2-categories and cyclic homology

The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. The work herein is based on the three papers 'Cyclic homology arising from adjunctions', 'Factorisations of distributive laws', and 'Hochschild homology, lax codescent,and duplicial structure', to which the current author has contributed. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan’s approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure.

A distributed, compact routing protocol for the Internet

The Internet has grown in size at rapid rates since BGP records began, and continues to do so. This has raised concerns about the scalability of the current BGP routing system, as the routing state at each router in a shortest-path routing protocol will grow at a supra-linearly rate as the network grows. The concerns are that the memory capacity of routers will not be able to keep up with demands, and that the growth of the Internet will become ever more cramped as more and more of the world seeks the benefits of being connected. Compact routing schemes, where the routing state grows only sub-linearly relative to the growth of the network, could solve this problem and ensure that router memory would not be a bottleneck to Internet growth. These schemes trade away shortest-path routing for scalable memory state, by allowing some paths to have a certain amount of bounded “stretch”. The most promising such scheme is Cowen Routing, which can provide scalable, compact routing state for Internet routing, while still providing shortest-path routing to nearly all other nodes, with only slightly stretched paths to a very small subset of the network. Currently, there is no fully distributed form of Cowen Routing that would be practical for the Internet. This dissertation describes a fully distributed and compact protocol for Cowen routing, using the k-core graph decomposition. Previous compact routing work showed the k-core graph decomposition is useful for Cowen Routing on the Internet, but no distributed form existed. This dissertation gives a distributed k-core algorithm optimised to be efficient on dynamic graphs, along with with proofs of its correctness. The performance and efficiency of this distributed k-core algorithm is evaluated on large, Internet AS graphs, with excellent results. This dissertation then goes on to describe a fully distributed and compact Cowen Routing protocol. This protocol being comprised of a landmark selection process for Cowen Routing using the k-core algorithm, with mechanisms to ensure compact state at all times, including at bootstrap; a local cluster routing process, with mechanisms for policy application and control of cluster sizes, ensuring again that state can remain compact at all times; and a landmark routing process is described with a prioritisation mechanism for announcements that ensures compact state at all times.

Tracing outsideness: young women's institutional journeys and the geographies of closed space

Understanding confinement and its complex workings between individuals and society has been the stated aim of carceral geography and wider studies on detention. This project contributes ethnographic insights from multiple sites of incarceration, working with an under-researched group within confined populations. Focussing on young female detainees in Scotland, this project seeks to understand their experiences of different types of ‘closed’ space. Secure care, prison and closed psychiatric facilities all impact on the complex geographies of these young women’s lives. The fluid but always situated relations of control and care provide the backdrop for their journeys in/out and beyond institutional spaces. Understanding institutional journeys with reference to age and gender allows an insight into the highly mobile, often precarious, and unfamiliar lives of these young women who live on the margins. This thesis employs a mixed-method qualitative approach and explores what Goffman calls the ‘tissue and fabric’ of detention as a complex multi-institutional practice. In order to be able to understand the young women’s gendered, emotional and often repetitive experiences of confinement, analysis of the constitution of ‘closed space’ represents a first step for inquiry. The underlying nature of inner regimes, rules and discipline in closed spaces, provide the background on which confinement is lived, perceived and processed. The second part of the analysis is the exploration of individual experiences ‘on the inside’, ranging from young women’s views on entering a closed institution, the ways in which they adapt or resist the regime, and how they cope with embodied aspects of detention. The third and final step considers the wider context of incarceration by recovering the young women’s journeys through different types of institutional spaces and beyond. The exploration of these journeys challenges and re-develops understandings of mobility and inertia by engaging the relative power of carceral archipelagos and the figure of femina sacra. This project sits comfortably within the field of carceral geography while also pushing at its boundaries. On a conceptual level, a re-engagement with Goffman’s micro-analysis challenges current carceral-geographic theory development. Perhaps more importantly, this project pushes for an engagement with different institutions under the umbrella of carceral geography, thus creating new dialogues on issues like ‘care’ and ‘control’. Finally, an engagement with young women addresses an under-represented population within carceral geography in ways that raise distinctly problematic concerns for academic research and penal policy. Overall, this project aims to show the value of fine grained micro-level research in institutional geographies for extending thinking and understanding about society’s responses to a group of people who live on the margins of social and legal norms.