In recent years quantum algorithms have become a popular area of mathematical research. Farhi and Gutmann introduced the concept of a quantum walk in 1998. In this thesis we investigate mixing properties of continuous-time quantum walks from a mathematical perspective. We focus on the connections between mixing properties and association schemes. There are three main goals of this thesis. Our primary goal is to develop the algebraic groundwork necessary to systematically study mixing properties of continuous-time quantum walks on regular graphs. Using these tools we achieve two additional goals: we construct new families of graphs that admit uniform mixing, and we prove that other families of graphs never admit uniform mixing. We begin by introducing association schemes and continuous-time quantum walks. Within this framework we develop specific algebraic machinery to tackle the uniform mixing problem. Our main algebraic result shows that if a graph has an irrational eigenvalue, then its transition matrix has at least one transcendental coordinate at all nonzero times. Next we study algebraic varieties related to uniform mixing to determine information about the coordinates of the corresponding transition matrices. Combining this with our main algebraic result we prove that uniform mixing does not occur on even cycles or prime cycles. However, we show that the probability distribution of a quantum walk on a prime cycle gets arbitrarily close to uniform. Finally we consider uniform mixing on Cayley graphs of elementary abelian groups. We utilize graph quotients to connect the mixing properties of these graphs to Hamming graphs. This enables us to find new results about uniform mixing on Cayley graphs of certain elementary abelian groups.

In biomolecules, the relationship among the sequence, molecular structure, and biological function are of very importance in the development of nanotechnology such as drug discovery. Previous studies involving multiple sequence alignment of biomolecules have demonstrated that interdependent or associated sites are indicative of the structural and functional characteristics of biomolecules, as an extension to methods such as consensus sequences analysis. In this thesis, a new method to detect associated sites in aligned sequence ensembles is proposed. It involves the use of multiple sub-tables (or levels) of two-dimensional contingency table analysis. The idea is to incorporate analysis by following an approach known as granular computing, which represents information at different levels of granularity or resolution. When associations of multiple sites in the sequence alignment converge, they reflect points of interrelatedness among the sites in the biomolecules. The study involves two different phases of analysis. The first phase includes labeling of the molecular sites in the p53 protein multiple sequence alignment according to the detected patterns. The sites are consequently labeled into three different types based on their site characteristics - conserved sites, associated sites, and hypervariate sites. To identify and label the associated sites, the proposed method is employed. In the second phase, the significance of the extracted site patterns is evaluated with respect to some of the structural and functional characteristics of the p53 protein. The results indicate that the extracted site patterns in combination with conserved sites are significantly associated with some of the known functionalities of p53 such as post translational modifications and the mutation frequency of the sites, hence establishing the link between these identified sites and the defined functionality. Furthermore, when these sites are aligned with p63 and p73, the homologs of p53, based on the common domains, the sites significantly discriminate between the human sequences of the p53 family. Therefore, the study confirms the importance of these detected sites that could indicate their differences in cancer suppressing property.

Data mining aims to discover interesting and unknown patterns in large-volume data. Association rule mining is one of the major data mining tasks, which attempts to find inherent relationships among data items in an application domain, such as supermarket basket analysis. An essential post-process in an association rule mining task is the evaluation of association rules by measures for their interestingness. Different interestingness measures have been proposed and studied. Given an association rule mining task, measures are assessed against a set of user-specified properties. However, in practice, given the subjectivity and inconsistencies in property specifications, it is a non-trivial task to make appropriate measure selections. In this work, we propose two novel approaches to assess interestingness measures. Our first approach utilizes the analytic hierarchy process to capture quantitatively domain-dependent requirements on properties, which are later used in assessing measures. This approach not only eliminates any inconsistencies in an end user’s property specifications through consistency checking but also is invariant to the number of association rules. Our second approach dynamically evaluates association rules according to a composite and collective effect of multiple measures. It interactively snapshots the end user’s domain- dependent requirements in evaluating association rules. In essence, our approach uses neural networks along with back-propagation learning to capture the relative importance of measures in evaluating association rules. Case studies and simulations have been conducted to show the effectiveness of our two approaches. / viii, 85 leaves : ill. ; 29 cm

Schema violation has been shown to have an impact on cognition. Previous research using reading tasks has shown that the impact is not the same across male and female characters, and research has shown that men and women hold different view of schemas. The Implicit Association Test (IAT) has been used as a method to investigate schema violation, but no study has effectively investigated gender differences. Therefore, this study specifically investigates the factors of participant and character gender on schema violation during the IAT. Event-related potentials (ERPs) were used to investigate the cognitive impact of schema violation while participants completed gender and sexuality IATs. Significant effects were found for participant gender and character gender in several ERP components (N100, P200, N400, and LPP), but only for the gender-career IAT. This suggests that on a basic cognitive level ERP activity is influenced by gender.

