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.

Novel insights into the inflammatory basis of gastrointestinal disease

It has become clear that inflammation is beneficial to man, there are situations though that the inflammatory response causes damage to the host that is harmful to health. When the inflammatory response fails or is too strong, the health of the host is damaged and disease can occur. The implication of intestinal disease caused by an ineffective immune response is of great social and economic burden to society. The overarching purpose of this thesis is to assess inflammatory signalling targets associated with immune mediated disorders such as IBD, IBS and inflammatory liver disease. By assessing these targets and modifying their function I hope to contribute and expand further the pre-existing information on these disorders and improve the therapeutic interventions available in these debilitating conditions. I will assess the role of inflammation in disorders of the GI tract and liver IBD, IBS, hepatic inflammatory injury and furthermore, I will use pharmaceutical agents to activate and suppress components of the immune system. I will examine the inflammatory response in experimental models of disease for IBD and liver injury, I will attempt to alter these pathways using pharmaceutical intervention to delineate the disease causing mechanism that may lead to clinically relevant therapeutic interventions. In regards to IBS, I will attempt to improve the existing knowledge that exists in relation to the pathogenesis of this functional bowel disorder. I will attempt to define a mechanism by which the low grade mucosal inflammation that has been demonstrated by others arises and what this inflammation is induced by. The overall aim of this thesis is to attempt to further understand the mechanisms behind GI and liver disease. Looking at the inflammatory response in these specific conditions and how they can be altered may lead to exciting new therapies for inflammatory conditions in the gastrointestinal tract.

Exploring the physicochemical basis of cheese texture, rheology and functionality, with emphasis on cation-casein interactions

The physicochemical properties of cheese and milk gels are greatly influenced by molecular interactions between the casein proteins involving calcium. Novel experiments were designed to investigate the relationship between insoluble caseinbound cations and rheological properties of Cheddar cheese and rennet-induced milk gels. Cheddar cheese and rennet-induced milk gels were supplemented with Mg2+ or Sr2+ to compare their effects on their rheological properties to those previously reported in literature for Ca2+ supplementation. Sr2+ displayed behaviour similar to Ca2+ as observed by its ability to increase the rigidity of cheese and rennet milk gels and also decrease cheese meltability. Mg+2 had no influence on cheese rheological properties and was greatly inferior to Ca2+ and Sr2+ in its ability to increase rennet milk gel elasticity. Cheddar cheese was supplemented with the calcium-chelating salts trisodium citrate, disodium hydrogen phosphate or disodium EDTA, in an attempt to reduce the CCP content of cheese and thereby modify its rheological and functional properties. TSC and EDTA were successful in decreasing cheese CCP, whereas DSP caused an initial increase in CCP content. Cheddar cheese was supplemented with chlorides of iron, copper and zinc at salting to investigate the effects of concentrations of these elements in excess of those found innately or commonly in fortification studies, with emphasis on mineral equilibria changes and resultant alteration of rheological properties. Zinc addition was the only added metal that significantly influenced cheese rheological properties, leading to an increase in cheese rigidity and decreased cheese melt at elevated temperatures. Gum tragacanth was used as a fat-replacer in the manufacture of reduced-fat Cheddar cheese, in an attempt to improve the rheological, functional and sensory properties of reduced-fat Cheddar. Overall, the experimental work reported in this thesis generated new knowledge and theories about how casein-mineral interactions influence rheological properties of casein systems.