Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams

The diameter of a disc filling a loop in the universal covering of a Riemannian manifold may be measured extrinsically using the distance function on the ambient space or intrinsically using the induced length metric on the disc. Correspondingly, the diameter of a van Kampen diagram filling a word that represents the identity in a finitely presented group can either be measured intrinsically its 1-skeleton or extrinsically in the Cayley graph of the group. We construct the first examples of closed manifolds and finitely presented groups for which this choice -- intrinsic versus extrinsic -- gives rise to qualitatively different min-diameter filling functions.Comment: 44 pages, 12 figures, to appear in the Journal of Differential Geometr

The role of affect and cognitive schemata in the assessment of psychopathy

This thesis examined psychopathy, cognitive schemata and affect in forensic and community populations. This was to identify whether cognitive schemata and affect would assist in the assessment of psychopathy. Study one was conducted on 38 male high secure hospital patients and 38 male prisoners. It focused on the assessment of psychopathy and cognitive schemata. It was predicted that psychopathy would be positively related to negative schemata and early maladaptive schemata and negatively related to positive schemata. This prediction was supported with the exception of Early Maladaptive Schemata. Study two was conducted on 38 male high secure hospital patients and 38 male prisoners and also examined psychopathy and affect. It further explored positive schemata that was significant in study one. It was predicted that psychopathy would be positively related to errors on affective word sentence completion with slower response times. These predictions were not supported. The third study included 101 male prisoners and 108 male university students. An assessment of cognitive schema and affect was also developed. A further core prediction was that psychopathy would have a positive relationship with detached affect and results supported this. Contrary to prediction, it was found that psychopathy was higher in the student group compared to the prisoner group. Study four further explored the core predictions and included an examination of psychopathy, cognitive schema, affect and the 'Big Five' in 174 prisoners and 200 male students. The predictions were supported that psychopathy would be negatively related to positive cognitive schemata and positively related to negative cognitive schemata, in both groups. The predictions that detached affect would be significant to psychopathy was again supported. Contrary to prediction psychopathy was found to be higher in the student group. The current research indicates that cognitive schemata and affect are related to psychopathy. It also shows that similar cognitive profiles of psychopathy are demonstrated in prison and student groups that relate to affect. Further, it highlights the neglected role of positive schemata in psychopathy. Future research could consider the role of positive schemata and refine the cognitive profile in psychopathy, it could also examine the newly proposed cognitive behavioural model of psychopathy

The absence of efficient dual pairs of spanning trees in planar graphs

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T* in the dual graph G such that T and T* do not intersect. We show that it is not always possible to find T in G, such that the diameters of T and T* are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.Comment: 7 pages, 3 figure

An Investigation into the Economic Thought of Medieval Arab-Islamic Scholars and Enlightenment Philosophers

This student-faculty collaborative research project focused on the contributions to economic thought of two distinct groups: medieval Arab-Islamic scholars and Enlightenment philosophers. The primary goal of the project was to generate two new chapters to supplement the Evolution of Economic Thought text. It looked to answer the research question, “How did the intellectual activity of medieval Arab-Islamic scholars and Enlightenment philosophers reflect and/or contribute to the development of modern economic thought?” The medieval Arab-Islamic chapter produced findings including a centrality of religion to economic life, the importance of specialization for increased efficiency, and an understanding of just price. Ibn Khaldūn, a prominent scholar of the medieval Arab-Islamic era, recognized a need for the division of labor, as individuals lack the capability of providing sufficient goods on their own to subsist. A holistic approach to thinking and an emphasis on rational methodology and objectivity were major contributions from the research on Enlightenment philosophers. Thomas Hobbes’s social contract theory is a philosophical idea that underlies modern economic theory, discussed at length in the Enlightenment chapter. Both chapters will be accessible online and available for instructors to use separately or in conjunction with existing online chapters as precursors to the main, physical text

The Potential for Public-Private Partnerships: Philanthropic Leaders Considering Housing as a Platform

Explores foundation leaders' approaches to housing as a platform for layering programs and services to improve quality of life, views on funding partnerships with the federal government, and suggestions for targeted collaborations. Includes case studies