On the role of subharmonic functions in the spectral theory of general Banach algebras

M.Sc

Metacognitive skills of second year extended and main stream University mathematics students: a case study

A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy to the Wits School of Education, Faculty of Humanities, University of the Witwatersrand, Johannesburg, Johannesburg, 2017Many universities have introduced so called extended degrees where students’ first year workload is spread over two years to prevent the decline of graduates in mathematics and science. It has been put forward that extended degree courses should include the explicit training of mathematics students in the use of metacognitive skills. This is based on research that shows that successful students in mathematics are able to apply such metacognitive skills and that these skills play an important role in mathematical problem solving. Such skills are concerned with the actual regulation, coordination and control of one’s own learning activities and cognitive processes. Given that extended degree students generally perform weakly in mathematics in comparison to main stream students (non-extended degree students) this research study sets out to consider the differences in the use of metacognitive skills of these two student groupings. A qualitative case study was used to investigate collaborative solving of mathematical problems of one student pair. Students were trained in the use of metacognitive skills by using the metacognitive intervention method called IMPROVE. The student pair was video-recorded during talk-aloud protocols twice before explicit training in the IMPROVE method, and after instruction in order to evaluate students’ development in the use of metacognitive skills. Video recordings were transcribed noting students’ verbal and non-verbal actions and the coding of transcriptions in conjunction with content analysis was used in determining differences in students’ metacognitive skills. Since students worked collaboratively, instances where students acted as so-called social triggers of each other’s metacognitive skills, were also investigated. With student-researcher interaction during observations, the researcher was also regarded as a social trigger of students’ metacognitive behaviour. Apart from these social triggers, environmental triggers of students’ metacognitive skills were also scrutinised. Environmental triggers included the effect of task difficulty and the intervention of the IMPROVE method on students’ metacognitive skills. This study on the social and environmental triggers of individual’s metacognitive skills contributes to the relatively young field in viewing metacognition as cognitive activity that operates on multiple levels during collaborative problem solving, and that metacognition cannot solely be explained in terms of individualistic conceptions but also by social and environmental triggers. Results from the study show that, in general, the main stream student exhibited a greater number of metacognitive skills compared to the extended degree student. Furthermore, it seems that the IMPROVE method as an environmental trigger, had an effect on the development of both students’ metacognitive behaviour. Research findings of the study also reveal that the researcher’s intervention mainly resulted in the students acting as social triggers for each other’s metacognitive behaviour. Furthermore, it was found that there were a greater number of occurrences in which the main stream student acted as social trigger for the extended degree student’ metacognitive behaviour. The level of task difficulty also seems to have acted as environmental trigger for students’ metacognitive behaviour. As an exploratory study, the findings of this study are not generalizable.MT 201

Impact of Dendritic Size and Dendritic Topology on Burst Firing in Pyramidal Cells

Neurons display a wide range of intrinsic firing patterns. A particularly relevant pattern for neuronal signaling and synaptic plasticity is burst firing, the generation of clusters of action potentials with short interspike intervals. Besides ion-channel composition, dendritic morphology appears to be an important factor modulating firing pattern. However, the underlying mechanisms are poorly understood, and the impact of morphology on burst firing remains insufficiently known. Dendritic morphology is not fixed but can undergo significant changes in many pathological conditions. Using computational models of neocortical pyramidal cells, we here show that not only the total length of the apical dendrite but also the topological structure of its branching pattern markedly influences inter- and intraburst spike intervals and even determines whether or not a cell exhibits burst firing. We found that there is only a range of dendritic sizes that supports burst firing, and that this range is modulated by dendritic topology. Either reducing or enlarging the dendritic tree, or merely modifying its topological structure without changing total dendritic length, can transform a cell's firing pattern from bursting to tonic firing. Interestingly, the results are largely independent of whether the cells are stimulated by current injection at the soma or by synapses distributed over the dendritic tree. By means of a novel measure called mean electrotonic path length, we show that the influence of dendritic morphology on burst firing is attributable to the effect both dendritic size and dendritic topology have, not on somatic input conductance, but on the average spatial extent of the dendritic tree and the spatiotemporal dynamics of the dendritic membrane potential. Our results suggest that alterations in size or topology of pyramidal cell morphology, such as observed in Alzheimer's disease, mental retardation, epilepsy, and chronic stress, could change neuronal burst firing and thus ultimately affect information processing and cognition

Development of a technique to identify advertisements in a video signal

Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013In recent years Content Based Information Retrieval (CBIR) has received a lot of research attention, starting with audio, followed by images and video. Video fingerprinting is a CBIR technique that creates a digital descriptor, also known as a fingerprint, for videos based on its content. These fingerprints are then saved to a database and used to detect unknown videos by comparing the unknown video's fingerprint to the fingerprints in the database to get a match. Many techniques have already been proposed with various levels of success, but most of the existing techniques focus mainly on robustness and neglect the speed of implementation. In this dissertation a novel video fingerprinting technique will be developed with the main focus on detecting advertisements in a television broadcast. Therefore the system must be able to process the incoming video stream in real-time and detect all the advertisements that are present. Even though the algorithm has to be fast, it still has to be robust enough to handle a moderate amount of distortions. These days video fingerprinting still holds many challenges as it involves characterizing videos, made up of sequences of images, effectively. This means the algorithm must somehow imitate the inherent ability of humans to recognize a video almost instantly. The technique uses the content of the video to derive a fingerprint, thus the features used by the fingerprinting algorithm should be robust to distortions that don't affect content according to humans.Master