This thesis describes building an iPhone application called FlipGlobe that finds a given location's antipode and then displays location-relevant content about it. FlipGlobe extracts knowledge from the many geo-tagged data sources available via RESTful APIs to give antipodes context and relevance. This thesis discusses the following challenges encountered while building FlipGlobe: accessing location-aware data stores on a mobile device simultaneously; locating and relating an iPhone's current location in a user-readable format; and optimizing performance using multithreading and asynchronous API calls. The process of learning iPhone development with Objective-C, too, will be discussed at length. The many technologies leveraged to build FlipGlobe that will be covered include: forward and reverse geocoding, asynchronous HTTP requests, asynchronous image fetching, multithreading with Grand Central Dispatch, automated reachability testing, and Google MapKit. Finally, the building and evaluation of FlipGlobe’s user interface using Agile and Lean development methodologies is discussed.

This thesis investigates small-scale mappae mundi, world maps, created in the thirteenth-century, which record the historical, mythical, social, and religious reality of the world for wealthy English patrons. My research focuses on two maps found in a Psalm book (British Library Add. MS 28681, f. 9 and f. 9v) on either side of a single page. One depicts the world in typical mappae mundi fashion, with Jerusalem at the centre of a network of cities, topographic features and monstrous creatures while the other lists place names and geographic descriptions. The maps depict the world in very different manners, one textually and the other visually, but their placement on the same leaf emphasizes their connection. This work explores the iconography, socio-historic context and literary precedence of mappae mundi in order to comprehend the distinct need for mixed-media to represent and understand a complex worldly existence in thirteenth-century England.

<p dir="ltr">In this thesis, we develop an algebraic framework for colored, colored connected, semi-grouplike-flavored, and pathlike co-/bi-/Hopf algebras, which are essential in combinatorics, topology, number theory, and physics. Moreover, we introduce and explore simply colored comonoid, which generalises the notion of colored conilpotent coalgebra. The simply colored structure captures the essence of being connected and give unified treatment of all connected co-/bi-algebras. </p><p dir="ltr">As a consequence, we establish precise conditions for the invertibility of characters essential for renormalization in the Connes-Kreimer formulation, supported by examples from these fields. In order to construct antipodes, we discuss formal localization constructions and quantum deformations. These allow to define and explain the appearance of Brown style coactions. We also investigate the relation between pointed coalgebras and color conilpotent coalgebras. </p><p dir="ltr">Using these results, we interpret all relevant coalgebras through categorical constructions, linking the bialgebra structures to Feynman categories and applying our developed theory in this context. This comprehensive framework provides a robust foundation for future research in mathematical physics and algebra.</p>