Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

Cornered Asymptotically Hyperbolic Metrics

Thesis (Ph.D.)--University of Washington, 2016-08

Almost quarter-pinched Kähler metrics and Chern numbers

Given n is an element of Z(+) and epsilon > 0, we prove that there exists delta = delta(epsilon, n) > 0 such that the following holds: If (M(n),g) is a compact Kahler n-manifold whose sectional curvatures K satisfy -1 -delta <= K <= -1/4 and c(I)(M), c(J)(M) are any two Chern numbers of M, then |c(I)(M)/c(J)(M) - c(I)(0)/c(J)(0)| < epsilon, where c(I)(0), c(J)(0) are the corresponding characteristic numbers of a complex hyperbolic space form. It follows that the Mostow-Siu surfaces and the threefolds of Deraux do not admit Kahler metrics with pinching close to 1/4.

Closed G2 forms and special metrics

170 p.

Latitudinal variation of the effect of aviation NOx emissions on atmospheric ozone and methane and related climate metrics

We evaluate the response to regional and latitudinal changes in aircraft NOx emissions using several climate metrics (radiative forcing (RF), Global Warming Potential (GWP), Global Temperature change Potential (GTP)). Global chemistry transport model integrations were performed with sustained perturbations in regional aircraft and aircraft-like NOx emissions. The RF due to the resulting ozone and methane changes is then calculated. We investigate the impact of emission changes for specific geographical regions (approximating to USA, Europe, India and China) and cruise altitude emission changes in discrete latitude bands covering both hemispheres. We find that lower latitude emission changes (per Tg N) cause ozone and methane RFs that are about a factor of 6 larger than those from higher latitude emission changes. The net RF is positive for all experiments. The meridional extent of the RF is larger for low latitude emissions. GWPs for all emission changes are positive, with tropical emissions having the largest values; the sign of the GTP depends on the choice of time horizon.

Einstein-like geometric structures on surfaces

An AH (affine hypersurface) structure is a pair comprising a projective equivalence class of torsion-free connections and a conformal structure satisfying a compatibility condition which is automatic in two dimensions. They generalize Weyl structures, and a pair of AH structures is induced on a co-oriented non-degenerate immersed hypersurface in flat affine space. The author has defined for AH structures Einstein equations, which specialize on the one hand to the usual Einstein Weyl equations and, on the other hand, to the equations for affine hyperspheres. Here these equations are solved for Riemannian signature AH structures on compact orientable surfaces, the deformation spaces of solutions are described, and some aspects of the geometry of these structures are related. Every such structure is either Einstein Weyl (in the sense defined for surfaces by Calderbank) or is determined by a pair comprising a conformal structure and a cubic holomorphic differential, and so by a convex flat real projective structure. In the latter case it can be identified with a solution of the Abelian vortex equations on an appropriate power of the canonical bundle. On the cone over a surface of genus at least two carrying an Einstein AH structure there are Monge-Amp`ere metrics of Lorentzian and Riemannian signature and a Riemannian Einstein K"ahler affine metric. A mean curvature zero spacelike immersed Lagrangian submanifold of a para-K"ahler four-manifold with constant para-holomorphic sectional curvature inherits an Einstein AH structure, and this is used to deduce some restrictions on such immersions.

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

Ricci flows on surfaces related to the Einstein weyl and Abelian vortex equations

There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the Abelian vortex equations, and it is shown that the property that a metric solve these equations is preserved by the Ricci flow. The equations are solved explicitly, and among the metrics obtained are all steady gradient Ricci solitons (e.g. the cigar soliton) and the sausage metric; there are found other examples of eternal, ancient, and immortal Ricci flows, as well as some Ricci flows with conical singularities.

Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity

Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in)homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann–Lamaître–Robertson–Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé–Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.

An institutional understanding of triple bottom line evaluations and the use of social and environmental metrics

Measuring social and environmental metrics of property is necessary for meaningful triple bottom line (TBL) assessments. This paper demonstrates how relevant indicators derived from environmental rating systems provide for reasonably straightforward collations of performance scores that support adjustments based on a sliding scale. It also highlights the absence of a corresponding consensus of important social metrics representing the third leg of the TBL tripod. Assessing TBL may be unavoidably imprecise, but if valuers and managers continue to ignore TBL concerns, their assessments may soon be less relevant given the emerging institutional milieu informing and reflecting business practices and society expectations.

