All discrete function representations become exponential in size in the worst case. Binary decision diagrams have become a common method of representing discrete functions in computer-aided design applications. For many functions, binary decision diagrams do provide compact representations. This work presents a way to represent large decision diagrams as multiple smaller partial binary decision diagrams. In the Boolean domain, each truth table entry consisting of a Boolean value only provides local information about a function at that point in the Boolean space. Partial binary decision diagrams thus result in the loss of information for a portion of the Boolean space. If the function were represented in the spectral domain however, each integer-valued coefficient would contain some global information about the function. This work also explores spectral representations of discrete functions, including the implementation of a method for transforming circuits from netlist representations directly into spectral decision diagrams.

Very high temperature (>900 °C) contact metamorphism and metasomatism of aluminous schist xenoliths in the mafic to ultramafic Cortlandt Complex, New York, resulted in formation of bodies of unusual Fe- and Al-oxide-rich rock called emery. During contact heating, disequilibrium thermal decomposition of the protolith schists in one closely examined xenolith produced two end-member materials: a quartzo-feldspathic water-undersaturated melt which partitioned much of the silica and calcium and all of the alkalis of the original schist; and a highly aluminous fine-grained emery residuum which contained spinel, magnetite, ilmenohematite, sillimanite, and sporadically corundum. During cooling, melt within the xenoliths was injected as cm-scale veinlets into the silica-poor solid residuum. Local increase in silica activity resulted in progressive silication reactions of spinel-rich residuum to several silicates. A simple model of progressive silication would require that reactions should occur from lower to higher silica content of product silicates in stages, e.g., spinel – sapphirine (Si/O=0.10), sapphirine – garnet (0.25), garnet – orthopyroxene (0.28), rather than directly from spinel to higher-silica minerals which would overstep intermediate reaction steps. However, observed reaction textures indicate the latter more complex behavior in which spinel may have reaction rims of, or occur as inclusions within, any of the three silicate minerals. Statistical analysis of several samples has shown the mode to be the spinel-orthopyroxene reaction rim boundary although orthopyroxene is the highest-silica product mineral, based on Si/O ratio. Chi-square test results are significant and show that the textural relations observed among spinel, sapphirine, garnet, and orthopyroxene are dependent. Increased silica activity therefore cannot be the only factor controlling the reaction sequence. Microprobe data has been collected in an attempt to correlate mineral compositions with the different textural occurrences. The effects of local equilibria appear to be the dominant factors in the overstepping of sequential reactions. Qualitative activity-activity diagrams proved useful for examining the effects of bulk composition on the relative stabilities of spinel and the three silicates, including variations in Fe/(Fe+Mg), bulk Mn and Zn contents, and minor local variation in oxygen fugacity. Matrix spinel compositions (i.e., those not modified by reaction to silicates) fall into two groups: a more magnesian one containing spinels with average Fe/(Fe+Mg) (Fe#) of 0.49 and a less magnesian one, average Fe# of 0.67. With regard to this bulk compositional effect, the more magnesian composition should reduce garnet stability due to the strong fractionation of Fe into garnet, thus favoring the reaction of spinel to orthopyroxene within silica-rich areas. In more aluminous areas, spinel will react to form sapphirine, then garnet, then possibly orthopyroxene. A less magnesian composition would expand the stability of garnet at the expense of sapphirine and, to a lesser extent, orthopyroxene. Zinc has a subtle effect on mineral stabilities. Because Zn is strongly partitioned into spinel, higher zinc contents (concentrations in some spinels are as high as 14.9 mol% gahnite) may expand the stability of that mineral considerably. Consequently, spinel stability may increase relative to the three silicates, but this may be quite variable due to variable reaction stoichiometry and different reaction-boundary slopes in the activity-activity diagram. In general, spinels with the highest Zn content occur next to orthopyroxene (ave. 4.9 mol% gahnite in spinels) for which the stability appears to be only slightly affected by this increase in Zn. The greatest decrease in silicate stability is observed in sapphirine. Spinels adjacent to sapphirine contain no more than 1.3 mol% gahnite. The effects of manganese and oxygen fugacity were also examined. Mn increases the stability of garnet due to strong partitioning of Mn into this mineral. It can be inferred using statistical and chemical data that this has some bearing on textural relations in garnet-bearing samples, but the lack of obvious Mn fractionation by other minerals examined makes it impossible to interpret the effects of Mn in the garnet-free samples. Calculated ferric-ferrous ratios in analyzed minerals were examined in an attempt to study the effect of oxygen fugacity on the stabilities of minerals. In the more magnesian compositions, which may correlate with slightly higher fO2 during reactions, spinels should react to form sapphirine, then possibly garnet or orthopyroxene with further silica activity increase. In lower-fO2 environments (perhaps those with higher bulk Fe#), spinel should react directly to form orthopyroxene. The coexistence of magnetite and ilmenohematite dictates T-fO2 conditions very nearly at those of the Hematite-Magnetite buffer. Minor fO2 variations that might have had an effect on silicate-forming reactions would only be recorded by small variations in magnetite and ilmenohematite solid solutions (ulvospinel and ilmenite contents, respectively). These data were not acquired in this study, however, so no definite conclusions could be made. / Master of Science

