The purpose of this study was to examine cognitive complexity, extremity, and the relationship between social repertory grids and life events repertory grids (LERG) in people who report a history of trauma. Effects of type of trauma on complexity and extremity scores of each type of grid were examined. Prior research into repertory grids and trauma has used only one type of grid, predominantly social grids or LERGs. Therefore, a natural, progressive step in the grid research involved investigating how individuals integrate social and life event constructs. It was hypothesized, and results show, that there is a positive correlation between complexity scores and extremity scores of social grids and LERGs. However it was not found that there was a negative correlation between trauma history and complexity scores, and that trauma acts as a moderator for cognitive complexity. Instead, it appears that the social facet of experience is key to understanding perception of traumatic experiences. Additionally, number of traumas experienced might affect social construct elaboration.

The ongoing sustainability crisis offer numerous, multifaced societal challenges as a result of the ongoing degradation of socio-ecological systems by human activity causing massive ecological damage and human suffering. Overcoming these difficulties begs for the rapid transition of society towards sustainability. This desire for urgent action has been hindered by the lack of coordinated global leadership focused on addressing these challenges and implementing a transition towards a sustainable future. The sustainability crisis and its manifestations, which include for example climate change, air and water pollution, deforestation and social segregation, are interconnected and volatile issues whose parts influence and impact each other causing the crisis to worsen. The earth system is pushed towards tipping points from beyond which it may become impossible to maintain the human civilization. The failure of leadership to address the wicked nature of these crises means humanity has been left ill-equipped to deal with the complex problems of sustainability.  This thesis considers the role of Education for Sustainable Development (ESD) in overcoming these issues and operating as a leverage point towards sustainability. It focuses on investigating how the development of sustainability leadership education in Higher Education can contribute to addressing the sustainability crisis. It looks at the role that educators can play in designing learning environments that ensure leaders and leadership capable of addressing wicked problems posed by global unsustainability. The aim of this research is to investigate what educators should consider when designing learning environments that promote the qualities needed for leading in complexity towards sustainability. It does this by examining a number of ESD programs as case studies to investigate the efficacy of those programs at creating sustainability outcomes within their students. It also undertakes a literature review to describe and articulate the unique challenges faced by sustainability leaders from a personal and professional perspective. The study is situated closely to the ongoing ESD discussion regarding competencies-based learning for sustainability and the research aims to provide some contribution to that dialogue. It does this through the investigation of competencies acquisition and the discussion of emerging areas of leadership that may hold beneficial outcomes for the development and practice of sustainability leaders.   The results of the thesis suggest a number of outcomes for consideration by educators and include a number of main findings. Firstly, educational programs can be capable of achieving the acquisition of ‘sustainability’ competencies within their students, but if these competencies are not taught within a larger sustainability contextualization, then students can fail to see the purpose of the competencies ‘for’ sustainability. Secondly, reflective practices, developed as the result of reflective pedagogies, can provide beneficial qualities in students as future sustainability leaders and require distinct pedagogical structures in order to guide reflective practices towards sustainability outcomes. Finally, a number of unique personal and professional challenges to sustainability leadership exist and need to be overcome if the domain of sustainability is to ensure the ongoing resilience and wellbeing of individuals and groups acting as sustainability leaders.   This research suggests a novel contribution to a number of areas within ESD research, including creating knowledge within the competencies discussion regarding emerging areas of study that may influence the future of defined sustainability competencies. It also highlights the need for educators to consider the role of wellbeing and resilience in current and future sustainability leaders.

Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.

Philosophiae Doctor - PhD / Health system in Sub-Saharan in Africa face multifaceted capacity challenges to fulfil their mandates of service provision and governance of their resources. Wide-ranging capacity development interventions exist to address these limitations. however, failure to take into account complexity into planning and implementation in the practice and research of these capacity development intervention predominate , hindering understanding and learning, and resulting in poor implementation or lack of sustainability of the capacity gains.

Massive MIMO systems are shown to be a promising technology for next generations of wireless communication networks. The realization of the attractive merits promised by massive MIMO systems requires advanced linear precoding and receiving techniques in order to mitigate the interference in downlink and uplink transmissions. This work considers the precoder and receiver design in massive MIMO systems. We first consider the design of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio (SINR) subject to a given power constraint. The analysis is carried out under the asymptotic regime in which the number of the BS antennas and that of the users grow large with a bounded ratio. This allows us to leverage tools from random matrix theory in order to approximate the parameters of the optimal linear precoder and receiver by their deterministic approximations. Such a result is of valuable practical interest, as it provides a handier way to implement the optimal precoder and receiver. To reduce further the complexity, we propose to apply the truncated polynomial expansion (TPE) concept on a per-user basis to approximate the inverse of large matrices that appear on the expressions of 4 the optimal linear transceivers. Using tools from random matrix theory, we determine deterministic approximations of the SINR and the transmit power in the asymptotic regime. Then, the optimal per-user weight coefficients that solve the max-min SINR problem are derived. The simulation results show that the proposed precoder and receiver provide very close to optimal performance while reducing significantly the computational complexity. As a second part of this work, the TPE technique in a per-user basis is applied to the optimal linear precoding that minimizes the transmit power while satisfying a set of target SINR constraints. Due to the emerging research field of green cellular networks, such a problem is receiving increasing interest nowadays. Closed form expressions of the optimal parameters of the proposed low complexity precoding for power minimization are derived. Numerical results show that the proposed power minimization precoding approximates well the performance of the optimal linear precoding while being more practical for implementation.