No description available.

Terrorism poses a significant challenge for psychology. Motivation to engage in such violent and anti-nonnative behavior has yet to be understood. The two studies described in the present thesis examined what psychological motivations might account for peoples' involvement in terrorism. Study 1 explored the collective narratives of participants with ties to the Liberation Tigers of Tamil Eelam. Participants' narratives conveyed the explicit theme of justice and the implicit theme of identity as motives for extreme violence. Based on these findings, study 2 investigated if social identity and justice motives would exceed a control condition in inciting participation in terrorism. In a laboratory setting, participants were recruited to partake in a fictitious terrorism plot. Recruitment that emphasized social identity motives was relatively more compelling for participants than justice motives. Results for both studies warrant further research into the psychological role that justice and identity might play in the use terrorism.

There is no abstract available for this thesis.

No description available.

<p>The visual system in humans provides the ability to interpret our surroundings from many distances. This complex system serves as a powerful sense which can drastically impact the quality of life when threatened or eliminated. While the mechanisms involved in visual interpretation are largely understood, many of the mechanisms of ocular diseases remain elusive. The most common ocular disorders are refractive errors, where failure of normal growth processes results in eye components with shape and sizes that are not matched to provide uncorrected sharp visual acuity without correction. Myopia, or nearsightedness, is a refractive error with prevalence rates of epidemic proportions in some urban Asian settings, and rising in other developed countries. Pathological, or high myopia, has an increased risk for potentially blinding ocular morbidities which can be irreversible and further negatively impact quality of life. Myopia, like other common ocular disorders, results from a combination of environmental and genetic factors. Over 20 candidate genomic regions have been identified as involved in myopic development progression. </p><p>One such locus, <italic>MYP3</italic>, on chromosome 12q21-23 spans nearly 44 Mb with more than 200 protein-encoding genes mapped within. Sizable candidate disease genomic regions typically require refinement to identify genes or variants within them which may contribute to disease development. Without an understanding of the underlying mechanistic framework of a disease, as is the case with myopia, biological inferences are difficult to make in prioritizing candidates, which can make finding true disease causing variants seem like finding a needle in a haystack. A better understanding of human ocular growth, as it relates to refractive error, may lead to more knowledgeable approaches to identifying the cause(s) of myopic development and associated ocular diseases. </p><p>To identify genes involved in ocular growth and development, whole genome expression patterns were assessed in human ocular tissues of fetal versus adult eyes, and adult posterior versus peripheral tissues. No database exists of fetal ocular tissue gene expression. In addition to providing insights into expression patterns during ocular development, these tissues were also compared as a surrogate to study rapid eye growth states such as in myopia. Only ocular tissue types with clinical phenotypes associated with myopic development were considered. Human retina/retinal pigment epithelium (RPE), choroid, sclera, cornea* and optic nerve* tissues were isolated from fetal (N=9; *N= 6) and adult (N=6) normal donor eyes. The Illumina® whole genome expression microarray platform was used to assess differential expression of genes. Fetal tissues were compared to their adult counterparts while adult posterior tissues were compared to their peripheral counterparts, and the differences in each were assessed using Ingenuity Pathway Analysis (IPA) for enriched functional groups and canonical pathways. Statistical significance for all tissue comparisons was determined using the Benjamin and Hochberg False Discovery Rate (FDR, 5%). Differentially expressed genes were compared to previously identified candidates for myopic development.</p><p>Additionally, qualitative and quantitative association studies in a large family (N=82) based high myopia cohort by genotyping 768 single nucleotide polymorphisms (SNPs) in the peak linkage area was performed to fine map the <italic>MYP3</italic> linkage peak. Qualitative testing for high myopia (&#8804; -5 diopter (D) affected, > -5 D unaffected) and quantitative testing on the average (avg) dioptric sphere (SPH) was performed. Five candidate SNPs were genotyped in a replicate high myopia cohort for independent validation. Additionally, the most significant SNPs were screened in a previously genotyped twin cohort as a second independent validation cohort.