Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 93-95).

Thesis (M. Phil.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In this article we suggest a beta regression model that accounts for the degree of preference in paired comparisons measured on a bounded metric paired comparison scale. The beta distribution for bounded continuous random variables assumes values in the open unit interval (0,1). However, in practice we will observe paired comparison responses that lie within a fixed or arbitrary fixed interval [-a,a] with known value of a. We therefore transform the observed responses into the interval (0,1) and assume that these transformed responses are each a realization of a random variable which follows a beta distribution. We propose a simple paired comparison regression model for beta distributed variables which allows us to model the mean of the transformed response using a linear predictor and a logit link function -- where the linear predictor is defined by the parameters of the logit-linear Bradley-Terry model. For illustration we applied the presented model to a data set obtained from a student survey of learning related emotions in mathematics. (authors' abstract)

Master of Science / Department of Biological & Agricultural Engineering / Philip L. Barnes / Wichita, Kansas water supply is derived from multiple sources. Unfortunately, these sources are not expected to meet the future needs of the population. This predicted water shortage led to the development of the Equus Beds Recharge Project, to investigate artificial recharge as a solution to meet future water demands. This project focuses on the Little Arkansas River as a source of this recharge water. The Kansas Department of Health and Environment set a daily 3[Mu]g/L standard for the recharged water as opposed to surface waters used directly for drinking water which can't exceed a yearly average atrazine concentration of 3[Mu]g/L. During 2005, five sub-watersheds within the Little Arkansas River watershed were instrumented to collect water quality samples and measure flow rate to calculate daily contaminant loadings. Three of the sub-watersheds used atrazine best management practices (BMPs) applied to grain sorghum while the remaining two sub-watersheds maintained existing farm practices. During 2007, monitoring continued and additional atrazine BMPs were applied to corn grown in the treated sub-watersheds. During both 2006 and 2007, water quality monitoring was used to examine water quality parameters throughout the entire watershed. Watershed-scale monitoring allowed for pollutant transport patterns to emerge both spatially and temporally and indicated potential sources of the pollutants. In this particular study, atrazine and sediment loss were the two most important water quality parameters. Results from this study showed that by using BMPs the concentration of atrazine was decreased by greater than 40% in 2006 when compared to the atrazine concentration from those areas without BMPs. A 5% reduction was seen in 2007, which was due to differences in precipitation and runoff between the two years. There was no reduction in sediment losses between the treated and untreated watersheds during 2006, leading to the conclusion that additional practices would be needed to reduce sediment losses as well as any pollutants associated with sediment loss (ex nutrients absorbed to the sediments). During 2007, sediment, nitrogen, and phosphorus were 66%, 60%, and 55% lower respectively in the treated versus untreated sub-watershed. These 2007 differences were related to rainfall pattern differences in the sub-watersheds.

An attempt was made to shed new light upon the controversy between semantic overlap (e.g., Rohwer, 1973) and interacting imagery (e.g., Paivio, 1970) interpretations of mnemonic effects in children's associative learning. Two approaches were taken to this task. First, several conflicting predictions of the semantic and imagery models were pinpointed and subjected to experimental analysis. Second, in an attempt to supercede the semantic versus imagery issue, the Piagetian (e.g., Piaget and Inhelder, 1973) conception of memory was considered and some predictions, derived from an extrapolation of this model to associative learning were examined experimentally. In terms of the former approach, the results of the four experiments generally were more consistent with the imagery perspective. However, since only peripheral features of the-semantic model were contradicted, no clear choice between the two positions was warranted. Inclusion of several measures of delayed recall in order to pursue the second, Piagetian-based, approach did point out the inadequacy of the semantic and imagery models with regard to longer retention intervals. From the Piagetian perspective the various memory-improving effects, rather than being attributable to operative (i.e., assirailatory) processes, instead, seemed more appropriately assigned to a figurative-level mnemonic. / Arts, Faculty of / Psychology, Department of / Graduate

Let G be a graph with vertex set V and no isolated vertices. A subset S⊆ V is a semipaired dominating set of G if every vertex in V\ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γpr 2(G) is the minimum cardinality of a semipaired dominating set of G. We show that if G is a connected graph of order n with minimum degree at least 2, then γpr2(G)≤12(n+1). Further, we show that if n≢3(mod4), then γpr2(G)≤12n, and we show that for every value of n≡3(mod4), there exists a connected graph G of order n with minimum degree at least 2 satisfying γpr2(G)=12(n+1). As a consequence of this result, we prove that every graph G of order n with minimum degree at least 3 satisfies γpr2(G)≤12n.

