This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jager [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L = f0; 1g:Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jager [2001]. Our principal category is shown to be a topological universe and contains a subconstruct isomorphic to the category of probabilistic convergence spaces discussed in Kent and Richardson [1996] when L = [0; 1]: Fundamental work in lattice-valued convergence from the more general perspective of monads can be found in Gahler [1995]. Secondly, diagonal axioms are defned in the category whose objects consist of all the lattice valued convergence spaces. When the latter lattice is linearly ordered, a diagonal condition is given which characterizes those objects in the category that are determined by probabilistic convergence spaces which are topological. Certain background information regarding filters, convergence spaces, and diagonal axioms with its dual are given in Chapter 1. Chapter 2 describes Probabilistic Convergence and associated Diagonal axioms. Chapter 3 defines Jager convergence and proves that Jager's construct is isomorphic to a bireáective subconstruct of SL-CS. Furthermore, connections between the diagonal axioms discussed and those given by Gahler are explored. In Chapter 4, further categorical properties of SL-CS are discussed and in particular, it is shown that SL-CS is topological, cartesian closed, and extensional. Chapter 5 explores connections between diagonal axioms for objects in the sub construct δ(PCS) and SL-CS. Finally, recommendations for further research are provided.

The purpose of this study is to determine whether children with autism recognize the same perceptual voicing boundaries of stop consonants as normally developing children of the same age group. This was explored using three groups of participants: ten children with autism between the ages of 8-14, five typically developing children between the ages of 8-14, and five typically developing seven-year-old children. Children in all groups listened to initial stop consonant syllables with voicing contrasts, with voiced and voiceless cognates presented. The initial consonants were altered along a voice onset time continuum within the typically perceived boundaries of each consonant. Participants were instructed to select the box containing the letter of the initial consonant they perceive when they hear each syllable. Results revealed greater difference between the responses of the children with autism when compared with the older control group, than when compared with the younger children. The responses of the children with autism were more similar to those of the children in the second control group. This could be indicative of a delay in the children with autism of perception of the categorical boundaries along the dimension of voice onset time compared to typical children's perception of these consonants.

Adults perceive basic emotional facial expressions as discrete categories using categorical perception. Within categorical perception, discrimination of facial emotional expressions is better for between category faces than within category faces. In this thesis, I examined the developmental trajectory of categorical perception in early childhood. I also examined the relationship between sensitivity to physical differences in facial emotional expressions and the use of emotion labels in toddlers. In Chapter 2, I found that infants before 12-months failed to discriminate between category faces along a happy-sad continuum. In contrast, evidence suggest that 9- and 12-month old infants categorically perceived faces along a happy-angry continuum. These findings suggest that categorical perception may not develop concurrently for all emotions. In Chapter 3, I found that toddlers by 26-months of age categorically perceived faces along a happy-sad continuum. These results highlight the long developmental trajectory of categorical perception of facial emotional expressions across early childhood. In Chapter 4, I found a relationship between perceptual sensitivity to physical differences between happy and sad faces, and the emotion vocabulary size in 26-month-olds. This relationship suggests that learning about emotions may utilize information from multiple domains, and that learning in one domain may influence the development of another. The perception of facial emotional expressions is an essential component of early social emotional development. Categorical perception is a mechanism that aids in organizing complex social information from faces into actionable categories. The research in this thesis advances our understanding of early social perceptual development and the process that allow us to successfully navigate in the social world. / Dissertation / Doctor of Philosophy (PhD) / Humans are experts at reading faces. Specifically, they are capable of interpreting complex social information from faces, including emotions, and using this information to navigate social situations. In order to organize facial emotional information, humans use a mechanism called categorical perception to quickly and efficiently sort facial emotional information into discrete categories. Inferences can be made about members within a category, which aids in the prediction and production appropriate behaviours. However, there has been limited research into the development of categorical perception in early childhood. The key goal of this thesis was to develop infant and toddler appropriate methodologies that capture the development categorical perception. In this thesis, I found that categorical perception does not develop uniformly across all ages and between different emotions. Results suggest that perceptual sensitivity to differences in facial emotional expression may be influenced by the use of emotion labels, or vice versa.

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability. In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based upon general trends in the data, we recommend potential actions the company could take. Additionally, we examine how a company can utilize predictive modeling to help them adapt their decision-making process as the trends identified from the initial analysis of the data evolve over time.

This paper serves to address the effect of time on the sales of clothing retail, from 2010 to May 2019. The data was retrieved from the US Census, where N=113 observations were used, which were plotted to observe their trends. Once outliers and transformations were performed, the best model was fit, and diagnostic review occurred. Inspections for seasonality and forecasting was also conducted. The final model came out to be an ARIMA (2,0,1). Slight seasonality was present, but not enough to drastically influence the trends. Our results serve to highlight the economic growth of clothing retail sales for the past 8 years, cementing the significance of the production economy's stability. The quarterly GDP data was collected in order to find out the relationship with the differenced clothing data. Some observations of GDP data were affected by the clothing data before removing the seasonality. After removing the seasonality, the clothing expense is white noise and not predictable from the historical GDP.

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