We begin with a disucssion of some of the serious deficiencies of first order predicate languages. These include the non-characterizability by first order sentences of such common mathematical structures as the class of well-ordered sets, the class of finite sets, the class of Archimedean fields and the standard models of arithmetic and analysis. Two methods of generalizing first order predicate languages are then studied. The first approach is to allow for "expressions of infinite length"; the second method is the introduction of "generalized quantifiers." For the languages resulting from each approach, we consider to what extent such deficiencies as those mentioned above may be overcome and also to what extent some of the elementary model-theoretic and proof-theoretic theorems of first order logic may be generalized to these new languages. Among the languages with expressions of infinite length, we first consider the Lω₁ω languages which generalize first order languages by extending the recursive definition of a formula to allow countable conjunctions and disjunctions of formulas as formulas. It is shown that with the use of such languages we are able to describe categorically the standard model of arithmetic, the class of finite sets, the class of Archimedean fields and other common mathematical structures which cannot be characterized in first order languages. Generalizations of the Lowenheim-Skolem and completeness theorems of first order logic are given as well as a countable isomorphism theorem due to Dana Scott. We make use of a characterization of rank equivalence due to Carol Karp to demonstrate that neither the standard model of analysis nor the class of well-ordered sets may be described in any Lω₁ω -language. In fact, our argument indicates that these characterizations are not possible in any extension of a Lω₁ω - language which, for any infinite cardinal α , allows as formulas conjunctions and disjunctions of less than a formulas. This result leads us naturally to a consideration of the class of Lω₁ω - languages, any element of which is obtained from a Lω₁ω - language by modifying the rules for formula formation to allow not only denumerable conjunctions and disjunctions but also quantifications over denumerable sets of variables. (These ideas are made more precise in the text of the thesis.) The standard model of analysis and the class of well-ordered sets are each seen to be characterizable by single Lω₁ω - sentences. Other infinitary languages are also mentioned, including languages with infinitely long atomic formulas. Among the languages with generalized quantifiers we restrict ourselves to the L(Qα) - languages, where α is an ordinal, which are obtained from first order languages by adding a new quantifier symbol Qα to be read "there exist Ɲα... .” In addition to being able to characterize sets of various cardinalities, we give a categorical description of the standard model of arithmetic by a single L(Qօ) - sentence. Among the model-theoretic results possible are generalizations of the compactness theorem, Lŏs's theorem and the downward Lowenheim - Skolem theorem of first order logic. Finally, on the proof-theoretic side, we show that in the case α = 0 there exists no recursive axiomatization which yields a completeness result; in the case α = 1 , however, such an axiomatization is possible. / Science, Faculty of / Mathematics, Department of / Graduate

Biological knowledge is widely represented in the form of ontologies and ontology-based annotations. Biomedical ontologies describe known phenomena in biology using formal axioms, and the annotations associate an entity (e.g. genes, diseases, chemicals, etc.) with a set of biological concepts. In addition to formally structured axioms, ontologies contain meta-data in the form of annotation properties expressed mostly in natural language which provide valuable pieces of information that characterize ontology concepts. The structure and information contained in ontologies and their annotations make them valuable for use in machine learning, data analysis and knowledge extraction tasks. I develop the first approaches that can exploit all of the information encoded in ontologies, both formal and informal, to learn feature embeddings of biological concepts and biological entities based on their annotations to ontologies. Notably, I develop the first approach to use all the formal content of ontologies in the form of logical axioms and entity annotations to generate feature vectors of biological entities using neural language models. I extend the proposed algorithm by enriching the obtained feature vectors through representing the natural language annotation properties within the ontology meta-data as axioms. Transfer learning is then applied to learn from the biomedical literature and apply on the formal knowledge of ontologies. To optimize learning that combines the formal content of biomedical ontologies and natural language data such as the literature, I also propose a new approach that uses self-normalization with a deep Siamese neural network that improves learning from both the formal knowledge within ontologies and textual data. I validate the proposed algorithms by applying them to the Gene Ontology to generate feature vectors of proteins based on their functions, and to the PhenomeNet ontology to generate features of genes and diseases based on the phenotypes they are associated with. The generated features are then used to train a variety of machinelearning based classifiers to perform different prediction tasks including the prediction of protein interactions, gene–disease associations and the toxicological effects of chemicals. I also use the proposed methods to conduct the first quantitative evaluation of the quality of the axioms and meta-data included in ontologies to prove that including axioms as background improves ontology-based prediction. The proposed approaches can be applied to a wide range of other bioinformatics research problems including similarity-based prediction and classification of interaction types using supervised learning, or clustering.

