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.

Police accountability in Ireland: an analysis of the problems posed by the legal, constitutional and political dimensions and how they might be addressed

The concept of police accountability is not susceptible to a universal or concise definition. In the context of this thesis it is treated as embracing two fundamental components. First, it entails an arrangement whereby an individual, a minority and the whole community have the opportunity to participate meaningfully in the formulation of the principles and policies governing police operations. Second, it presupposes that those who have suffered as victims of unacceptable police behaviour should have an effective remedy. These ingredients, however, cannot operate in a vacuum. They must find an accommodation with the equally vital requirement that the burden of accountability should not be so demanding that the delivery of an effective police service is fatally impaired. While much of the current debate on police accountability in Britain and the USA revolves around the issue of where the balance should be struck in this accommodation, Ireland lacks the very foundation for such a debate as it suffers from a serious deficit in research and writing on police generally. This thesis aims to fill that gap by laying the foundations for an informed debate on police accountability and related aspects of police in Ireland. Broadly speaking the thesis contains three major interrelated components. The first is concerned with the concept of police in Ireland and the legal, constitutional and political context in which it operates. This reveals that although the Garda Siochana is established as a national force the legal prescriptions concerning its role and governance are very vague. Although a similar legislative format in Britain, and elsewhere, have been interpreted as conferring operational autonomy on the police it has not stopped successive Irish governments from exercising close control over the police. The second component analyses the structure and operation of the traditional police accountability mechanisms in Ireland; namely the law and the democratic process. It concludes that some basic aspects of the peculiar legal, constitutional and political structures of policing seriously undermine their capacity to deliver effective police accountability. In the case of the law, for example, the status of, and the broad discretion vested in, each individual member of the force ensure that the traditional legal actions cannot always provide redress where individuals or collective groups feel victimised. In the case of the democratic process the integration of the police into the excessively centralised system of executive government, coupled with the refusal of the Minister for Justice to accept responsibility for operational matters, project a barrier between the police and their accountability to the public. The third component details proposals on how the current structures of police accountability in Ireland can be strengthened without interfering with the fundamentals of the law, the democratic process or the legal and constitutional status of the police. The key elements in these proposals are the establishment of an independent administrative procedure for handling citizen complaints against the police and the establishment of a network of local police-community liaison councils throughout the country coupled with a centralised parliamentary committee on the police. While these proposals are analysed from the perspective of maximising the degree of police accountability to the public they also take into account the need to ensure that the police capacity to deliver an effective police service is not unduly impaired as a result.

‘Doing’ separation in contemporary Ireland: the experiences of women who separate in midlife

This study explores the experiences of fourteen Irish women who separated in midlife. The rationale for choosing to study this age group of women is because they are the first generation of Irish women to publically separate in midlife in such large numbers. All of them entered marriage at a time when divorce was not possible in Ireland and as such they are broadly without a cultural ‘script’ for how to ‘do’ separation. An exploratory study was conducted to try to capture the processes and events that are part of the lived experiences of separation for women in midlife. In-depth interviews were conducted with fourteen women who were recruited following their attendance at post-separation courses. The participants came from predominantly middle class backgrounds. Narrative interviews were conducted which covered topics such as the attitudes to separation internalised during childhood, the genesis of the marital problems, the events that triggered the separations, the women’s emotional reactions at the time of separating and their social, housing and financial outcomes of having separated. A theoretical framework using concepts related to connectedness and fragmentation was used to analyse the data. Significant diversity was found in the experiences of the interviewees. Most of the women retained connectedness to their children, to their families of origin and to friends who were not joint friends. Significant fragmentation was found in relationships with ex-husbands, with in-laws and with joint friends. All of the women were worse off financially than if they had remained married. They felt socially isolated in the aftermath of separation. Many of the women were struggling to establish positive identities as separated women. While a few of them were very relieved that their marriages had ended, for most, separation was experienced as a painful episode in their lives.

