### Recent Submissions

• #### CEO Overconfidence and the Probability of Bankruptcy

This thesis examines the relation between CEO overconfidence and the probability of bankruptcy. In addition to the main research question, we develop two additional hypotheses. We evaluate the potential link or channel between CEO overconfidence and the probability of bankruptcy. In the relationship between CEO overconfidence and the probability of bankruptcy, we seek for any interaction effects of CEO dominance. It is not uncommon for CEOs to be overconfident about their firms' prospects. In our sample, we use data from the year 2000 to 2019 for US companies. We proxy the bankruptcy probability using Altman’s Z Score. We use a stock option-driven measure of overconfidence, and this measure assumes that non-overconfident CEO will exercise their stock options if it is in the money, while overconfident CEOs will hold stock options beyond a rational threshold. We construct both continuous and indicator-based measures of overconfidence to test the hypotheses. The empirical findings reveal that CEO overconfidence increases the probability of bankruptcy. We do not find any evidence in favor of overinvestment which we consider as a channel through which overconfidence leads to increased bankruptcy risk. We also find that dominant and overconfident CEOs are suited for innovative firms, implying that giving an overconfident CEO a dominant position can minimize a firm's probability of bankruptcy. The implications of this study are that firms should be cautious in hiring overconfident CEO and they should take measures to reduce the negative effects of CEO overconfidence like the probability of bankruptcy. One way to reduce the probability of bankruptcy in innovative firms is to appoint overconfident CEO into a dominant position.
• #### Implications of Non-Operating Room Anesthesia Policy for Operating Room Efficiency

This thesis focuses on examining the use of Non-Operating Room Anesthesia (NORA) policy in Operating Room (OR) scheduling. A NORA policy involves a practice whereby the administration of anesthesia stage is performed outside the OR. The goal of the thesis is to determine whether NORA policy can improve OR efficiency measured by the performance of total costs, which consists of a weighted sum of patient waiting time, OR overtime and idle time. A simulation optimization method is adopted to find near-optimal schedules for elective surgeries in an outpatient setting. The results of a traditional OR scheduling model, where all stages of the surgery are performed in the OR, will be compared to the results of a NORA OR model where the initial anesthesia stage is performed outside of the OR. Two cases are considered for the NORA model given the decrease on mean durations: (1) a model with the same number of surgery appointments and shorter session length and (2) a models with the same session length and more surgery appointments. . The impact of a NORA policy on OR performance is further analyzed by considering scenarios that capture Surgery duration variability and mean surgery durations which are two traits for surgeries that have been shown to impact OR performance. This thesis aims to investigate how a NORA policy performs when standard deviations and mean surgery durations change. The results show that NORA policy can improve OR efficiency in all settings.
• #### A Study on Immersion and Emotions’ Influence on Impulse Buying in Virtual Environments

Impulse buying has always been an interesting phenomenon that is observed in our daily lives. Statistics have shown that impulse purchases make up almost 40% of all purchases made online. Many studies have examined impulse buying, and they have found that emotions accompany impulsive behaviors naturally. With the recent development in virtual reality (VR) technology, this phenomenon is observable in online virtual environments. Retailers can create immersive virtual shops where the customer can walk among the aisles of a virtual store and make purchases. This study examines whether the effects of emotions on impulse buying vary across different immersion levels (2D vs. VR) and gender. To test our hypotheses, we collected data from the 2D and VR setting using experiments. The results provide evidence that gender plays a significant role in the three-way relationship between positive/negative emotions, immersion, and impulse buying. The unique setting of our research extends the literature on impulse buying, marketing, and virtual reality. The results offer valuable insights to marketers and retailers who want to develop virtual shops and influence impulse buying in these virtual shops.
• #### Examining The Influence of Social Augmented Reality Apps on Customer Relationships: The Mediating Role of Shared Social Experience

The development of augmented reality (AR) has provided firms with increasing opportunities to improve customer experiences, especially in a shared context where customers are encouraged to communicate with others. This study investigates the effectiveness of social AR in building relationships among customers through a shared social experience, one which includes shared sense of place, social interaction, and social identity. Data was collected from 378 active users of a social AR application and was analyzed using the partial least squares structural equation modelling (PLS-SEM) and Hayes’ PROCESS Macro. Results from this study show that shared sense of place, social interaction, and social identity mediate the influence of social AR past usage on customer-to-customer relationships, which consequently enhance customers’ continuance intention to use the social AR application. Additionally, the results of the moderated mediation analysis reveal that the indirect effect of social AR past usage on continuance intention is positively moderated by extraversion, such that at higher level of extraversion the mediated relationship becomes stronger. These findings offer important contributions to the AR marketing literature and add valuable insights for practitioners to advance the use of AR technology.
• #### The Effect of Perceived Deception on Consumer Repurchase Intention

