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

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

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's Terrorist, Amy Waldman's, The Submission, and Don DeliIIo's 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 questionEnglis

Flows of linear orders on sparse graphs

We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre, partially answering a question of Tsankov regarding results of Evans, Hubicka and Nesetril on the topological dynamics of automorphism groups of sparse graphs.Comment: 17 page

Dyadic Characteristics and Intimate Partner Violence among Men Who Have Sex with Men.

OBJECTIVE: Although the research community has begun to recognize intimate partner violence (IPV) as an important issue in same-sex relationships, there has been a lack of attention to characteristics of these relationships that may be associated with IPV. In particular, there has been a lack of attention paid to the associations between dyadic characteristics and IPV in same-sex relationships. This paper examined associations between dyadic characteristics, including relationship satisfaction, communal coping and efficacy, and perpetrating and experiencing IPV among a sample of United States men who have sex with men (MSM). METHODS: We collected data via an online survey with 528 MSM, who were greater than 18 years of age and reported at least one male sex partner in the last 12 months. The analysis examined dyadic factors associated with reporting of experiencing and perpetrating emotional violence, physical violence, and sexual violence. RESULTS: The prevalence of violence in the sample ranged from nine percent reporting perpetrating sexual violence to 33% of men reporting experiencing emotional violence. MSM who reported greater satisfaction with their relationship or who reported a higher degree of concordance with their partner on lifestyle choices were less likely to report experiencing or perpetrating emotional violence. MSM who perceived a stigma to being in a male same-sex couple were less likely to report experiencing or perpetrating sexual violence. CONCLUSION: The results presented here demonstrate high levels of IPV among MSM and that dyadic characteristics are associated with the occurrence of IPV. Understanding relationship characteristics associated with increased IPV among same-sex male couples can contribute to the development of more accurate IPV screening tools, and more sensitively and appropriately designed intervention messages

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

SensorWeb 3G: Extending On-Orbit Sensor Capabilities to Enable Near Realtime User Configurability

This research effort prototypes an implementation of a standard interface, Web Coverage Processing Service (WCPS), which is an Open Geospatial Consortium(OGC) standard, to enable users to define, test, upload and execute algorithms for on-orbit sensor systems. The user is able to customize on-orbit data products that result from raw data streaming from an instrument. This extends the SensorWeb 2.0 concept that was developed under a previous Advanced Information System Technology (AIST) effort in which web services wrap sensors and a standardized Extensible Markup Language (XML) based scripting workflow language orchestrates processing steps across multiple domains. SensorWeb 3G extends the concept by providing the user controls into the flight software modules associated with on-orbit sensor and thus provides a degree of flexibility which does not presently exist. The successful demonstrations to date will be presented, which includes a realistic HyspIRI decadal mission testbed. Furthermore, benchmarks that were run will also be presented along with future demonstration and benchmark tests planned. Finally, we conclude with implications for the future and how this concept dovetails into efforts to develop "cloud computing" methods and standards

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