Beginning primary teachers’ perspectives on becoming a teacher in the workplace: Contextual, emotional, and temporo-spatial dimensions of identity shaping

The issue, with international and national overtones, of direct relevance to the present study, relates to the shaping of beginning teachers’ identities in the workplace. As the shift from an initial teacher education programme into initial practice in schools is a period of identity change worthy of investigation, this study focuses on the transformative search by nine beginning primary teachers for their teaching identities, throughout the course of their initial year of occupational experience, post-graduation. The nine beginning teacher participants work in a variety of primary school settings, thus strengthening the representativeness of the research cohort. Privileging ‘insider’ perspectives, the research goal is to understand the complexities of lived experience from the viewpoints of the participating informants. The shaping of identity is conceived of in dimensional terms. Accordingly, a framework composed of three dimensions of beginning teacher experience is devised, namely: contextual; emotional; temporo-spatial. Data collection and analysis is informed by principles derived from sociocultural theories; activity theory; figured worlds theory; and, dialogical self theory. Individual, face-to-face semi-structured interviews, and the maintenance of solicited digital diaries, are the principal methods of data collection employed. The use of a dimensional model fragments the integrated learning experiences of beginning teachers into constituent parts for the purpose of analysis. While acknowledging that the actual journey articulated by each participant is a more complex whole than the sum of its parts, key empirically-based claims are presented as per the dimensional framework employed: contextuality; emotionality; temporo-spatiality. As a result of applying the foci of an international literature to an under-researched aspect of Irish education, this study is offered as a context-specific contribution to the knowledge base on beginning teaching. As the developmental needs of beginning teachers constitute an emerging area of intense policy focus in Ireland, this research undertaking is both relevant and timely.

Problems with drawing lines: Theo-geographies of the Catholic parish in Ireland

While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.

Peer rejection and social information-processing factors in the development of aggressive behavior problems in children.

The relation between social rejection and growth in antisocial behavior was investigated. In Study 1,259 boys and girls (34% African American) were followed from Grades 1 to 3 (ages 6-8 years) to Grades 5 to 7 (ages 10-12 years). Early peer rejection predicted growth in aggression. In Study 2,585 boys and girls (16% African American) were followed from kindergarten to Grade 3 (ages 5-8 years), and findings were replicated. Furthermore, early aggression moderated the effect of rejection, such that rejection exacerbated antisocial development only among children initially disposed toward aggression. In Study 3, social information-processing patterns measured in Study 1 were found to mediate partially the effect of early rejection on later aggression. In Study 4, processing patterns measured in Study 2 replicated the mediation effect. Findings are integrated into a recursive model of antisocial development.

Response decision processes and externalizing behavior problems in adolescents.

Externalizing behavior problems of 124 adolescents were assessed across Grades 7-11. In Grade 9, participants were also assessed across social-cognitive domains after imagining themselves as the object of provocations portrayed in six videotaped vignettes. Participants responded to vignette-based questions representing multiple processes of the response decision step of social information processing. Phase 1 of our investigation supported a two-factor model of the response evaluation process of response decision (response valuation and outcome expectancy). Phase 2 showed significant relations between the set of these response decision processes, as well as response selection, measured in Grade 9 and (a) externalizing behavior in Grade 9 and (b) externalizing behavior in Grades 10-11, even after controlling externalizing behavior in Grades 7-8. These findings suggest that on-line behavioral judgments about aggression play a crucial role in the maintenance and growth of aggressive response tendencies in adolescence.

Detection methods for common problems in solar home systems

Gemstone Team SHINE (Students Helping to Implement Natural Energy)

Component Neural Systems for the Creation of Emotional Memories during Free Viewing of a Complex, Real-World Event.

