Philosophiae Doctor - PhD / In this study the construct of personal theories is used to represent the teacher's conceptions, which are interpreted as the consciously held beliefs. The teacher's personal theories encompass beliefs, images, values and attitudes as well as understanding about teaching and learning. This study investigates the influence of the teacher's conceptions of mathematics, of the teaching and learning of mathematics and of the context before and after a structured learning experience. The interest in the teacher's conceptions is derived from the assumption that these serve as a primary component that influence how teachers think about their professional responsibilities and how they act in their classrooms. Furthermore, the extent of implementation of a new curriculum has been linked to the scope of congruence between the teachers' conceptions and the underpinning philosophy of the intended curriculum. The study of the teacher's conceptions is especially relevant during a time of educational reform, such as the current transition to an Outcomes Based Education curriculum in South Africa. The participants in this study consist of four primary school mathematics teachers with various educational backgrounds, who teach at schools situated in different physical environments. The conceptions that these teachers have of mathematics, of the teaching and learning of mathematics and the influence of the context are investigated using a variety of instruments. Data collection was done with a questionnaire, a repertory grid, a semi-structured interview and lesson observations. The teachers participated in the Teaching Intervention and Support Programme (TISP), as a structured teacher learning experience. The programme is centred on the integration of the developmental and socio-cultural perspectives on teacher learning. With the developmental perspective the focus is on the acquisition of intellectual skills, while the socio-cultural perspective emphasizes participation in social practice. Both are directed at effecting conceptual change. With the developmental approach the process of conceptual change involves the development of new conceptions from existing conceptions. From the socio-cultural perspective the context is paramount and conceptual change is seen as new ways of being and acting within a particular context. The teachers were invited to attend a two-week intervention session, followed by a six months support programme that was aimed at establishing a teacher learning community. The learning experiences provided during the intervention session were drawn mainly from Realistic Mathematics Education. On completion of the programme, the teachers' conceptions of mathematics, of the teaching and learning of mathematics and the influence of the context were again investigated. The results of this study show that two of the participants had highly mechanistic conceptions of mathematics, and the teaching and learning of mathematics. The remaining two had a more empiristic approach with its high focus on environmental activities. After the programme, the teachers with the mechanistic views adopted a mixed. conception with some of the mechanistic conceptions retained, but now interspersed with some empiristic and realistic conceptions. The participants with the empiristic conceptions adopted a more realistic conception, but again to varying degrees. Thompson's (1991) hierarchical structure for the development of conceptions was also used to describe the extent of conceptual change. However, it was found that a concentric, rather than a hierarchical representation is a more appropriate to describe these changes. With regards to the socio-cultural view of conceptual change, all the participants perceived the context differently. The teachers' actions were also more commensurate with the practices associated with teachers that encourage learner autonomy, mathematical investigations and a facilitative role for the teacher.

<p>  </p> <p>Mathematics teacher educators have suggested that approximations of practice provide preservice mathematics teachers (PMTs) with opportunities to engage with, develop, and demonstrate subdomains of Mathematical Knowledge for Teaching ([MKT], Ball et al., 2008) because MKT provides a way for PMTs to understand how to contextualize their discipline-specific content knowledge for effective mathematics teaching and learning. However, the affordances and limitations of commonly used forms of approximations of practice (i.e., lesson planning and peer teaching) coupled with reflective practices to engage PMTs in subdomains of MKT are still being explored. In this study, I investigated how lesson planning, peer teaching, and associated reflections individually and collectively afforded opportunities for PMTs to demonstrate and develop the MKT subdomains. Eleven PMTs enrolled in a secondary mathematics methods course at a large Midwestern University participated in the study. My dissertation comprises three sub-studies (Sub-study “1”, “2”, and “3”), and I produced three manuscripts to individually report findings from those sub-studies. I investigated how lesson planning, peer teaching, and reflections afforded opportunities for PMTs to demonstrate and describe MKT subdomains in Sub-studies 1, 2, and 3, respectively. The findings across the sub-studies suggested that several MKT subdomains (e.g., Knowledge of Content and Teaching, Knowledge of Content and Students) were evidenced in the PMTs’ planned teacher and student actions (e.g., selecting mathematical tasks, formulating and sequencing questions), and in-the-moment actions and decisions (e.g., mathematically representing students’ responses, implementing mathematical tasks). Several aspects of MKT subdomains (e.g., evaluate the diagnostic potential of tasks) were strongly evidenced only in the PMTs’ lesson plans whereas other aspects (e.g., modifying tasks based on students’ responses) were evidenced only in peer teaching. These findings suggested that various forms of approximations of practice (planned and enacted actions) created unique opportunities for the PMTs to engage with and demonstrate MKT. I also found that the PMTs reflected on some subdomains of MKT that were not evidenced in their approximated practices, indicating that how PMTs describe the MKT subdomains is not entirely a result of what subdomains they engage in during approximations of practice. My findings also revealed limitations of using approximations of practice to engage PMTs with MKT subdomains. The MKT subdomains that required the PMTs to think about students’ alternative mathematical concepts, big mathematical ideas, and non-standard mathematics problem-solving strategies were least evidenced across the approximations of practice and reflections. These findings have two primary implications for mathematics teacher educators. First, I invite mathematics teacher educators to engage PMTs in multiple forms of approximations of practice to optimize their opportunities to engage with, demonstrate, and develop the MKT subdomains. Second, I suggest potential instructional activities (e.g., inviting PMTs to reflect on their roles as students and teachers during peer teaching) that could be incorporated into approximations of practice to address the existing limitations. Broadly, I invite mathematics teacher educators to design instructional activities at the intersection of mathematics content and pedagogy, collaborating with colleagues to enhance these opportunities across programs.</p> <p>  </p>

