Stable concordance of knots in 3-manifolds

Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide obstructions to the existence of a singular concordance which can be homotoped to an embedding after stabilization by connected sums with $S^2\times S^2$. Results include classifications of stably slice links in orientable 3-manifolds, stable knot concordance in products of an orientable surface with the circle, and stable link concordance for many links of null-homotopic knots in orientable 3-manifolds.Comment: 59 pages, 28 figure

The zero forcing polynomial of a graph

Zero forcing is an iterative graph coloring process, where given a set of initially colored vertices, a colored vertex with a single uncolored neighbor causes that neighbor to become colored. A zero forcing set is a set of initially colored vertices which causes the entire graph to eventually become colored. In this paper, we study the counting problem associated with zero forcing. We introduce the zero forcing polynomial of a graph $G$ of order $n$ as the polynomial $\mathcal{Z}(G;x)=\sum_{i=1}^n z(G;i) x^i$, where $z(G;i)$ is the number of zero forcing sets of $G$ of size $i$. We characterize the extremal coefficients of $\mathcal{Z}(G;x)$, derive closed form expressions for the zero forcing polynomials of several families of graphs, and explore various structural properties of $\mathcal{Z}(G;x)$, including multiplicativity, unimodality, and uniqueness.Comment: 23 page

On Barrier Graphs of Sensor Networks

The study of sensor networks begins with a model, which usually has a geometric component. This thesis focuses on networks of sensors modeled as collections of rays in the plane whose use is to detect intruders, and in particular a graph derived from this geometry, called the barrier graph of the network, which captures information about the network\u27s coverage. Every such ray-barrier sensor network corresponds to a barrier graph, but not every graph is the barrier graph of some network. We show that any barrier graph is not just tripartite, but perfect. We describe how to find networks which have certain designated graphs as their barrier graphs. We show that the size of a minimum vertex cover (in this context called the resilience) of a given graph can yield information about whether and how one can find a sensor network whose barrier graph is the given graph. Finally, we demonstrate that barrier graphs have certain strong structural properties, as a result of the geometry of ray-barrier networks, which represent progress towards a full characterization of barrier graphs

Barrier Graphs and Extremal Questions on Line, Ray, Segment, and Hyperplane Sensor Networks

A sensor network is typically modeled as a collection of spatially distributed objects with the same shape, generally for the purpose of surveilling or protecting areas and locations. In this dissertation we address several questions relating to sensors with linear shapes: line, line segment, and rays in the plane, and hyperplanes in higher dimensions. First we explore ray sensor networks in the plane, whose resilience is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is described by a particular tripartite graph, the barrier graph of the network. We show that barrier graphs are perfect (Berge) graphs and have a rigid neighborhood structure due to the rays\u27 geometry. We introduce two extremal problems for networks in the plane made of line sensors, line segment sensors, or ray sensors, which informally ask how well it is possible to simultaneously protect k locations with n (line/ray/segment)-shaped sensors from intruders. The first question allows any number of intruders, while the second assumes there is a lone intruder. We show these are questions to be answered separately, and provide complete answers for k = 2 in both cases. We provide asymptotically tight answers for question (1) when k = 3, 4 and the locations are in convex position. We also provide asymptotic lower bounds for question (1) for any k. Finally, we generalize these extremal problems to d dimensions. For the d-dimensional version of question (1) we provide asymptotic lower and upper bounds for any combination of k and d, though these bounds do not meet

Development of Extended Unimpaired Streamflow Records in the Saluda Basin, South Carolina

This paper presents the steps involved and the methodologies employed in the first phase of the South Carolina Surface Water Assessment - development of extended and unimpaired streamflow estimates based on USGS gage data in the Saluda basin. Streamflow data are first adjusted to remove effects of anthropogenic impairments. Adjustments are made for reservoirs, withdrawals, and discharges based on available documentation. Where documentation is insufficient, hindcasting methods are used. The resulting datasets are called unimpaired flows (UIFs). The UIFs are then extended in time from 1925, the starting date of the first continuous stream discharge data available in the basin, through 2013. Candidate reference gages for each short-record gage are selected based on a qualitative assessment. Area ratio and Maintenance of Variance Extension (Hirsch, 1982) methods are applied. Statistical and graphical evaluation of the extension results is followed by composition of extended UIFs

Bi-cultural dynamics for risk and protective factors for cardiometabolic health in an Alaska Native (Yup\u27ik) population

Alaska Native people experience disparities in mortality from heart disease and stroke. This work attempts to better understand the relationships between socioeconomic, behavioral, and cardiometabolic risk factors among Yup\u27ik people of southwestern Alaska, with a focus on the role of the socioeconomic, and cultural components. Using a cross-sectional sample of 486 Yup\u27ik adults, we fitted a Partial Least Squares Path Model (PLS-PM) to assess the associations between components, including demographic factors [age and gender], socioeconomic factors [education, economic status, Yup\u27ik culture, and Western culture], behavioral factors [diet, cigarette smoking and smokeless tobacco use, and physical activity], and cardiometabolic risk factors [adiposity, triglyceride-HDL and LDL lipids, glycemia, and blood pressure]. We found relatively mild associations of education and economic status with cardiometabolic risk factors, in contrast with studies in other populations. The socioeconomic factor and participation in Yup\u27ik culture had potentially protective associations with adiposity, triglyceride-HDL lipids, and blood pressure, whereas participation in Western culture had a protective association with blood pressure. We also found a moderating effect of participation in Western culture on the relationships between Yup\u27ik culture participation and both blood pressure and LDL lipids, indicating a potentially beneficial additional effect of biculturalism. Our results suggest that reinforcing protective effects of both Yup\u27ik and Western cultures could be useful for interventions aimed at reducing cardiometabolic health disparities

Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS

We present the results of a search for new, heavy particles that decay at a significant distance from their production point into a final state containing charged hadrons in association with a high-momentum muon. The search is conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS detector operating at the Large Hadron Collider. Production of such particles is expected in various scenarios of physics beyond the standard model. We observe no signal and place limits on the production cross-section of supersymmetric particles in an R-parity-violating scenario as a function of the neutralino lifetime. Limits are presented for different squark and neutralino masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final version to appear in Physics Letters