</p><p>Ocular growth expression data were used to help prioritize the resulting association candidates as supporting evidence and was not used on its own to identify or exclude candidates. Candidate genes (within 100 kilobases (kb) of highly associated SNPs) identified through either qualitative or quantitative association testing were screened in the most disease relevant tissues (retina/ retinal pigment epithelium (RPE), choroid and sclera) for differential expression during ocular growth and by physical regions of the tissues within the eye. Genes that were identified by microarray studies as being differentially expressed in one or more tissue were validated using quantitative real time PCR (RT-qPCR). </p><p>Significant gene expression changes with fold changes > 1.5 were found in adult versus fetal retina/RPE (N=1185), choroid (N=6446), sclera (N=1349), and cornea (N=3872), but not the optic nerve nor any of the central versus peripheral tissues. In all adult versus fetal tissues, differentially expressed genes belonging to cancer, development, and cell death/growth functional groups, as well as signaling canonical pathways were enriched. Seventeen genes previously associated with increased susceptibility for non-syndromic high myopia were in the most significant functional assignments for at least one adult versus fetal ocular tissue. In adult central versus peripheral tissues, there was considerably more variation by tissue in enriched functions and canonical pathways of differentially expressed genes. The only functional category shared by all three tissue types was development. </p><p><italic>MYP3</italic> association testing yielded several genetic markers as nominally significant in association with high myopia in qualitative testing including <italic>rs3803036</italic> (p=9.1X10-4), a missense mutation in <italic>PTPRR</italic>; and <italic>rs4764971</italic> (p = 6.1X10-4), an intronic SNP in <italic>UHRF1BP1L</italic>. After correction for multiple testing, quantitative tests found statistically significant SNPs<italic> rs4764971</italic> (p = 3.1x10-6), also found by qualitative testing; <italic>rs7134216</italic> (p = 5.4X10-7), in the 3<super>1</super> UTR of <italic>DEPDC4</italic>; and <italic>rs17306116<iitalic> (p < 9X10-4), intronic within <italic>PPFIA2<italic>. The intronic SNP in <italic>UHRF1BP1L</italic>, <italic>rs4764971</italic>, was validated for association with the quantitative trait of sphere (SPH) using an independently collected non-syndromic, high myopia cohort. SNPs within <italic>PTPRR</italic> (for quantitative association) and <italic>PPFIA2</italic> (for qualitative and quantitative association) both approached significance in the independent high myopia cohort.</p><p>As with screening genes previously implicated in myopic development, qualitative and quantitative association candidates were screened in the independent whole genome expression array analyses, comparing normal rapidly growing fetal to normal grown adult ocular tissues. <italic>PTPRR</italic> and <italic>PPFIA2<italic>, candidates from qualitative and quantitative association respectively, were both validated by RT-qPCR with differential expression in at least one disease relevant ocular tissue. <italic>PTPRR</italic> and <italic>PPFIA2<italic> belong to the same gene family- that of protein tyrosine phosphatase (PTP) genes. This family of genes relays extracellular signals that regulate cell growth, division, maturation and function, and its differential expression is consistent with our myopia surrogate model. </p><p>Many genes implicated in either syndromic or non-syndromic myopia were present in the most significantly enriched adult versus fetal functional and/or canonical pathways together. The adult versus fetal choroid and cornea tissue types had the most overlap with known non-syndromic myopic-associated genes in the most significantly enriched functional groups. Further exploration of the connections amongst these known genes may elucidate possible mechanistic roles for disease progression and/or reveal related novel candidate genes. Differentially expressed genes in central versus peripheral tissues yielded minimal overlap with genes implicated in myopia; however, in addition to broadening our understanding of the spatial variances in these tissues they may contain clues to the development and/or progression of other ocular diseases such as retinopathy of prematurity development.</p><p>The overlap with previously identified myopia-associated genes supports the model of eye growth for studying myopic development in human tissues. This expression data can be used both in prioritizing candidate genes other proposed genomic myopia loci, and also in detailed pathway analyses to identify potential biological mechanisms for candidates within these loci. Our most strongly associated candidate gene both in the discovery and replicate cohort was <italic>UHRF1BP1L</italic>, which was not differentially expressed in our data; however, interacting genes regulate the expression of at least one differentially expressed gene, indicating a possibly pathway connection. It is possible that differential expression may have been missed by the microarray data, or it may not be differentially expressed and affects myopic development through alternative or indirect means. While the expression data is a useful tool in prioritizing and inferring mechanistic roles for candidates, it cannot be used to exclude candidates. Deeper study of the pathways of candidate genes for myopic development may reveal connections to genes involved in ocular growth. Despite these potential limitations, two of the three novel candidates, <italic>PTPRR</italic> and <italic>PPFIA2</italic>, were supported by genomic convergence with the expression data, in addition to our discovery genetic association data. The other novel candidate, <italic>UHRF1BP1L</italic>, was validated in an independent Caucasian high-grade myopia cohort. Further validation and refinement of these three novel <italic>MYP3<italic> candidate genes is necessary to make further claims about their possible involvement in myopic progression.</p> / Dissertation

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