The Firefighter Process models the spread and defence of a fire using a simple graph. We consider the following discrete-time process: at t = 0 some vertex of the graph begins burning. At each subsequent step we may defend a vertex from burning and the fire spreads from all burning vertices to all undefended neighbours. We consider the related problems of maximising the number of saved vertices, protecting a specified set from burning and maximising the weight of the saved vertices. We close three open problems concerning these decision problems and their related optimisation problems using the notion of a strategy, the sequence of defended vertices. / Graduate

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The objective of this work is to use complexity theory to propose a new interpretation of industrial clusters. Industrial clusters constitute a specific type of econosphere, whose driving principles are self-organisation, economies of diversity and a configuration that optimises the exploration of diversity starting from the configuration of connectivity of the system. This work shows the centrality of diversity by linking complexity theory (intended as "a method for understanding diversity"') to different concepts such as power law distributions, self-organisation, autocatalytic cycles and connectivity.I propose a method to distinguish self-organising from non self-organising agglomerations, based on the correlation between self-organising dynamics and power law network theories. Self-organised criticality, rank-size rule and scale-free networks theories become three aspects indicating a common underlying pattern, i.e. the edge of chaos dynamic. I propose a general model of development of industrial clusters, based on the mutual interaction between social and economic autocatalytic cycle. Starting from Kauffman's idea(^2) on the autocatalytic properties of diversity, I illustrate how the loops of the economies of diversity are based on the expansion of systemic diversity (product of diversity and connectivity). My thesis provides a way to measure systemic diversity. In particular I introduce the distinction between modular innovation at the agent level and architectural innovation at the network level and show that the cluster constitutes an appropriate organisational form to manage the tension and dynamics of simultaneous modular and architectural innovation. The thesis is structured around two propositions: 1. Self-organising systems are closer to a power law than hierarchical systems or aggregates (collection of parts). For industrial agglomerations (SLLs), the closeness to a power law is related to the degree of self-organisation present in the agglomeration, and emerges in the agglomeration’s structural and/or behavioural properties subject to self-organising dynamic.2. Self-organising systems maximise the product of diversity times connectivity at a rate higher than hierarchical systems.

Given a finite set X of states, a finite set of transformations of X (generators), and another transformation f of X, we analyze the complexity of the membership problem, which consists in deciding whether f can be obtained by composition of the generators. This problem is studied for various classes (pseudovarieties) of monoids. It is shown that the complexity is NP-hard for monoids of threshold 2 or more, and NP-complete in commutative, J- and R-trivial monoids. For idempotent monoids (aperiodic of threshold one), the problem is NP-complete in the general case; subcases are analyzed, and a largest class of aperiodic monoids is identified for which the problem is in FL, as well as a largest class for which the problem is not NP-hard. / The problem which consists in characterizing an idempotent monoid is also addressed: given a set of transformations, it can be decided in NC$ sp2$ whether the monoid they generate is idempotent. Similar tests are given for three subclasses of idempotent monoids: R$ sb1$, L$ sb1$, and N$ sb3$; in all three cases, the complexity is NC$ sp1$. / A sequential upper bound is also given for each of the parallel complexities given above.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Mar. 10, 2009). PDF text: vi, 77 p. : ill. ; 634 K. UMI publication number: AAT 3336828. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (M. Sc.)--University of Sydney, 2002. / Title from title screen (viewed Apr. 24, 2008). Submitted in fulfilment of the requirements for the degree of Master of Science to the Unit for the History and Philosophy of Science, Faculty of Science. Degree awarded 2002; thesis submitted 2001. Includes bibliography. Also available in print form.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Risto Miikkulainen. Vita. Includes bibliographical references. Also available from UMI.

Thesis (Ph. D.)--University of Hong Kong, 1998. / Includes bibliographical references (leaf 123-128).

Thesis (M.S.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 19, 2009) Includes bibliographical references.

Thesis (M.S.)--University of Florida, 2004. / Title from title page of source document. Document formatted into pages; contains 53 pages. Includes vita. Includes bibliographical references.