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After a review of the literature on Pivotal Response Treatment (PRT) in young children with developmental delays, less was known on its effects on challenging behavior and functional communication in preschool age children receiving services in a traditional public school. A multiple baseline design across three participants was used to evaluate the effects of PRT on the functional communication of three preschool students with developmental delays. Based on a functional analysis, we also observed the effects of PRT on challenging behavior. A visual analysis of the data revealed a functional relation between PRT and functional communication and provided promising evidence regarding the effectiveness of function aligned mands in reducing problem behavior. Brief surveys and interviews revealed that the intervention was feasible and effective based on staff and family reports. This research study adds to the evidence supporting the use of the intervention and expands on the knowledge base surrounding function aligned communication. Implications for research and practice are discussed.

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In this thesis we examine properties of Gelfand-Shilov spaces Ssσ and Pilipović spaces Σsσ. These are spaces of smooth functions which, along with their Fourier transforms, decay sub-exponentially. Results for the two types of spaces relating to Fourier transforms, analyticity of functions, triviality of the spaces and short-time Fourier transforms are explored. It is determined that Σsσ is nontrivial if and only if s+σ>1, and that results for Ssσ when s+σ≥1 can generally be found to have corresponding counterparts for Σsσ when s+σ>1.

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Since their discovery in the early 1950's, frames have emerged as an important tool in areas such as signal processing, image processing, data compression and sampling theory, just to name a few. Our purpose of this dissertation is to investigate dual frames and the ability to find dual frames which are optimal when coping with the problem of erasures in data transmission. In addition, we study a special class of frames which exhibit algebraic structure, discrete Gabor frames. Much work has been done in the study of discrete Gabor frames in Rn, but very little is known about the l2(Z) case or the l2(Zd) case. We establish some basic Gabor frame theory for l2(Z) and then generalize to the l2(Zd) case.

Tolerating transitions between activities and locations is an essential daily-living skill, as transitions are inevitable in most typical settings. However, for some individuals, requests to transition may occasion problem behavior which can interfere with daily routines and result in a more restrictive lifestyle. The unpredictability of transitions is often assumed to be aversive and functionally related to transition-related problem behavior. As a result, advance notice procedures are often recommended to reduce problem behavior during transitions. However, Brewer et al. (2014) found mixed results for the use of advance notice highlighting some studies where advance notice procedures reduced problem behavior and others where the procedures were inefficacious. In this study, we reviewed the relevant literature between 1994 and 2020, including studies reviewed by Brewer et al. (2014) and extended Brewer et al.’s (2014) review in a number of ways. We first summarized the current literature, including new studies published since Brewer et al.’s (2014) review, which included a total of 28 applications of advance notice published in 14 papers. Next, we identified key features of each study, including the presence or absence of demonstrated functional relations, inclusion of additional antecedent or consequent interventions, and evaluation and control of the effects of pre- and post-transition reinforcers on responding. Then we identified gaps in current knowledge regarding predictability and made research recommendations for addressing these gaps. Finally, we discuss practice recommendations for transition-related problem behavior based on current research.

The individual functional analysis (FA) is the most widely used method to identify variables that influence the occurrence of problem behavior. Researchers often modify the FA after the analysis reveals undifferentiated responding. The interview-informed synthesized contingency analysis (IISCA) is one of the most substantial variations of the FA that builds upon the FA modifications. We evaluated the use of the two different functional analytic methods, the FA and IISCA, and the subsequent function-based treatment to reduce problem behavior for three children with autism spectrum disorder (ASD). The individual FA and the IISCA demonstrated differentiated responding for all participants. The treatment based on the results from the traditional FA was effective for all children. We discuss the implications of these findings.

While descriptive assessment outcomes show limited correspondence with experimental analysis outcomes, they are still often used in the treatment of problem behavior. The most effective way of treating problem behavior is by manipulating its controlling variables; however, if descriptive analyses are not depicting accurate environment-behavior relations, then treatments based off of descriptive analysis results have a higher chance of failing. The current study looks to replicate and extend the literature on utility descriptive assessments by analyzing three different data analysis methods. Three children with a diagnosis of autism were exposed to two types of experimental analyses. Following experimental analyses, descriptive assessments were completed and analyzed to determine correlations between the behavior and environmental events. The results from the three investigated data analysis methods were then compared to the outcomes of the experimental analyses.

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