<p>The increasing volume and availability of Electronic Health Records (EHRs) open up opportunities for computational models to improve patient care. Key factors in improving patient outcomes include identifying patient sub-groups with distinct patient characteristics and providing personalized treatment actions with expected improved outcomes. This thesis investigates how well-formulated matrix decomposition and causal inference techniques can be leveraged to tackle the problem of disease sub-typing and inferring treatment recommendations in healthcare. In particular, the research resulted in computational techniques based on archetypal analysis to identify and analyze disease sub-types and a causal reinforcement learning method for learning treatment recommendations. Our work on these techniques are divided into four part in this thesis:</p> <p><br></p> <p>In the first part of the thesis, we present a retrospective study of Sepsis patients in intensive care environments using patient data. Sepsis accounts for more than 50% of hospital deaths, and the associated cost ranks the highest among hospital admissions in the US. Sepsis may be misdiagnosed because the patient is not thoroughly assessed or the symptoms are misinterpreted, which can lead to serious health complications or even death. An improved understanding of disease states, progression, severity, and clinical markers can significantly improve patient outcomes and reduce costs. We have developed a computational framework based on archetypal analysis that identifies disease states in sepsis using clinical variables and samples in the MIMIC-III database. Each identified state is associated with different manifestations of organ dysfunction. Patients in different states are observed to be statistically significantly composed of distinct populations with disparate demographic and comorbidity profiles. We furthermore model disease progression using a Markov chain. Our progression model accurately characterizes the severity level of each pathological trajectory and identifies significant changes in clinical variables and treatment actions during sepsis state transitions. Collectively, our framework provides a holistic view of sepsis, and our findings provide the basis for the future development of clinical trials and therapeutic strategies for sepsis. These results have significant implications for a large number of hospitalizations.</p> <p><br></p> <p><br></p> <p>In the second part, we focus on the problem of recommending optimal personalized treatment policies from observational data. Treatment policies are typically based on randomized controlled trials (RCTs); these policies are often sub-optimal, inconsistent, and have potential biases. Using observational data, we formulate suitable objective functions that encode causal reasoning in a reinforcement learning (RL) framework and present efficient algorithms for learning optimal treatment policies using interventional and counterfactual reasoning. We demonstrate the efficacy of our method on two observational datasets: (i) observational data to study the effectiveness of right heart catheterization (RHC) in the initial care of 5735 critically ill patients, and (ii) data from the Infant Health and Development Program (IHDP), aimed at estimating the effect of the intervention on the neonatal health for 985 low-birth-weight, premature infants. For the RHC dataset, our method's policy prescribes right heart catheterization (RHC) for 11.5% of the patients compared to the best current method that prescribes RHC for 38% of the patients. Even with this significantly reduced intervention, our policy yields a 1.5% improvement in the 180-day survival rate and a 2.2% improvement in the 30-day survival rate. For the IHDP dataset, we observe a 3.16% improvement in the rate of improvement of neonatal health using our method's policy.</p> <p><br></p> <p>In the third part, we consider the Supervised Archetypal Analysis (SAA) problem, which incorporates label information to compute archetypes. We formulate a new constrained optimization problem incorporating Laplacian regularization to guide archetypes towards groupings of similar data points, resulting in label-coherent archetypes and label-consistent soft assignments. We first use the MNIST dataset to show that SAA can can yield better cluster quality over baselines on any chosen number of archetypes. We then use the CelebFaces Attributes dataset to demonstrate the superiority of SAA in terms of cluster quality and interpretability over competing supervised and unsupervised methods. We also demonstrate the interpretability of SAA decompositions in the context of a movie rating application. We show that the archetypes from SAA can be directly interpreted as user ratings and encode class-specific movie preferences. Finally, we demonstrate how the SAA archetypes can be used for personalized movie recommendations. </p> <p><br></p> <p>In the last part of this thesis, we apply our SAA technique to clinical settings. We study the problem of developing methods for ventilation recommendations for Sepsis patients. Mechanical ventilation is an essential and commonly prescribed intervention for Sepsis patients. However, studies have shown that mechanical ventilation is associated with higher mortality rates on average, it is generally believed that this is a consequence of broad use of ventilation, and that a more targeted use can significantly improve average treatment effect and, consequently, survival rates. We develop a computational framework using Supervised Archetypal Analysis to stratify our cohort to identify groups that benefit from ventilators. We use SAA to group patients based on pre-treatment variables as well as treatment outcomes by constructing a Laplacian regularizer from treatment response (label) information and incorporating it into the objective function of AA. Using our Sepsis cohort, we demonstrate that our method can effectively stratify our cohort into sub-cohorts that have positive and negative ATEs, corresponding to groups of patients that should and should not receive mechanical ventilation, respectively. </p> <p>We then train a classifier to identify patient sub-cohorts with positive and negative treatment effects. We show that our treatment recommender, on average, has a high positive ATE for patients that are recommended ventilator support and a slightly negative ATE for those not recommended ventilator support. We use SHAP (Shapley Additive exPlanations) techniques for generating clinical explanations for our classifier and demonstrate their use in the generation of patient-specific classification and explanation. Our framework provides a powerful new tool to assist in the clinical assessment of Sepsis patients for ventilator use.</p>

