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.

Simplified decoding techniques for linear block codes

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications.

Characterisation of the microbiota of traditional fermented beverages and screening these and other populations for novel antimicrobial producers and gene clusters

To screen for novel ribosomally synthesised antimicrobials, in-silico genome mining was performed on all publically available fully sequenced bacterial genomes. 49 novel type 1 lantibiotic clusters were identified from a number of species, genera and phyla not usually associated with lantibiotic production, and indicates high prevalence. A crucial step towards the commercialisation of fermented beverages is the characterisation of the microbial content. To achieve this goal, we applied next-generation sequencing techniques to analyse the bacterial and yeast populations of the organic, symbiotically-fermented beverages kefir, water kefir and kombucha. A number of minor components were revealed, many of which had not previously been associated with these beverages. The dominant microorganism in each of the water kefir grains and fermentates was Zymomonas, an ethanol-producing bacterium that had not previously been detected on such a scale. These studies represent the most accurate description of these populations to date, and should aid in future starter design and in determining which species are responsible for specific attributes of the beverages. Finally, high-throughput robotics was applied to screen for the presence of antimicrobial producers associated with these beverages. This revealed a low frequency of bacteriocin production amongst the bacterial isolates, with only lactococcins A, B and LcnN of lactococcin M being identified. However, a proteinaceous antimicrobial produced by the yeast Dekkera bruxellensis, isolated from kombucha, was found to be active against Lactobacillus bulgaricus. This peptide was patially purified.

The treatment of landfill leachate using natural systems

Leachate may be defined as any liquid percolating through deposited waste and emitted from or contained within a landfill. If leachate migrates from a site it may pose a severe threat to the surrounding environment. Increasingly stringent environmental legislation both at European level and national level (Republic of Ireland) regarding the operation of landfill sites, control of associated emissions, as well as requirements for restoration and aftercare management (up to 30 years) has prompted research for this project into the design and development of a low cost, low maintenance, low technology trial system to treat landfill leachate at Kinsale Road Landfill Site, located on the outskirts of Cork city. A trial leachate treatment plant was constructed consisting of 14 separate treatment units (10 open top cylindrical cells [Ø 1.8 m x 2.0 high] and four reed beds [5.0m x 5.0m x 1.0m]) incorporating various alternative natural treatment processes including reed beds (vertical flow [VF] and horizontal flow [HF]), grass treatment planes, compost units, timber chip units, compost-timber chip units, stratified sand filters and willow treatment plots. High treatment efficiencies were achieved in units operating in sequence containing compost and timber chip media, vertical flow reed beds and grass treatment planes. Pollutant load removal rates of 99% for NH4, 84% for BOD5, 46% for COD, 63% for suspended solids, 94% for iron and 98% for manganese were recorded in the final effluent of successfully operated sequences at irrigation rates of 945 l/m2/day in the cylindrical cells and 96 l/m2/day in the VF reed beds and grass treatment planes. Almost total pathogen removal (E. coli) occurred in the final effluent of the same sequence. Denitrification rates of 37% were achieved for a limited period. A draft, up-scaled leachate treatment plant is presented, based on treatment performance of the trial plant.

Becoming a father of a child with an intellectual disability- a narrative inquiry of Irish fathers’ stories

Background: This thesis explored men’s experiences of becoming a father of a child with an intellectual disability in the early years. In Ireland, it is estimated that there are almost 97% (n= 9,914) children with intellectual disabilities living at home in the care of parents, siblings, relatives or foster parents. While mothers and fathers are the primary caregivers, mothers’ experiences are well documented in comparison to the dearth of reports on fathers’ experiences. This descriptive narrative study aims to redress this gap in knowledge and understanding of men’s experiences of becoming a father of a child with an intellectual disability in the early years. Method: Narrative inquiry was employed for this study as it allows stories told by fathers to be collected as a means of exploring men’s transition to becoming a father of a child with an intellectual disability. A sample of 10 fathers of children with intellectual disabilities aged between thirteen months and five years of age were recruited from a large intellectual disability Health Service Provider (HSP) in the South of Ireland. Data were collected through semi-structured interviews which were audio-recorded, transcribed, and analysed using a narrative thematic approach. Findings: Findings are presented in four themes: i) ‘becoming a father’, ii) ‘something wrong with my child’, iii) ‘entering the world of disability’ and iv) ‘living a different life’. For all 10 fathers the time of being told that their child had an intellectual disability was laden with negative emotional responses irrespective of whether the diagnosis was at birth or more gradual over the child’s early developmental period. When fathers found out that ‘something was wrong’ they spoke of ‘moving on’ and entering the world of disability. In their narratives, becoming the father of a child with an intellectual disability had changed their lives and would inevitably change their futures. Fathers’ positivity was clearly evident with many fathers identifying that the diagnosis of their child with an intellectual disability was not a life ending event but rather a life changing event. Conclusions: Healthcare professionals have a critical role in supporting fathers during the transition to becoming a father of a child with an intellectual disability. Factors which require consideration include recognising that each father’s experience is unique; that fathers require support; and that fathers achieve personal growth because of their experiences of their transition to becoming a father of a child with an intellectual disability in the early years.