Many contemporary metaphysicians think that for any two distinct things, it is always possible for them to coexist with one another. Leibniz gives a somewhat different answer: two distinct things are able to coexist with one another only when they are compossible. God cannot cre…
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This PhD thesis is formed of work completed while studying at Royal Holloway, University of London. The three chapters that form the majority of the thesis each represent distinct projects that were studied in this time. Chronologically, the research forming the first chapter, o…
This thesis exhibits a range of applications of combinatoric methods to string theory. The concepts and techniques used in the counting of ribbon graphs, the theory of finite groups, and the construction of cell complexes can give powerful methods and interesting insights into t…
This thesis lies in the field of probabilistic and extremal combinatorics: we study discrete structures, with a focus on thresholds, when the behaviour of a structure changes from one mode into another. From a probabilistic perspective, we consider models for a random structure …
The simple relational structures form the units, or atoms, upon which all other relational structures are constructed by means of the substitution decomposition. This decomposition appears to have first been introduced in 1953 in a talk by Fraïssé, though it did not appear in …
Bacterial cells during many cell division cycles accumulate spontaneous mutations, which result in the birth of novel clones – cells that carry identical set of mutations. As a result of this clonal expansion, an evolving bacterial population has different clonal composition ove…
In recent years, mathematicians working in nonlinear algebra have actively explored the use of algebraic geometry, combinatorics and symbolic computations to answer questions in a diverse field of applications, with an emphasis on statistics and optimization. This dissertation i…