A metapopulation is defined as a set of potential local populations among which dispersal may occur. Metapopulation theory has grown rapidly in recent years, but much has focused on the mathematical properties of metapopulations rather than their relevance to real systems. Indeed, barring some notable exceptions, metapopulation theory remains largely untested in the field. This thesis investigates the importance of metapopulation structure in the ‘real world’, firstly by building additional realism into metapopulation models, and secondly through a 3-year field study of a real metapopulation system. The modelling analyses include discrete-and continuous-time models, and cover single species, host-parasitoid, and disease-host systems, with and without stochasticity. In all cases, metapopulation structure enhanced species persistence in time, and often allowed long-term continuance of otherwise non-persistent interactions. Spatial heterogeneity and patterning was evident whenever local populations were stochastic or deterministically unstable in isolation. In metapopulations, the latter case often gave rise to self-organising spatial patterns. These were composed of spiral wave fronts (or ‘arcs of infection’ in disease models) of different sizes, and were related to the stability characteristics of local populations as well as the dispersal rates. There was no evidence for self-organising spatial patterns in the host-parasitoid system studied in the field (the weevil Sitona discoideus and its braconid parasitoid Microctonus aethiopoides), and a new model for the interaction suggested that this is probably due to the strong host density-dependence and stabilising parasitism acting on local populations. Dispersal may be important because of very high mortality in dispersing weevils, which may be related to the scarcity of their host plant in the landscape. If this is the case, the model suggested that local weevil density may be sensitive to the area of crop grown. Stochastic models showed that species in suitably large metapopulations may persist for very long times at relatively low overall density and with very low incidence of density-dependence. This suggests that metapopulation processes may explain a general inability to detect density-dependence in many real populations, and may also play an important part in the persistence of rare species. For host-parasitoid metapopulation models, persistence often depended on the way in which they were initialised. Initial conditions corresponding to a biological control release were the least likely to persist, and the maximum host suppression observed in this case was 84%, as compared with 60% for the corresponding non-spatial models and >90% often observed in the field. Metapopulation structure also allowed persistence of ‘boom-bust’ disease models, although the dynamics of these were particularly dependent on assumptions about what happens to disease classes at very low densities. Models assuming infinitely divisible units of density, models incorporating a non-zero extinction threshold, and individual-based models all gave differing results in terms of disease persistence and rate of spatial spread. Fitting models to overall metapopulation dynamics often gave misleading results in terms of underlying local dynamics, emphasising the need to sample real populations at an appropriate scale when seeking to understand their behaviour.

