Navigating New Trade Routes: The rise of Value chains, and the Challenges for Canadian Trade Policy

In the new paradigm of international trade, Canada needs a trade policy that recognizes both the increasing importance of global value chains and the critical role of Canada-US commercial and regulatory integration in gaining full benefit from their exploitation.border papers, international policy

Mapping nn grid points onto a square forces an arbitrarily large Lipschitz constant

We prove that the regular $n\times n$ square grid of points in the integer lattice $\mathbb{Z}^{2}$ cannot be recovered from an arbitrary $n^{2}$-element subset of $\mathbb{Z}^{2}$ via a mapping with prescribed Lipschitz constant (independent of $n$). This answers negatively a question of Feige from 2002. Our resolution of Feige's question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly the present work contains a detailed investigation of Lipschitz regular mappings on Euclidean spaces, with emphasis on their bilipschitz decomposability in a sense comparable to that of the well known result of Jones. Secondly, we build on work of Burago and Kleiner and McMullen on non-realisable densities. We verify the existence, and further prevalence, of strongly non-realisable densities inside spaces of continuous functions.Comment: 60 pages (43 pages of the main part, 13 pages of appendices), 10 figures. This is a revised version according to referees' comments. Our version of the proof of the theorem about bilipschitz decomposition of Lipschitz regular mappings was greatly simplified. To appear in GAF

Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces

We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $\sigma$-porous subset. For separable metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical points of its domain. These results contain the case of nonexpansive self-mappings and the case of nonexpansive set-valued mappings as particular cases.Comment: 35 pages; accepted version of the manuscript; accepted for publication in Topological Methods in Nonlinear Analysi

Evaluation of Continuous Monitoring as a Tool for Municipal Stormwater Management Programs

The purpose of this study is to evaluate the uncertainty attributable to inadequate temporal sampling of stormwater discharge and water quality, and understand its implications for meeting monitoring objectives relevant to municipal separate storm sewer systems (MS4s). A methodology is presented to evaluate uncertainty attributable to inadequate temporal sampling of continuous stormflow and water quality, and a case study demonstrates the application of the methodology to six small urban watersheds (0.8-6.8 km2) and six large rural watersheds (30-16,192 km2) in Virginia. Results indicate the necessity of high-frequency continuous monitoring for accurately capturing multiple monitoring objectives, including illicit discharges, acute toxicity events, and stormflow pollutant concentrations and loads, as compared to traditional methods of sampling. For example, 1-h sampling in small urban watersheds and daily sampling in large rural watersheds would introduce uncertainty in capturing pollutant loads of 3–46% and 10–28%, respectively. Overall, the outcomes from this study highlight how MS4s can leverage continuous monitoring to meet multiple objectives under current and future regulatory environments

Rethinking Resurrection: Choosing Interdisciplinary Dialogue Over Dualism

Christianity is plagued by two dualistic concepts: first, an ontological dualism that divides the human person into body and soul, and second, an epistemological dualism that claims science and theology are incompatible. However, these polarized (and polarizing) theological frameworks are no longer sufficient, especially as scientific research provides new understanding about the brain and human identity. The existence of the nonphysical soul has long been called into question, thereby creating a theological crisis at the very core of Christian belief: the resurrection. This thesis will examine the crisis as it manifests itself in contemporary Christian society, pointing to the perpetuation of dualistic philosophies as the source of a theological impasse. Finally, it will propose an interdisciplinary solution, revisiting resurrection theology in dialogue with modern science, and providing a way forward for those who seek a way both to participate in the resurrected life, and to proclaim the promise of general resurrection without dismissing scientific research

The estates of the Norman dukes and the Norman kings of England 911-1135

This thesis examines the Norman ducal estates between 911 and 1106 and the English royal estates between 1066 and 1135. The stability and cohesion of these polities, during a period in which socio-political changes led to political decentralization in western Europe, is often explained by the strength of Norman and English institutions. This thesis argues that such institutions were built upon the tangible foundations of wealth and authority provided by the ducal and royal estates. The Introduction sets out the research questions, sketches the source material, and situates the thesis within the existing literature. Chapter 1 discusses the Norman evidence, and the methodological challenges it poses, for reconstructing ducal land. Chapter 2 analyses the early ducal estates between 911 and 1035, demonstrating their geographical distribution within Normandy and the fundamental role they played in the duchy’s formation. Chapter 3 continues the analysis of the ducal estates down to 1106 and discusses how they fit into the duchy’s wider tenurial framework by comparing them with the estates of the Norman aristocracy. Chapter 4 turns to England and explains how Domesday Book is used to identify, reconstruct, and estimate the value of the royal estates under the Confessor and the Conqueror. Chapter 5 demonstrates that royal land doubled in size between 1066 and 1086 but was also conceptually transformed by the conquest. By examining the Conqueror’s antecessores and the narrative accounts, Chapter 5 reconstructs the chronology and process by which this transformation occurred. Chapter 6 looks at the royal demesne under the Conqueror’s sons, who, out of political necessity, granted out considerable portions of Domesday’s terra regis, reducing it to its pre-conquest value. The Conclusion summarizes the principal findings of the thesis, emphasizing the importance of land in underpinning ducal and royal power to shape political structures in Normandy and England. Three appendices, in a separate volume, tabulate the data behind the analysis