CAT(0) is an algorithmic property

In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is non-positively curved. In particular, given such a complex we show how to define a boolean combination of polynomial equations and inequalities in real variables, i.e. a real semi-algebraic set, which is empty if and only if the complex is non-positively curved. Once this equivalence has been shown, the main result follows from a standard theorem in real algebraic geometry.Comment: (23 pages) To appear in Geometriae Dedicat

Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piecewise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The proof involves a mixture of computer computation and techniques from small cancellation theory.Comment: (21 pages) To appear in Topolog

Recreational Boating in Virginia: a preliminary analysis

Increasingly, recreational boating and its supporting industries are being affected by governmental policy and regulatory and allocation decisions. Clearly, those charged with making these decisions cannot understand the impacts of their decisions on related business, individuals, and their livelihoods without possessing some knowledge of the general linkages between boating and local economies. This initial estimate of the economic impacts of boating in Virginia is a first step in that direction. Hopefully, a better knowledge of the nature, recent growth and present magnitude of boating in the Commonwealth will insure that decisions made which influence its existence will be\u27based on the best information possible

Where the Green Grants Went 6 : Patterns of UK Funding for Environmental and Conservation Work

The sixth edition of Where the Green Grants Went provides a comprehensive overview of grants to environmental initiatives from UK foundations, the National Lottery, and public sector funding programmes. The report focuses on 5,857 grants from foundations and the lottery which together were worth £383 million across the two financial years 2010/11 and 2011/12. Highlights include:detailed analysis of environmental grants from 180 foundations, with UK environmental philanthropy reaching £112 million in 2011/12, its highest ever levelinsights into the types of funding most needed by environmental groups, and the comparative advantages of foundation grants relative to other income sourcesperspectives from more than 100 chief executives on why they value philanthropic fundinginterviews with four experienced environmental philanthropistsa list of the 100 environmental organisations receiving the most money from UK foundationsanalysis of environmental grants from 31 lottery programmes, together worth £182.9 million across 2010/11 and 2011/12an overview of public sector grants programmes, and top-level analysis of their thematic and geographic focu

Remote sensing tools for the objective quantification of tree structural condition from individual trees to landscape scale assessment

Tree management is the practice of protecting and caring for trees for sustainable, defined objectives. However, there are often conflicts between maintaining trees and the obligation to protect targets, such as people or infrastructure, from the risks associated with the failure of trees and major limbs. Where there are targets worthy of protection, tree structural condition is typically monitored relative to the prescribed management objectives. Traditionally, field methods for capturing data on tree structural condition are manual with a tree surveyor taking very limited direct measurements, and only from parts of the tree that are within reach from the ground. Consequently, large sections of the tree remain unmeasured due to the logistical complications of accessing the aerial structure. Therefore, the surveyor estimates tree part sizes, approximates counts of relevant tree features and uses personal interpretation to infer the significance of the observations. These techniques are temporally and logistically demanding, and largely subjective. This thesis develops solutions to the limitations of traditional methods through the development of remote sensing (RS) tools for assessing tree structural condition, in order to inform tree management interventions. For individual trees, a proximal photogrammetry technique is developed for objectively quantifying tree structural condition by measuring the self-affinity of tree crowns in fractal dimensions. This can identify the individual tree crown complexity along a structural condition continuum, which is more effective than the traditional categorical approach for monitoring tree condition. Moving out in scale, a framework is developed which optimises the matchpairing agreement between ground reference tree data and RS-derived individual tree crown (ITC) delineations in order to quantify the accuracy of different ITC delineation algorithms. The framework is then used to identify an optimal ITC delineation algorithm which is applied to aerial laser scanning data to map individual trees and extract a point cloud for each tree. Metrics are then derived from the point cloud to classify a tree according to its structural condition, a process which is then applied to the tree population across an entire landscape. This provides information with which to spatially optimise tree survey and management resources, improve the decision making process and move towards proactive tree management. The research presented in this thesis develops RS tools for assessing tree structural condition, at a range of investigative scales. These objective, data-rich tools will enable resource-limited tree managers to direct remedial interventions in an optimised and precise way

Qualifying Prosecutorial Immunity Through Brady Claims

This Article considers the soundness of the doctrine of absolute immunity as it relates to Brady violations. While absolute immunity serves to protect prosecutors from civil liability for good-faith efforts to act appropriately in their official capacity, current immunity doctrine also creates a potentially large class of injury victims—those who are subjected to wrongful imprisonment due to Brady violations—with no access to justice. Moreover, by removing prosecutors from the incentive-shaping forces of the tort system that are thought in other contexts to promote safety, absolute immunity doctrine may under-incentivize prosecutorial compliance with constitutional and statutory requirements and increase criminal justice system error. The Article seeks to identify ways to use the civil justice system to promote prosecutorial compliance with Brady, while recognizing the need to provide appropriate civil protections to enable prosecutors to fulfill their unique role within the criminal justice system. After developing a novel taxonomy of Brady cases, evaluating such cases against basic tort principles, and considering the prosecutorial community’s views regarding appropriate Brady remedies, it proposes a statutory modification of absolute immunity that might better regulate and incentivize prosecutor behavior, reduce wrongful convictions, and improve access to justice