UNSW Canberra
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(2023) Lee, EthanThesisTo study the distribution of prime ideals in a number field, there are two important results which must be considered: Mertens’ theorems for number fields and the prime ideal theorem. The prime ideal theorem is a stronger result on average, but its effective version can face significant technical issues. It is not immediately obvious, but an effective version of Mertens' theorems for number fields (which we prove in Theorem 1.1.3) avoids all of the technical issues that present in the effective prime ideal theorem. Several ingredients are needed to prove Theorem 1.1.3. The most important ingredient is an explicit estimate for the idealcounting function. This explicit estimate is of independent interest too, because it generalises the widely useful floor function into the number fields setting. Therefore, we update the latest explicit estimate for the idealcounting function in Theorem 3.1.1. Because there are no technical obstructions to consider, Theorem 1.1.3 can be applied more broadly than the prime ideal theorem. In particular, for an irreducible polynomial g with integer coefficients and sufficiently large rational primes p, there is an explicit connection between the number of solutions to the congruence g(x) = 0 modulo p and the prime ideals in a certain number field; we prove this in Lemma 5.2.1. Now, this number at each p defines a multiplicative function that unlocks nice applications in sieve methods, such as bounds on the number of rational primes represented by a polynomial. Therefore, we use Lemma 5.2.1 and Theorem 1.1.3 to establish explicit Nagell theorems in Corollary 5.1.1; these are weighted Mertens' theorems that appear in the literature pertaining to sieve methods. Using Corollary 5.1.1, we then prove an explicit formula for the number k of irreducible factors of a polynomial with integer coefficients; this is presented in Corollary 5.1.3. A deterministic algorithm to compute k emerges from this formula. To demonstrate what would be possible if the farreaching Generalised Riemann Hypothesis (GRH) was proven, we establish conditional versions of our main results throughout as well.

(2023) Rana, Md JuelThesisThis thesis focuses on improving the energy management strategies for Community Microgrids (CMGs), which are expected to play a crucial role in the future smart grid. CMGs bring many benefits, including increased use of renewable energy, improved reliability, resiliency, and energy efficiency. An Energy Management System (EMS) is a key tool that helps in monitoring, controlling, and optimizing the operations of the CMG in a costeffective manner. The EMS can include various functionalities like dayahead generation scheduling, realtime scheduling, uncertainty management, and demand response programs. Generation scheduling in a microgrid is a challenging optimization problem, especially due to the intermittent nature of renewable energy. The power balance constraint, which is the balance between energy demand and generation, is difficult to satisfy due to prediction errors in energy demand and generation. Realtime scheduling, which is based on a shorter prediction horizon, reduces these errors, but the impact of uncertainties cannot be completely eliminated. In regards to demand response programs, it is challenging to design an effective model that motivates customers to voluntarily participate while benefiting the system operator. Mathematical optimization techniques have been widely used to solve power system problems, but their application is limited by the need for specific mathematical properties. Metaheuristic techniques, particularly Evolutionary Algorithms (EAs), have gained popularity for their ability to solve complex and nonlinear problems. However, the traditional form of EAs may require significant computational effort for complex energy management problems in the CMG. This thesis aims to enhance the existing methods of EMS in CMGs. Improved techniques are developed for dayahead generation scheduling, multistage realtime scheduling, and demand response implementation. For generation scheduling, the performance of conventional EAs is improved through an efficient heuristic. A new multistage scheduling framework is proposed to minimize the impact of uncertainties in realtime operations. In regards to demand response, a memetic algorithm is proposed to solve an incentivebased scheme from the perspective of an aggregator, and a pricebased demand response driven by dynamic price optimization is proposed to enhance the electric vehicle hosting capacity. The proposed methods are validated through extensive numerical experiments and comparison with stateoftheart approaches. The results confirm the effectiveness of the proposed methods in improving energy management in CMGs.