Security metrics for object-oriented class designs

Measuring quality attributes of object-oriented designs (e.g. maintainability and performance) has been covered by a number of studies. However, these studies have not considered security as much as other quality attributes. Also, most security studies focus at the level of individual program statements. This approach makes it hard and expensive to discover and fix vulnerabilities caused by design errors. In this work, we focus on the security design of an object oriented application and define a number of security metrics. These metrics allow designers to discover and fix security vulnerabilities at an early stage, and help compare the security of various alternative designs. In particular, we propose seven security metrics to measure Data Encapsulation (accessibility) and Cohesion (interactions) of a given object-oriented class from the point of view of potential information flow.

Assessment of Speech Dialog Systems using Multi-Modal Cognitive Load Analysis and Driving Performance Metrics

In this paper, cognitive load analysis via acoustic- and CAN-Bus-based driver performance metrics is employed to assess two different commercial speech dialog systems (SDS) during in-vehicle use. Several metrics are proposed to measure increases in stress, distraction and cognitive load and we compare these measures with statistical analysis of the speech recognition component of each SDS. It is found that care must be taken when designing an SDS as it may increase cognitive load which can be observed through increased speech response delay (SRD), changes in speech production due to negative emotion towards the SDS, and decreased driving performance on lateral control tasks. From this study, guidelines are presented for designing systems which are to be used in vehicular environments.

The right person, in the right job, with the right skills, at the right time. A workforce-planning model that goes beyond metrics

Purpose – The paper aims to describe a workforce-planning model developed in-house in an Australian university library that is based on rigorous environmental scanning of an institution, the profession and the sector. Design/methodology/approach – The paper uses a case study that describes the stages of the planning process undertaken to develop the Library’s Workforce Plan and the documentation produced. Findings – While it has been found that the process has had successful and productive outcomes, workforce planning is an ongoing process. To remain effective, the workforce plan needs to be reviewed annually in the context of the library’s overall planning program. This is imperative if the plan is to remain current and to be regarded as a living document that will continue to guide library practice. Research limitations/implications – Although a single case study, the work has been contextualized within the wider research into workforce planning. Practical implications – The paper provides a model that can easily be deployed within a library without external or specialist consultant skills, and due to its scalability can be applied at department or wider level. Originality/value – The paper identifies the trends impacting on, and the emerging opportunities for, university libraries and provides a model for workforce planning that recognizes the context and culture of the organization as key drivers in determining workforce planning. Keywords - Australia, University libraries, Academic libraries, Change management, Manpower planning Paper type - Case study

Multi-modal object tracking using dynamic performance metrics

Intelligent surveillance systems typically use a single visual spectrum modality for their input. These systems work well in controlled conditions, but often fail when lighting is poor, or environmental effects such as shadows, dust or smoke are present. Thermal spectrum imagery is not as susceptible to environmental effects, however thermal imaging sensors are more sensitive to noise and they are only gray scale, making distinguishing between objects difficult. Several approaches to combining the visual and thermal modalities have been proposed, however they are limited by assuming that both modalities are perfuming equally well. When one modality fails, existing approaches are unable to detect the drop in performance and disregard the under performing modality. In this paper, a novel middle fusion approach for combining visual and thermal spectrum images for object tracking is proposed. Motion and object detection is performed on each modality and the object detection results for each modality are fused base on the current performance of each modality. Modality performance is determined by comparing the number of objects tracked by the system with the number detected by each mode, with a small allowance made for objects entering and exiting the scene. The tracking performance of the proposed fusion scheme is compared with performance of the visual and thermal modes individually, and a baseline middle fusion scheme. Improvement in tracking performance using the proposed fusion approach is demonstrated. The proposed approach is also shown to be able to detect the failure of an individual modality and disregard its results, ensuring performance is not degraded in such situations.