Biological knowledge is widely represented in the form of ontologies and ontologybased annotations. Biomedical ontologies describe known phenomena in biology using formal axioms, and the annotations associate an entity (e.g. genes, diseases, chemicals, etc.) with a set of biological concepts. In addition to formally structured axioms, ontologies contain meta-data in the form of annotation properties expressed mostly in natural language which provide valuable pieces of information that characterize ontology concepts. The structure and information contained in ontologies and their annotations make them valuable for use in machine learning, data analysis and knowledge extraction tasks. I develop the rst approaches that can exploit all of the information encoded in ontologies, both formal and informal, to learn feature embeddings of biological concepts and biological entities based on their annotations to ontologies. Notably, I develop the rst approach to use all the formal content of ontologies in the form of logical axioms and entity annotations to generate feature vectors of biological entities using neural language models. I extend the proposed algorithm by enriching the obtained feature vectors through representing the natural language annotation properties within the ontology meta-data as axioms. Transfer learning is then applied to learn from the biomedical literature and apply on the formal knowledge of ontologies. To optimize learning that combines the formal content of biomedical ontologies and natural language data such as the literature, I also propose a new approach that uses self-normalization with a deep Siamese neural network that improves learning from both the formal knowledge within ontologies and textual data. I validate the proposed algorithms by applying them to the Gene Ontology to generate feature vectors of proteins based on their functions, and to the PhenomeNet ontology to generate features of genes and diseases based on the phenotypes they are associated with. The generated features are then used to train a variety of machinelearning based classi ers to perform di erent prediction tasks including the prediction of protein interactions, gene{disease associations and the toxicological e ects of chemicals. I also use the proposed methods to conduct the rst quantitative evaluation of the quality of the axioms and meta-data included in ontologies to prove that including axioms as background improves ontology-based prediction. The proposed approaches can be applied to a wide range of other bioinformatics research problems including similarity-based prediction and classi cation of interaction types using supervised learning, or clustering.

I consider how the nature and meaning of space shape middle-class women's topophobia in the new town of Secunda (with a particular focus on symbolic violence). In Lefebvre's 'terrorist societies' fear becomes latent as citizens seek to maintain status quos which maintain systems of privilege. I demonstrate that one such system is white privilege. Secunda assists in maintaining these systems as its design draws heavily on Eurocentric values and new town 'best practices'. As a company town developed in reaction to international sanctions during apartheid, its design also resulted in the preservation of certain privileged groups. I argue that white privilege is a white problem and thus base my study on the (white) middle-class as a dominant group. I show that the identities of women (although traditionally viewed as passive and fearful) are diverse, falling both victim to and inflicting symbolic violence and topophobia. I focus on topophobia, or spatial fear, as fear affects us all and influences our shaping of urban space. The mutually reinforcing nature (abstract representations of the ideologies of planners) and meaning (infused through emotions, identities and power relations) of space are explored. I dispute the bias against emotion-based research that exists within planning, arguing that this has debilitating consequences for transformation. I suggest the use of intersecting emotion-spectra rather than the dichotomous approach conventionally taken by emotion research. A feminist ethnography is used with an iterative inductive research process engaging a variety of techniques, including digital/social media. My own multiple insider identities (of middle-class, white, English-Afrikaans woman, and planner) are used to critique systems of dominance. Findings highlight various forms of symbolic violence (in addition to white privilege) including codes of 'respectability' and 'purity', consumerism, fat talk, and persistent gender roles. Further, possible influences of dominant systems on space (particularly in reinforcing persistent social segregation in Secunda) are demonstrated. Symbolic violence can be used to deflect accountability, but this research shows that topophobia is a planning problem, worthy of consideration.

Due to the increasing complexity of today\'s cyber-physical systems, defects become inevitable and harder to detect. The complexity of such software is generally huge, with millions of lines of code. The impact of failure of such systems could be hazardous. The reliability of the system depends on the effectiveness and rigor of the testing procedures. Verification of the software behind such cyber-physical systems is required to ensure stability and reliability before the systems are deployed in field. We have investigated the verification of the software for Autonomous Underwater Vehicles (AUVs) to ensure safety of the system at any given time in the field. To accomplish this, we identified useful invariants that would aid as monitors in detecting abnormal behavior of the software. Potential invariants were extracted which had to be validated. The investigation attempts to uncover the possibility of performing this method on existing Software verification platforms. This was accomplished on Cloud9, which is built on KLEE and using the Microsoft\'s VCC tool. Experimental results show that this method of extracting invariants can help in identifying new invariants using these two tools and the invariants identified can be used to monitor the behavior of the autonomous vehicles to detect abnormality and failures in the system much earlier thereby improving the reliability of the system. Recommendations for improving software quality were provided. The work also explored safety measures and standards on software for safety critical systems and Autonomous vehicles. Metrics for measuring software complexity and quality along with the requirements to certify AUV software were also presented. The study helps in understanding verification issues, guidelines and certification requirements. / Master of Science

