The subject of this thesis is the fractional order Sobolev space, H[superscript]r[subscript]p, as considered by Nikol'skii; the goal is to demonstrate an imbedding theorem for H[superscript]r[subscript]p analogous to the classical imbedding theorem for W[superscript]m[subscript]p which was first shown by Sobolev. The properties established here for spaces H[superscript]r[subscript]p defined over all of Rn, including completeness and imbedding theorems, are demonstrated by a technique involving the approximation of functions in those spaces by entire functions of the exponential type. Properties of such entire functions, which are of interest in theire own right, are developed in a separate chapter. An extension theorem for differentiable developed in a separate chapter. An extension theorem for differentiable functions defined over an open subset of Rn is also proved. / Science, Faculty of / Mathematics, Department of / Graduate

In this thesis we are concerned with obtaining an integral representation of a class of nonlinear additive and biadditive functionals on function spaces of measurable functions and on L[superscript] p-spaces, p > 0 . The associated measure space is essentially atom-free finite and o-finite. Also we are concerned to the extend the presence of atoms in a measure space complicates the representation theory for functionals of the type under consideration here. A class of nonlinear transformations on L[superscript] p-spaces, 1 ≤ p ≤ ∞, called Urysohn operators. [11] taking measurable functions to measurable functions is studied and we describe an integral representation for this class when the associated measure space is an arbitrary 0-finite measure space and this characterization extends our previous results where the measure space considered was atom-free. / Science, Faculty of / Mathematics, Department of / Graduate

The aim of this study is to compare and contrast the teaching of the adult illiterates as done by Cora Stewart in the United States of America, James Yen in China, and Frank Laubach in Africa. / Typescript. / "September 1949." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts under Plan II." / Advisor: Nita K. Pyburn, Professor Directing Paper. / Includes bibliographical references (leaves 51-54).

In typed functional programming there is often the need for combining pure and monadic (or other effectful) computations, but the required lifting must be done manually by the programmer and may result in cluttered code. This thesis explores ways to allow the compiler to perform this task automat- ically. Several possible approaches are described, where the final one reduces the task to solving a system of linear diophantine equations. Apart from monads, the described method is also considered for the case of applicative functors as another abstraction to represent effectful operations. 1

This thesis has two overall themes, both of which involve the word functional, albeit in different contexts. The theme that motivates two of the chapters is the development of methods that enable a deeper understanding of the variability of functional data. The theme of the final chapter is the development of methods that enable a deeper understanding of the landscape of functionality across the human genome in different human tissues. The first chapter of this thesis provides a framework for quantifying the variability of functional data and for analyzing the factors that affect this variability. We extend functional principal components analysis by modeling the variance of principal component scores. We pose a Bayesian model, which we estimate using variational Bayes methods. We illustrate our model with an application to a kinematic dataset of two-dimensional planar reaching motions by healthy subjects, showing the effect of learning on motion variability. The second chapter of this thesis provides an alternative method for decomposing functional data that follows a Poisson distribution. Classical methods pose a latent Gaussian process that is then linked to the observed data via a logarithmic link function. We pose an alternative model that draws on ideas from non-negative matrix factorization, in which we constrain both scores and spline coefficient vectors for the functional prototypes to be non-negative. We impose smoothness on the functional prototypes. We estimate our model using the method of alternating minimization. We illustrate our model with an application to a dataset of accelerometer readings from elderly healthy Americans. The third chapter of this thesis focuses on functional genomics, rather than functional data analysis. Here we pose a method for unsupervised clustering of functional genomics data. Our method is non-parametric, allowing for flexible modeling of the functional genomics data without binarization. We estimate our model using variational Bayes methods, and illustrate it by calculating genome-wide functional scores (based on a partition of our clusters into functional and non-functional clusters) for 127 different human tissues. We show that these genome-wide and tissue-specific functional scores provide state-of-the-art functional prediction.

The current study evaluated the effectiveness of delivering behavioral assessment and treatment to reduce challenging behavior shown by Korean children with ASD by using in-home telehealth from the U.S. The participants were five young children diagnosed with autism who lived in Korea and displayed challenging behavior. The children’s mothers, who had no previous experience in functional analysis (FA) and functional communication training (FCT) procedures, implemented all procedures with coaching provided by a behavior consultant during assessment and treatment sessions via telehealth. The results of the current study showed that functional analyses conducted via telehealth from the U.S. to the children’s homes in Korea were effective in identifying the function of challenging behavior for each participant. Furthermore, the results also showed that challenging behavior was reduced by 100% across all children by the end of treatment. These results suggest that telehealth can be an effective and efficient way to deliver behavior analytic services for underserved populations in countries like Korea.