Online commerce changes the way products are displayed. Bounded by less chance to present information of the product, e-retailers always face misunderstandings on the consumer side, and consequently, unfavourable consumer behaviour. This makes online retailing prone to perceived deceptive practice. Past research has mainly integrated perceived deception into existing consumer behavior theories. In the same vein, this research further examines the factors moderating the relationship between perceived deception and repurchase intention. Specifically, we tested how product type (hedonic versus utilitarian), consumer regulatory focus (promotion versus prevention), and their interaction can help mitigate perceived deception's negative effect on consumer repurchase intention. This research expands the literature on perceived deception. With the prior work establishing the negative effect of perceived deception on consumer purchase behaviour, this research further investigates the factors that may attenuate the unfavourable outcome. It also helps marketers increase repurchase rates by emphasizing the hedonic attribute and instigating promotion intention to help mitigate the negative effects of perceived deception.
• #### How Virtual Reality Leads to Positive Responses to Persuasion Attempts: The Implications of VR Brand Placement

Facebook has started to test advertising in virtual reality, yet consumers’ responses toward this phenomenon have been neglected in the virtual reality and consumer behaviour literature. Most of the previous research has focused on VR as the primary tool for representing the service or product and not a medium for advertising purposes. Therefore, brand placement in virtual environments, as one of the most common persuasive advertising efforts by brands, is the focus of this study. More specifically, this research analyzes the effect of brand placement context (VR, 360 or 2D) and placement congruity on consumers’ persuasion knowledge and their responses towards brands, using the cognitive load theory and persuasion knowledge model to predict and explain the effect. The research model was tested using PLS-SEM and the PROCESS macro with a sample of 209 participants. The results confirmed that participants who experienced a higher sense of telepresence and interactivity (VR condition) were more likely to report lower persuasion knowledge and better brand evaluations and behavioural intentions. It was also found that compared to the 360 condition, in VR and 2D environments, participants were more likely to recall the brand embedded into the environment. Placement congruity was found to moderate the underlying mechanism through which interactivity and telepresence affect persuasion knowledge. These findings provide helpful insights to marketers and brand managers, who think of VR as an advertising tool, on how the technology factor impacts consumers’ responses to their persuasion attempts, such as brand placements.
• #### The Influence of Perceived Value on Exploratory Behaviour Towards Future Patronage Intention in M-Commerce: An S-O-R Approach.

The exploratory behaviour issue has received considerable attention in both online and brick-and-mortar consumer behaviour literature so far. However, regarding the widely prevalent use of mobile commerce in daily life, surprisingly, mobile exploratory behaviour has seldom been investigated. It is unclear to what extent mobile commerce characteristics can facilitate explorative behaviour. Thus, this study aims to fill the gap in the extant literature by examining the positive relationship between the perceived value, namely, functional, emotional and social and exploration (diversive and specific), which in turn, directly impacts future patronage intention. Due to the pivotal role of flow state in computer-mediated and online behaviour in the extant literature, the current study set out to examine the mediation role of flow between the relationship of perceived values and divisive vs specific exploration. This thesis begins with a brief overview of the recent history of noted research elements and proposes the conceptual model based on the stimulate-organism-response (S-O-R) model. It then discussed the hypotheses development. The remaining part of the paper proceeds with details on the data collection process and the methodological approach adopted to test these relationships.
• #### Firm Performance and CEO Compensation: CEO Pay Slice vs Pay-Performance Sensitivity

I study the relationship between CEO incentive compensation and firm performance in the presence of CEO dominance to examine how incentive compensation improves firm performance by reducing agency conflicts between shareholders and managers. I estimate pay-performance sensitivity (PPS) as a measure of CEO incentive compensation and the CEO pay slice (CPS) as a measure of CEO dominance. Controlling for standard control variables, I conduct multiple OLS regressions and find that at the high level of CPS, PPS improves firm performance, but at the low level of CPS, impact of PPS diminishes. This shows that determining stand-alone associations of PPS or CPS to firm value—a popular practice in the literature—might not be adequate because of an unexplored interaction effect between executive incentive and executive dominance. To address the potential endogeneity issues, I conduct robustness check by employing instrumental variables with a two-stage least square (2SLS) estimation procedure. As an additional robustness check, I account for the year effect and confirm that the results still stand to the same level of significance.
• #### When Moneyball Meets the Beautiful Game: A Predictive Analytics Approach to Exploring Key Drivers for Soccer Player Valuation