archives@tulane.edu / 1 / Joseph Skelton

Despite the emergence of narrative and humanistic anthropological perspectives on thriving indigenous textile technologies, indigo dyed textile products are often read as homogenous products, devoid of Yoruba women-dyers' symbolic narratives. This ethnographic research on indigo textile dyeing in Osogbo examines the relationship between textile production and ritual by focusing on how indigenous peoples are stimulated to create what they make and the textile makers' unit of expression. A key argument throughout the thesis is that the dyeing act is a ritual performance by women dyers in Osogbo a re-enacted symbolic performance of the formation and evolution of human sociality and the socialization of human beings. It is also a symbolic representation of motherhood (parenthood when it comes to the societal level) a process of inscribing the kadara (destiny) of a child and the development of iwa (character) and ewa (beauty) to be an omoluabi (good and cultured child) in Yoruba ontology. The thesis also explores alkaline water production processes as part of the indigenous indigo textile dyeing processes and the use of adire textile for communication in Osogbo the notions of colour and colour symbolism and the use of texts, proverbs and images on dyed textiles as communicative tools specifically to show the transformatory nature of rituals in indigo textile dyeing. / Thesis (DPhil)--University of Pretoria, 2017. / Anthropology and Archaeology / DPhil / Unrestricted

This paper describes the tension between intuition about number theory and attempts to formalize it. I will first examine the root of the dilemma, Godel's First Incompleteness Theorem, which demonstrates that in any reasonable formalization of number theory, there will be independent statements. After proving the theorem, I consider some of its consequences on intuition, focusing on Freiling's "Dart Experiment" which is based on our usual notion of the real numbers as a line. This experiment gives an apparent refutation of the Axiom of Choice and the Continuum Hypothesis; however, it also leads to an equally apparent paradox. I conclude that such paradoxes are inevitable as the formalization of mathematics takes us further from our initial intuitions.

In this study I investigate the impact different director types have on firm commitments to voluntary labor regulation. Using an author-constructed dataset of eight focal firm’s boards of directors for a nineteen-year period, I examine the impacts of gender and racial diversity, as well as the inclusion of independent interlocking board members on firm commitments to voluntary labor regulation following a legitimacy crisis in the 1990s. Framing firms’ responses within a chronological approach to institutional theory, I test how trends for these three director types varied for firms most and least committed to voluntary labor regulation, as well as for firms that underwent bankruptcy, an acquisition, or split into various firms between 1996 and 2014. Findings suggest that firms view gender and racial diversity in similar ways, but independent interlocks as a separate strategy. All firms increased the number of women and racial minorities on their boards, with least committed firms having the highest percentages of both over this entire period. Use of independent interlocks increased at a moderate rate for most committed firms, decreased over time for least committed firms, and increased significantly for firms going through additional crises (bankruptcy, an acquisition, or splitting up). This study contributes to theory and research on organizational change by extending understanding of mechanisms that drive organizational change in response to crisis by analyzing internal normative mechanisms that shaped firms’ responses. It extends research on board composition by analyzing the conditions under which board diversity and interlocked board members are sought by focal firms. Understanding how and why board diversity and independent interlock membership serve as mechanisms of internal, normative change provides insight into what internal mechanisms shape organizational policies and practices, and provide a correction to the over-focus on external, coercive mechanisms in existing scholarship.

To ensure the correctness of real time systems, it is important to determine the execution time of tasks. The worst case execution time of each task needs to be found in order to determine if the system is schedulable. This thesis aims at bounding the execution time of programs analyzed by KLEE, a symbolic execution engine. This is done by estimating the cycles required on the Cortex-M4 processor. A custom fork of KLEE has been created which outputs additional information about the program under analysis. This information is used by a tool written in Rust which reconstructs the corresponding control flow in optimized assembly code. KLEE analyzes an intermediate representation language, LLVM IR. This representation is used in the compilation process of many programming languages. One of these languages is Rust which has been the primary focus of the tool. Testing has been done on applications written with the RTIC framework. The measured cycles of these applications has been correctly bounded for all test cases.