(2023) Le, AnhThesisAlthough forest biomass estimation has attracted a great number of studies using remote sensing data, its usage still contains high uncertainties. After transitioning from deforestation to reforestation under the development of Payments for Environmental Services (PES) programmes, young forests that are dominated by numerous small regenerating understory trees are found in many areas of many developing countries. However, the lack of analysis on the effect of this understory vegetation on total AGB is one the limitations of biomass studies. Moreover, it is always challenging to estimate the biomass of tropical forest due to its complex structure, high diversity of species, and dense canopy of understory trees. Taking into account these factors, this study, therefore, aims to investigate the effect of including understory trees in accuracy of AGB estimation in complex tropical heterogeneous forest at the local scale. The research conducted three consecutive experiments, using different remote sensing data sources, being: optical data, synthetic aperture radar (SAR) data and the integration of optical and SAR data, across various forest types in different test site locations. The results provide comprehensive insights into the impact of small regenerating trees on improving AGB estimation. This major finding alone demonstrates that the role of small regenerating trees should not be automatically discounted, especially for tropical forest where a number of different tree layers is common. This is especially important in areas with a large number of small regenerating trees and where open canopy layers are young. The thesis reveals that the level of influence of small regenerating trees on each forest type is different. Therefore, the study recommends an approach to including small regenerating trees for each forest type. This thesis argues there is a need to develop localspecific allometric equations for both overstory and understory layers to improve the accuracy of biomass models. Methods required for collecting field data and calculating biomass for small regenerating trees should be considered carefully in terms of evaluating costeffective biomass estimation for each ecological region and each species. This requirement is most critical for young forest sites where there are mixtures of mature trees and young regenerating trees.

(2023) Cotton, AnthonyThesisThe study of employee engagement has been a key focus of management for over three decades. The academic literature on engagement has generated multiple definitions but there are two primary models of engagement: the Personal Engagement Model of Kahn (1990), and the Work Engagement Model (WEM) of Schaufeli et al., (2002). While the former is cited by most authors as the seminal work on engagement, research has tended to focus on elements of the model and most theoretical work on engagement has predominantly used the WEM to consider the topic. The purpose of this study was to test all the elements of the nomological network of the PEM to determine whether the complete model of personal engagement is viable. This was done using data from a large, complex public sector workforce. Survey questions were designed to test each element of the PEM and administered to a sample of the workforce (n = 3,103). The scales were tested and refined using confirmatory factor analysis and then the model was tested determine the structure of the nomological network. This was validated and the generalisability of the final model was tested across different work and organisational types. The results showed that the PEM is viable but there were differences from what was originally proposed by Kahn (1990). Specifically, of the three psychological conditions deemed necessary for engagement to occur, meaningfulness, safety, and availability, only meaningfulness was found to contribute to employee engagement. The model demonstrated that employees experience meaningfulness through both the nature of the work that they do and the organisation within which they do their work. Finally, the findings were replicated across employees in different work types and different organisational types. This thesis makes five contributions to the engagement paradigm. It advances engagement theory by testing the PEM and showing that it is an adequate representation of engagement. A model for testing the causal mechanism for engagement has been articulated, demonstrating that meaningfulness in work is a primary mechanism for engagement. The research has shown the key aspects of the workplace in which employees experience meaningfulness, the nature of the work that they do and the organisation within which they do it. It has demonstrated that this is consistent across organisations and the type of work. Finally, it has developed a reliable measure of the different elements of the PEM which will support future research in this area.

(2023) Francis, ForrestThesisIn analytic number theory, the most natural generalisations of the famous Riemann zeta function are the Dirichlet Lfunctions. Each Dirichlet Lfunction is attached to a qperiodic arithmetic function for some natural number q, known as a Dirichlet character modulo q. Dirichlet characters and Lfunctions encode with them information about the primes, especially in reference to their remainders modulo q. For this reason, number theorists are often interested in bounds on short sums of a Dirichlet character over the integers. For one, such sums appear as an intermediate step in partial summation bounds for Dirichlet Lfunctions. However, short character sum estimates may also be used directly to tackle other number theoretic problems. In this thesis, we wish to examine the application of character sum estimates in some specific settings. There are three main estimates that we are interested in: the trivial bound, Burgess’ bound, and the Pólya–Vinogradov inequality. Of these, we will focus primarily on Burgess’ bound; the main result of this thesis will be the computation of explicit constants versions of Burgess’ bound for a variety of parameters, improving upon the work of Treviño [54]. The interplay between Burgess’ bound and the Pólya–Vinogradov inequality is vital in this explicit setting, and we will dedicate a portion of this thesis to investigating these interactions. This makes precise the work of Fromm and Goldmakher [21], who demonstrated a counterintuitive influence the Pólya–Vinogradov inequality has on Burgess’ bound. Once we have established improvements to Burgess’ bound in the explicit setting, we will “test” these improvements by tackling several applications where Burgess’ bound has been used previously. Primary among these is an explicit bound for Lfunctions across the critical strip. We also include applications to normEuclidean cyclic fields and least kth power nonresidues.

