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Classifying individuals into binary disease categories can be challenging due to complex relationships across different exposures of interest. In this thesis, we investigate three different approaches for disease classification using multiple biomarkers. First, we consider combining information from literature reviews and INTERHEART data set to identify the threshold of ApoB, ApoA1 and the ratio of these two biomarkers to classify individuals at risk of developing myocardial infarction. We develop a Bayesian estimation procedure for this purpose that utilizes the conditional probability distribution of these biomarkers. This method is flexible compared to standard logistic regression approach and allows us to identify a precise threshold of these biomarkers. Second, we consider the problem of disease classification using two dependent biomarkers. An independently identified threshold for this purpose usually leads to a conflicting classification for some individuals. We develop and describe a method of determining the joint threshold of two dependent biomarkers for a disease classification, based on the joint probability distribution function constructed through copulas. This method will allow researchers uniquely classify individuals at risk of developing the disease. Third, we consider the problem of classifying an outcome using a gene and miRNA expression data sets. Linear principal component analysis (PCA) is a widely used approach to reduce the dimension of such data sets and subsequently use it for classification, but many authors suggest using kernel PCA for this purpose. Using real and simulated data sets, we compare these two approaches and assess the performance of components towards genetic data integration for an outcome classification. We conclude that reducing dimensions using linear PCA followed by a logistic regression model for classification seems to be acceptable for this purpose. We also observe that integrating information from multiple data sets using either of these approaches leads to a better performance of an outcome classification. / Thesis / Doctor of Philosophy (PhD)

Contracts are legally enforceable agreements between two or more parties. The agreements can contain temporally based conditions, such as actions taken by the contract parties or events that happen, that trigger changes to the state of the contract when the conditions become true. Since the structure of these conditions can be very complex, it can be difficult to write contracts in a natural language in a clear and unambiguous way. A better approach is to have a formal language with a precise semantics to represent contracts. Contracts expressed in such a language have a mathematically precise meaning and can be written, analyzed, and manipulated by software. This thesis presents FCL, a formal language with a precise semantics for writing general contracts that may depend on temporally based conditions. Motivated by carefully selected examples of contracts, we derive a set of desirable requirements that a formal language of contracts should support. Based on the requirements, we clearly de ne the notion of contract and address what it means to fulfill or breach a contract. We present the formal syntax and semantics of FCL. We also successfully formalize different kinds of contracts in FCL and develop a reasoning system for FCL. / Thesis / Doctor of Philosophy (PhD)

In the era of big data, it is essential to implement practical security and privacy measures to ensure the lawful use of data and provide users with trust and assurance. In the dissertation, I address this issue through several key steps. Firstly, I delve into the problem of conditional secret disclosure, representing it using graphs to determine the most efficient approach for storing and disclosing secrets. Secondly, I extend the conditional disclosure of secrets problem from a single secret to multiple secrets and from a bipartite graph to an arbitrary graph. Thirdly, I remove security constraints to observe how they affect the efficiency of storage and recovery. In our final paper, I explore the secure summation problem, aiming to determine the capacity of total noise. Throughout the dissertation, I leverage information-theoretic tools to address security and privacy concerns.

No / We examine the short-term price reaction of 424 UK stocks to large one-day price changes. Using the GJR-GARCH(1,1), we find no statistical difference amongst the cumulative abnormal returns (CARs) of the Single Index, the Fama–French and the Carhart–Fama–French models. Shocks ⩾5% are followed by a significant one-day CAR of 1% for all the models. Whilst shocks ⩽−5% are followed by a significant one-day CAR of −0.43% for the Single Index, the CARs are around −0.34% for the other two models. Positive shocks of all sizes and negative shocks ⩽−5% are followed by return continuations, whilst the market is efficient following larger negative shocks. The price reaction to shocks is unaffected when we estimate the CARs using the conditional covariances of the pricing variables.

In recent years, a number of arguments have been put forward stating that regular conditional clauses preceding theirmatrix clause are derived bymeans ofmovement: They are base-generated low in the tree and then moved to the high clause-initial position. Using data from English and German, I show in this short paper that these arguments carry over straightforwardly to less canonical conditional constructions such as V1-conditionals and conditional conjunction constructions. That suggests that, if the original argu- ments hold, then V1-conditionals and conditional conjunction constructions should be derived bymovement as well.

Focusing on Environmental, Social and Governance (ESG) responsible investments, this study examines the historical and forecasted volatility and dynamic correlations between Emerging Markets in Europe, Asia and Latin America. By complementing the previous studies that provide evidence for how high ESG-ratings can reduce volatility in stock prices, regardless of which market, we seek to find if this is true in Emerging Markets. We additionally incorporate an analysis of dynamic correlations between Emerging Markets to see potential diversification benefits, which can be crucial in risk management. Data selection is based on daily closing prices of six different Emerging Markets indices. Three indices capturing the traditional Emerging Markets and three more only consisting of firms with a high ESG-rating, considered to be ESG Leaders. The sampled period is between January 2020 to January 2024. Data was processed through the DCC- GARCH(1,1) model to measure historical and forecasted volatility and dynamic correlations. The model uses past information to predict future values, meaning that past volatility and correlations influence forecasted volatility and correlations. This allows for a nuanced understanding of how the volatility and correlations have evolved and how they are forecast to change between these Emerging Markets. Key findings suggest that Asia can work as the diversification benefactor, as it is the least volatile Emerging Market and the ESG Leaders in Asia are showing a lower dynamic correlation with the ESG Leaders in the other Emerging Markets. Further results indicate that Europe is the most volatile Emerging Market, including the ESG Leaders. Furthermore, ESG Leaders in Europe and Latin America were seen to have the best DCC-GARCH filtered daily returns, while also having the highest dynamic correlation. This means that a portfolio with these two assets tends to be more volatile as shocks in daily returns move in tandem.