Vaccination has been used to control the spread of infectious diseases for centuries with widespread success. Deterministic models studying the spread of infectious disease often use the assumption of mass vaccination; however, these models do not allow for the inclusion of human behaviour. Since current vaccination campaigns are voluntary in nature, it is important to extend the study of infectious disease models to include the effects of human behaviour. To model the effects of vaccination behaviour on the spread of influenza, we examine a series of models in which individuals vaccinate according to memory or individual decision-making processes based upon self-interest. Allowing individuals to vaccinate proportionally to an exponentially decaying memory function of disease prevalence, we demonstrate the existence of a Hopf bifurcation for short memory spans. Using a game-theoretic influenza model, we determine that lowering the perceived vaccine risk may be insufficient to increase coverage to established target levels. Utilizing evolutionary game theory, we examine models with imitation dynamics both with and without a decaying memory function and show that, under certain conditions, periodic dynamics occur without seasonal forcing. Our results suggest that maintaining diseases at low prevalence with voluntary vaccination campaigns could lead to subsequent epidemics following the free-rider dilemma and that future research in disease control reliant on individual-based decision-making need to include the effects of human behaviour.

The relevance of places to people has been questioned in recent times, as the world has become increasingly globalised and people more mobile. The aim of this research was to explore the relationship between sense of place and people’s behaviour in ‘ordinary’, everyday places. This contrasts with much prior research, which has focused on ‘special’ places, such as national parks and impressive landscapes in order to investigate the components of sense of place. Most people do not live in such places, but inhabit ordinary places in (sub) urban contexts. The research questions were: How does sense of place manifest in an ordinary, everyday landscape? In what ways can social learning impact upon the dynamics of sense of place? Can a more salient sense of place affect people’s attitudes towards and behaviour within their local area? Using an action research approach, pre- and post-interviews and three workshops to create a sustainable future vision at a neighbourhood level of scale, and the town as a whole, were held with fourteen residents of East Bolton, in the North West of England. The activities were designed to facilitate interaction between the participants, so that meanings attributed to places could be shared and discussed. This approach allowed participants to see familiar places in new ways and to share perspectives. The key themes that emerged from this research were: the importance of childhood places; the impact of mobility – both physical and social mobility; the interdependence of places at various scales; and also self-efficacy and people’s ability to influence their surroundings. A key finding was that sense of place can be made more salient for people in ‘ordinary’ landscapes, particularly if people are given direct experience of their places and opportunities to share and reflect on their perceptions relating to place. Social learning, however, takes time and requires resources to create opportunities to influence the salience of sense of place. The findings point to the value of promoting social learning through engagement activities. Planners, regeneration project officers and citizen groups could utilise sense of place as an organising principle to explore place meanings and as a catalyst for stimulating local action. Participants found it more difficult to discuss sense of place at the neighbourhood level of scale than the town level of scale, partly owing to their differing conception of boundaries and lack of awareness of the neighbourhood beyond the home. This has implications for implementing the localism agenda, suggesting that local action and visioning needs to be situated within activities nested at a range of scales in order to be most effective. The drive towards localism may lead to more self-organising and activism emerging from outside of the formal planning system and becoming a force for collective place shaping. Thus, the benefits of developing a more salient sense of place may also have impacts in less formal ways, such as greater interest and involvement in neighbourhood affairs and increased capacity-building, from which community action could potentially emerge.

We introduce a new framework of generalized operators to handle vector valued distributions, intertwined evolution operators of B-evolution equations and Fokker Planck type evolution equations. Generalized operators capture these operators. The framework is a marriage between vector valued distribution theory and abstract harmonic analysis: a new convolution algebra is the offspring. The new algebra shows that convolution is more fundamental than operator composition. The framework is complete with a Hille-Yosida theorem for implicit evolution equations for generalized operators. Feller semigroups and processes fit perfectly into the framework of generalized operators. Feller semigroups are intertwined by the Chapman Kolmogorov equation. Our framework handles more complex intertwinements which naturally arise from a dynamic boundary approach to an absorbing barrier of a fly trap model: we construct an entwined pseudo Poisson process which is a pair of stochastic processes entwined by the extended Chapman Kolmogorov equation. Similarly, we introduce the idea of an entwined Brownian motion. We show that the diffusion equation of an entwined Brownian motion involves an implicit evolution equation on a suitable scalar test space. We end off by constructing a new convolution of operator valued measures which generalizes the convolution of Feller convolution semigroups. / Thesis (PhD)--University of Pretoria, 2015. / Mathematics and Applied Mathematics / Unrestricted