(2023) Liu, BoThesisThere are a large number of settlement records in the literature showing that the creep settlement of shallow foundations on sand can increase over decades to a magnitude comparable to the immediate settlement. However, in most of the existing settlement prediction methods, the creep settlement of footings on sand is either ignored or accounted for using an arbitrary empirical multiplier, which has been identified as one of the major reasons for the poor predictability of these methods. The objectives of this study are to establish a method that can explicitly account for the timedependent behaviour of footings on sand in a realistic manner and to explore its potential use in practice. To achieve the goal, the research included three parts, starting with understanding the timedependent behaviour of sand that derives the timedependency of footings on sand using the discrete element method (soil element scale), followed by the formulation and validation of the footing modelling method (footing scale), and the application of the proposed method in soil–structure analysis (structure system scale). At the soil element scale, the creep and aging behaviour of sand in triaxial conditions is studied using the discrete element method. The macro and microscopic responses of the discrete element models of sand subjected to successive triaxial shear, creep and postcreep shear are studied and analysed. Increases in soil stiffness and strength are observed in the simulations as the consequence of imposing a creep period. The analysis of the stress–dilatancy behaviour reveals that the development of interlocking between sand particles during creep is the cause of these aging effects. At the foundation scale, an elastoviscoplastic macroelement model that can simulate the timedependent behaviour of footings on sand is constructed based on the nonstationary flow surface theory. The macroelement model with only three parameters is found capable of replicating the time effects of footings seen in practice, such as postcreep stiffening and settlements induced by unloadreload cycles. The data from more than fifty fullscale footing load tests are employed to validate the macroelement model, which confirms the applicability of the proposed method to foundations on sand under typical working load conditions. Guidelines are provided for the determination of model parameters based on cone penetration test results. Besides, the macroelement model is applied to formulate a settlement correction factor for creep. With the correction factor, the longterm settlement of a footing on sand can be predicted from the observed immediate settlement. At the scale of a structure system, centrifuge experiments are performed to study the soil–structure interaction in 3Dprinted framed structures of different stiffnesses supported by spread footings on different soils. The magnitude of load redistribution induced by soil–structure interaction is found to be greatly influenced by the relative structure–soil stiffness. The effect of the timedependent behaviour of foundations on soil–structure interaction is further studied based on a proposed numerical method that integrates the macroelement model with superstructure analysis. The method is validated with the results from the centrifuge experiments and applied to shed light on the timedependent soil–structure interaction in the long term.

(2023) Sharififar, ArmanThesisThis thesis considers the problem of efficient broadcast in a system where a single server transmits a set of messages to a number of users via a noiseless broadcast channel. Each user requests one specific message and may know some of the other messages a priori as its side information. This problem is known as the index coding problem and was first introduced by Birk and Kol [Birk and Kol, 1998], in the context of satellite communications. Exploiting the side information of the receivers along with the coding techniques at the server can reduce the number of transmissions to satisfy all the receivers. The simple model in index coding can establish a useful framework for studying other research areas, including network coding, distributed storage systems, and coded caching. In this thesis, index coding is approached from a new perspective to propose a new scalar linear coding scheme called the updatebased maximum column distance (UMCD) coding scheme. In the beginning, the receivers are sorted based on the size of their side information. Then, in each transmission, a linear combination of the messages is designed to instantaneously satisfy one of the receivers with the minimum size of side information. Then, the problem is updated by eliminating all receivers who are able to decode their requested message from the coded messages received so far along with the messages in their side information. This process is repeated until all receivers can successfully decode their requested message. Concrete instances are provided to show that the proposed UMCD coding scheme has a better broadcast performance compared to the most efficient existing coding schemes, including the recursive coding scheme (Arbabjolfaei and Kim, 2014) and the interlinkedcycle cover coding scheme (Thapa et al., 2017). Also in this thesis, the insufficiency of linear coding and the necessity of nonlinear codes for index coding problem are investigated, with two main contributions. First, while the insufficiency of linear coding has been proved for network coding (Dougherty et al., 2005), groupcast index coding (Effros et al., 2015), and asymmetricrate unicast index coding (Maleki et al., 2014), it remained an open problem for symmetricrate unicast index coding. In this thesis, we settle this open question by constructing two symmetricrate unicast index coding instances of sizes 33 and 36 for which optimal linear coding is outperformed by nonlinear codes. Second, while it has been known that the insufficiency of linear coding is due to the dependency of its rate on the field size, this dependency has been illustrated only over fields with characteristic two. In this thesis, we extend this limit to the fields with characteristic three by constructing two index coding instances of size 29. It is shown that while for the first instance, linear coding is optimal only over fields with characteristic three, for the second instance, linear coding over any fields with characteristic three can never be optimal. Finally in this thesis, a new coding scheme called the independent user partition multicast (IUPM) is proposed for the groupcast index coding. It is proved that the proposed IUPM coding scheme includes the two most efficient coding schemes, namely the user partition multicast (Shanmugam et al., 2015) and the packet partition multicast (Tehrani et al., 2012), as special cases. Then, a new polynomialtime algorithm for solving the general groupcast index coding problem is proposed. We show that the proposed heuristic algorithm can outperform the approximation partition multicast coding scheme (Unal and Wagner, 2016) for a class of groupcast index coding instances.

