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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.

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This study evaluated the effects of the type of language used by the therapist during a functional analysis on rates of challenging behavior with individuals who came from families where Spanish was the primary language. Three individuals with autism spectrum disorder who live in a residential treatment facility participated in a multi-element (i.e., demand, attention, play- verbal, and play-nonverbal) functional analysis (FA). The FA was conducted in an ABAB experimental design with the A conditions conducted in Spanish and the B conditions conducted in English. Language did not have an effect on rates of challenging behavior during the FA. One participant displayed no responding across conditions and the other two participants responded similarly during the demand conditions regardless of the language in which the conditions were conducted. Functional communication training (FCT) was conducted for one of these two participants in both languages. The results for this individual that there was no difference according to language in rates of challenging behavior as well as acquisition and maintenance of a functionally communicative response. Keywords: functional analysis, language, functional communication training, Autism Spectrum Disorder, problem behavior / Applied Behavioral Analysis

Proper formation of the heart is a critical developmental event which requires strict regulation of coordinated cardial cell adhesion, alignment, and migration. The simple, tube-like heart of the fruit fly, Drosophila melanogaster, has proven to be an attractive system in which to study the regulatory pathways which control cardiogenesis. This is mainly due to its strikingly similarity to the vertebrate heart during early embryogenesis. In addition, many genes identified in association with congenital heart disease in humans have homologues in Drosophila, suggesting that this model organism has great potential to contribute to cardiovascular research. The extracellular matrix protein encoded by slit is a ligand for the receptors Robo, and Robo2 (lea). Recently, a third receptor for Slit has been identified as the heparin sulfate proteoglycan Syndecan. The main objective of this thesis was to use time lapse confocal imaging in order to develop further understanding of the mechanisms which result in heart assembly defects in slit, robo, lea, and syndecan mutants. We also aimed to gain a better understanding of the role of Syndecan within the Slit-Robo pathway and elucidate its relative contribution to development of the mature heart. In mutants homozygous for slit, as well as mutants doubly heterozygous for robo and lea, cardial cell alignment, adhesion, and synchronized migration were disrupted. The heart phenotype of syndecan homozygous mutants was similar that of slit and robo, lea, however the migration speed of cells to the midline did not seem to be affected. Based on our findings, we hypothesize that Slit may have Syndecan-dependent and Syndecan-independent functions in the heart. / Thesis / Master of Science (MSc)

In this dissertation I am using M. truncatula as a model legume that forms indeterminate nodules with rhizobia under limited nitrogen conditions. I take advantage of an M. truncatula Tnt1 mutant population that provides a useful resource to uncover and characterize novel genes. Here, I focused on several objectives. First, I carried out forward and reverse genetic screening of M. truncatula Tnt1 mutant populations to uncover novel genes involved in symbiotic nitrogen fixation. Second, I focused on reverse genetic screening of two genes, identified as encoding blue copper proteins, and characterization of their mutants' potential phenotypes. Third, I further characterized a nodule essential gene, M. truncatula vacuolar iron transporter like 8 (MtVTL8), which encodes a nodule specific iron transporter. I characterized the expression pattern, expression localization and function of MtVTL8. Additionally, I characterized several residues predicted to be essential to function using a model based on the known crystal structure of Eucalyptus grandis vacuolar iron transporter 1 (EgVIT1), a homologous protein to MtVTL8. I identified several potential essential residues of the MtVTL8 protein, mutagenized them, and through complementation experiments in planta and in yeast assessed functionality of the resulting protein. This helped us to better understand the potential mechanism by which MtVTL8 functions.

A nonlinear movmg contact algorithm has been implemented to model the sticking-sliding inelastic behavior in the interlocks of steel sheet pile sections subjected to axial tension. Previously, numerical instabilities were encountered during the solution process while conducting a series of verification problems for the algorithm by the Newton-Raphson method. In an attempt to identify the cause of these instabilities, an in-depth study of the effect of fineness of the finite element mesh on the convergence of the solution has been undertaken. The solution process credited to Riks and Wempner has been used to find the postbuckling equilibrium path of shallow reticulated domes. This algorithm, with some modifications, is used to move from one load step to another step in this study. As in most nonlinear problems, the size of the load step influences the rate of convergence. In addition, in the moving contact problem nodes can move along the sides of an element on the contact surface. Thus, the mesh refinement also affects the rate of convergence. To study the effects of both of these parameters, a series of test problems was run with variable load steps and mesh refinements. The modified Riks-Wempner algorithm, which automatically adjusts the load step size as the solution process advances, successfully solved all the inelastic and large displacement problems attempted. From the mesh refinement studies two conclusions were reached: for curved boundaries use curved elements and avoid the use of irregularly shaped elements. Finally, the improved solution algorithm is applied fo sheet pile interlocks loaded in axial tension. Results for progressively increasing load show the spread of yielding in the thumbs and fingers of the interlocks and the sliding of one past another as the deformations increase. / Master of Science