Co-constructing self-efficacy narratives : a study of four mature age university students

This thesis reports on a study in which research participants, four mature aged females starting an undergraduate degree at a regional Australian university, collaborated with the researcher in co-constructing a self-efficacy narrative. For the purpose of the study, self-efficacy was conceptualized as a means by which an individual initiates action to engage in a task or set of tasks, applies effort to perform the task or set of tasks, and persists in the face of obstacles encountered in order to achieve successful completion of the task or set of tasks. Qualitative interviews were conducted with the participants, initially investigating their respective life histories for an understanding of how they made the decision to embark on their respective academic program. Additional data were generated from a written exercise, prompting participants to furnish specific examples of self-efficacy. These data were incorporated into the individual's self-efficacy narrative, produced as the outcome of the "narrative analysis". Another aspect of the study entailed "analysis of narrative" in which analytic procedures were used to identify themes common to the self-efficacy narratives. Five main themes were identified: (a) participants' experience of schooling . for several participants their formative experience of school was not always positive, and yet their narratives demonstrated their agency in persevering and taking on university-level studies as mature aged persons; (b) recognition of family as an early influence . these influences were described as being both positive, in the sense of being supportive and encouraging, as well as posing obstacles that participants had to overcome in order to pursue their goals; (c) availability of supportive persons – the support of particular persons was acknowledged as a factor that enabled participants to persist in their respective endeavours; (d) luck or chance factors were recognised as placing participants at the right place at the right time, from which circumstances they applied considerable effort in order to convert the opportunity into a successful outcome; and (e) self-efficacy was identified as a major theme found in the narratives. The study included an evaluation of the research process by participants. A number of themes were identified in respect of the manner in which the research process was experienced as a helpful process. Participants commented that: (a) the research process was helpful in clarifying their respective career goals; (b) they appreciated opportunities provided by the research process to view their life from a different perspective and to better understand what motivated them, and what their preferred learning styles were; (c) their past successes in a range of different spheres were made more evident to them as they were guided in self-reflection, and their self-efficacious behaviour was affirmed; and (d) the opportunities provided by their participation in the research process to identify strengths of which they had not been consciously aware, to find confirmation of strengths they knew they possessed, and in some instances to rectify misconceptions they had held about aspects of their personality. The study made three important contributions to knowledge. Firstly, it provided a detailed explication of a qualitative narrative method in exploring self-efficacy, with the potential for application to other issues in educational, counselling and psychotherapy research. Secondly, it consolidated and illustrated social cognitive theory by proposing a dynamic model of self-efficacy, drawing on constructivist and interpretivist paradigms and extending extant theory and models. Finally, the study made a contribution to the debate concerning the nexus of qualitative research and counselling by providing guidelines for ethical practice in both endeavours for the practitioner-researcher.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Application of electrical resistivity method to detect deep cracks in unsaturated residual soil slope

Crack is a significant influential factor in soil slope that could leads to rainfall-induced slope instability. Existence of cracks at soil surface will decrease the shear strength and increase the hydraulic conductivity of soil slope. Although previous research has shown the effect of surface-cracks in soil stability, the influence of deep-cracks on soil stability is still unknown. The limited availability of deep crack data due to the difficulty of effective investigate methods could be one of the obstacles. Current technology in electrical resistivity can be used to detect deep-cracks in soil. This paper discusses deep cracks in unsaturated residual soil slopes in Indonesia using electrical resistivity method. The field investigation such as bore hole and SPT tests was carried out at multiple locations in the area where the electrical resistivity testing have been conducted. Subsequently, the results from bore-hole and SPT test were used to verify the results of the electrical resistivity test. This study demonstrates the benefits and limitations of the electrical resistivity in detecting deep-cracks in a residual soil slopes.

Inexact uniformization method for computing transient distributions of Markov chains

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.