A biological reaction diusion model has gained much attention recently. This model is formulated as a system of nonlinear partial dierential equations that contains an unknown function of one dependent variable. How to determine this unknown function is complicated but also useful. This model is considered in this master thesis. The generators of the equivalence groups and invariant solutions are calculated.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 104-105).

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 226-232).

We give examples of two non nuclear non normal Hilbert-Schmidt operators that are not unitarily equivalent but have the same traces and kernel.

Psychological flexibility has been identified as an important construct within Relational Frame Theory and the examination of third-wave behavioral therapies. While psychological flexibility is defined within the context of relational responding, there is no research that directly assesses its relationship to measures of equivalence. The current study examined the relationship between PEAK Equivalence Pre-Assessment and scores of psychological inflexibility (via the AFQ-Y) in school-aged children with disabilities. Pearson correlations were utilized to examine the relationships between scores on PEAK and the AFQ-Y, as well as to examine the correlations among PEAK subtests. A large negative and statistically significant correlation (r =-.64, p < .05) was found between measures of psychological inflexibility and PEAK equivalence scores. Correlations among PEAK Equivalence Pre-Assessment subtests were line with previous research by Dixon, Belisle, & Stanley (in review), providing additional information for the relationship among measured components of equivalence. These findings have implications for guiding educational and therapeutic intervention, as well as provide additional evidence of the utility of the PEAK Equivalence Module.

Research surrounding psychological flexibility has begun to develop in recent decades. It has proven to be an important construct within the examination of third wave behavioral therapies and Relational Frame Theory. Though defined within the context of relational responding, there is little research directly assessing the relationship of psychological flexibility to measures of equivalence. The current study compared the scores of the PEAK Equivalence Pre-Assessment (to measure equivalence) and the scores from the AFQ-Y (to measure psychological inflexibility) to examine this relationship in school-aged children with ASD. The relationship between the total scores of the PEAK assessment and the scores of the AFQ-Y was examined by using a Pearson correlation. Results showed a statistically significant negative correlation (r = -.63, p<.05) between these measures. A Pearson correlation was then also used to examine the correlations among the PEAK subtests. As anticipated, the results showed a significant positive correlation among each of the components of equivalence providing additional information regarding the relationship among measured components of equivalence. These findings support recent research, and can help guide future educational and therapeutic interventions. Keywords: Autism (ASD), equivalence, PEAK, psychological flexibility

AN ABSTRACT OF THE THESIS OF Hailey Williams, for the Master’s Degree in Behavior Analysis, presented on 7/8/16, at Southern Illinois University Carbondale. TITLE: TEACHING EQUIVALENCE RELATIONS THROUGH DRAWING USING THE PEAK-E CURRICULUM MAJOR PROFESSOR: Dr. Mark R. Dixon The purpose of this study was to observe the formation of equivalence response classes using drawing to demonstrate the transformation of stimulus function from arbitrary textual words to simple drawings. Two children with Autism were taught directly trained relations, which paired together three stimuli from three separate class formations. The children were taught to relate A-B and B-C relations in trial blocks, and then tested with B-A and C-A relations. This train-test method was used to see if derived relations had emerged. Both participants demonstrated adequate learning in achieve mastery criteria in all the directly trained and derived relations from this study. The data is represented in a multiple baseline graph with an embedded multiple probe design. The outcome of this study indicates that the use of drawing and other creative behaviors have value in both relation frame theory and PEAK. There are also several implications of the study addressed here, including drawing as a verbal behavior and the role of internal events and covert behaviors in learning.

The current study evaluated the methods outlined in the Promoting the Emergence of Advanced Knowledge Relational Training System Transformation Module (PEAK-T). Researches evaluated the validity and efficacy of the PEAK-T assessment at identifying skill deficits as well as its ability to identify appropriate intervention to target those deficits. Additionally, the current study evaluated the efficacy and validity of the methods as outline by the PEAK-T curriculum at teaching target skills. The PEAK-T assessment was conducted to identify three programs for each of the participants. Baseline probes of three boys with autism suggested that programs identified by the PEAK-T assessment were not in their repertories prior to treatment. Following treatment each of the participants was able to achieve mastery of all three programs this included directly trained as well as derived relations. The PEAK-T assessment was run following the intervention, all participants exhibited an increase in total PEAK-T score.

No description available.

In this thesis, we explain the term CCZ-equivalence in more detail to- gether with an analysis of a special type of matrices of this equivalence. We also clarify the higher order differential cryptanalysis and its generalized ver- sion. To demonstrate this method we present several attacks on a simple five round Feistel cipher, two of these attacks are our own. We have implemented the most important attacks and results of these experiments can be found in the text. We also explore how to use a decomposition F = F2 ◦F−1 1 (where F1 and F2 are permutations) to construct a generalized higher order differential attack to a block cipher with an S-box F. This construction may be used while searching for an attack to F using the CCZ-equivalence which is gener- ally a hard question. The result of our research is a theorem which presents a necessary condition on a degree of F which is needed for an existence of such a decomposition. 1