Cellulose Biodegradation Models; An Example of Cooperative Interactions in Structured Populations

We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the population of micro-organisms. We then use the corresponding models in the context of multiple-trait populations. This leads to classical, logistic type, reproduction rates limiting the growth of large populations but also, and more surprisingly, limiting the growth of populations which are too small in a manner similar to the effects seen in populations requiring cooperative interactions (or sexual reproduction). This study hence offers a striking example of how some mechanisms resembling cooperation can occur in structured biological populations, even in the absence of any actual cooperation.Comment: 37 pages, accepted to ESAIM: Mathematical Modelling and Numerical Analysis (2017

Unification and limitations of error suppression techniques for adiabatic quantum computing

While adiabatic quantum computation (AQC) possesses some intrinsic robustness to noise, it is expected that a form of error control will be necessary for large scale computations. Error control ideas developed for circuit-model quantum computation do not transfer easily to the AQC model and to date there have been two main proposals to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that these two methods are fundamentally related and may be analyzed within the same formalism. We analyze the effectiveness of such error suppression techniques and identify critical constraints on the performance of error suppression in AQC, suggesting that error suppression by itself is insufficient for fault-tolerant, large-scale AQC and that a form of error correction is needed. This manuscript has been superseded by the articles, "Error suppression and error correction in adiabatic quantum computation I: techniques and challenges," arXiv:1307.5893, and "Error suppression and error correction in adiabatic quantum computation II: non-equilibrium dynamics," arXiv:1307.5892.Comment: 9 pages. Update replaces "Equivalence" with "Unification." This manuscript has been superseded by the two-article series: arXiv:1307.5892 and arXiv:1307.589

The use of Bayes factors in fine-scale genetic association studies

The aim of this thesis is to explore and compare methods that can be used for the purposes of finding possible genetic effects in the context of fine-scale genotype-phenotype association studies. Fine-scale genetic association studies present unique challenges for attempts at finding genetic effects, due to the strong linkage that can exist between different variants and issues that exist as a result of multiple testing. However, unlike Genome-Wide Association Studies (GWAS), there is potential to use the information from haplotypes arising from areas of low genetic recombination. In order to test the effectiveness of approaches involved in fine-scale studies, the PheGe-Sim (Phenotype Genotype Simulation) application has been developed in order to simulate fine-scale phenotype-genotype data sets under a variety of scenarios. The simulations are based upon the coalescent model with extensions of population expansion, recombination, and finite sites mutations, that allow for real data sets to be more closely mirrored. The simulated data sets are subsequently used to assess the effectiveness of each of the methods that are used in this thesis, in attempting to find the known simulated causal variants. One of the methods suitable for use in fine-scale genetic association studies for testing associations is Treescan (Templeton et al., 2005). Treescan is a method that attempts to use relationships between closely related haplotypes in an attempt to increase the power of finding genetic determinants of a phenotype. A haplotype tree is constructed, and each branch can be sequentially tested for any evidence of association from the resultant groups. To provide comparisons with the Treescan method, similar methods to the Treescan approach using each SNP (single nucleotide polymorphism) and haplotype have been implemented. As a result of the issues of multiple testing in the context of GWAS, Balding (2006) advocated the use of Bayes factors as an alternative to the standard use of p-values for categorical data sets. In this thesis Bayes factors have been formulated that are suitable for continuous phenotype data, and for the context of fine-scale association studies. Bayes factors are used in a method that utilizes the Treescan approach of assessing various groupings from a haplotype tree, with the method being adapted to take advantage of the flexibility offered by Bayes factors. Single SNP and haplotype approaches have also been programmed using the same implementation of Bayes factors. The PheGe-Find (Phenotype Genotype-Find) application has been developed that implements the association methods when supplied with the appropriate genotype and phenotype input files. In addition to testing the methods on simulated data, the approaches are also tested on two real data sets. The first of these concerns genotypes and phenotypes of the Drosophila Melanogaster fruit fly, that has previously been assessed using the original Treescan approach of Templeton et al. (2005). This allows for comparisons to be made between the different approaches upon a data set where there is strong evidence of a causal link between the genotype and phenotypes concerned. A second data set of genetic variants surrounding the human ADRA1A gene is also assessed for any potential causative genetic effects on blood pressure and heart rate phenotype measurements