The inverse limit of GIT quotients of Grassmannians by the maximal torus

There are finitely many GIT quotients of

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

Characterisation of bacteriophage-host interactions in Lactococcus lactis

Lactococcus lactis is used extensively world-wide for the production of fermented dairy products. Bacteriophages (phages) infecting L. lactis can result in slow or incomplete fermentations, or may even cause total fermentation failure. Therefore, bacteriophages disrupting L. lactis fermentation are of economic concern. This thesis employed a multifaceted approach to investigate various molecular aspects of phage-host interaction in L. lactis. The genome sequence of an Irish dairy starter strain, the prophage-cured L. lactis subsp. cremoris UC509.9, was studied. The 2,250,427 bp circular chromosome represents the smallest among its sequenced lactococcal equivalents. The genome displays clear genetic adaptation to the dairy niche in the form of extensive reductive evolution. Gene prediction identified 2066 protein-encoding genes, including 104 which showed significant homology to transposase-specifying genes. Over 9 % of the identified genes appear to be inactivated through stop codons or frame shift mutations. Many pseudogenes were found in genes that are assigned to carbohydrate and amino acid transport and metabolism orthologous groups, reflecting L. lactis UC509.9’s adaptation to the lactose and casein-rich dairy environment. Sequence analysis of the eight plasmids of L. lactis revealed extensive adaptation to the dairy environment. Key industrial phenotypes were mapped and novel lactococcal plasmid-associated genes highlighted. In addition to chromosomally-encoded bacteriophage resistance systems, six functional such systems were identified, including two abortive infection systems, AbiB and AbiD1, explaining the observed phage resistance of L. lactis UC509.9 Molecular analysis suggests that the constitutive expression of AbiB is not lethal to cells, suggesting the protein is expressed in an un/inactivated form. Analysis of 936 species phage sk1-escape mutants of AbiB revealed that all such mutants harbour mutations in orf6, which encodes the major capsid protein. Results suggest that the major capsid protein is required for activation of the AbiB system, although this requires furrther investigations. Temporal transcriptomes of L. lactis UC509.9 undergoing lytic infection with either one of two distinct bacteriophages, Tuc2009 and c2, was determined and compared to the transcriptome of uninfected UC509.9 cells. Whole genome microarrays performed at various time-points post-infection demonstrated a rather modest impact on host transcription. Alterations in the UC509.9 transcriptome during lytic infection appear phage-specific, with a relatively small number of differentially transcribed genes shared between infection with either Tuc2009 or c2. Transcriptional profiles of both bacteriophages during lytic infection was shown to generally correlate with previous studies and allowed the confirmation of previously predicted promoter sequences. Bioinformatic analysis of genomic regions encoding the presumed cell wall polysaccharide (CW PS) biosynthesis gene cluster of several strains of L. lactis was performed. Results demonstrate the presence of three dominant genetic types of this gene cluster, termed type A, B and C. These regions were used for the development of a multiplex PCR to identify CW PS genotype of various lactococcal strains. Analysis of 936 species phage receptor binding protein phylogeny (RBP) and CW PS genotype revealed an apparent correlation between RBP phylogeny and CW PS type, thereby providing a partial explanation for the observed narrow host range of 936 phages. Further analysis of the genetic locus encompassing the presumed CW PS biosynthesis operon of eight strains identified as belonging to the CW PS C (geno)type, revealed the presence of a variable region among the examined strains. The obtained comparative analysis allowed for the identification of five subgroups of the C type, named C1 to C5. We purified an acidic polysaccharide from the cell wall of L. lactis 3107 (C2 subtype) and confirmed that it is structurally different from the CW PS of the C1 subtype L. lactis MG1363. Combinations of genes from the variable region of C2 subtype were amplified from L. lactis 3107 and introduced into a mutant of the C1 subtype L. lactis NZ9000 (a direct derivative of MG1363) deficient in CW PS biosynthesis. The resulting recombinant mutant synthesized a CW PS with a composition characteristic for that of the C2 subtype L. lactis 3107 and not the wildtype C1 L. lactis NZ9000. The recombinant mutant exhibited a changed phage resistance/sensitivity profile consistent with that of L. lactis 3107, which unambiguously demonstrated that L. lactis 3107 CW PS is the host cell surface receptor of two bacteriophages belonging to the P335 species as well as phages that are member of the 936 species. The research presented in this thesis has significantly advanced our understanding of L. lactis bacteriophage-host interactions in several ways. Firstly, the examination of plasmidencoded bacteriophage resistance systems has allowed inferences to be made regarding the mode of action of AbiB, thereby providing a platform for further elucidation of the molecular trigger of this system. Secondly, the phage infection transcriptome data presented, in addition to previous work, has made L. lactis a model organism in terms of transcriptomic studies of bacteriophage-host interactions. And finally, the research described in this thesis has for the first time explicitly revealed the nature of a carbohydrate bacteriophage receptor in L. lactis, while also providing a logical explanation for the observed narrow host ranges exhibited by 936 and P335 phages. Future research in discerning the structures of other L. lactis CW PS, combined with the determination of the molecular interplay between receptor binding proteins of these phages and CW PS will allow an in depth understanding of the mechanism by which the most prevalent lactococcal phages identify and adsorb to their specific host.

Reasoning with imprecise trade-offs in decision making under certainty and uncertainty

In many real world situations, we make decisions in the presence of multiple, often conflicting and non-commensurate objectives. The process of optimizing systematically and simultaneously over a set of objective functions is known as multi-objective optimization. In multi-objective optimization, we have a (possibly exponentially large) set of decisions and each decision has a set of alternatives. Each alternative depends on the state of the world, and is evaluated with respect to a number of criteria. In this thesis, we consider the decision making problems in two scenarios. In the first scenario, the current state of the world, under which the decisions are to be made, is known in advance. In the second scenario, the current state of the world is unknown at the time of making decisions. For decision making under certainty, we consider the framework of multiobjective constraint optimization and focus on extending the algorithms to solve these models to the case where there are additional trade-offs. We focus especially on branch-and-bound algorithms that use a mini-buckets algorithm for generating the upper bound at each node of the search tree (in the context of maximizing values of objectives). Since the size of the guiding upper bound sets can become very large during the search, we introduce efficient methods for reducing these sets, yet still maintaining the upper bound property. We define a formalism for imprecise trade-offs, which allows the decision maker during the elicitation stage, to specify a preference for one multi-objective utility vector over another, and use such preferences to infer other preferences. The induced preference relation then is used to eliminate the dominated utility vectors during the computation. For testing the dominance between multi-objective utility vectors, we present three different approaches. The first is based on a linear programming approach, the second is by use of distance-based algorithm (which uses a measure of the distance between a point and a convex cone); the third approach makes use of a matrix multiplication, which results in much faster dominance checks with respect to the preference relation induced by the trade-offs. Furthermore, we show that our trade-offs approach, which is based on a preference inference technique, can also be given an alternative semantics based on the well known Multi-Attribute Utility Theory. Our comprehensive experimental results on common multi-objective constraint optimization benchmarks demonstrate that the proposed enhancements allow the algorithms to scale up to much larger problems than before. For decision making problems under uncertainty, we describe multi-objective influence diagrams, based on a set of p objectives, where utility values are vectors in Rp, and are typically only partially ordered. These can be solved by a variable elimination algorithm, leading to a set of maximal values of expected utility. If the Pareto ordering is used this set can often be prohibitively large. We consider approximate representations of the Pareto set based on ϵ-coverings, allowing much larger problems to be solved. In addition, we define a method for incorporating user trade-offs, which also greatly improves the efficiency.