0.1 Gaps in Optimizing A comparison of the levels of development of Operations Research, Simulation Technique and Optimal Control Theory appears to gain increasing interest. Operations Research Sciences achieved very high mathematical standards and solved a great amount of important optimization problems, mainly at the level of management of private corporation and civil or military government tasks, however, these achievements are seldom incorporated in the mathematical curriculum of modern universities. Nevertheless, Operations Research seems to have failed in solving long range or strategical problems as they arise in any broader social, economical or political context (MUller-Merbach, 1976). Also for the weakest task, namely that of improving theory building, system simulation works as an optimization tool. Simulation models of large complex systems, like socio economical or political ones, failed until now to fit large empirical data bases. This was, in fact, one of the few serious objections against the form in which Forrester solved some problems modelling and simulating urban and world de velopments (Forrester, 1969; Forrester, 1971; IEEE-SCC October 197o; IEEE-SMC April 1972; Mass, 1974; Schroeder, 1975).

This book is a presentation of my recent research work into the theory and applications of mathematical relations between finite sets. The consequent results and concepts are expressed in 'conjunction' with the idea of a union of simplicial complexes and the algorithms and overall methodology have become known as Q-Analysis. The mathematical ideas are essentially comhinatorial and are developed in Section-A of the book, whilst Section-R contains an application to a community study (that of the IJniversity of Rssex). All of the work has been published elsewhere, in the usual form of papers, and a comprehensive introduction to the whole approach will be found in my earlier book, Mathematical Structure in Human Affairs (Heinemann, London 1974). Much of the research work referred to in this present hook would not have been possible without the co-operation of my research team, of whom I would particularly like to thank J.II. Johnson, and its puhlication owes a lot to the secretarial help provided by ~Iary Low. R.H. Atkin IJniversity of Rssex U.K.

First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.

1.1 Statement of the Problem This work describes a new and effective computer algorithm for detecting the contours of ribs in ehest radiographs. The problem, which is common to both the research areas of Machine Vision and Biomedical Computing, is to extract graphical information, such as that represented in Figure 1-lb, from a picture such as Figure 1-la. Figure 1-la shows a typical posterior-anterior (PA) ehest radiograph while Figure 1-lb shows a drawing of the ventral aspect of the thorax. lt is hoped that this researchwill contribute significantly toward developing an automated system for interpreting ehest radio graphs. 1.2 Why Have We Carried Out This Research? Since about one-third of the 650,000,000 medical radiographs (X-ray photographs) taken annually in the United States areehest radiographs, there is a growing awareness of the need for a computer aided system to help diagnose these radiographs. The detection of rib contours is, of course, a necessary element in such a system. In addition to being able to accommodate the need for a mass screening program, an automated systemalso has the ability to detect anomalies at earlier stages. Ziskin et al (1971) state that reliable 2 {a) Original Chest Radiograph Figure 1-1. A Chest Radiograph 3 VENTRAL CONTOUR CARTILAGE {b) THE THORAX; VENTRAL ASPECT OF A CHEST RADIOGRAPH Figura 1-1 A CHEST RADIOGRAPH studies indicate that even under routine conditions radiologists fail to detect approximately 30% of abnormalities in ehest X-ray films.

This volume is the product of the Conference on Cognitive Process Models of Foreign Policy Decision-Making which was held in London at the Richardson Institute for Conflict and Peace Research from March 17-24, 1973. We would like to thank Michael Nicholson, Director of the Richardson Institute, for acting as the host of the Conference. Support for the Conference and the preparation of the Conference papers for publication was provided by the Mathematical Social Sciences Board (MSSB). The MSSB is funded by aNational Science Foundation grant which is administered by the Center for Advanced Study in the Behavioral Sciences as the primary grantee. We are grateful to Hayward Alker, Jr. and William H. Riker of the MSSB for their help and encouragement. The graph shown on the cover is a cognitive map representation of the output from our computer simulation of foreign pOlicy decision-making. We would like to thank Robert Axelrod and Gary Raffel of the University of Michigan for generating the graph. PART I INTRODUCTION 1 CHAPTER 1 THOUGHT AND ACTION IN FOREIGN POLICY G. MATTHEW BONHAM The American University MICHAEL J. SHAPIRO University of Hawaii Introduction The papers assembled here constitute, and to some extent represent, widely disparate views of foreign policy thinking and decision-making. As is the case with almost any collective enterprise, it is possible to suggest some noteworthy resemblances among the contributions to this volume and to indicate grounds for distinguishing them from other "approaches.

Picture processing by computer has found its application in various fields. Character recognition has shown the most practical success. Furthermore, the techniques span much more sophisticated applications such as interpretation of biomedical images and X-ray films, measurement of images in nuclear physics, processing of a large volume of pictorial data sent from the satellites, etc. The particular problem attacked in this thesis is computer analysis and identification of human faces. Pictures of human faces are successfully analyzed by a computer program which extracts face feature points, such as nose, mouth, eyes, and so on. The program was tested with more than 800 photographs The research has been done with main emphasis on the method of how to incorporate the picture structures into the picture anlysis program. The success of the program is due to the employment of a flexible picture analysis scheme with feedbacks, which will be described in the next chapter. An experiment on face identification of 20 people was also conducted. I-1. Picture Analysis and Recognition- New Aspects When shown the pictures of the human face of Fig. 1-1, we can immediately tell the positions of the nose, mouth and eyes; and more- over, we can say that both pictures surely portray the same person. Picture analysis and recognition by computer concerns itself with this type of two-dimensional image processing. In this thesis, I selected human-face pictures as objects of processing.