(2023) Rajamohan, DeepakThesisThe future of applications such as lastmile delivery, infrastructure inspection and surveillance bets big on employing small autonomous drones and ground robots in cluttered urban settings where precise positioning is critical. However, when navigating close to buildings, GPSbased localisation of robotic platforms is noisy due to obscured reception and multipath reflection. Localisation methods using introspective sensors like monocular and stereo cameras mounted on the platforms offer a better alternative as they are suitable for both indoor and outdoor operations. However, the inherent drift in the estimated trajectory is often evident in the 7 degrees of freedom that captures scaling, rotation and translation motion, and needs to be corrected. The theme of the thesis is to use a preexisting 3D model to supplement the pose estimation from a visual navigation system, reducing incremental drift and thereby improving localisation accuracy. The novel framework developed for the monocular camera first extracts the geometric relationship between the pixels of the calibrated camera and the 3D points on the model. These geometric constraints, when used in addition to the relative pose constraints typically used in Simultaneous Localisation and Mapping (SLAM) algorithms, provide superior trajectory estimation. Further, scale drift correction is proposed using a novel $SIM_3$ optimisation procedure and successfully demonstrated using a unique dataset that embodies many urban localisation challenges. Techniques developed for Stereo camera localisation aligns the textured 3D stereo scans with respect to a 3D model and estimates the associated camera pose. The idea is to solve the image registration problem between the projection of the 3D scan and images whose poses are accurately known with respect to the 3D model. The 2D motion parameters are then mapped to the 3D space for camera pose estimation. Novel image registration techniques are developed which use image edge information combined with traditional approaches to show successful results.

(2023) CullyHugill, MichaelaThesisThis thesis presents new explicit results on the distribution of prime numbers. The results largely fall into the categories of error estimates for the prime number theorem (PNT) and interval estimates for primes. The error in the PNT can be estimated with the truncated Riemannvon Mangoldt explicit formula \begin{equation*} \psi(x) = x  \sum_{\gamma \leq T} \frac{x^\rho}{\rho} + E(x,T), \end{equation*} where $\rho=\beta + i\gamma$ represents the nontrivial zeros of the Riemann zetafunction. A new explicit version of Goldston's estimate for $E(x,T)$ \cite{Goldston_83} is proved, of order \begin{equation*} E(x,T) = O\left( \frac{x\log x \log\log x}{T} \right). \end{equation*} This estimate is used to update two shortinterval results: we prove that there are primes between cubes, i.e., in intervals $(n^3,(n+1)^3)$, for all $n\geq \exp(\exp(32.537))$, and primes between $n^{155}$ and $(n+1)^{155}$ for all $n\geq 1$. The proof follows the original method of Ingham \cite{Ingham_37}, and builds on work of Dudek \cite{Dudek_16p}. We also prove and use a new update to Bertrand's conjecture of primes in $(n, 2n2)$ for integers $n > 3$. The methods of Ramar{\'e} and Saouter \cite{R_S_2003intervals} and Kadiri and Lumley \cite{K_L_14} are used to give new pairs $(\Delta, x_0)$ for which there exist at least one prime in $((1  \Delta^{1})x, x]$ for all $x\geq x_0$. For instance, we can take $(x_0,\Delta) = (e^{150}, 2.07\cdot 10^{11})$. Lastly, new conditional results are proved for the error in the PNT. Under the Riemann hypothesis (RH), we prove an explicit error estimate for the PNT in short intervals, and a meanvalue estimate of the same. The latter is based on the work of Selberg \cite{Selberg_43}. The meanvalue estimate is particularly of interest for its applications, of which two are given. We first prove that under RH, there is a prime in $(y, y+ 37 \log^2 y]$ for at least half the $y\in [x,2x]$ and all $x\geq 2$. The second application is to Goldbach numbers: we prove that under RH there is a Goldbach number in $(x,x+ 864 \log^2 x]$ for all $x\geq 2$.