Philosophiae Doctor - PhD / The purpose of the present study is to enrich academic knowledge, the understanding of management theory, and professional management practice for leaders in a South African Higher Education Institution (HEI) under volatile, uncertain, complex, and ambiguous (VUCA) conditions. Due to increased globalisation and rapid changes in the technological, social, economic, and political spheres, the environment in which organisations function has become increasingly VUCA. These factors create a unique set of challenges for the leaders of these organisations. Traditionally tested and proven methods of leading organisations no longer guarantee high performance. The dynamic environment is challenging leaders to find new ways to be successful. To further complicate matters, the speed, frequency, and intensity with which the organisational environment is changing are ascending in nature. The field of Higher Education in South Africa demonstrates the challenges and opportunities VUCA imposes on organisational leadership.

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<div>In this dissertation, we study two important problems in the area of modern deep learning: adversarial robustness and adversarial generative model. In the first part, we study the generalization performance of deep neural networks (DNNs) in adversarial learning. Recent studies have shown that many machine learning models are vulnerable to adversarial attacks, but much remains unknown concerning its generalization error in this scenario. We focus on the $\ell_\infty$ adversarial attacks produced under the fast gradient sign method (FGSM). We establish a tight bound for the adversarial Rademacher complexity of DNNs based on both spectral norms and ranks of weight matrices. The spectral norm and rank constraints imply that this class of networks can be realized as a subset of the class of a shallow network composed with a low dimensional Lipschitz continuous function. This crucial observation leads to a bound that improves the dependence on the network width compared to previous works and achieves depth independence. We show that adversarial Rademacher complexity is always larger than its natural counterpart, but the effect of adversarial perturbations can be limited under our weight normalization framework. </div><div></div><div>In the second part, we study deep generative models that receive great success in many fields. It is well-known that the complex data usually does not populate its ambient Euclidean space but resides in a lower-dimensional manifold instead. Thus, misspecifying the latent dimension in generative models will result in a mismatch of latent representations and poor generative qualities. To address these problems, we propose a novel framework called Latent Wasserstein GAN (LWGAN) to fuse the auto-encoder and WGAN such that the intrinsic dimension of data manifold can be adaptively learned by an informative latent distribution. In particular, we show that there exist an encoder network and a generator network in such a way that the intrinsic dimension of the learned encodes distribution is equal to the dimension of the data manifold. Theoretically, we prove the consistency of the estimation for the intrinsic dimension of the data manifold and derive a generalization error bound for LWGAN. Comprehensive empirical experiments verify our framework and show that LWGAN is able to identify the correct intrinsic dimension under several scenarios, and simultaneously generate high-quality synthetic data by samples from the learned latent distribution. </div><div><br></div>

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Context: Node.js is an established web framework built using JavaScript. As a result, there are a wide variety of frameworks that have emerged that specialize in different quality attributes and functionalities. Some of which are heavily geared to performance and benchmarking while others might focus on security, availability, robustness, etc. Objectives: The project aims to explore different Node.js server-side frameworks and determine their maintainability using metrics such as Halstead metrics, Maintainability index, source line of code as well as Logical source lines of code. This thesis also explores if there is a correlation between the quality attributes maintainability and performance. Realization: In order to explore the different quality attributes, the thesis relied upon experiments and a literature review. The hierarchical method in this thesis was first to examine their performance, later examine their overall maintainability. Examined is also the impact of comments and how they can affect the results of the maintainability index Results: The results indicate all the selected frameworks have a low-to borderline medium cyclomatic complexity, also a high degree of maintainability using two different 3 metric maintainability index formulas. The latency tests indicate the different frameworks produce similar performance results. Conclusion: Concluded in this thesis is, there seems to be no relationship between both lines of code, logical lines of code, and cyclomatic complexity. There also seems to be no correlation between Halstead volume and the overall maintainability index for both the 3 metric formulas used. There is a slight indication of a relationship between Halstead Effort and Cyclomatic Complexity using one of the 3 metric formulas i.e., as the cyclomatic complexity decreases the overall maintainability (using Halsted’s effort instead of Halstead’s volume) increases.