Constructing compact 8-manifolds with holonomy Spin(7) from Calabi-Yau orbifolds

Compact Riemannian 7- and 8-manifolds with holonomy G(2) arid Spin(7) were first constructed by the author in 1994-5, by resolving orbifolds T-7/Gamma and T-8/Gamma. This paper describes a new construction of compact 8-manifolds with holonomy Spin(7). We start with a Calabi-Yau 4-orbifold Y with isolated singularities of a special kind. We divide by an antiholomorphic involution a of Y to get a real 8-orbifold Z = Y/. Then we resolve tire singularities of Z to get a compact 8-manifold M, which has metrics with holonomy Spin(7). Manifolds constructed in this way typically have large fourth Betti number b(4)(M).</sigma

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

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

A change in temperature modulates defence to yellow (stripe) rust in wheat line UC1041 independently of resistance gene Yr36

Background Rust diseases are of major importance in wheat production worldwide. With the constant evolution of new rust strains and their adaptation to higher temperatures, consistent and durable disease resistance is a key challenge. Environmental conditions affect resistance gene performance, but the basis for this is poorly understood. Results Here we show that a change in day temperature affects wheat resistance to Puccinia striiformis f. sp tritici (Pst), the causal agent of yellow (or stripe) rust. Using adult plants of near-isogenic lines UC1041 +/- Yr36, there was no significant difference between Pst percentage uredia coverage in plants grown at day temperatures of 18°C or 25°C in adult UC1041 + Yr36 plants. However, when plants were transferred to the lower day temperature at the time of Pst inoculation, infection increased up to two fold. Interestingly, this response was independent of Yr36, which has previously been reported as a temperature-responsive resistance gene as Pst development in adult UC1041 -Yr36 plants was similarly affected by the plants experiencing a temperature reduction. In addition, UC1041 -Yr36 plants grown at the lower temperature then transferred to the higher temperature were effectively resistant and a temperature change in either direction was shown to affect Pst development up to 8 days prior to inoculation. Results for seedlings were similar, but more variable compared to adult plants. Enhanced resistance to Pst was observed in seedlings of UC1041 and the cultivar Shamrock when transferred to the higher temperature. Resistance was not affected in seedlings of cultivar Solstice by a temperature change in either direction. Conclusions Yr36 is effective at 18°C, refining the lower range of temperature at which resistance against Pst is conferred compared to previous studies. Results reveal previously uncharacterised defence temperature sensitivity in the UC1041 background which is caused by a change in temperature and independently of Yr36. This novel phenotype is present in some cultivars but absent in others, suggesting that Pst defence may be more stable in some cultivars than others when plants are exposed to varying temperatures

Modelling the Northeast Atlantic circulation : implications for the spring invasion of shelf regions by Calanus finmarchicus

The appearance in spring of the copepod Calanus finmarchicus in continental shelf waters of the northeastern Atlantic has been hypothesized to be mainly attributable to invasion from across the continental slope rather than in situ overwintering. This paper describes the application of a hydrodynamic circulation model and a particle-tracking model to Northeast Atlantic waters in order to assess the influence of the flow field and ascent migration parameters on the spring invasion of C. finmarchicus. For hydrodynamic modelling, the Hamburg Shelf-Ocean Model (HAMSOM) was applied to the North Atlantic and Nordic Seas and forced with daily mean atmospheric data. Simulated flow fields from HAMSOM serve as forcing functions for a particle-tracking model of the same region. The robustness of the simulated shelf invasion in three target boxes of the Northeast Atlantic Shelf was assessed by means of a sensitivity analysis with respect to variations in four key migration parameters: overwintering depth, ascent rate, ascent timing, and depth during residence in upper layers. The invasion of the northern North Sea and Norwegian Shelf waters is more sensitive to ascent migration parameters than invasion of the Faroese Shelf. The main reason for enhanced sensitivity of the North Sea invasion is the time and space-dependent flow structure in the Faroe-Shetland Channel. Dense aggregations of overwintering C. finmarchicus are found in the Channel, but because of the complex flow field only a proportion of the overwintering stock has the capacity to reach the North Sea

On the geometry of closed G2-structure

We give an answer to a question posed recently by R.Bryant, namely we show that a compact 7-dimensional manifold equipped with a G2-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G2. This could be considered to be a G2 analogue of the Goldberg conjecture in almost Kahler geometry. The result was generalized by R.L.Bryant to closed G2-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G2-manifold with closed fundamental form and divergence-free Weyl tensor is a G2-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G2-structure again imply that the induced metric has holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main theorem is generalized to the assumption that the Weyl tensor is divergence-free, clarity improved, typos correcte

Sis I See You!: Stories of Black Women Administrators – Lifting the Veil, Stories of Black Women Administrators at HWIs

Black women play a vital role in the success of higher education. However, Black women administrators are often successful in the profession without the necessary tools and support. Although Black women administrators experience several barriers in the profession, they still find ways to connect, engage, and find a sense of community. Black women administrators must have an understanding of how to navigate these challenges in the academy as reoccurring issues can become detrimental to their careers. This chapter focuses on the challenges and successes of Black women administrators in higher education at historically white institutions

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

Water redistribution determines photosynthetic responses to warming and drying in two polar mosses

Predicting impacts of climate change requires an understanding of the sensitivity of species to temperature, including conflated changes in humidity. Physiological responses to temperature and clump-to-air vapour pressure difference (VPD) were compared in two Antarctic moss species, Ceratodon purpureus (Hedw.) Brid. and Schistidium antarctici (Cardot) L.I. Savicz &amp; Smirnova. Temperatures from 8 to 24°C had no significant effects on photosynthesis or recovery from drying, whereas high VPD accelerated drying. In Schistidium, which lacks internal conduction structures, shoots dried more slowly than the clump, and photosynthesis ceased at high shoot relative water content (RWC), behaviour consistent with a strategy of drought avoidance although desiccation tolerant. In contrast, shoots of Ceratodon have a central vascular core, but dried more rapidly than the clump. These results imply that cavitation of the hydroid strand enables hydraulic isolation of extremities during rapid drying, effectively slowing water loss from the clump. Ceratodon maintained photosynthetic activity during drying to lower shoot RWC than Schistidium, consistent with a strategy of drought tolerance. These ecophysiological characteristics may provide a functional explanation for the differential distribution of Schistidium and Ceratodon along moisture gradients in Antarctica. Thus, predicting responses of non-vascular vegetation to climate change at high latitudes requires greater focus on VPD and hydraulics than temperature

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