In 1985 I first began my research on the life and work of Harold Hotel ling. That year, Harold Hotelling's widow had donated the collection of his private p:;tpers, correspondence and manuscripts to the Butler Library, Columbia University. This is a most appropriate place for them to reside, in that Hotelling's most productive period as an active researcher in eco nomics and statistics coincides with the years when he was Professor of Mathematical Economics at Columbia (1931-1946). The Hotelling Collection comprises some 13,000 separate items and contains numerous unpublished letters and manuscripts of great importance to historians of economics and statistics. In the course of the following year I was able, with the generous financial assistance of the Nuffield Foundation, the Economic and Social Research Council, the British Academy and the University of Durham, to spend six weeks over the Easter period working on the collection. I returned to New York in September 1986 while on sabbatical leave from the University of Durham, and I spent most of the following eight months examining the many documents in the collection. During that academic year I was grateful to Columbia University who gave me the title of Visiting Research Professor and gave me the freedom to work in their many well-stocked libraries.
Abstract
For the linear Hotelling model with firms located at the boundaries of the segment line, we study the price competition in a scenario of incomplete information in the production costs of both firms. We introduce the bounded uncertain costs (BUC) condition in the production costs and we prove that there is a local optimum price strategy if and only if the BUC condition holds. We compute explicitly the local optimum price strategy and we prove that it does not depend upon the distributions of the production costs of the firms, except on their first moments. We prove that the ex-post profit of a firm is smaller than its ex-ante profit if and only if the production cost of the other firm is greater than its expected cost.
The practice of robotics and computer vision both involve the application of computational algorithms to data. Over the fairly recent history of the fields of robotics and computer vision a very large body of algorithms has been developed. However this body of knowledge is something of a barrier for anybody entering the field, or even looking to see if they want to enter the field — What is the right algorithm for a particular problem?, and importantly, How can I try it out without spending days coding and debugging it from the original research papers?
The author has maintained two open-source MATLAB Toolboxes for more than 10 years: one for robotics and one for vision. The key strength of the Toolboxes provide a set of tools that allow the user to work with real problems, not trivial examples. For the student the book makes the algorithms accessible, the Toolbox code can be read to gain understanding, and the examples illustrate how it can be used —instant gratification in just a couple of lines of MATLAB code. The code can also be the starting point for new work, for researchers or students, by writing programs based on Toolbox functions, or modifying the Toolbox code itself.
The purpose of this book is to expand on the tutorial material provided with the toolboxes, add many more examples, and to weave this into a narrative that covers robotics and computer vision separately and together. The author shows how complex problems can be decomposed and solved using just a few simple lines of code, and hopefully to inspire up and coming researchers. The topics covered are guided by the real problems observed over many years as a practitioner of both robotics and computer vision. It is written in a light but informative style, it is easy to read and absorb, and includes a lot of Matlab examples and figures. The book is a real walk through the fundamentals of robot kinematics, dynamics and joint level control, then camera models, image processing, feature extraction and epipolar geometry, and bring it all together in a visual servo system.
