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Title: Computational mechanics in practice : mathematical adaptions and experimental applications
Author: Kelly, David
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2011
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The definition and quantification of complexity is a source of debate. A promising answer, from Crutch field, Shalizi and co-workers, identifies complexity with the amount of information required to optimally predict the future of a process. Computational mechanics computes this quantity for discrete time series; quantifying the complexity and generating minimal, optimally predictive models. Here we adapt and apply these methods to two very different problems. First, we extend computational mechanics to continuous data which cluster around discrete values. This is applied to the analysis of single molecule experimental data; allowing us to infer hidden Markov models without the necessity of assuming model architecture and allowing for the inference of degenerate states, giving advantages over previous analysis methods. The new analysis methods are demonstrated to perform well on both simulated data, in high noise and sparse data conditions; and experimental data, namely fluorescence resonance energy transfer spectra of Holliday junction conformational dynamics. Secondly, we apply computational mechanics to investigations of the HP model of protein folding. Computational mechanics was used to investigate the properties of the sequence sets folding to the highly designable structures. A hypothesised correlation between structures' designability and the statistical complexity of its sequence set was unsupported. However, methods were developed to succinctly encapsulate the non-local statistical regularities of sequence sets and used to accurately predict the structure of designing and randomly generated sequences. Finally, limitations of the standard algorithm for reconstructing predictive models are addressed. The algorithm can fail due to pair-wise comparisons of conditional distributions. A clustering method, considering all distributions simultaneously has been developed. This also makes clear when the algorithm may be effectively employed. A second issue concerns a class of processes for which computational mechanics cannot infer the correct, optimally predictive models. Adaptions to allow the inference of these processes have been devised.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available