fungi, plants, and animals

Measurement of flavor asymmetry of light-quark sea in the proton with Drell-Yan dimuon production in p+pp+p and p+dp+d collisions at 120 GeV

Evidence for a flavor asymmetry between the $\bar u$ and $\bar d$ quark distributions in the proton has been found in deep-inelastic scattering and Drell-Yan experiments. The pronounced dependence of this flavor asymmetry on $x$ (fraction of nucleon momentum carried by partons) observed in the Fermilab E866 Drell-Yan experiment suggested a drop of the $\bar d\left(x\right) / \bar u\left(x\right)$ ratio in the $x > 0.15$ region. We report results from the SeaQuest Fermilab E906 experiment with improved statistical precision for $\bar d\left(x\right) / \bar u\left(x\right)$ in the large $x$ region up to $x=0.45$ using the 120 GeV proton beam. Two different methods for extracting the Drell-Yan cross section ratios, $\sigma^{pd} /2 \sigma^{pp}$, from the SeaQuest data give consistent results. The $\bar{d}\left(x\right) / \bar{u}\left(x\right)$ ratios and the $\bar d\left(x\right) - \bar u\left(x\right)$ differences are deduced from these cross section ratios for $0.13 < x < 0.45$. The SeaQuest and E866/NuSea $\bar{d}\left(x\right) / \bar{u}\left(x\right)$ ratios are in good agreement for the $x\lesssim 0.25$ region. The new SeaQuest data, however, show that $\bar d\left(x\right)$ continues to be greater than $\bar u\left(x\right)$ up to the highest $x$ value ($x = 0.45$). The new results on $\bar{d}\left(x\right) / \bar{u}\left(x\right)$ and $\bar{d}\left(x\right) - \bar{u}\left(x\right)$ are compared with various parton distribution functions and theoretical calculations

Dirty and 40 days in the wilderness: Eliciting childbirth and postnatal cultural practices and beliefs in Nepal.

Background: Pregnancy and childbirth are socio-cultural events that carry varying meanings across different societies and cultures. These are often translated into social expectations of what a particular society expects women to do (or not to do) during pregnancy, birth and/or the postnatal period. This paper reports a study exploring beliefs around childbirth in Nepal, a low-income country with a largely Hindu population. The paper then sets these findings in the context of the wider global literature around issues such as periods where women are viewed as polluted (or dirty even) after childbirth. Methods: A qualitative study comprising five in-depth face-to-face interviews and 14 focus group discussions with mainly women, but also men and health service providers. The qualitative findings in Nepal were compared and contrasted with the literature on practices and cultural beliefs related to the pregnancy and childbirth period across the globe and at different times in history. Results: The themes that emerged from the analysis included: (a) cord cutting & placenta rituals; (b) rest & seclusion; (c) purification, naming & weaning ceremonies and (d) nutrition and breastfeeding. Physiological changes in mother and baby may underpin the various beliefs, ritual and practices in the postnatal period. These practices often mean women do not access postnatal health services. Conclusions: The cultural practices, taboos and beliefs during pregnancy and around childbirth found in Nepal largely resonate with those reported across the globe. This paper stresses that local people’s beliefs and practices offer both opportunities and barriers to health service providers. Maternity care providers need to be aware of local values, beliefs and traditions to anticipate and meet the needs of women, gain their trust and work with them