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.

There exists heightened research attention afforded to the pivotal demands - both internal and external - that exist within the salesperson role set. Unprecedented pressures on salespersons to acquire, retain, and build enduring customer relationships to enhance the firm's bottom-line performance coincides with increasing complexities within the work environment. This relevant and timely research introduces an original construct derived from the long-standing attention afforded to relationship selling, relational incongruity that exists within the buyer-seller exchange. Relational incongruity, defined, is the relational tension spawned between the salesperson, the customer, and the firm when situational psychological incongruity exists within the buyer-seller exchange itself. Framed in resource-advantage theory, this research investigates divergent demands and the increasing complexity of sales relationships through the lens of relational incongruity. A research program based on minimizing relational incongruity will augment the sales management and B2B literature by looking at how he salesperson and the customer build strong relationships as well as the antecedents that can undermine these relationships by generating realtional incongruity.

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.

This dissertation thesis describes the phenomenon of audiovisual performance in different connotations. A substantial part is devoted to psychological survey into my own subconscious and subsequently to metaphorical processing of this introspection. An important part of the work is a resume of the general knowledge of the physical properties and its metaphorical application on mental and creative processes. This analysis and explanation of internal cognitive models are implemented in terms of the study of relationships, interactions based on cooperation or confrontation, but also the inability to grasp the objective reality from the subjective position due to the merged distinctions of real and fictional. The importance of audiovisual performance is also studied in linear perspective of history, in order to point out the general principle of repetition patterns, which reveals that audiovisual performances is an activity which is a necessary expression of life itself and not just the concept in the field of arts.