Analyses of human oral microbiomes reveal substantial amounts of information about health, diet, and diseases of individuals and their communities within the archaeological record. In order to examine bacterial genomes from the past, specific archaeological samples that contain remnants of the microbial communities in question must be utilized. Recent developments in high-throughput, next-generation DNA sequencing have enabled the characterization of entire oral microbiomes and genomes from the remains of the bacteria trapped in calcified dental plaque. This project analyzed samples of ancient human dental calculus from North and Central America, which were examined for the changes within the oral microbiome in relation to the adoption of agriculture. Additionally, the conditional presence of pathogens associated with an increasingly agricultural and carbohydrate-rich diet was examined. The overarching goal was to examine and determine the level of microbial shifts within the past oral microbiomes of North and Central America, and by virtue of using the associated archaeological reports and analyses, place the data into the proper context. Three distinct sets of dental calculus were used for this Dissertation; The first is from Indigenous samples (N=56), spanning from the Archaic to the Mississippian, recovered from excavations in the Guntersville Basin in Northern Alabama. The second set is from a Late-Terminal Classic Maya city center and satellite village in the Upper Belize Valley (N=11). The final sample set comes from an archaeologically recovered early 20th century Cemetery near Jackson Mississippi (N=12). After individual analyses, they are all examined along a temporal axis to examine the effect of agriculture on the human oral microbiome. The findings from this study have shown that oral microbiomes of the Americas were affected by the introduction of agriculture, but remained biologically diverse. Because various subsistence strategies can shape and affect the oral microbiome, the composition is seen to change over time. Our understanding of the evolution of oral microbiomes throughout human history is more complex than previously thought; there is no global trend for the oral microbiome, but is highly location dependent.

<p> In this thesis, we undertake a study of imperative reasoning. Beginning with a philosophical analysis of the distinction between imperative and functional language features, we define a (pure) imperative language as one whose constructs are inherently referentially opaque. We then give a definition of a reasoning language by identifying desirable properties such a language should have.</p> <p> The rest of the thesis presents a new pure imperative reasoning language, Assignment Calculus AC. The main idea behind AC is that R. Montague's modal operators of intension and extension are useful tools for modeling procedures in programming languages. This line of thought builds on T. Janssen's demonstration that Montague's intensional logic is well suited to dealing with assignment statements, pointers, and other difficult features of imperative languages.</p> <p> AC consists of only four basic constructs, assignment 'X := t', sequence 't; u', procedure formation 'it' and procedure invocation '!t'. Three interpretations are given for AC: an operational semantics, a denotational semantics, and a term-rewriting system. The three are shown to be equivalent. Running examples are used to illustrate each of the interpretations.</p> <p> Five variants of AC are then studied. By removing restrictions from AC's syntactic and denotational definitions, we can incorporate L-values, lazy evaluation, state backtracking, and procedure composition into AC. By incorporating procedure composition, we show that AC becomes a self-contained Turing complete language in the same way as the untyped λ-calculus: by encoding numerals, Booleans, and control structures as AC terms. Finally we look at the combination of AC with a typed λ-calculus.</p> / Thesis / Doctor of Philosophy (PhD)

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Several years ago an experimental re-entry program for women was initiated at the University of Central Florida. Women with B.S. degrees in Math or Science dating back 10 and 20 years ago were given a review course in Mathematics, primarily calculus, preparatory to subsequent courses in their M.S. programs of study. The complete course is available on tape and many students have viewed it since the course’s inception. This project involved generation of software for testing the manipulative skills presented in the Calculus review. A skeleton format is presented which demonstrates all the features of the different programming modules being developed. The user has the option of requesting a cross reference between problems which emphasize those topics deemed most appropriate. A series of menus direct the student to subproblems in response to a level of difficulty stipulated. Each subproblem presents the user with a multiple choice of answers. A random number generator is used to assure that the same subproblem produces a different correct answer each time. Window graphics is used extensively to highlight the important aspects of each problem as well as a choice of graphs relating the variables within a specific problem. A user’s manual with detailed analytical solutions of all the problems is available to supplement the software.

<p> The pattern matching calculus introduced by Kahl provides a fine-grained mechanism of modelling non-strict pattern matching in modern functional programming languages. By changing the rule of interpreting the empty expression that results from matching failures, the pattern matching calculus can be transformed into another calculus that abstracts a "more successful" evaluation. Kahl also showed that the two calculi have both a confluent reduction system and a same normalising strategy, which constitute the operational semantics of the pattern matching calculi.</p> <p> As a new technique based on Haskell's language extensions of type-saft cast, arbitrary-rank polymorphism and generalised algebraic data types, type-indexed expressions introduced by Kahl demonstrate a uniform way of defining all expressions as type-indexed to guarantee type safety.</p> <p> In this thesis, we implemented the type-indexed syntax and operational semantics of the pattern matching calculi using type-indexed expressions. Our type-indexed syntax mirrors the definition of the pattern matching calculi. We implemented the operational semantics of the two calculi perfectly and provided reduction and normalisation examples that show that the pattern matching calculus can be a useful basis of modelling non-strict pattern matching.</p> <p> We formalised and implemented the bimonadic semantics of the pattern matching calculi using categorical concepts and type-indexed expressions respectively. The bimonadic semantics employs two monads to reflect two kinds of computational effects, which correspond to the two major syntactic categories of the pattern matching calculi, i.e. expressons and matchings. Thus, the resulting implementation provides the detotational model of non-strict pattern matching with more accuracy.</p> <p> Finally, from a practical programming viewpoint, our implementation is a good demonstration of how to program in the pure type-indexed setting by taking fully advantage of Haskell's language extensions of type-safe cast, arbitrary-rank polymorphism and generalised algebraic data types.</p> / Thesis / Master of Science (MSc)

<p> Mechanized mathematics systems, especially Theorem Provers (TP) and Computer Algebra Systems (CAS), can play a very helpful role in handling relational calculus. Computer Algebra Systems help to automate tedious symbolic computations. However, they lack the ability to make sophisticated derivations of logical formulas. Correspondingly, a Theorem Prover is powerful in deriving the truth-value of a logical formula. Nevertheless, it is not suitable for dealing with symbolic expressions.</p> <p> The main goal for our research is to investigate the automation of relational calculus using existing mechanized mathematics technologies. Particularly, we elaborated a heuristic that enables the assignment of tasks to PVS and Maxima to help perform relational calculus. As well we built a proof-of-concept tool that supports this calculus.</p> <p> To fulfill our objective, we adopted the following steps: 1. Investigated and evaluated the characteristics and capabilities of TPs and CASs. This step led us to select PVS and Maxima as the tools to be used by our system. 2. Explored a strategy that governs setting tasks to PVS and Maxima in order to perform relational calculus. Then, we propose a task assignment heuristic based on this strategy. 3. Designed and built a proof-of-concept tool that makes use of PVS and Maxima to help perform relational calculus. 4. Assessed our tool by using it to handle some illustrative examples of operations on concrete relations.</p> <p> In our work, relations are given by their characteristic predicates. We assume as well that predicates that are provided to our proof-of-concept tool are in a Disjunctive Normal Form. We adopt a linear notation for the representation of propositions, quantifications, and expressions. We fall short of providing a user interface, which makes the use of the tool that we built slightly difficult.</p> / Thesis / Master of Science (MSc)

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