The approach to a theory of non-finitary matroids, as outlined by the author in [20], is here extended to the case in which the relevant closure operators are defined on arbitrary complete Boolean algebras, rather than on the power sets of sets. As a preliminary to this study, the theory of derivatives of operators on complete Boolean algebras is developed and the notion, having interest in its own right, of an analytic closure operator is introduced . The class of B-matroidal closure operators is singled out for especial attention and it is proved that this class is closed under Whitney duality. Also investigated is the class of those closure operators which are both matroidal and topological. / Thesis / Doctor of Philosophy (PhD)

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

<p dir="ltr">We analyze the query complexity of multiple search problems.</p><p dir="ltr">Firstly, we provide lower bounds on the complexity of "Local Search". In local search we are given a graph G and oracle access to a function f mapping the vertices to numbers, and seek a local minimum of f; i.e. a vertex v such that f(v) <= f(u) for all neighbors u of v. We provide separate lower bounds in terms of several graph parameters, including congestion, expansion, separation number, mixing time of a random walk, and spectral gap. To aid in showing these bounds, we design and use an improved relational adversary method for classical algorithms, building on the prior work of Scott Aaronson. We also obtain some quantum bounds using the traditional strong weighted adversary method.</p><p dir="ltr">Secondly, we show a multiplicative duality gap for Yao's minimax lemma by studying unordered search. We then go on to give tighter than asymptotic bounds for unordered and ordered search in rounds. Inspired by a connection through sorting with rank queries, we also provide tight asymptotic bounds for proportional cake cutting in rounds.</p>

The objective of this thesis is not only to design a building or investigate an idea, but also to explore and learn to appreciate what is truly important and, hope- fully, to discover that part of truth which may lead us to a serenity in our souls. My entire struggle is basically to try to achieve a comprehension of the order of nature. At some point in my life as an architect, if I have to build an artifact, that artifact should remind people of the everlasting merits of the invisible world and awaken the imagination of others in the pursuit of truth. This book recounts the attempt to articulate an idea, one which I believe to be a part of the order of nature, into the design environment. / Master of Architecture

This essay discusses the becomings of the character Saya in the visual novel Saya no Uta (2003), developed by Nitroplus. Being perceived as either girl or monster, Saya is trapped between these notions, within the endless becomings of her conceptualisation. Using the idea of becomings developed by Gilles Deleuze in Logic of Sense (1969) this essay aims to understand how Saya could be perceived through her becomings. Compared to the character of Alice from Alice in Wonderland, which is a prevalent subject through Logic of Sense, Saya shows many similarities with Deleuze's unofficial heroine. Donna Haraway's A Cyborg Manifesto (1985) is used to understand the underlying machinic desires of Saya, and how she becomes a productive force through consumption of the notions that try to define her. The dichotomy of girl and monster is further explained using Rosi Bradiotti's Nomadic subjects (1994), where the monster not only becomes a manifestation of the grotesque, but also a subject of the monstrosity within its discursive concept. The ambivalence of the monster is the duality between the abhorrent and the adored. The analysis shows that Saya, whether she is released to the world or not, renders the dichotomy useless in relation to the force of the materiality that somehow persists through, whatever its meaning, and what it ultimately is subjected to.