O estudo da evolução da concentração de elementos de uma reação química, conhecida como Cinética Química, é de extrema importância para a compreensão das complexas interações em sistemas biológicos. Uma maneira de descrever a cinética de uma reação química é utilizando um sistema de equações diferenciais ordinárias (EDOs). Uma vez que para resolver um sistema de equações diferenciais ordinárias pode ser uma tarefa difícil (ou mesmo inviável), métodos numéricos são utilizados para realizar simulações, ou seja, para obter concentrações aproximadas das espécies químicas envolvidas durante um determinado período de tempo. No entanto, quanto maior for o sistema simulado de EDOs, mais os métodos numéricos estão sujeitos a erros. Além disso, o aumento do tamanho do sistema muitas vezes resulta em simulações que são mais exigentes do ponto de vista computacional. Assim, o objetivo deste projeto de mestrado é o desenvolvimento de regras para simplificar os sistemas de equações diferenciais ordinárias que modelam a cinética de reações químicas e, portanto, a obtenção de um algoritmo para executar simulações numéricas de um modo mais rápido e menos propenso a erros. Mais do que diminuir o erro e o tempo de execução, esta simplificação possibilita o biólogo escolher a solução mais factível do ponto de vista de medida. Isso porque, a identificação dos sistemas (i.e., inferência dos parâmetros) requer que a concentração de todas as espécies químicas seja conhecida, ao menos em um certo intervalo de tempo. Contudo, em muitos casos, não é possível medir a concentração de todas as espécies químicas consideradas. Esta simplificação gera sistemas equivalentes ao original, mas que dispensa a utilização de certas concentrações de espécies químicas. Um sistema de equações diferenciais ordinárias pode ser simplificado considerando as relações de conservação de massa, que são equações algébricas. Além disso, no caso de reações enzimáticas, o sistema de equações diferenciais ordinárias pode ser simplificado pelo pressuposto de que a concentração do complexo enzima-substrato mantém-se constante, o que permite a utilização da equação de Michaelis-Menten. De todas as combinações possíveis das equações algébricas com as equações diferenciais, uma família de sistemas simplificados de EDOs foi construída, permitindo a escolha do sistema mais simples. Esta escolha segue um critério guloso que favorece a minimização do número de equações diferenciais e do número total de termos. As regras em desenvolvimento de simplificação dos sistemas de equações diferenciais ordinárias foram utilizados para projetar um algoritmo, que foi implementado usando a linguagem de programação Python. O algoritmo concebido foi testado utilizando instâncias artificiais. / The study of the evolution of the concentration of species in a chemical reaction, known as Chemical Kinetics, is of paramount importance for the understanding of complex interactions in biological systems. One way to describe the kinetics of a chemical reaction is using a system of ordinary differential equations (ODEs). Once to solve a system of ODEs can be a difficult (or even unfeasible) task, numerical methods are employed to carry out simulations, that is, to obtain approximated concentrations of the involved chemical species for a certain time frame. However, the larger is the simulated system of ODEs, the more numerical methods are subject to error. Moreover, the increase of the system size often results in simulations that are more demanding from the computational point of view. Thus, the objective is the development of rules to simplify systems of ODEs that models the kinetics of chemical reactions, hence obtaining an algorithm to execute numerical simulations in a faster way and less prone to error. More than decrease error and run time, this simplification allows the biologist to choose the most feasible solution from the point of view of measurement. This is because the identification of systems (i.e., inferring parameters) requires that the concentration of all chemical species is known, at least in a certain time interval. However, in many cases it is not possible to measure the concentration of all chemical species considered. This simplification creates systems equivalent to the original, but that does not require the use of certain concentrations of chemical species. A system of ODEs can be simplified considering the relations of mass conservation, which are algebraic equations. Furthermore, in the case of enzymatic reactions, the system of ODEs can be simplified under the assumption that the concentration of enzyme-substrate complex remains constant, which allows us to use the Michaelis-Menten equation. From all possible combinations of the algebraic equations with differential equations, a family of simplified systems of ODEs will be built, allowing the choice of a simplest system. This choice will follow a greedy criterion which favors the minimization of number of differential equations and the total number of terms. The rules under development to simplify systems of ODEs will be used to design an algorithm, which will be implemented using Python programming language. The designed algorithm will be tested using synthetic data.