The New Zealand Wool Industry (NZWI) contributes over a billion dollars a year to NZ gross output. However, this industry is at a crossroads and the incumbent practitioners are looking for ways to increase the value of the New Zealand wool clip. The value of the industry to the economy is directly related to the price which buyers are prepared to pay for wool, primarily as a result of the marketing approaches used, physical parameters of wool as well as intra and inter-fibre competition. The inflation adjusted price has steadily decreased over recent years and understanding of its dynamics is a fundamental problem for the stakeholders. Among the stakeholders, buyers / exporters, heavily involved in the process of price formation currently face a real time problem of sourcing strong wool from two parallel but different marketing systems operated simultaneously – auction and direct supply. The underlying mathematics which governs the decision making of buyers on the price dynamics in these sourcing options is poorly understood. This study developed system models for price formation in both auction and direct supply sourcing and an associated optimization model for the buyer / exporter of the New Zealand wool clip. All three of these models were original and none appear to have been described previously. It is hoped that these three models will be of quite general utility and also be useful therefore for other agricultural commodities that are traded simultaneously via auction and direct supply. The average price for a given wool type, which is the output from this new modelling exercise is precisely what is required as input data for solving the minimization problem in wool blending models.

Thesis (MSc (Computer Science))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: The aim of this thesis is to develop a generic 3D virtual environment development platform for autism spectrum disorder (ASD) therapy tools. The potential of using computerised therapy tools for ASD therapy is well known. However, the development of such tools is expensive and time-consuming, and is language and culture speci c. This work intends to alleviate these problems. The design of the platform is based on known game engine designs, but adapted for the requirements of ASD therapy tools. It supports standard features such as 3D rendering, animation and audio output. Speci c features, aimed at ASD therapy tools and educational games, included in our engine are: replays, data capturing, remote monitoring over a network and language localisation. We also implemented an input hardware abstraction layer to allow support for non-standard input peripherals in the future, without modifying existing game implementations. Furthermore, to separate the development of games and tools from the engine, we include wrapper libraries in our engine for Lua and Java. We successfully developed our engine and implemented a number of prototype therapy tools and educational games. These implementations confirmed that the engine works as expected. Some of these programs are currently in use at a local primary school. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om 'n 3D virtuele omgewing en ontwikkelingsplatform vir outistiese spektrum versteuring (OSV) terapiemiddels te ontwikkel. Die gebruik van rekenaargebaseerde terapiemiddels vir OSV terapie is bekend. Om sulke terapiemiddels te ontwikkel is egter duur, tydrowend en is dikwels gerig op spesi eke taal- en kultuurgroepe. Hierdie werk het dit ten doel om hierdie probleme te bowe te kom. Die ontwerp van die platform is gebaseer op die ontwerp van bekende videospeletjie-enjins, maar is aangepas vir die benodigdhede van OSV terapiemiddels. Dit ondersteun standaard funksionaliteit soos 3D uitbeelding, animasie en klank. Ons platform sluit in spesi eke funksionaliteit, wat gerig is op OSV terapiemiddels en opvoedkundige speletjies, naamlik: kykweer, datavaslegging, afstandswaarneming oor 'n netwerk en taal-lokalisering. Verder is 'n abstrakte koppelvlak vir toevoerapparatuur ontwikkel, wat dit moontlik maak om in die toekoms nie-standaard toevoerapparatuur te ondersteun, sonder om bestaande speletjies se implementasies aan te pas. Verder, om die ontwikkeling van speletjies en terapiemiddels te skei van die enjin, is koppelvlakke ontwikkel wat dit moontlik maak om die enjin in Lua en Java te gebruik.

