Selmer Martin Johnson

Solution of a Large-Scale Traveling-Salesman Problem

The RAND Corporation in the early 1950s contained “what may have been the most remarkable group of mathematicians working on optimization ever assembled” [6]: Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names. Groups like this need their challenges. One of them appears to have been the traveling salesman problem (TSP) and particularly its instance of finding a shortest route through Washington, DC, and the 48 states [4, 7].

Chemical Equilibrium in Complex Mixtures

A new method for the determination of the equilibrium composition of complex mixtures is described. The general method, which is based on the minimization of free energy, states the problem with unusual simplicity, avoiding many of the usual difficulties of description and computation. Two specific computation procedures are shown, one using a steepest descent technique applied to a quadratic fit, the other making use of linear programing.

A mathematical model of the human external respiratory system.

This study examines the thesis that a part of the human physiological system can be simulated by a suitably constructed mathematical model. The model employed derives from a class of mathematical programming methods that were originally developed for representing complex military and industrial activities and have recently been used to represent involved chemical equilibria. The motivation for this research is the long-range view that a successful mathematical simulation of the human system or of human subsystems would provide an important tool for biological investigations. A sufficiently complex mathematical model-that is, a model that embodies sufficiently complex mathematical model-that is, a model that embodies sufficient chemical and biological detail to represent a whole, functioning human system or subsystem-could be used to explore biological hypotheses, environmental stress reactions, and interplay of dependent subsystems, and could serve as a pedagogical tool or even as an aid to medical diagnosis. Of course, the foregoing long-range view is an ultimate goal. For the moment, only the techniques, concepts, and characteristics of such a mathematical model are being explored. This paper presents the results of a simulation of the external respiratory function. Respiration, and the consequent gas exchanges at the lung surfaces, involves many chemical reactions and a transformation of venous blood into arterial blood. This activity was chosen as a test cast to explore the feasibility of constructing a mathematical model of a human subsystem.