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Title
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Minimum embedding dimension from the perspective of persistent homology
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Creator
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Sukhu, Christopher Lloyd
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Date
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2019
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Collection
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Electronic Theses & Dissertations
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Description
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"We investigate the use of 1-dimensional persistence diagrams to determine minimum embedding dimension. In particular, we test the claim that persistence diagrams look qualitatively the same once the correct dimension is reached. In some cases, this appears to not be true so we turn to a quantitative measure, the bottleneck distance, to see if the persistence diagrams are close once the minimum embedding dimension is attained. In some instances, we see that the persistence diagrams fail to...
Show more"We investigate the use of 1-dimensional persistence diagrams to determine minimum embedding dimension. In particular, we test the claim that persistence diagrams look qualitatively the same once the correct dimension is reached. In some cases, this appears to not be true so we turn to a quantitative measure, the bottleneck distance, to see if the persistence diagrams are close once the minimum embedding dimension is attained. In some instances, we see that the persistence diagrams fail to converge experimentally under the bottleneck distance. The main issue appears to be that it is difficult to explicitly characterize the persistent homology of delay embeddings of arbitrary time series. Instead we restrict to periodic time series where there exists such an explicit characterization. We apply Fourier analysis to see that that number of peaks in the frequency spectrum of a delay embedded time series is related to the minimum embedding dimension. Moreover, we give a method to filter out less significant peaks while not altering the persistent homology much, with respect to the bottleneck distance."--Page ii.
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Title
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The effectiveness of mirror imitation training on the generalization of imitation skills for children with autism spectrum disorder
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Creator
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Galimberti, Anjela Janai
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Date
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2019
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Collection
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Electronic Theses & Dissertations
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Description
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"The ability to imitate is a foundational skill related to multiple aspects of social, play, and language development in children. However, many children with autism spectrum disorder (ASD) do not imitate as effectively as their typically developing peers and therefore need direct instruction to acquire imitative repertoires. The current study investigated the effectiveness of Mirror Imitation Training: a relatively novel instructional procedure which uses a mirror as a tool to teach...
Show more"The ability to imitate is a foundational skill related to multiple aspects of social, play, and language development in children. However, many children with autism spectrum disorder (ASD) do not imitate as effectively as their typically developing peers and therefore need direct instruction to acquire imitative repertoires. The current study investigated the effectiveness of Mirror Imitation Training: a relatively novel instructional procedure which uses a mirror as a tool to teach imitation skills. Three children with autism spectrum disorder who did not demonstrate a generalized imitation repertoire despite exposure to conventional imitation training methods were selected for participation. For all three participants, mirror imitation training was effective at producing skill acquisition across two sets of imitation targets and increased responding to the remaining untrained sets of imitation targets. Supplemental findings also showed 2 of the 3 participants required fewer sessions to criteria on set 2 after meeting criterion for their set 1 with MIT. These findings identify mirror imitation training as a promising teaching method to promote generalized imitation skills in children with ASD who do not demonstrate generalized imitation skills when taught with more traditional methods of imitation instruction."--Page ii.
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Title
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A comparison of two mediation analysis methods with sequential mediators
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Creator
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Bennett, Kyle
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Date
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2019
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Collection
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Electronic Theses & Dissertations
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Description
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"Two methods for mediation analysis with sequential mediators were compared using multiple simulation scenarios. The performances of each method were assessed using three key metrics: relative bias, root mean square error, and coverage. The methods shared both similarities and key differences and some modification and adjustment were necessary to perform comparable simulations across the scenarios. Overall performance was assessed primarily using relative bias, where each simulated effect...
Show more"Two methods for mediation analysis with sequential mediators were compared using multiple simulation scenarios. The performances of each method were assessed using three key metrics: relative bias, root mean square error, and coverage. The methods shared both similarities and key differences and some modification and adjustment were necessary to perform comparable simulations across the scenarios. Overall performance was assessed primarily using relative bias, where each simulated effect estimate was compared to a "true" effect generated by simulating from a theoretical super population. Simulation scenarios included correctly specified models using both methods and various mis-specified estimation models by incorrectly specifying a critical parameter in the model to assess the performance and robustness of each mediation analysis method. The results of the simulations suggest that one method was particularly more resilient to mis-specification of the model over the other, and that proper specification of the marginal structural model is also critical to minimizing bias and maximizing coverage."--Page ii.
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