We study a multivariate version of the Bernstein–Sato polynomial, the so-called Bernstein–Sato ideal, associated to an arbitrary factorization of an analytic germ <i>f - f</i>₁···<i>f</i>_r. We identify a large class of geometrically characterized germs so that the <i>D</i>_X,x[<i>s</i>₁,...,<i>s</i>_r]-annihilator of <i>f</i>^s₁¹···<i>f</i>^s_r^r admits the simplest possible description and, more-over, has a particularly nice associated graded object. As a consequence we are able to verify Budur’s Topological Multivariable Strong Monodromy Conjecture for arbitrary factorizations of tame hyperplane arrangements by showing the zero locus of the associated Bernstein–Sato ideal contains a special hyperplane. By developing ideas of Maisonobe and Narvaez-Macarro, we are able to find many more hyperplanes contained in the zero locus of this Bernstein–Sato ideal. As an example, for reduced, tame hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial contained in [−1,0) are combinatorially determined; for reduced, free hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial are all combinatorially determined. Finally, outside the hyperplane arrangement setting, we prove many results about a certain <i>D</i>_X,x-map ∇_<i>A</i> that is expected to characterize the roots of the Bernstein–Sato ideal.

This thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.

科学研究費補助金 研究種目:基盤研究(A)(1) 課題番号: 研究代表者:三井 斌友 研究期間:1996-1998年度

The sap beetle genus Carpophilus Stephens (Coleoptera: Nitidulidae) is a large genus consisting of over 200 species and are found worldwide. Several species are important pests of crops and stored products, and are frequently intercepted as part of biosecurity operations. The genus is poorly known taxonomically, and there are several species groups that are challenging to identify by morphological methods. In particular, two species found across the Pacific, C. maculatus Murray and C. oculatus Murray are frequently confused with each other. These two species are similar in size and colour, but differ primarily by the shape of the colour pattern on their elytra. However, this colour pattern is highly variable within both species, leading to ambiguity in the indentification of these species. Within C. oculatus, three subspecies have been described based on differences in the male genitalia and pronotal punctation: C. o. oculatus and C. o. gilloglyi Dobson are distributed widely across the Pacific, while C. o. cheesmani Dobson is known only from Vanuatu. A search of literature records and specimen collections revealed 32 species of Carpophilus recorded from the Pacific region. In addition there remain several unidentified specimens representing at least four species, two of which will be described subsequent to this research. A number of species recorded in the literature may have been misidentified, and these require further field collections and inspection of museum specimens to confirm their presence in the Pacific. To test the validity of the subspecies of C. oculatus, and its distinctiveness from C. maculatus, a phylogeny of available specimens of Carpophilus was inferred from one mitochondrial gene (cytochrome c oxidase subunit I (COI)), and two nuclear genes (28S ribsomal RNA (28S) and the internal transcribed spacer 2 (ITS2)). These data show large genetic distances between the three subspecies of C. oculatus of 7-12%. Given these distances are similar to those between other species in the genus, this indicates these subspecies may be elevated to full species. The data also consistently support a monophyletic relationship between C. o. oculatus and C. o. gilloglyi. Nuclear genes also support C. o. cheesmani as part of a clade with the other subspecies, but these relationships are unresolved in COI. Carpophilus maculatus was not supported as being the sister taxon of the C. o. oculatus and C. o. gilloglyi clade. Other relationships within Carpophilus were unresolved, possibly due to a combination of incomplete taxon sampling, and saturation of substitutions within the COI gene. Phylogeographic analysis of specimens collected from several localities within the range of C. oculatus showed that, with only one exception, there were no shared haplotypes between archipelagoes. This result suggests it may be possible to determine the provenence of intercepted specimens, providing further information regarding potential invasion pathways. A degree of geographic structuring was also present within C. o. gilloglyi, being separated into a western clade found in Fiji and Rotuma and an eastern clade distributed from the Kermadec Islands and Tonga to French Polynesia. This separation was most profound in COI data, with a mean pairwise distance between the clades of 7%. ITS2 data also demonstrates a degree of differentiation between the two clades, based on differences in the insertions and deletions between the clades. The variability in the shape and colour of the elytral pattern of C. oculatus was also investigated. Colour was quantified using a method based on Red-Green-Blue (RGB) colour values derived from digital photographs, while an outline analysis of the elytral pattern was conducted using elliptic Fourier analysis (EFA). Principal Components Analysis of the RGB values and EFA coefficients showed no clear separation between subspecies, nor were any trends correlated with host fruit or collection localities. Variation at all levels and all measures studied in this thesis show that this geographic region and this genus of beetles offer intruiging insights into speciation, biogeography and biological invasions. There is much scope for further research on the causes and consequences of this variation and the lives of these interesting insects.