Rainbow Graphs and Switching Classes

A rainbow graph is a graph that admits a vertex-coloring such that every color appears exactly once in the neighborhood of each vertex. We investigate some properties of rainbow graphs. In particular, we show that there is a bijection between the isomorphism classes of n-rainbow graphs on 2n vertices and the switching classes of graphs on n vertices.Comment: Added more reference, fixed some typos (revision for journal submission

Chaos at the border of criticality

The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techniques. The bifurcation structure of the continuous system (specifically, the proximity to a degenerate AHB) endows the Poincare map with distinct qualitative features such as unimodality and the presence of the boundary layer, where the map is strongly expanding. This structure of the map in turn explains the bifurcation scenarios in the continuous system including chaotic mixed-mode oscillations near the border between the regions of sub- and supercritical AHB. The proposed mechanism yields the statistical properties of the mixed-mode oscillations in this regime. The statistics predicted by the analysis of the Poincare map and those observed in the numerical experiments of the continuous system show a very good agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science (tentatively, Sept 2008

An Empirical Examination of the Associations between Social Tags and Web Queries

Introduction. We aim to discover the associations between social tags for a Web page and Web queries that would retrieve the same Webpage in three major search engines. Method. 4,827 query terms were submitted to the three major search engines to acquire search engine results pages. A series of Perl scripts were written to read search engine results pages and to identify, analyse, and extract organic links Analysis. Web pages from the organic links in search engine results pages were examined to see whether and how they had been tagged in Delicious. Only the Webpages tagged by at least 100 taggers were included in this study. The top thirty popular social tags used were harvested. The two sets of data were quantitatively analysed to investigate the research questions. Results. At least 60% of search engines\u27 query terms overlapped with social tags in Delicious; higher ranked social tags were more likely to be used as query terms for the same Web resources; and the co-occurring pattern of query terms and social tags over social ranking resembled a power law distribution. Conclusions. Socially tagged resources are likely to be highly ranked in search engine results pages. The findings can be applicable to the future study of Web resource related tasks such as Web searching and Web indexing

Meaning of Wearing Faux Fur

The purpose of this study is to Understand meanings of consuming faux fur from the perspective of consumer culture theory

Case-control association analysis of rheumatoid arthritis with candidate genes using related cases

We performed a case-control association analysis of rheumatoid arthritis (RA) for several candidate genes using the North American Rheumatoid Arthritis Consortium (NARAC) data provided in Genetic Analysis Workshop 15. We conducted the case-control association analysis using all related cases and unrelated controls and compared the results with those from the analysis of samples using only one randomly selected case from each family and all unrelated controls. For both analyses we used a weighted composite likelihood ratio test based on single-nucleotide polymorphism (SNP) markers or haplotypes accounting for the correlation among samples within a family. Several SNPs, including R620W in the candidate gene PTPN22, showed an association with RA status, which confirmed previously reported results. Several other SNPs in the candidate genes, such as CTLA4, HAVCR1, and SUMO4, also had rather small p-values (<0.05), suggesting the associations between them and RA. Our results showed that the p-values obtained from the analysis including all related cases were generally smaller than those obtained from the analysis including only one randomly selected case per family. These results, together with the results, based on simulated data, showed that higher power could be achieved using all related cases