http://hdl.handle.net/10468/88 2013-06-20T01:45:06Z 2013-06-20T01:45:06Z McCarthy, Stephen Patrick http://hdl.handle.net/10468/1138 2013-05-28T02:00:18Z 2013-01-01T00:00:00Z

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs McCarthy, Stephen Patrick Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

2013-01-01T00:00:00Z Lane, Ciara Mary Frances http://hdl.handle.net/10468/1096 2013-04-30T02:00:16Z 2013-01-01T00:00:00Z

An investigation of post-primary students' images of mathematics Lane, Ciara Mary Frances This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

2013-01-01T00:00:00Z Fitzgerald, Anthony P. Perry, Ivan J. Corcoran, Paul Keeley, Helen S. Ruelbach, Udo Arensman, Ella http://hdl.handle.net/10468/875 2013-01-24T12:49:13Z 2012-01-01T00:00:00Z

The incidence and repetition of hospital-treated deliberate self harm: findings from the world's first national registry Fitzgerald, Anthony P.; Perry, Ivan J.; Corcoran, Paul; Keeley, Helen S.; Ruelbach, Udo; Arensman, Ella Background: Suicide is a significant public health issue with almost one million people dying by suicide each year worldwide. Deliberate self harm (DSH) is the single most important risk factor for suicide yet few countries have reliable data on DSH. We developed a national DSH registry in the Republic of Ireland to establish the incidence of hospital-treated DSH at national level and the spectrum and pattern of presentations with DSH and repetition. Methods and Findings: Between 2003 and 2009, the Irish National Registry of Deliberate Self Harm collected data on DSH presentations to all 40 hospital emergency departments in the country. Data were collected by trained data registration officers using standard methods of case ascertainment and definition. The Registry recorded 75,119 DSH presentations involving 48,206 individuals. The total incidence rate fell from 209 (95% CI: 205–213) per 100,000 in 2003 to 184 (95% CI: 180–189) per 100,000 in 2006 and increased again to 209 (95% CI: 204–213) per 100,000 in 2009. The most notable annual changes were successive 10% increases in the male rate in 2008 and 2009. There was significant variation by age with peak rates in women in the 15–19 year age group (620 (95% CI: 605–636) per 100,000), and in men in the 20–24 age group (427 (95% CI: 416–439) per 100,000). Repetition rates varied significantly by age, method of self harm and number of previous episodes. Conclusions: Population-based data on hospital-treated DSH represent an important index of the burden of mental illness and suicide risk in the community. The increased DSH rate in Irish men in 2008 and 2009 coincided with the advent of the economic recession in Ireland. The findings underline the need for developing effective interventions to reduce DSH repetition rates as a key priority for health systems.

2012-01-01T00:00:00Z Cashman, Kevin D. Fitzgerald, Anthony P. Kiely, Mairead Seamans, Kelly M. http://hdl.handle.net/10468/863 2012-12-21T03:00:10Z 2011-12-01T00:00:00Z

A systematic review and meta-regression analysis of the vitamin D intake-serum 25-hydroxyvitamin D relationship to inform European recommendations Cashman, Kevin D.; Fitzgerald, Anthony P.; Kiely, Mairead; Seamans, Kelly M. The present study used a systematic review approach to identify relevant randomised control trials (RCT) with vitamin D and then apply meta-regression to explore the most appropriate model of the vitamin D intake–serum 25-hydroxyvitamin D (25(OH)D) relationship to underpin setting reference intake values. Methods included an updated structured search on Ovid MEDLINE; rigorous inclusion/exclusion criteria; data extraction; and meta-regression (using different model constructs). In particular, priority was given to data from winter-based RCT performed at latitudes >49•58°N (n 12). A combined weighted linear model meta-regression analyses of natural log (Ln) total vitamin D intake (i.e. diet and supplemental vitamin D) versus achieved serum 25(OH)D in winter (that used by the North American Dietary Reference Intake Committee) produced a curvilinear relationship (mean (95% lower CI) serum 25(OH)D (nmol/l) = 9•2 (8•5) Ln (total vitamin D)). Use of non-transformed total vitamin D intake data (maximum 1400 IU/d; 35µg/d) provided for a more linear relationship (mean serum 25(OH)D (nmol/l) = 0•044 × (total vitamin D) + 33•035). Although inputting an intake of 600 IU/d (i.e. the RDA) into the 95% lower CI curvilinear and linear models predicted a serum 25(OH)D of 54•4 and 55•2 nmol/l, respectively, the total vitamin D intake that would achieve 50 (and 40) nmol/l serum 25(OH)D was 359 (111) and 480 (260) IU/d, respectively. Inclusion of 95% range in the model to account for inter-individual variability increased the predicted intake of vitamin D needed to maintain serum 25(OH)D ≥50 nmol/l to 930 IU/d. The model used to describe the vitamin D intake–status relationship needs to be considered carefully when setting new reference intake values in Europe.

2011-12-01T00:00:00Z