To investigate the neural systems that contribute to the formation of complex, self-relevant emotional memories, dedicated fans of rival college basketball teams watched a competitive game while undergoing functional magnetic resonance imaging (fMRI). During a subsequent recognition memory task, participants were shown video clips depicting plays of the game, stemming either from previously-viewed game segments (targets) or from non-viewed portions of the same game (foils). After an old-new judgment, participants provided emotional valence and intensity ratings of the clips. A data driven approach was first used to decompose the fMRI signal acquired during free viewing of the game into spatially independent components. Correlations were then calculated between the identified components and post-scanning emotion ratings for successfully encoded targets. Two components were correlated with intensity ratings, including temporal lobe regions implicated in memory and emotional functions, such as the hippocampus and amygdala, as well as a midline fronto-cingulo-parietal network implicated in social cognition and self-relevant processing. These data were supported by a general linear model analysis, which revealed additional valence effects in fronto-striatal-insular regions when plays were divided into positive and negative events according to the fan's perspective. Overall, these findings contribute to our understanding of how emotional factors impact distributed neural systems to successfully encode dynamic, personally-relevant event sequences.

Mental hoop diaries: emotional memories of a college basketball game in rival fans.

The rivalry between the men's basketball teams of Duke University and the University of North Carolina-Chapel Hill (UNC) is one of the most storied traditions in college sports. A subculture of students at each university form social bonds with fellow fans, develop expertise in college basketball rules, team statistics, and individual players, and self-identify as a member of a fan group. The present study capitalized on the high personal investment of these fans and the strong affective tenor of a Duke-UNC basketball game to examine the neural correlates of emotional memory retrieval for a complex sporting event. Male fans watched a competitive, archived game in a social setting. During a subsequent functional magnetic resonance imaging session, participants viewed video clips depicting individual plays of the game that ended with the ball being released toward the basket. For each play, participants recalled whether or not the shot went into the basket. Hemodynamic signal changes time locked to correct memory decisions were analyzed as a function of emotional intensity and valence, according to the fan's perspective. Results showed intensity-modulated retrieval activity in midline cortical structures, sensorimotor cortex, the striatum, and the medial temporal lobe, including the amygdala. Positively valent memories specifically recruited processing in dorsal frontoparietal regions, and additional activity in the insula and medial temporal lobe for positively valent shots recalled with high confidence. This novel paradigm reveals how brain regions implicated in emotion, memory retrieval, visuomotor imagery, and social cognition contribute to the recollection of specific plays in the mind of a sports fan.

Memory and coping with stress: the relationship between cognitive-emotional distinctiveness, memory valence, and distress.

Cognitive-emotional distinctiveness (CED), the extent to which an individual separates emotions from an event in the cognitive representation of the event, was explored in four studies. CED was measured using a modified multidimensional scaling procedure. The first study found that lower levels of CED in memories of the September 11 terrorist attacks predicted greater frequency of intrusive thoughts about the attacks. The second study revealed that CED levels are higher in negative events, in comparison to positive events and that low CED levels in emotionally intense negative events are associated with a pattern of greater event-related distress. The third study replicated the findings from the previous study when examining CED levels in participants' memories of the 2004 Presidential election. The fourth study revealed that low CED in emotionally intense negative events is associated with worse mental health. We argue that CED is an adaptive and healthy coping feature of stressful memories.

The spatiotemporal dynamics of autobiographical memory: neural correlates of recall, emotional intensity, and reliving.

We sought to map the time course of autobiographical memory retrieval, including brain regions that mediate phenomenological experiences of reliving and emotional intensity. Participants recalled personal memories to auditory word cues during event-related functional magnetic resonance imaging (fMRI). Participants pressed a button when a memory was accessed, maintained and elaborated the memory, and then gave subjective ratings of emotion and reliving. A novel fMRI approach based on timing differences capitalized on the protracted reconstructive process of autobiographical memory to segregate brain areas contributing to initial access and later elaboration and maintenance of episodic memories. The initial period engaged hippocampal, retrosplenial, and medial and right prefrontal activity, whereas the later period recruited visual, precuneus, and left prefrontal activity. Emotional intensity ratings were correlated with activity in several regions, including the amygdala and the hippocampus during the initial period. Reliving ratings were correlated with activity in visual cortex and ventromedial and inferior prefrontal regions during the later period. Frontopolar cortex was the only brain region sensitive to emotional intensity across both periods. Results were confirmed by time-locked averages of the fMRI signal. The findings indicate dynamic recruitment of emotion-, memory-, and sensory-related brain regions during remembering and their dissociable contributions to phenomenological features of the memories.