Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

The biodiversity, control and genetic characterisation of the lactococcal 936 group phages

Phages belonging to the 936 group represent one of the most prevalent and frequently isolated phages in dairy fermentation processes using Lactococcus lactis as the primary starter culture. In recent years extensive research has been carried out to characterise this phage group at a genomic level in an effort to understand how the 936 group phages dominate this particular niche and cause regular problems during large scale milk fermentations. This thesis describes a large scale screening of industrial whey samples, leading to the isolation of forty three genetically different lactococcal phages. Using multiplex PCR, all phages were identified as members of the 936 group. The complete genome of thirty eight of these phages was determined using next generation sequencing technologies which identified several regions of divergence. These included the structural region surrounding the major tail protein, the replication region as well as the genes involved in phage DNA packing. For a number of phages the latter genomic region was found to harbour genes encoding putative orphan methyltransferases. Using small molecule real time (SMRT) sequencing and heterologous gene expression, the target motifs for several of these MTases were determined and subsequently shown to actively protect phage DNA from restriction endonuclease activity. Comparative analysis of the thirty eight phages with fifty two previously sequenced members of this group showed that the core genome consists of 28 genes, while the non-core genome was found to fluctuate irrespective of geographical location or time of isolation. This study highlights the continued need to perform large scale characterisation of the bacteriophage populations infecting industrial fermentation facilities in effort to further our understanding dairy phages and ways to control their proliferation.

Job control and ambulatory blood pressure

Objective: The effect of work on blood pressure (BP) in a general population with appropriate adjustment for confounders is not well defined. High job control has been found to be associated with lower BP and with nocturnal BP dipping. However, with older workers this may be compromised and has not been studied extensively. Methods: A cross-sectional study was carried out on a primary care-based sample (N=2047) aged 50–69 years. Data were collected on sociodemographic factors, medication, clinic, and ambulatory blood pressure. Job control was measured using two scales from the Copenhagen Psychosocial Questionnaire (COPSOQ) (possibility for development and influence at work). Nocturnal systolic BP (SBP) dipping was the reduction in SBP from day- to night-time using ambulatory SBP readings. Results: In general, BP increased with age, male gender, and higher body mass index. Workers with high influence at work and high possibility for development were more likely to have high asleep SBP [odds ratio (OR) 2.13, 95% confidence interval (95% CI) 1.05–4.34, P=0.04], (OR 2.27, 95% CI 1.11–4.66, P=0.03) respectively. Influence at work and awake BP were inversely associated: awake SBP (OR 2.44, 95% CI 1.35–4.41, P<0.01), awake DBP (OR 2.42, 95% CI 1.24–4.72, P=0.01). No association was seen between job control and nocturnal SBP dipping. Conclusion: Older workers with high job control may be more at risk of cardiovascular disease resulting from high day- and night-time BP with no evidence of nocturnal dipping.