In the last three decades, strategic management scholars have explored the organization’s need to reconfigure its capabilities to leverage opportunities in a changing environment. The first objective of this study was to identify the underlying elements of the managerial processes of dynamic capabilities, and to offer a reconceptualization of the dynamic capabilities construct. The second objective of this investigation was to determine how the reconceptualized dynamic capabilities construct could influence the alignment of ordinary capabilities. Findings from this investigation indicate that organizational processes and managerial processes are unique components of dynamic capabilities. In addition, these organizational processes were found to be significantly and positively correlated with the alignment of ordinary capabilities. Furthermore, managerial processes were found to moderate the relationship between organizational processes and one type of ordinary capability alignment (i.e. innovation-operations capability alignment). Taken together, the findings of this study support the notion that dynamic capabilities are context specific, and that understanding how they influence the organization’s ability to change is complex. The developments and findings in this study offer a reconceptualized and empirically tested framework for the capability alignment process, thereby providing a more comprehensive picture of the underlying processes.

The purpose of this paper is to investigate the impact of cross-listing on companies' performance. It is divided into two aspects, one in short-term and the other in long-term. In short-run study, 6 companies cross-listing in NYSE and Chinese market are in the sample. In pre-cross-listing period, the abnormal returns are mostly positive and remain stable; the cumulative abnormal returns are close to 0 and the difference among them is very small; but on the cross-listing day, all the companies' abnormal returns decline, and after that day, the abnormal returns still fluctuate around 0 while most of them are negative, and the difference among each company's cumulative abnormal return become large. In long-run study, by using multiple regression of 99 Chinese companies listed in th U.S. markets form 2007 to 2012, there is a significant positive relationship between total asset turnover and cross-listing at 5% significance level and there is a significantly negative relation between market value and cross-listing at 10%significance level; return on equity and return on asset are both positive with cross-llisting, but not significant.

abstract: Patients suffering from Retinitis Pigmentosa (RP), the most common type of inherited retinal degeneration, experience irreversible vision loss due to photoreceptor degeneration. The preservation of cone photoreceptors has been deemed medically relevant as a therapy aimed at preventing blindness in patients with RP. Cones rely on aerobic glycolysis to supply the metabolites necessary for outer segment (OS) renewal and maintenance. The rod-derived cone viability factor (RdCVF), a protein secreted by the rod photoreceptors that preserves the cones, accelerates the flow of glucose into the cone cell stimulating aerobic glycolysis. This dissertation presents and analyzes ordinary differential equation (ODE) models of cellular and molecular level photoreceptor interactions in health and disease to examine mechanisms leading to blindness in patients with RP. First, a mathematical model composed of four ODEs is formulated to investigate the progression of RP, accounting for the new understanding of RdCVF’s role in enhancing cone survival. A mathematical analysis is performed, and stability and bifurcation analyses are used to explore various pathways to blindness. Experimental data are used for parameter estimation and model validation. The numerical results are framed in terms of four stages in the progression of RP. Sensitivity analysis is used to determine mechanisms that have a significant affect on the cones at each stage of RP. Utilizing a non-dimensional form of the RP model, a numerical bifurcation analysis via MATCONT revealed the existence of stable limit cycles at two stages of RP. Next, a novel eleven dimensional ODE model of molecular and cellular level interactions is described. The subsequent analysis is used to uncover mechanisms that affect cone photoreceptor functionality and vitality. Preliminary simulations show the existence of oscillatory behavior which is anticipated when all processes are functioning properly. Additional simulations are carried out to explore the impact of a reduction in the concentration of RdCVF coupled with disruption in the metabolism associated with cone OS shedding, and confirms cone-on-rod reliance. The simulation results are compared with experimental data. Finally, four cases are considered, and a sensitivity analysis is performed to reveal mechanisms that significantly impact the cones in each case. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

Reading is regarded as one of the most important, but also most complex skills utilised to attain fluency (Snyman, 2016). In this study I argue that Namibians have not yet adopted reading as part of their culture, and this is believed to have contributed immensely to the high failure rate of learners and students in primary, secondary, and tertiary education. The purpose of this study was to investigate the contribution that reading can make towards ESL learning at Ordinary Level (OL) in Namibian Senior Secondary Schools. The research focused on the challenges pertaining to reading by contemplating the nature of the reading culture of OL learners, how the curriculum and textbooks model reading for OL learners, and how ESL teachers expose OL learners to reading in the classroom. This research was informed by the principles of the multiliteracies pedagogy of the New London Group (NLG) (1999), the work on social constructivism of Lev Vygotsky (1978), Stephen Krashen’s (1985) Input Hypothesis, as well as Jim Cummins’ (1984) distinction between BICS and CALP. Following a qualitative approach, a descriptive case study design was employed to explore why OL learners lack analytical and critical reading skills that would enable them to learn English from their engagement with the texts they read. Four purposively selected ESL teachers and eight stratified randomly selected learners from four Secondary Schools in the Khomas education region, Windhoek, participated in the study. Data were collected using open-ended surveys, non-participant classroom observation, semi-structured interviews, and document analysis. Using qualitative content analysis, five themes on the role of reading in ESL emerged from the raw data: reading experience, access to reading materials, inadequate curriculum, inadequate infrastructure, and the use of textbooks to enhance reading. The findings indicate that reading is not developed as a culture for the majority of OL learners, as OL learners indicated that they only read for school purposes, as opposed to reading for fun. The OL curriculum was found not to support reading, because reading is not part of the OL syllabus. As opposed to the Higher Level (HL), there are no prescribed reading materials for OL and the OL syllabus lacks proper guidance regarding integration of reading in ESL lessons. The study concludes that a great deal needs to be done to instil the love of reading in OL learners for them to reach the same level as HL learners. / Thesis (PhD)--University of Pretoria, 2019. / Humanities Education / PhD / Unrestricted

