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In this thesis we consider two classes of binary matroids, even cycle matroids and even cut matroids. They are a generalization of graphic and cographic matroids respectively. We focus on two main problems for these classes of matroids. We first consider the Isomorphism Problem, that is the relation between two representations of the same matroid. A representation of an even cycle matroid is a pair formed by a graph together with a special set of edges of the graph. Such a pair is called a signed graph. A representation for an even cut matroid is a pair formed by a graph together with a special set of vertices of the graph. Such a pair is called a graft. We show that two signed graphs representing the same even cycle matroid relate to two grafts representing the same even cut matroid. We then present two classes of signed graphs and we solve the Isomorphism Problem for these two classes. We conjecture that any two representations of the same even cycle matroid are either in one of these two classes, or are related by a local modification of a known operation, or form a sporadic example. The second problem we consider is finding the excluded minors for these classes of matroids. A difficulty when looking for excluded minors for these classes arises from the fact that in general the matroids may have an arbitrarily large number of representations. We define degenerate even cycle and even cut matroids. We show that a 3-connected even cycle matroid containing a 3-connected non-degenerate minor has, up to a simple equivalence relation, at most twice as many representations as the minor. We strengthen this result for a particular class of non-degenerate even cycle matroids. We also prove analogous results for even cut matroids.

Probability matching is the tendency to predict outcomes in accordance with their actual contingencies in a binary choice task. It is, however, a suboptimal response if the aim is to maximize correct predictions. I review two theories that attempt to explain why probability matching occurs: the pattern-search hypothesis and dual-systems theory. These theories are tested in two studies which suggest that dual-systems theory provides a better account of probability matching behavior. Studies 3, 4, and 5 then provide evidence for an extension of the dual-systems theory, called expectation matching, which is intended to explain why probability matching is the intuitive response to a binary choice problem.

Thesis (M.A.)--West Virginia University, 1998. / Title from document title page. Document formatted into pages; contains viii, 79 p. : ill. Includes abstract. Includes bibliographical references (p. 66-68).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Results are presented from molecular dynamics simulations of binary liquid crystal mixtures using a generalisation of a well established Gay-Berne intermolecular potential. The simulations are undertaken in both the microcanonical (NVE) and the isoenthalpic-isobaric (NPH) ensembles. Firstly a 50:50 mixed system is simulated in the NVE ensemble containing generalised Gay-Berne (GGB) rod-like molecules with length to breadth axial ratios of 3.5:1 (molecules A) and 3:1 (molecules B). The molecules in this system differs only slightly from the well-characterised Gay-Berne (GB) potential with length to breadth ratio of 3:1. It is shown that the system exhibits isotropic (/), nematic (N) and smectic-B (SmB) phases with both the I-N and N-SmB phase boundaries not clearly defined. Competition between two density waves parallel to the director of the same wavelength but different phase lead to a pre-smectic ordering preceding the N-SmB phase transition. The longer molecules are shown to have a consistently higher order parameter the difference being greatest in the nematic phase and decrease with lowering temperature. Although a degree of local ordering is shown within each smectic layer the smectic phase is fully commensurate. Secondly, phase behaviour diagrams are presented from a series of constant-NPH simulations over a range of pressures and concentrations. The binary mixtures exhibit a rich phase behaviour, displaying isotropic, nematic, smectic-A (SmA), induced smectic-A and smectic-B phases depending on the choice of pressure and concentration. It is shown that the temperature range over which the nematic phase is stable can be extended greater than either homogeneous system by elevating the system pressure and/or by choice of concentration, agreeing with experimental results. The mixture exhibits a stable SmA island at a mole fraction of xa = 0.50 depending on the choice of pressure and a narrow induced SmA phase at xa = 0.25.

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abstract: A significant portion of stars occur as binary systems, in which two stellar components orbit a common center of mass. As the number of known exoplanet systems continues to grow, some binary systems are now known to harbor planets around one or both stellar components. As a first look into composition of these planetary systems, I investigate the chemical compositions of 4 binary star systems, each of which is known to contain at least one planet. Stars are known to vary significantly in their composition, and their overall metallicity (represented by iron abundance, [Fe/H]) has been shown to correlate with the likelihood of hosting a planetary system. Furthermore, the detailed chemical composition of a system can give insight into the possible properties of the system's known exoplanets. Using high-resolution spectra, I quantify the abundances of up to 28 elements in each stellar component of the binary systems 16 Cyg, 83 Leo, HD 109749, and HD 195019. A direct comparison is made between each star and its binary companion to give a differential composition for each system. For each star, a comparison of elemental abundance vs. condensation temperature is made, which may be a good diagnostic of refractory-rich terrestrial planets in a system. The elemental ratios C/O and Mg/Si, crucial in determining the atmospheric composition and mineralogy of planets, are calculated and discussed for each star. Finally, the compositions and diagnostics of each binary system are discussed in terms of the known planetary and stellar parameters for each system. / Dissertation/Thesis / M.S. Astrophysics 2013

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