On b-chromatic Number of Prism Graph Families

A b-coloring of graph is a proper -coloring that verifies the following property: for every color class , 1≤≤, there exists a vertex , with color , such that all the other colors in are utilized in neighbors. The b-chromatic number of a graph , denoted by (), is the largest integer such that may have a b-coloring by colors. In this paper we discuss the b-coloring of prism graph , central graph of prism graph (), middle graph of prism graph () and the total graph of prism graph () and we obtain the b-chromatic number for these graphs

Design of Randomized Experiments in Networks

Over the last decade, the emergence of pervasive online and digitally enabled environments has created a rich source of detailed data on human behavior. Yet, the promise of big data has recently come under fire for its inability to separate correlation from causation-to derive actionable insights and yield effective policies. Fortunately, the same online platforms on which we interact on a day-to-day basis permit experimentation at large scales, ushering in a new movement toward big experiments. Randomized controlled trials are the heart of the scientific method and when designed correctly provide clean causal inferences that are robust and reproducible. However, the realization that our world is highly connected and that behavioral and economic outcomes at the individual and population level depend upon this connectivity challenges the very principles of experimental design. The proper design and analysis of experiments in networks is, therefore, critically important. In this work, we categorize and review the emerging strategies to design and analyze experiments in networks and discuss their strengths and weaknesses

Networked Experiments

This chapter considers the design and analysis of networked experiments, one of the most precise tools available for studying social behavior. As a result of digitization, the scale, scope and complexity of networked experiments have expanded significantly in recent years, creating a need for more robust design and analysis strategies. I first review innovations in networked experimental design, assessing the implications of the experimental setting, sampling, randomization procedures and treatment assignment. I then discuss the analysis of networked experiments, with particular emphasis on modeling treatment response assumptions, inference and estimation, and recent approaches to interference and uncertainty in dependent data. I conclude by discussing important challenges facing the future of networked experimentation, focusing on adaptive treatment assignment, novel randomization techniques, linking online treatments to offline responses and experimental validation of observational methods. I hope this framework can help guide future work toward a cumulative research tradition in networked experimentation

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

Graduate Academic Catalog (1993-94)

This Graduate Catalog is provided by the Graduate Faculty of the University of Nebraska at Omaha in the hope that it will be a source of information to you on the graduate programs available through our University. We are proud of our University and of its programs. We encourage you to become acquainted with us and with the many sources available to the community through the University. The lamp of learning which you see on this page is the symbol of the scholarship and creative activity which characterizes every graduate program at the University of Nebraska at Omaha. It is this emphasis which distinguishes graduate studies from undergraduate studies. We have tried to include as much information as possible, but obviously we could not include everything. If you have questions which are not answered here, please feel free to call on the Office of Graduate Studies, 204 Eppley Administration Building, telephone (402) 554-2341

Graduate Academic Catalog (1990-91)

This Graduate Catalog is provided by the Graduate Faculty of the University of Nebraska at Omaha in the hope that it will be a source of information to you on the graduate programs available through our University. We are proud of our University and of its programs. We encourage you to become acquainted with us and with the many sources available to the community through the University. The lamp of learning which you see on this page is the symbol of the scholarship and creative activity which characterizes every graduate program at the University of Nebraska at Omaha. It is this emphasis which distinguishes graduate studies from undergraduate studies. We have tried to include as much information as possible, but obviously we could not include everything. If you have questions which are not answered here, please feel free to call on the Office of Graduate Studies, 204 Eppley Administration Building, telephone (402) 554-2341