On the Minimum Ropelength of Knots and Links

The ropelength of a knot is the quotient of its length and its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are $C^{1,1}$ curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp.Comment: 29 pages, 14 figures; New version has minor additions and corrections; new section on asymptotic growth of ropelength; several new reference

Terrorizing Islam: Building American Identity in the 9/11 Novel

In the years after 9/11, a number of novels appeared that purported to examine the perspectives of both Islamic fundamentalist terrorists and American Muslims . While ostensibly giving their American audiences an insight into an Islamic perspective, what these novels are actually unconsciously doing is using their Muslim characters to create a new sense of American identity in the post-9/11world where older conceptions of American identity have been disrupted by the violent intrusion of an alien presence . Drawing upon the work of Edward Said and Toni Morrison, this thesis will examine the ways John Updike\u27s Terrorist, Amy Waldman\u27s, The Submission, and Don DeliIIo\u27s Falling Man, construct a Muslim Other in order to create an American identity. The presence of the Muslims in these novels serves as an occasion for the Americans to explore their new identities after 9/11,where American exceptionalism and such American qualities once constructed as intrinsic and essential as freedom, inviolability, and tolerance are called into questio

Sparse graphs and the fixed points on type spaces property

We examine the topological dynamics of the automorphism groups of omega-categorical sparse graphs resulting from Hrushovski constructions. Specifically, we consider the fixed points on type spaces property, which a structure M has if, for each positive integer n, every Aut(M)-subflow of the space of n-types has a fixed point. Extending a result of Evans, Hubicka and Nesetril, we show that there exists an omega-categorical structure M, resulting from a Hrushovski construction, such that no omega-categorical expansion of M has the fixed points on type spaces property.Comment: 23 pages, 1 figur

The Second Hull of a Knotted Curve

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.Comment: 7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Mat

The externally definable Ramsey property and fixed points on type spaces

We discuss the externally definable Ramsey property, a weakening of the Ramsey property for ultrahomogeneous structures, where the only colourings considered are those that are externally definable: that is, definable with parameters in an elementary extension. We show a number of basic results analogous to the classical Ramsey theory, and show that, for an ultrahomogeneous structure M, the externally definable Ramsey property is equivalent to the dynamical statement that, for each natural number n, every subflow of the space of n-types with parameters in M has a fixed point. We discuss a range of examples, including results regarding the lexicographic product of structures.Comment: 42 pages, 1 figur

Reporting of Intimate Partner Violence among Men Who Have Sex with Men in an Online Survey

Objective: A growing body of literature suggests that IPV occurs within same-sex relationships and that members of the LGBT community face a number of unique challenges in accessing IPV related services. This paper examines the use of an on-line survey, marketed through a popular social networking site, to collect data on the experience and perpetration of IPV among men who have sex with men (MSM) in the US.Methods: Internet-using MSM were recruited through selective placement of banner advertisements on MySpace.com. Participants were eligible for the baseline survey if they were males ≥ 18 years of age, and reported at least one male sex partner in the last 12 months. In total 16, 597 men responded to the ad, of which 11, 681 were eligible for the study, and 5602 completed the questionnaire: in total 543 men completed the follow-up survey which included questions on the experience and perpetration of IPV. The final analysis sample was 402 MSM.Results: The prevalence of violence among the sample was relatively high: 11.8% of men reported physical violence from a current male partner, and about 4% reported experiencing coerced sex. Reporting of perpetration of violence against a partner was generally lower, with approximately 7% reporting perpetrating physical violence and less than 1% reporting perpetration of sexual violence.Conclusion: The results presented here find lower levels of experiencing both physical and sexual IPV than have been shown in previous studies, yet show relatively high levels of reporting of perpetration of IPV. Collecting IPV data through surveys administered through social networking sites is feasible and provides a new opportunity to reach currently over-looked populations in IPV research

Criticality for the Gehring link problem

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November 200

Factors Associated with Self-Reported HBV Vaccination among HIV-Negative MSM Participating in an Online Sexual Health Survey: A Cross-Sectional Study

Background: A substantial proportion of men who have sex with men (MSM) in the United States remain unvaccinated against hepatitis B. We sought to understand which factors are associated with vaccination among HIV-negative MSM. Methodology/Principal Findings: Data were from a 2010 web-based survey of adult MSM. We calculated the prevalence of self-reported hepatitis B vaccination among 1,052 HIV-negative or HIV-untested men who knew their hepatitis B vaccination status, and used multivariate logistic regression to determine associated factors. 679 (64.5%) MSM reported being vaccinated. Younger men were more likely to report being vaccinated than older men, and there was a significant interaction between age and history of hepatitis B testing. Men with at least some college education were at least 2.1 times as likely to be vaccinated as men with a high school education or less (95 % CI = 1.4–3.1). Provider recommendation for vaccination (aOR = 4.2, 95 % CI = 2.4–7.4) was also significantly associated with receipt of vaccination. Conclusions/Significance: Providers should assess sexual histories of male patients and offer those patients with male sex partners testing for hepatitis infection and vaccinate susceptible patients. There may be particular opportunities fo

Intimate Partner Violence and Sexual Risk-taking among Men Who Have Sex with Men in South Africa

Objective: A growing body of literature suggests that men who have sex with men (MSM) represent a high risk group for human immunodeficiency virus (HIV) infection in Africa, but are often overlooked in the development of HIV interventions and programming. Little attention has been paid to the presence of intimate partner violence (IPV) among MSM in African settings. This paper examines reporting of IPV among a sample of predominantly white, gay internet-recruited MSM in South Africa and examines associations between IPV and sexual risk-taking.Methods: Internet-using MSM were recruited through selective placement of banner advertisements on Facebook.com. Eligibility criteria were over 18-years-old, residence in South Africa and self-reporting of recent male-male sexual behavior. There were 777 eligible respondents, of which 521 MSM with complete data are included in the final analysis. Ninety percent of the sample reported a White/ European race, and 96% self-identified as gay.Results: The prevalence of IPV, both experienced and perpetrated, was relatively high, with 8% of men reporting having experienced recent physical IPV and 4.5% of men reporting recent experiences of sexual IPV. Approximately 4.5% of MSM reported recently perpetrating physical IPV, while the reporting of perpetration of recent sexual IPV was much lower at 0.45%. Reporting of experiencing and perpetration of physical IPV was significantly associated with race, level of education and reporting recent unprotected anal sex. Reporting of experiencing recent sexual IPV was significantly associated with reported experiences of homophobia.Conclusion: There is a limited amount of data on IPV within same-sex relationships in South Africa, and the results presented here suggest that the prevalence of IPV within this White/European and gay population is cause for concern. Collection of IPV data through surveys administered via social networking sites is feasible and represents a way of reaching otherwise marginalized population groups in IPV research; although in this instance Black Africans and MSM who did not identify as gay were severely under-represented. [West J Emerg Med. 2011;12(3):343-347.