Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate submanifolds of S^n. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey-Lawson for submanifolds in R^n in their pioneering paper. We also construct calibrated submanifolds in complete metrics with special holonomy G_2 and Spin(7) discovered by Bryant and Salamon on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds in a compact manifold with special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some paragraphs rewritten for improved clarit

Combining community-based research and local knowledge to confront asthma and subsistence-fishing hazards in Greenpoint/Williamsburg, Brooklyn, New York.

Activists in the environmental justice movement are challenging expert-driven scientific research by taking the research process into their own hands and speaking for themselves by defining, analyzing, and prescribing solutions for the environmental health hazards confronting communities of the poor and people of color. I highlight the work of El Puente and The Watchperson Project--two community-based organizations in the Greenpoint/Williamsburg neighborhood in Brooklyn, New York, that have engaged in community-based participatory research (CBPR) to address asthma and risks from subsistence-fish diets. The CBPR process aims to engage community members as equal partners alongside scientists in problem definition, information collection, and data analysis--all geared toward locally relevant action for social change. In the first case I highlight how El Puente has organized residents to conduct a series of asthma health surveys and tapped into local knowledge of the Latino population to understand potential asthma triggers and to devise culturally relevant health interventions. In a second case I follow The Watchperson Project and their work surveying subsistence anglers and note how the community-gathered information contributed key data inputs for the U.S. Environmental Protection Agency Cumulative Exposure Project in the neighborhood. In each case I review the processes each organization used to conduct CBPR, some of their findings, and the local knowledge they gathered, all of which were crucial for understanding and addressing local environmental health issues. I conclude with some observations about the benefits and limits of CBPR for helping scientists and communities pursue environmental justice

Pressure perturbations from geologic carbon sequestration: Area-of-review boundaries and borehole leakage driving forces

We investigate the possibility that brine could be displaced upward into potable water through wells. Because of the large volumes of CO2 to be injected, the influence of the zone of elevated pressure on potential conduits such as well boreholes could extend many kilometers from the injection site—farther than the CO2 plume itself. The traditional approach to address potential brine leakage related to fluid injection is to set an area of fixed radius around the injection well/zone and to examine wells and other potentially open pathways located in the “Area-of-Review” (AoR). This suggests that the AoR needs to be defined in terms of the potential for a given pressure perturbation to drive upward fluid flow in any given system rather than on some arbitrary pressure rise. We present an analysis that focuses on the changes in density/salinity of the fluids in the potentially leaking wellbore.Bureau of Economic Geolog

Neighborhoods of trees in circular orderings

In phylogenetics, a common strategy used to construct an evolutionary tree for a set of species X is to search in the space of all such trees for one that optimizes some given score function (such as the minimum evolution, parsimony or likelihood score). As this can be computationally intensive, it was recently proposed to restrict such searches to the set of all those trees that are compatible with some circular ordering of the set X. To inform the design of efficient algorithms to perform such searches, it is therefore of interest to find bounds for the number of trees compatible with a fixed ordering in the neighborhood of a tree that is determined by certain tree operations commonly used to search for trees: the nearest neighbor interchange (nni), the subtree prune and regraft (spr) and the tree bisection and reconnection (tbr) operations. We show that the size of such a neighborhood of a binary tree associated with the nni operation is independent of the tree’s topology, but that this is not the case for the spr and tbr operations. We also give tight upper and lower bounds for the size of the neighborhood of a binary tree for the spr and tbr operations and characterize those trees for which these bounds are attained

Integrable vortex-type equations on the two-sphere

We consider the Yang-Mills instanton equations on the four-dimensional manifold S^2xSigma, where Sigma is a compact Riemann surface of genus g>1 or its covering space H^2=SU(1,1)/U(1). Introducing a natural ansatz for the gauge potential, we reduce the instanton equations on S^2xSigma to vortex-type equations on the sphere S^2. It is shown that when the scalar curvature of the manifold S^2xSigma vanishes, the vortex-type equations are integrable, i.e. can be obtained as compatibility conditions of two linear equations (Lax pair) which are written down explicitly. Thus, the standard methods of integrable systems can be applied for constructing their solutions. However, even if the scalar curvature of S^2xSigma does not vanish, the vortex equations are well defined and have solutions for any values of the topological charge N. We show that any solution to the vortex equations on S^2 with a fixed topological charge N corresponds to a Yang-Mills instanton on S^2xSigma of charge (g-1)N.Comment: 14 pages; v2: clarifying comments added, published versio

Collaborative development of diffraction-limited beamline optical systems at US DOE light sources

An ongoing collaboration among four US Department of Energy (DOE) National Laboratories has demonstrated key technology prototypes and software modeling tools required for new high-coherent flux beamline optical systems. New free electron laser (FEL) and diffraction-limited storage ring (DLSR) light sources demand wavefront preservation from source to sample to achieve and maintain optimal performance. Fine wavefront control was achieved using a novel, roomtemperature cooled mirror system called REAL (resistive element adjustable length) that combines cooling with applied, spatially variable auxiliary heating. Single-grating shearing interferometry (also called Talbot interferometry) and Hartmann wavefront sensors were developed and used for optical characterization and alignment on several beamlines, across a range of photon energies. Demonstrations of non-invasive hard x-ray wavefront sensing were performed using a thin diamond single-crystal as a beamsplitter

Magnetic Field Response Measurement Acquisition System

Magnetic field response sensors designed as passive inductor-capacitor circuits produce magnetic field responses whose harmonic frequencies correspond to states of physical properties for which the sensors measure. Power to the sensing element is acquired using Faraday induction. A radio frequency antenna produces the time varying magnetic field used for powering the sensor, as well as receiving the magnetic field response of the sensor. An interrogation architecture for discerning changes in sensor s response kequency, resistance and amplitude is integral to the method thus enabling a variety of measurements. Multiple sensors can be interrogated using this method, thus eliminating the need to have a data acquisition channel dedicated to each sensor. The method does not require the sensors to be in proximity to any form of acquisition hardware. A vast array of sensors can be used as interchangeable parts in an overall sensing system

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

Circular Networks from Distorted Metrics

Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into this elementary framework. Alternatively, various network representations have been developed. Circular networks are a natural generalization of leaf-labeled trees interpreted as split systems, that is, collections of bipartitions over leaf labels corresponding to current species. Although such networks do not explicitly model specific evolutionary events of interest, their straightforward visualization and fast reconstruction have made them a popular exploratory tool to detect network-like evolution in genetic datasets. Standard reconstruction methods for circular networks, such as Neighbor-Net, rely on an associated metric on the species set. Such a metric is first estimated from DNA sequences, which leads to a key difficulty: distantly related sequences produce statistically unreliable estimates. This is problematic for Neighbor-Net as it is based on the popular tree reconstruction method Neighbor-Joining, whose sensitivity to distance estimation errors is well established theoretically. In the tree case, more robust reconstruction methods have been developed using the notion of a distorted metric, which captures the dependence of the error in the distance through a radius of accuracy. Here we design the first circular network reconstruction method based on distorted metrics. Our method is computationally efficient. Moreover, the analysis of its radius of accuracy highlights the important role played by the maximum incompatibility, a measure of the extent to which the network differs from a tree.Comment: Submitte