To measure the market value of a professional soccer (i.e., association football) player is of great interest to soccer clubs. Several gaps emerge from the existing soccer transfer market research. Economics literature only tests the underlying hypotheses between a player’s market value or wage and a few economic factors. Finance literature provides very theoretical pricing frameworks. Sports science literature uncovers numerous pertinent attributes and skills but gives limited insights into valuation practice. The overarching research question of this work is: what are the key drivers of player valuation in the soccer transfer market? To lay the theoretical foundations of player valuation, this work synthesizes the literature in market efficiency and equilibrium conditions, pricing theories and risk premium, and sports science. Predictive analytics is the primary methodology in conjunction with open-source data and exploratory analysis. Several machine learning algorithms are evaluated based on the trade-offs between predictive accuracy and model interpretability. XGBoost, the best model for player valuation, yields the lowest RMSE and the highest adjusted R2. SHAP values identify the most important features in the best model both at a collective level and at an individual level. This work shows a handful of fundamental economic and risk factors have more substantial effect on player valuation than a large number of sports science factors. Within sports science factors, general physiological and psychological attributes appear to be more important than soccer-specific skills. Theoretically, this work proposes a conceptual framework for soccer player valuation that unifies sports business research and sports science research. Empirically, the predictive analytics methodology deepens our understanding of the value drivers of soccer players. Practically, this work enhances transparency and interpretability in the valuation process and could be extended into a player recommender framework for talent scouting. In summary, this work has demonstrated that the application of analytics can improve decision-making efficiency in player acquisition and profitability of soccer clubs.
• #### Risk-Taking and CEO Compensation: CEO Pay Slice Versus Pay-Volatility Sensitivity

This paper aims to analyze the impacts of compensation incentives and CEO power on firm’s risk-taking by using stock return volatility (Srisk) and earnings volatility (Erisk) as the proxies of firm’s risk-taking level, and by using pay-volatility sensitivity (PVS) and CEO-pay slice (CPS) as the proxies of compensation incentives and CEO power, respectively. By applying ordinary least square (OLS) regression and two-stage least square (2SLS) regression on obtained data, this paper provides strong empirical evidence that PVS and CPS have negative impact on earnings volatility and stock return volatility. In addition, the negative impact of PVS on managerial risk-taking is greater for CEOs with lower CPS than that for CEOs with higher CPS. That is, EBC discourages CEOs from taking more risks, and more powerful CEOs are less risk-averse than less powerful CEOs when granted EBC.
• #### Some New Estimator in Linear Mixed Models with Measurement error

Linear mixed models (LMMs) are an important tool for the analysis of a broad range of structures including longitudinal data, repeated measures data (including cross-over studies), growth and dose-response curve data, clustered (or nested) data, multivariate data, and correlated data. In many practical situations, the observation of variables is subject to measurement errors, and ignoring these in data analysis can lead to inconsistent parameter estimation and invalid statistical inference. Therefore, it is necessary to extend LMMs by taking the effect of measurement errors into account. Multicollinearity and fixed-effect variables with measurement errors are two well-known problems in the analysis of linear regression models. Although there exists a large amount of research on these two problems, there is by now no single technique superior to all other techniques for the analysis of regression models when these problems are present. In this thesis, we propose two new estimators using Nakamura's approach in LMM with measurement errors to overcome multicollinearity. We consider that prior information is available on fixed and random effects. The first estimator is the new mixed ridge estimator (NMRE) and the second estimator is the weighted mixed ridge estimator (WMRE). We investigate the asymptotic properties of these proposed estimators and compare the performance of them over the other estimators using the mean square error matrix (MSEM) criterion. Finally, a data example and a Monte Carlo simulation are also provided to show the theoretical results.
• #### Distress Effects in Stock Returns

This thesis addresses a fundamental topic in financial economics: the effects of distress risk in the cross section of equities returns. Initial results show that both raw and risk-adjusted excess returns are rising in distress risk, and the remainder of this thesis examines the general robustness of the distress premium. Accordingly, the additional excess returns to stocks having heightened levels of financial distress are contingent upon the stock price being low. These findings are then extended to demonstrate that these same stocks are also microcap firms, thus attributing the anomalous behaviour of distressed stocks to a common factor with many other market anomalies. The economic implication is that arbitrage profits are likely to be limited due to the high transaction costs alongside the limited investment capacity with associated low-priced, microcap stocks.
• #### Linear Forms in Logarithms and Fibonacci Numbers

The main work included in these pages is from a paper co-written by myself and my brother, Simon Earp-Lynch, under the supervision of Omar Kihel, pertaining to Diophantine triples of Fibonacci numbers. To go along with this will be introductory material not included in said paper which establishes the mathematical concepts therein and offers some historical perspective and motivation. The initial aim of the paper was to explore the possibility of a generalization of the main result in [2] on D(4)-Diophantine triples of Fibonacci numbers. The paper managed to extend the ideas in [2] to results for D(9)-Diophantine triples and D(64)-Diophantine triples. A generalization of Lemma 1 of [1] was also found, a lemma on Diophantine triples and Pellian equations which is key in establishing the main result in [2]. This paper includes this result and its proof, which involves a correction of the proof of Lemma 1 of [1]. This result may prove useful in the extension of the results in the paper, and potentially others as well. I will begin by introducing Diophantine equations, leading to Diophantine triples, followed by a section on the necessary preliminaries on Fibonacci num- bers, which concludes with the statements of our main results. Following this, I establish the primary machinery used in the proof of the main result, linear forms in logarithms. I then move to the generalization of the aforementioned Lemma 1 of [1], before finally commencing the proof of the main results.
• #### Diophantine Triples and Linear Forms in Logarithms

