A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

CHARACTERISTICS OF PRIVATE HIGH SCHOOLS FOR STUDENTS WITH EMOTIONAL DISABILITIES AND PERCEPTIONS OF THEIR PUBLIC SCHOOL CASE MANAGERS

Placement of students with disabilities in private special-education schools remains costly and controversial. This is particularly concerning, given the lack of research on the characteristics and quality of these restrictive settings. The purpose of this study was to identify the academic and vocational course offerings and behavioral supports provided in private special-education schools the serve high school students with emotional disabilities (ED). Second, the research examined the perceptions of the quality of services in these setting from the perspectives of public school case managers. Using a mixed-method design to collect data, 9 administrative heads of private special-education schools were surveyed, and 7 public school case managers were interviewed. Results indicated that (a) private special-education schools offer the basic academic core courses needed to meet graduation requirements, (b) vocational options for students enrolled in these schools are quite limited, (c) these schools provide a variety of behavioral interventions and supports, and (d) case managers are concerned with the lack of academic rigor and inconsistent programming at these schools but applauded the notion that students with ED are exiting with a high school diploma. Findings from this study may have policy implications for improving and developing programming options for high school students with ED.