A computer program that symbolically generates and evaluates all Feynman diagrams required for scattering amplitude for exclusive processes is tested, corrected, extended, and brought to operational status. The sensitivity of perturbative QCD predictions for the nucleon form factors, ψ → pp̅, and 𝛾𝛾 → pp̅, to the theoretical uncertainties of the nucleon wave function and the form of the running coupling constant is investigated. A new prediction for the cross-section for 𝛾𝛾 → Δ++ Δ̅++ with sum-rule wave functions is presented. As a product of the development of the computer program, the quark amplitudes for meson-baryon scattering are obtained. Integrations of the quark amplitudes over wave functions are carried out by cutting off singularities. The numerical reliability of the integration and its sensitivity to the cut-off’s and the choice of wave function are investigated. / Ph. D. / incomplete_metadata

Yes / It is important for the formulators of biopharmaceuticals to predict the folding–unfolding transition of proteins. This enables them to process proteins under predetermined conditions, without denaturation. Depending on the apparent denaturation temperature (Tm) of lysozyme, we have derived an equation describing its folding–unfolding transition diagram. According to the water content and temperature, this diagram was divided into three different areas, namely, the area of the water-folded lysozyme phase, the area of the water-folded lysozyme phase and the bulk water phase, and the area of the denatured lysozyme phase. The water content controlled the appearance and intensity of the Raman band at ∼1787 cm–1 when lysozyme powders were thermally denatured at temperatures higher than Tm. / MAM gratefully acknowledges CARA (Stephen Wordsworth and Ryan Mundy) and University of Bradford for providing an academic fellowship.

Doctor of Philosophy / Department of Computing and Information Sciences / David A. Gustafson / The Unified Modeling Language (UML) has been designed to be a full standard notation for Object-Oriented Modeling. UML 2.0 consists of thirteen types of diagrams: class, composite structure, component, deployment, object, package, activity, use case, state, sequence, communication, interaction overview, and timing. Each one is dedicated to a different design aspect. This variety of diagrams, which overlap with respect to the information depicted in each, can leave the overall system design specification in an inconsistent state. This dissertation presents Super State Analysis (SSA) for analyzing UML multiple state and sequence diagrams to detect the inconsistencies. SSA model uses a transition set that captures relationship information that is not specifiable in UML diagrams. The SSA model uses the transition set to link transitions of multiple state diagrams together. The analysis generates three different sets automatically. These generated sets are compared to the provided sets to detect the inconsistencies. Because Super State Analysis considers multiple UML state diagrams, it discovers inconsistencies that cannot be discovered when considering only a single UML state diagram. Super State Analysis identifies five types of inconsistencies: valid super states, invalid super states, valid single step transitions, invalid single step transitions, and invalid sequences.

Master of Science / Department of Civil Engineering / Asadollah Esmaeily / Realistic strength assessment of reinforced concrete structural elements, especially columns in bridges and tall buildings is a critical need not only at design time, but also when an accurate evaluation of the strength is needed for decisions such as retrofit or replacement of an existing structure. Assessment of the flexural strength of a column under a specific axial load level is usually done by constructing the axial force-bending moment interaction response curve of the section. This assessment can be done using the code procedure. However, the code does not consider the confinement effect, and is based on the “stress block” assumption for a pre-assumed failure strain for concrete. It has been shown by various experimental and analytical studies that the performance of a reinforced concrete section is affected by different factors such loading history and material behavior. A realistic performance assessment should consider not only proper models for the monotonic and cyclic response of the material, but also analytical methods and procedures that can capture the effects of loading pattern and provide realistic predictions of the section capacity. Accuracy of the analytical methods in strength assessment of reinforced concrete sections was explored in a comparative study. These methods were compared and validated against the existing experimental data. The factors considered in these analytical procedures, included the effect of confinement, and the method employed in assessment of the axial-force-bending moment interaction response of a column section. The experimental data were collected from tests conducted on circular and rectangular columns under a constant axial load. It has been shown that the axial force-bending moment interaction curve, constructed based on the moment-curvature response of a section using a more detailed analytical method such as fiber-model, considering the confining effect of the lateral reinforcement, represents the most realistic and optimal response of a cross section.