This is the thesis for my master's degree in mathematics which I undertook with Dr. Omar Kihel. Over the last couple of years I have studied number theory with the aim being to develop a broader understanding of the theory of Diophantine equations and their (at times) elusive solutions. I begin my thesis by establishing some of the preliminary results while touching on their place within the history of number theory. This section finishes with an account of Alan Baker's work on linear forms in logarithms and some of its applications, after which the two theorems on Diophantine triples that this paper will aim to prove are stated. In the second section, I list a series of definitions and results of which the reader must be aware, but which I could not fit into the first section due to its historical slant. Following this, I prove a lemma on Pellian equations which generalizes the first lemma of [1]. This requires that a mistake from the proof of that lemma be fixed. Since this lemma was used in [2], this section serves to buttress that result as well. In the next two sections, I prove the two main theorems using results on linear forms in logarithms of algebraic numbers, extending the main result in [2] to $D(9)$ and $D(64)$ triples. The thesis ends with a few words on potential generalization and improvement of the main results, as well as other potential avenues of inquiry, and draws attention to some potential difficulties. The main results closely follow a paper co-written with my brother, Benjamin Earp-Lynch.
• #### Upper Bounds for the Number of solutions for the Diophantine Equation $y^2=px(Ax^2-C), C \in {2, \pm 1, \pm 4}$

A Diophantine equation is an equation of more than one variable where we are looking for strictly integer solutions. The purpose of this paper is to give a new upper bounds for the number of positive solutions for the Diophantine equation $y^2 = px(Ax^2 − C), C \in {2, ±1, ±4}. Where p is an odd prime and A is an integer greater than 1. The case where C = −2 is already complete, which we go over in detail here. We look through examples of Diophantine equations starting with linear Diophantine equations. We then look at Pell’s equation,$x^2 − Dy^2 = C$where D and C are natural numbers. We show the continued fraction algorithm and how to use it to solve Pell’s equation. We will look at proofs and lemmas surrounding particular cases of the Diophantine equation$y^2 = px(Ax^2 − C)$. Then focus on finding the upper bounds of the equation. Then we conclude by showing the new upper bounds of the Diophantine equation$y^2 = px(Ax^2 − C), C \in {2, ±1, ±4}.
• #### Towards a New Algorithm for Event Recommendation System

We develop a recommendation algorithm for a local entertainment and ticket provider company. The recommender system predicts the score of items, i.e. event, for each user. The special feature of these events, which makes them very different from similar settings, is that they are perishable: each event has a relatively short and specific lifespan. Therefore there is no explicit feedback available for a future event. Moreover, there is a very short description provided for each event and thus the keywords play a more than usual important role in categorizing each event. We provide a hybrid algorithm that utilizes content-based and collaborative filtering recommendations. We also present an axiomatic analysis of our model. These axioms are mostly derived from social choice theory.
• #### Dynamics in large scale networks

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the massively multiplayer online game (MMOG) Planetside 2. We are particularly interested in removal patterns in these networks. Our main finding is that in both of these networks the nodes which are most commonly removed are minor near isolated nodes. We also investigate the process of merging of two large networks using data captured during the merger of servers of Planetside 2. We found that the original network structures do not really merge but rather they get gradually replaced by newcomers not associated with the original structures. In the final part of the thesis we investigate the concept of motifs in the Barabási-Albert random graph. We establish some bounds on the number of motifs in this graph.
• #### Community Detection in Multi-Layer Networks

In the scope of the current thesis we review and analyse networks that are formed by nodes with several attributes. We suppose that different layers of communities are embedded in such networks, besides each of the layers is connected with nodes' attributes. For example, examine one of a variety of online social networks: an user participates in a plurality of different groups/communities – schoolfellows, colleagues, clients, etc. We introduce a detection algorithm for the above-mentioned communities. Normally the result of the detection is the community supplemented just by the most dominant attribute, disregarding others. We propose an algorithm that bypasses dominant communities and detects communities which are formed by other nodes' attributes. We also review formation models of the attributed networks and present a Human Communication Network (HCN) model. We introduce a High School Texting Network (HSTN) and examine our methods for that network.
• #### Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.
• #### Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.