In this thesis, the dynamics of an isolated cavitation bubble submerged in a steady flow is studied numerically. A Lagrangian-Eulerian approach is considered, in which properties of the fluid are computed first by means of Eulerian methods (in this study the commercial CFD software Ansys Fluent 19 was used) and the trajectory of the bubble is then computed in a Lagrangian fashion, i.e. the bubble is considered as a small particle moving relative to the fluid, due to the effect of several forces depending on fluid's pressure field, fluid's velocity field and bubble's radius. Bubble's radius dynamics, modeled by Rayleigh-Plesset equation, has a big influence on its kinetics, so a special attention is given to it. Two study cases are considered. The first one, motivated by acoustic cavitation is concerned with the response of the bubble's radius in a static flow under the influence of an oscillatory pressure field, the second one studies the trajectory of the bubble submerged in a fluid passing by a Venturi tube and a sharp-edged orifice plate.

[pt] Na engenharia geotécnica, o conhecimento das propriedades geomecânicas de subsuperfície é fundamental aos cálculos de estabilidade. Na prática cotidiana, a estimativa dessa distribuição é realizada pelo geólogo/geotécnico responsável, que traça seções geológico- geotécnicas em função de sua experiência e da observação dos dados das investigações de campo e laboratório. Tais estimativas bidimensionais, porém, não contemplam a distribuição espacial. Assim, o objetivo deste trabalho é enriquecer a compreensão global do maciço com a previsão da distribuição tridimensional dessas propriedades. Utilizou-se o modelador geológico PETREL(TM) para a estimativa geoestatística da variação espacial dos valores de RMR e grau de fraturamento ao longo do maciço rochoso destinado à implantação da casa de força do Aproveitamento Hidrelétrico de Simplício. Essa distribuição foi estimada em função da disposição dos dados ao longo dos furos de sondagem localizados espacialmente no modelo. Também foi lançada a geometria da futura superfície de escavação, para que se pudesse avaliar qual a seção crítica de qualidade do maciço em relação aos taludes de corte. Essa seção foi então extraída do modelo com a distribuição ponto a ponto do valor de RMR, de onde foram obtidos os parâmetros de resistência c e Ø para a análise de estabilidade. Analisou-se então a estabilidade desse talude em um programa que permite essa variação espacial de parâmetros de resistência e, em paralelo também foram realizadas as análises convencionais de estabilidade de taludes rochosos, de forma a apresentar a importância da modelagem tridimensional para tal estudo. / [en] In geotechnical engineering, the knowledge of geomechanical subsurface properties is fundamental to stability analyses. The usual practice is that a geologist/geotechnical engineer does this distribution estimate. The professional makes some geologic-geotechnical sections based on his/her experience and by the observation of field/laboratory investigations data. But these 2D sections cannot take spatial distribution. To solve this problem and provide a better global comprehension of rock mass, this work presents a study of 3D property distribution. The geological modeler PETREL(TM) has been used to do a geostatistical estimate of RMR and fracture density spatial variety at the rock mass where the AHE Simplício`s power house will be installed. This distribution has been estimated based on data linked to the boreholes, spatially arranged at the model. The geometry of the future excavated surface was introduced in the model. The purpose was to carry out a study to find the critical quality section of the model related to the excavated slopes. This section was extracted with its RMR value distribution. Before the stability analysis, the resistance parameters c and Ø were calculated to every point on this section from the RMR correlations. The slope stability of the critical section was calculated in a program where the resistance parameters can vary point by point. The conventional rock slope stability analysis has been done too. At the end of the study, the first analysis was compared against the last one, proving the importance of the subsurface tridimensional modeling.