Let G be a graph with vertex set V and no isolated vertices, and let S be a dominating set of V. The set S is a semitotal dominating set of G if every vertex in S is within distance 2 of another vertex of S. And, S is a semipaired dominating set of G if S can be partitioned into 2-element subsets such that the vertices in each 2-set are at most distance two apart. The semitotal domination number γt 2(G) is the minimum cardinality of a semitotal dominating set of G, and the semipaired domination number γpr 2(G) is the minimum cardinality of a semipaired dominating set of G. For a graph without isolated vertices, the domination number γ(G) , the total domination γt(G) , and the paired domination number γpr(G) are related to the semitotal and semipaired domination numbers by the following inequalities: γ(G) ≤ γt 2(G) ≤ γt(G) ≤ γpr(G) and γ(G) ≤ γt 2(G) ≤ γpr 2(G) ≤ γpr(G) ≤ 2 γ(G). Given two graph parameters μ and ψ related by a simple inequality μ(G) ≤ ψ(G) for every graph G having no isolated vertices, a graph is (μ, ψ) -perfect if every induced subgraph H with no isolated vertices satisfies μ(H) = ψ(H). Alvarado et al. (Discrete Math 338:1424–1431, 2015) consider classes of (μ, ψ) -perfect graphs, where μ and ψ are domination parameters including γ, γt and γpr. We study classes of perfect graphs for the possible combinations of parameters in the inequalities when γt 2 and γpr 2 are included in the mix. Our results are characterizations of several such classes in terms of their minimal forbidden induced subgraphs.

In honor of Professor Peter Slater's work on paired domination, we introduce a relaxed version of paired domination, namely semipaired domination. Let G be a graph with vertex set V and no isolated vertices. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γPr2(G) is the minimum cardinality of a semipaired dominating set of G. In this paper, we study the semipaired domination versus other domination parameters. For example, we show that γ(G) ≤ γPr2(G) ≤ 2γ(G) and 2/3γt(G) ≤ γPr2(T) ≤ γ 4/3γt(G), where γ(G) and γt(G) denote the domination and total domination numbers of G. We characterize the trees G for which γPr2(G) = 2γ(G).

<p>Historically, music theorists have claimed that the major triad functions as a strong instantiator of key, and that each of its inversions are harmonically equivalent. To examine these assumptions, subjects were tested with the Method of Paired Comparisons, and asked to judge the similarity of root, first inversion, and second inversion major triads drawn from keys of different degrees of musical relatedness. In Experiment 1, where triads were built on the tonics of two maximally-related keys (A and E major), only professional musicians demonstrated a separation of the triads on the basis of key, indicating that inversions of triads built on the same root-note were perceived as sounding similar to one another. The majority of moderately trained and inexperienced subjects tended to use a pitch-height strategy, in which triads containing upper notes that were close in absolute frequency were judged as sounding similar to one another. In Experiment 2, where triads were also included from a distantly related key (Bb major), the majority of professional musicians continued to group all triads on the basis of key, while some moderately-trained subjects confused the maximally-related keys, but perceived them as distinct from the more distant key. Other moderately-trained and musically-inexperienced subjects used a pitch·height strategy for judging similarity. In Experiments 3 and 4, chords were built on seven different rootnotes moving counterclockwise and clockwise, respectively, from a constant standard chord on the Circle of Fifths. The professional and moderately trained subjects tested did not show an especially strong tendency to judge chord similarity on the basis of musical key in either experiment. Inversion equivalence was demonstrated in each of these four experiments by subjects who judged triads built on the same root-note as sounding similar to one another. In Experiment 5, where seven Shepard chords (chords built to obscure pitch-height and inversion cues) were presented to only moderately-trained subjects, similarity judgements now appeared to be based on key. Conclusions are made regarding musical representation in a form described by the theoretic Circle of Fifths in musically-trained individuals.</p> / Thesis / Doctor of Philosophy (PhD)

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