Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces

We use a modified S-iterative process to prove some strong and Δ-convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature

A Three-Dimensional Heat Map Matrix for Showing Co-relationships in Network Analysis

Many datasets are representation of networks in the real world. Exploratory data analysis, as a proven method in data science, can be used to discover patterns in networks and lead to meaningful questions for detailed data analysis. Showing co-occurrence of two related items is a widely used method in the exploratory data analysis of networks. The discovered co-occurrence patterns not only make the association visible, but also provide clues to predict future co-occurrence if the networks scale up. There are many visual techniques to show the co-occurrence association, such as D3 heat map and nodes-relationship cluster graph. Most of those techniques generate two dimensional diagrams as the visualization output. This thesis focuses on adding one more dimension to existing two dimensional heat map to show the co-occurrence between three items. The output is represented in a user interactive three-dimensional matrix. Several functions are developed to support the interactions between the user and the dataset. Among them a key function is a selection panel so, instead of load a huge dataset, the user can choose records of interest to analyze. The usefulness of the developed three-dimensional heat map is reflected in two successful case studies. One is the co-occurrence of elements in the formation of minerals species, and the other is the co-occurrence of topics in the research interests of people at the University of Idaho. The exploratory data analysis carried out in these two case studies shows interesting patterns of co-occurrence, and helps generate a few more thoughts and ideas for further data analysis. With small adaptations, the output of this research can also be applied to conduct visual co-occurrence analysis in other disciplines.masters, M.S., Computer Science -- University of Idaho - College of Graduate Studies, 2016-0