Purpose: An important challenge for eye care practitioners is meeting the needs of an ever-increasing elderly population. Standard vision tests are inadequate for determining performance in real life situations. One test that was developed to address this issue is the Attended Field of View (AFOV) test (Coeckelbergh et al, 2004). This test was designed to assess the functional field of view when people are allowed to make habitual head and eye movements. The original AFOV test is no longer available. This research seeks to develop a replacement AFOV test and to demonstrate its reliability as an assessment tool. Methods: Two groups of participants were recruited. The first group consisted of seven participants between the ages of 15-41 years. The second group consisted of seven participants between the ages of 59–79 years. All subjects had visual acuities equal or better than 20/25 and no history of visual field loss. A computer-generated display was observed from a 60cm distance. The display consisted of 24 white circles on a gray background and one open circle (target). The circles were organized with one circle in the centre and eight located radially at three eccentricities (4, 8, and 12 degrees). Participants were required to locate the target circle and identify the gap direction. A response was considered correct when both the location and gap direction were accurate. Using a weighted staircase method based on presentation time each location was evaluated independently. Viewing efficiency [log (1/threshold presentation time)] was obtained for each location. The data was analyzed using repeated measures ANOVA. Results: A comparison of viewing efficiency for the two age groups demonstrates that viewing efficiency is consistently lower for the older group at all three visits. The main effect of age was observed (F1,12=25.842;p=0.000). In the older group, a significant difference was found between the second and third visits. This difference was not found in the younger group. A main effect of eccentricity was found in both groups (F2,36=30.84;p<0.000), but no interaction was observed between eccentricity and group (F2,36=0.42;p=0.662). Viewing efficiency values in the older group were lower in all directions (main effect of age) (F1,96=150.36;p<0.000). Directional variations in viewing efficiency were observed showing higher values in the horizontal axes (directions Right and Left) than along the vertical axes (directions Up and Down) in both groups. A comparison of superior and inferior hemifield data shows consistent differences for both age groups. The superior hemifield (average of directions located superiorly to the horizontal axis) demonstrate higher viewing efficiency values (better performance) than the inferior hemifield. Conclusions: The use of the new AFOV test requires a practice time before its use in order to avoid the confound of a learning effect, but subsequent data is reliable in young people. The learning effect was more significant in older people and for this reason the use of the test should be preceded by a longer practice session in this population. When interpreting the results of this test one must account for eccentricity, direction, and age.

Purpose: An important challenge for eye care practitioners is meeting the needs of an ever-increasing elderly population. Standard vision tests are inadequate for determining performance in real life situations. One test that was developed to address this issue is the Attended Field of View (AFOV) test (Coeckelbergh et al, 2004). This test was designed to assess the functional field of view when people are allowed to make habitual head and eye movements. The original AFOV test is no longer available. This research seeks to develop a replacement AFOV test and to demonstrate its reliability as an assessment tool. Methods: Two groups of participants were recruited. The first group consisted of seven participants between the ages of 15-41 years. The second group consisted of seven participants between the ages of 59–79 years. All subjects had visual acuities equal or better than 20/25 and no history of visual field loss. A computer-generated display was observed from a 60cm distance. The display consisted of 24 white circles on a gray background and one open circle (target). The circles were organized with one circle in the centre and eight located radially at three eccentricities (4, 8, and 12 degrees). Participants were required to locate the target circle and identify the gap direction. A response was considered correct when both the location and gap direction were accurate. Using a weighted staircase method based on presentation time each location was evaluated independently. Viewing efficiency [log (1/threshold presentation time)] was obtained for each location. The data was analyzed using repeated measures ANOVA. Results: A comparison of viewing efficiency for the two age groups demonstrates that viewing efficiency is consistently lower for the older group at all three visits. The main effect of age was observed (F1,12=25.842;p=0.000). In the older group, a significant difference was found between the second and third visits. This difference was not found in the younger group. A main effect of eccentricity was found in both groups (F2,36=30.84;p<0.000), but no interaction was observed between eccentricity and group (F2,36=0.42;p=0.662). Viewing efficiency values in the older group were lower in all directions (main effect of age) (F1,96=150.36;p<0.000). Directional variations in viewing efficiency were observed showing higher values in the horizontal axes (directions Right and Left) than along the vertical axes (directions Up and Down) in both groups. A comparison of superior and inferior hemifield data shows consistent differences for both age groups. The superior hemifield (average of directions located superiorly to the horizontal axis) demonstrate higher viewing efficiency values (better performance) than the inferior hemifield. Conclusions: The use of the new AFOV test requires a practice time before its use in order to avoid the confound of a learning effect, but subsequent data is reliable in young people. The learning effect was more significant in older people and for this reason the use of the test should be preceded by a longer practice session in this population. When interpreting the results of this test one must account for eccentricity, direction, and age.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Coq; monads; functional reactive programming; formal verification. Includes bibliographical references (leaves 31-32).

Students commonly engage in problem behaviors, yet teachers report handling difficult behavior as their biggest challenge. Some research over the last few decades has used functional analyses (FAs) to determine the function of student’s problem behavior and then developed functional-based interventions based on the FA findings. Despite the success of the studies, research has indicated traditional FA methodologies are not always feasible for teachers and/or schools. Therefore, a need still exists to develop better and more efficient ways to train teachers how to conduct FAs in the classroom. Thus, the purpose of the current study was to evaluate the effectiveness of using virtual video models to train future teachers how to conduct trial based functional analyses (TBFAs). Additionally, the current study sought to assess if the participants could generalize their skills learned virtually to an in person setting. Three future teachers enrolled in education courses at a southeastern university participated in the study and watched video models of each of the TBFA conditions (attention, demand, tangible, and ignore). After watching the videos, participants were then asked to conduct each trial virtually, and then complete each trial the following day in person. A multiple baseline design across participants was used, and results indicated the videos were effective at teaching the participants to conduct a TBFA. Specifically, all three future teachers successfully conducted every trial of a TBFA with high procedural integrity virtually. The virtual training then generalized well into an in person setting, with only one participant needing additional feedback. Additionally, results indicate the virtual intervention was socially valid for all participants. Limitations and directions for future research are also discussed.