Research into the usefulness of scientific diagrams as teaching and learning tools has revealed their great effectiveness in reinforcing and replacing text; summarizing, clarifying, grouping and comparing information; illustrating abstract concepts and spatial relations between concepts; and aiding understanding and integration of knowledge. However, these advantages are not always realised as diagram effectiveness depends on the student's cognitive ability, visual literacy and prior knowledge. In biochemistry, flow diagrams are used as tools for the visualisation of biochemical processes, the abstract nature of which presents problems to students, probably because the depicted content is beyond their perceptual experience. In this study, we define visualisation as the entire process from the perception of an external representation (e.g. diagram), its internal processing, and the expression of a mental model of the represented content. Therefore, visualisation incorporates reasoning processes and interactions with a student's conceptual knowledge, in their construction of a mental model. Students' visualisation difficulties, in terms of conceptual and reasoning difficulties, have been well researched in areas such as physics and chemistry, but neglected in biochemistry, especially with respect to the use of diagrams as visualisation tools. Thus the aim of this study was to investigate students' use of diagrams for the visualisation of biochemical processes, and to identify the nature, and potential sources of students' conceptual, reasoning and diagram-related difficulties revealed during the visualisation process. The study groups ranged from 27 to 95 biochemistry students from the University of Natal and 2 to 13 local and international experts. Propositional knowledge was obtained from textbooks and from a questionnaire to experts. Data on student visualisation of biochemical processes was obtained from their responses to written and interview probes as well as student-generated diagrams. All data was subjected to inductive analysis according to McMillan and Schumacher (1993) and any difficulties that emerged were classified at levels 1- 3 on the framework of Grayson et al. (2001). The possible sources of difficulties were considered in terms of a model by Schonborn et al. (2003 & 2002). The results revealed the following major findings. The meaning of linear, cyclic and cascade biochemical processes was partially resolved by means of an extensive list of generic and distinguishing functional features obtained from experts. Attempts to clarify propositional knowledge of the complement system revealed a deficiency in our understanding of the functional relationship between the complement pathways and highlighted the need for further experimental laboratory work. Several students literally interpreted diagrams of the functional characteristics of biochemical processes (e.g. cyclic) as the spatial arrangement of the intermediates within cells (e.g. occur in "circles"), although in some cases, their verbal responses revealed that they did not hold this difficulty suggesting that they might hold more than one internal model of the process. Some students also showed difficulty using textbook diagrams to visualise the chemistry of glycolytic and complement reactions. In this regard, besides students' conceptual knowledge and reasoning ability, a major source of these difficulties included misleading symbolism and visiospatial characteristics in the diagrams, suggesting the need for improvement of diagram design through the use of clearer symbolism, the standardization of conventions, and improvement of visiospatial properties of diagrams. The results constituted further empirical evidence for the model of Schonbom et al. (2003 & 2002) and led to the proposal of a model of visualisation aimed at clarifying the highly complex and cognitive processes involved in individuals' visualisation of biochemical processes in living systems. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 2003.

An n-Venn diagram is defined as a collection of n finitely intersecting closed curves dividing the plane into 2^n distinct regions, where each region is in the interior of a unique subset of the curves. A Venn diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. An n-Venn diagram has n-fold rotational symmetry if a rotation of 180 degrees about a centre point in the plane leaves the diagram unchanged, up to a relabeling of the curves. It has been known that rotationally symmetric Venn diagrams could exist only if the number of curves is prime. Moreover, non-simple Venn diagrams with rotational symmetry have been proven to exist for any prime number of curves. However, the largest prime for which a simple rotationally symmetric Venn diagram was known prior to this, was 7. In this thesis, we are concerned with generating simple monotone Venn diagrams, especially those that have some type(s) of symmetry. Several representations of these diagrams are introduced and different backtracking search algorithms are provided based on these representations. Using these algorithms we show that there are 39,020 non-isomorphic simple monotone 6-Venn diagrams in total. In the case of drawing Venn diagrams on a sphere, we prove that there exists a simple symmetric n-Venn diagram, for any n >= 6, with the following set(s) of isometries : (a) a 4-fold rotational symmetry about the polar axis, together with an additional involutional symmetry about an axis through the equator, or (b) an involutional symmetry about the polar axis together with two reflectional symmetries about orthogonal planes that intersect at the polar axis. Finally, we introduce a new type of symmetry of Venn diagrams which leads us to the discovery of the first simple rotationally symmetric Venn diagrams of 11 and 13 curves. / Graduate / 0984 / Khalegh@GMail.com

This thesis presents an in-depth investigation into the practical use of 3D for software visualisation. This work presents the first comprehensive user-centred study which examines the software engineering tasks users undertake currently, the issues that 3D addresses and a measure of benefit of the 3D solution compared to traditional approaches. This thesis also presents a mechanism for creating 3D software visualisations, a refined evaluation methodology and visualisation heuristics that together provide a valuable resource for further research into this area. The research results have been structured so they are directly applicable to industry and as such are already undergoing industrial adoption. This has been achieved through the following: Firstly the research augments current and accepted software visualisation approaches by basing the visual notation on the Unified Modelling Language (UML). This has enabled the current visual software engineering tasks to be studied and for representative user tasks to be captured and quantified. The 3D visualisations then complement the current working practices by solving

This thesis presents an in-depth investigation into the practical use of 3D for software visualisation. This work presents the first comprehensive user-centred study which examines the software engineering tasks users undertake currently, the issues that 3D addresses and a measure of benefit of the 3D solution compared to traditional approaches. This thesis also presents a mechanism for creating 3D software visualisations, a refined evaluation methodology and visualisation heuristics that together provide a valuable resource for further research into this area. The research results have been structured so they are directly applicable to industry and as such are already undergoing industrial adoption. This has been achieved through the following: Firstly the research augments current and accepted software visualisation approaches by basing the visual notation on the Unified Modelling Language (UML). This has enabled the current visual software engineering tasks to be studied and for representative user tasks to be captured and quantified. The 3D visualisations then complement the current working practices by solving