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 human impacts of flower farm development in the Ethiopian Rift Valley region

The flower industry has a reputation for heavy usage of toxic chemicals and polluting the environment, enormous consumption of water, and poor working condition and low wage level in various parts of the world. It is unfortunate that this industry is adamant to change and repeating the same mistakes in Ethiopia. Because of this, - there is a growing concern among the general public and the international community about sustainability of the Ethiopian flower industry. Consequently, working conditions in the flower industry, impacts of wage income on the livelihoods of employees, coping strategies of low wage flower farm workers, impacts of flower farms on the livelihoods of local people and environmental pollution and conflict, were analysed. Both qualitative and quantitative research methods were employed. Four quantitative data sets: labour practice, employees’ income and expenditure, displaced household, and flower grower views survey were collected between 2010 and 2012. Robust regression to identify the determinants of wage levels, and Multinomial logit to identify the determinants of coping strategies of flower farm workers and displaced households were employed. The findings show the working conditions in flower farms are characterized by low wages, job insecurity and frequent violation of employees’ rights, and poor safety measures. To ensure survival of their family, land dispossessed households adopt a wide range of strategies including reduction in food consumption, sharing oxen, renting land, share cropping, and shifting staple food crops. Most experienced scarcity of water resources, lack of grazing areas, death of herds and reduced numbers of livestock due to water source pollution. Despite the Ethiopian government investment in attracting and creating conducive environment for investors, not much was accomplished when it comes to enforcing labour laws and environmental policies. Flower farm expansion in Ethiopia, as it is now, can be viewed as part of the global land and water grab and is not all inclusive and sustainable. Several recommendations are made to improve working conditions, maximize the benefits of flower industry to the society, and to the country at large.

Alcohol income and health: a complicated but desirable mix

The aim of this thesis is to examine if a difference exists in income for different categories of drinkers in Ireland using the 2007 Slán data set. The possible impact of alcohol consumption on health status and health care utilisation is also examined. Potential endogeneity and selection bias is accounted for throughout. Endogeneity is where an independent variable included in the model is determined within the context of the model (Chenhall and Moers, 2007). An endogenous relationship between income and alcohol and between health and alcohol is accounted for by the use of separate income equations and separate health status equations for each category of drinker similar to what was done in previous studies into the effects of alcohol on earnings (Hamilton and Hamilton, 1997; Barrett, 2002). Sample selection bias arises when a sector selection is non-random due to individuals choosing a particular sector because of their personal characteristics (Heckman, 1979; Zhang, 2004). In relation to alcohol consumption, selection bias may arise as people may select into a particular drinker group due to the fact that they know that by doing so it will not have a negative effect on their income or health (Hamilton and Hamilton, 1997; Di Pietro and Pedace, 2008; Barrett, 2002). Selection bias of alcohol consumption is accounted for by using the Multinomial Logit OLS Two Step Estimate as proposed by Lee (1982), which is an extension of the Heckman Probit OLS Two Step Estimate. Alcohol status as an ordered variable is examined and possible methods of estimation accounting for this ordinality while also accounting for selection bias are looked at. Limited Information Methods and Full Information Methods of estimation of simultaneous equations are assessed and compared. Findings show that in Ireland moderate drinkers have a higher income compared with abstainers or heavy drinkers. Some studies such as Barrett (2002) argue that this is as a consequence of alcohol improving ones health, which in turn can influence ones productivity which may ultimately be reflected in earnings, due to the fact that previous studies have found that moderate levels of alcohol consumption are beneficial towards ones health status. This study goes on to examine the relationship between health status and alcohol consumption and whether the correlation between income and the consumption of alcohol is similar in terms of sign and magnitude to the correlation between health status and the consumption of alcohol. Results indicate that moderate drinkers have a higher income than non or heavy drinkers, with the weekly household income of moderate drinkers being €660.10, non drinkers being €546.75 and heavy drinkers being €449.99. Moderate Drinkers also report having a better health status than non drinkers and a slightly better health status than heavy drinkers. More non-drinkers report poor health than either moderate or heavy drinkers. As part of the analysis into the effect of alcohol consumption on income and on health status, the relationship between other socio economic variables such as gender, age, education among others, with income, health and alcohol status is examined.

Between respectability and disgrace: schismogenesis and the regeneration of inequality, stigma and social exclusion in Limerick

The thesis examines cultural processes underpinning the emergence, institutionalisation and reproduction of class boundaries in Limerick city. The research aims to bring a new understanding to the contemporary context of the city’s urban regeneration programme. Acknowledging and recognising other contemporary studies of division and exclusion, the thesis creates a distinctive approach which focuses on uncovering the cultural roots of inequality, educational disadvantage, stigma and social exclusion and the dynamics of their social reproduction. Using Bateson’s concept of schismogenesis (1953), the thesis looks to the persistent, but fragmented culture of community and develops a heuristic ‘symbolic order of the city’. This is defined as “…a cultural structure, the meaning making aspect of hierarchy, the categorical structures of world understanding, the way Limerick people understand themselves, their local and larger world” (p. 37). This provides a very different departure point for exploring the basis for urban regeneration in Limerick (and everywhere). The central argument is that if we want to understand the present (multiple) crises in Limerick we need to understand the historical, anthropological and recursive processes underpinning ‘generalised patterns of rivalry and conflict’. In addition to exploring the historical roots of status and stigma in Limerick, the thesis explores the mythopoesis of persistent, recurrent narratives and labels that mark the boundaries of the city’s identities. The thesis examines the cultural and social function of ‘slagging’ as a vernacular and highly particularised form of ironic, ritualised and, often, ‘cruel’ medium of communication (often exclusion). This is combined with an etymology of the vocabulary of Limerick slang and its mythological base. By tracing the origins of many normalised patterns of Limerick speech ‘sayings’, which have long since forgotten their roots, the thesis demonstrates how they perform a significant contemporary function in maintaining and reinforcing symbolic mechanisms of inclusion/exclusion. The thesis combines historical and archival data with biographical interviews, ethnographic data married to a deep historical hermeneutic analysis of this political community.

The effect of alcohol consumption on household income in Ireland

This paper presents a study of the effects of alcohol consumption on household income in Ireland using the Slán National Health and Lifestyle Survey 2007 dataset, accounting for endogeneity and selection bias. Drinkers are categorised into one of four categories based on the recommended weekly drinking levels by the Irish Health Promotion Unit; those who never drank, non-drinkers, moderate and heavy drinkers. A multinomial logit OLS Two Step Estimate is used to explain individual's choice of drinking status and to correct for selection bias which would result in the selection into a particular category of drinking being endogenous. Endogeneity which may arise through the simultaneity of drinking status and income either due to the reverse causation between the two variables, income affecting alcohol consumption or alcohol consumption affecting income, or due to unobserved heterogeneity, is addressed. This paper finds that the household income of drinkers is higher than that of non-drinkers and of those who never drank. There is very little difference between the household income of moderate and heavy drinkers, with heavy drinkers earning slightly more. Weekly household income for those who never drank is €454.20, non-drinkers is €506.26, compared with €683.36 per week for moderate drinkers and €694.18 for heavy drinkers.