(2023) Sarfaraz, AaliyaThesisSupply chains have progressed through time from being limited to a few regional traders to becoming complicated business networks. As a result, supply chain management systems now rely significantly on the digital revolution for the privacy and security of data. Due to key qualities of blockchain, such as transparency, immutability and decentralization, it has recently gained a lot of interest as a way to solve security, privacy and scalability problems in supply chains. However conventional blockchains are not appropriate for supply chain ecosystems because they are computationally costly, have a limited potential to scale and fail to provide trust. Consequently, due to limitations with a lack of trust and coordination, supply chains tend to fail to foster trust among the network’s participants. Assuring data privacy in a supply chain ecosystem is another challenge. If information is being shared with a large number of participants without establishing data privacy, access control risks arise in the network. Protecting data privacy is a concern when sending corporate data, including locations, manufacturing supplies and demand information. The third challenge in supply chain management is scalability, which continues to be a significant barrier to adoption. As the amount of transactions in a supply chain tends to increase along with the number of nodes in a network. So scalability is essential for blockchain adoption in supply chain networks. This thesis seeks to address the challenges of privacy, scalability and trust by providing frameworks for how to effectively combine blockchains with supply chains. This thesis makes four novel contributions. It first develops a blockchainbased framework with AttributeBased Access Control (ABAC) model to assure data privacy by adopting a distributed framework to enable fine grained, dynamic access control management for supply chain management. To solve the data privacy challenge, AccessChain is developed. This proposed AccessChain model has two types of ledgers in the system: local and global. Local ledgers are used to store business contracts between stakeholders and the ABAC model management, whereas the global ledger is used to record transaction data. AccessChain can enable decentralized, finegrained and dynamic access control management in SCM when combined with the ABAC model and blockchain technology (BCT). The framework enables a systematic approach that advantages the supply chain, and the experiments yield convincing results. Furthermore, the results of performance monitoring shows that AccessChain’s response time with four local ledgers is acceptable, and therefore it provides significantly greater scalability. Next, a framework for reducing the bullwhip effect (BWE) in SCM is proposed. The framework also focuses on combining data visibility with trust. BWE is first observed in SC and then a blockchain architecture design is used to minimize it. Full sharing of demand data has been shown to help improve the robustness of overall performance in a multiechelon SC environment, especially for BWE mitigation and cumulative cost reduction. It is observed that when it comes to providing access to data, information sharing using a blockchain has some obvious benefits in a supply chain. Furthermore, when data sharing is distributed, parties in the supply chain will have fair access to other parties’ data, even though they are farther downstream. Sharing customer demand is important in a supply chain to enhance decisionmaking, reduce costs and promote the final end product. This work also explores the ability of BCT as a solution in a distributed ledger approach to create a trustenhanced environment where trust is established so that stakeholders can share their information effectively. To provide visibility and coordination along with a blockchain consensus process, a new consensus algorithm, namely Reputationbased proofof cooperation (RPoC), is proposed for blockchainbased SCM, which does not involve validators to solve any mathematical puzzle before storing a new block. The RPoC algorithm is an efficient and scalable consensus algorithm that selects the consensus node dynamically and permits a large number of nodes to participate in the consensus process. The algorithm decreases the workload on individual nodes while increasing consensus performance by allocating the transaction verification process to specific nodes. Through extensive theoretical analyses and experimentation, the suitability of the proposed algorithm is well grounded in terms of scalability and efficiency. The thesis concludes with a blockchainenabled framework that addresses the issue of preserving privacy and security for an openbid auction system. This work implements a bid management system in a private BC environment to provide a secure bidding scheme. The novelty of this framework derives from an enhanced approach for integrating BC structures by replacing the original chain structure with a tree structure. Throughout the online world, user privacy is a primary concern, because the electronic environment enables the collection of personal data. Hence a suitable cryptographic protocol for an openbid auction atop BC is proposed. Here the primary aim is to achieve security and privacy with greater efficiency, which largely depends on the effectiveness of the encryption algorithms used by BC. Essentially this work considers Elliptic Curve Cryptography (ECC) and a dynamic cryptographic accumulator encryption algorithm to enhance security between auctioneer and bidder. The proposed ebidding scheme and the findings from this study should foster the further growth of BC strategies.