This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned."

Intelligence and security informatics (ISI) can be broadly defined as the study of the development and use of advanced information technologies and systems for national and international security-related applications, through an integrated technological, organizational, and policy-based approach. In the past few years, ISI research has experienced tremendous growth and attracted substantial interest from academic researchers in related fields as well as practitioners from both government agencies and industry. The first two meetings (ISI 2003 and ISI 2004) in the ISI symposium and conference series were held in Tucson, Arizona, in 2003 and 2004, respectively. They provided a stimulating intellectual forum for discussion among previously disparate communities: academic researchers in information technologies, computer science, public policy, and social studies; local, state, and federal law enforcement and intelligence experts; and information technology industry consultants and practitioners. Building on the momentum of these ISI meetings and with sponsorship by the IEEE, we held the IEEE International Conference on Intelligence and Security Informatics (ISI 2005) in May 2005 in Atlanta, Georgia. In addition to the established and emerging ISI research topics covered at past ISI meetings, ISI 2005 included a new track on Terrorism Informatics, which is a new stream of terrorism research leveraging the latest advances in social science methodologies, and information technologies and tools. ISI 2005 was jointly hosted by Rutgers, the State University of New Jersey; the University of Arizona (UA); and the Georgia Institute of Technology (GATECH).

Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics. After introducing fundamental counting rules and the tools of graph theory and relations, the authors focus on three basic problems of combinatorics: counting, existence, and optimization problems. They discuss advanced tools for dealing with the counting problem, including generating functions, recurrences, inclusion/exclusion, and P lya theory. The text then covers combinatorial design, coding theory, and special problems in graph theory. It also illustrates the basic ideas of combinatorial optimization through a study of graphs and networks.