Multipartite graph decomposition: cycles and closed trails

This paper surveys results on cycle decompositions of complete multipartite graphs (where the parts are not all of size 1, so the graph is not <em>K</em>_<em>n</em> ), in the case that the cycle lengths are “small”. Cycles up to length <em>n</em> are considered, when the complete multipartite graph has <em>n</em> parts, but not hamilton cycles. Properties which the decompositions may have, such as being gregarious, are also mentioned.<br /

Multipartite graph decomposition: cycles and closed trails

This paper surveys results on cycle decompositions of complete multipartite graphs (where the parts are not all of size 1, so the graph is not K_n ), in the case that the cycle lengths are “small”. Cycles up to length n are considered, when the complete multipartite graph has n parts, but not hamilton cycles. Properties which the decompositions may have, such as being gregarious, are also mentioned

The argument of the broken pane: Suffragette consumerism and newspapers

Within the cut-throat world of newspaper advertising the newspapers of Britain's Women's Social and Political Union (WSPU) Votes for Women and the Suffragette managed to achieve a balance that has often proved to be an impossible challenge for social movement press—namely the maintenance of a highly political stance whilst simultaneously exploiting the market system with advertising and merchandising. When the militant papers advocated window smashing of West End stores in 1912–1913, the companies who were the target still took advertisements. Why? What was the relationship between news values, militant violence and advertising income? ‘Do-it-yourself’ journalism operated within a context of ethical consumerism and promotionally orientated militancy. This resulted in newspaper connections between politics, commerce and a distinct market profile, evident in the customisation of advertising, retailer dialogue with militants and longer-term loyalty—symptomatic of a wider trend towards newspaper commercialism during this period

Ovine pedomics : the first study of the ovine foot 16S rRNA-based microbiome

We report the first study of the bacterial microbiome of ovine interdigital skin based on 16S rRNA by pyrosequencing and conventional cloning with Sanger-sequencing. Three flocks were selected, one a flock with no signs of footrot or interdigital dermatitis, a second flock with interdigital dermatitis alone and a third flock with both interdigital dermatitis and footrot. The sheep were classified as having either healthy interdigital skin (H), interdigital dermatitis (ID) or virulent footrot (VFR). The ovine interdigital skin bacterial community varied significantly by flock and clinical condition. The diversity and richness of operational taxonomic units was greater in tissue from sheep with ID than H or VFR affected sheep. Actinobacteria, Bacteriodetes, Firmicutes and Proteobacteria were the most abundant phyla comprising 25 genera. Peptostreptococcus, Corynebacterium and Staphylococcus were associated with H, ID and VFR respectively. Sequences of Dichelobacter nodosus, the causal agent of ovine footrot, were not amplified due to mismatches in the 16S rRNA universal forward primer (27F). A specific real time PCR assay was used to demonstrate the presence of D. nodosus which was detected in all samples including the flock with no signs of ID or VFR. Sheep with ID had significantly higher numbers of D. nodosus (104-109 cells/g tissue) than those with H or VFR feet

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

The intersection problem for m‐cycle systems

Let I(v) denote the set of integers k for which a pair of m‐cycle systems of K, exist, on the same vertex set, having k common cycles. Let J(v) = {0, 1, 2,…, t −2, t} where t = v(v − 1)/2m. In this article, if 2mn + x is an admissible order of an m‐cycle system, we investigate when I(2mn + x) = J(2mn + x), for both m even and m odd. Results include J(2mn + 1) = I(2mn + 1) for all n > 1 if m is even, and for all n > 2 if n is odd. Moreover, the intersection problem for even cycle systems is completely solved for an equivalence class x (mod 2m) once it is solved for the smallest in that equivalence class and for K. For odd cycle systems, results are similar, although generally the two smallest values in each equivalence class need to be solved. We also completely solve the intersection problem for m = 4, 6, 7, 8, and 9. (The cased m = 5 was done by C‐M. K. Fu in 1987.) © 1993 John Wiley & Sons, Inc. Copyrigh

On Mendelsohn and directed triple systems with repeated elements allowed in triples

The definitions of both Mendelsohn triple systems and directed (or transitive) triple systems are extended to include triples with repeated elements. It is shown that such systems exist if and only if the number of elements in the underlying set is divisible by three. Moreover, every balanced ternary design with suitable parameters may have its triples directed to form a directed (transitive) triple system with repeats. Finally provided the underlying set is of size at least nine, there exists a balanced ternary design on this set with block size three, the triples of which cannot be oriented to form a Mendelsohn triple system with repeats

5-cycle decompositions from paired 3- and 4-cycle decompositions

Let (V,T) be a 3-fold triple system and (V,C) a 4-fold 4-cycle system on the same set V. This choice of indices 3 and 4 ensures that each system contains the same number of cycles: {pipe}T{pipe} = {pipe}C{pipe}. We pair up the cycles, {t, c}, where t ∈ T and c ∈ C, in such a way that t and c share one edge. If t = (x, y, z) and c = (x, y, u, v), so t and c share the edge {x, y}, then we retain the 5-cycle (z, x, v, u, y) and remove the repeated edge {x, y}. Doing this for all the pairs {t, c}, we rearrange all the shared edges, common to t and c, into further 5-cycles, so that the result is a 7-fold 5-cycle system on V. The necessary conditions are that the order {pipe}V {pipe} is 1 or 5 (mod 10); these conditions are shown to be sufficient for such a "metamorphosis" from pairs of 3- and 4-cycles into 5-cycles

More balanced ternary designs with block size three

A balanced ternary design (BTD) is a balanced design on V elements with constant block size, in which each element may occur 0, 1 or 2 times in each block. Thus blocks may be collections of elements rather than subsets of elements. A regular BTD is one in which each element occurs singly in ρ{variant} blocks, and is repeated in ρ{variant} blocks. The condition V ≡ 0(mod 3) was shown in an earlier paper to be both necessary and sufficient for the existence of a regular BTD on V elements with block size 3, index 2 and ρ{variant}=1. We show in this paper that if ρ{variant} = 2, necessary and sufficient conditions for existence of a regular BTD with block size 3 and index 2 are V ≡0 or 2(mod 3), V ≥5, and if ρ{variant}=3 the necesary and sufficient conditions are V ≡ 0 or 1(mod 3), V ≥ 7. Hence by allowing ρ{variant} to be as large as 3, we have a regular BTD on V elements with block size 3 and index 2 for all V ≠1,2,4