Some remarks on the central nervous system

It is pointed out that the successes obtained in the mathematical biology of the central nervous system are based mostly on a number of more or less complicated neuronic circuit models, each inventedad hoc for the purpose of explaining a given phenomenon. The individual models remain disconnected from each other, however, and the unity of the CNS is not apparent. (Rashevsky,Mathematical Biophysics, 3rd Edition, Vol. II, 1960. New York, Dover Publications, Inc.) Some “field theories” of the CNS, as for example that of Griffith (Bull. Math. Biophysics,25, 111–120, 1963;27, 187–195, 1965), give more expression to this unity but lose in the explanation of specific phenomena. The present paper starts with the picture thatevery neuron in the brain isdirectly or indirectly affected to some extent byevery other neuron. This leads to a system of equations with a very large number of variables. Such a system can be replaced in the limiting case by an integral equation of the first kind. At least two specific results can be obtained with this approach and suggestions for further improvement are made.     

Some remarks on the dynamics of molecular self-organization

The dynamics of a self-organizing molecular system is described in terms of its normal modes. Each normal mode is associated with a certain eigenvalue, the average of which reflects most directly the overall process of self-organization. For the temporal change of this quantity a maximum principle holds.     

Essay review: The history of ecology

Joel B. Hagen,An Entangled Bank: The Origins of ecosystem Ecology (New Brunswick, N.J.: Rutgers University Press, 1992); Gregg Mitman,The State of Nature: Ecology, Community, and American Social Thought, 1900–1950 (Chicago and London: University of Chicago Press, 1992).     

Some remarks on the Kedem-Katchalsky equations for non-electrolytes

The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ _ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf _sm andf _sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL _p .     

Essay review: The Correspondence of the young Darwin

The Correspondence of Charles Darwin: Volume I, 1821–1836; Volume II, 1837–1843 (Cambridge: Cambridge University Press, 1985, 1986).     

Some remarks on the mathematical aspects of automobile driving

Some aspects which involve the interaction of the human element and of the machine element in driving are discussed. As an example a simple equation is derived for the maximum safe speed of a car on an empty road. The parameters of the equation are partly of physiological nature, partly of mechanical nature. Another example treats in a similar manner the problem of a car passing another car moving in the same direction.     

Some remarks on the mathematical biophysics of organic assymetry

Zusammenfassung Das Vorhandensein bilateraler Asymmetrie bei Organismen ist an und für sich biophysikalisch verständlich. Schwierigkeiten entstehen jedoch beim Versuch die auffallende Ungleichheit in den Häufigkeiten des Vorkommens von Rechts- und Linksasymmetrie biophysikalisch zu deuten. Es werden zwei Möglichkeiten für solch'eine Deutung besprochen. Die eine stützt sich auf die fundamentale Asymmetrie des elektromagnetischen Feldes, und wird als biologisch weniger geeignet angesehen. Die andere, welche dem Verfasser als wahrscheinlicher erscheint, beruht auf der Asymmetrie der organischen Moleküle.

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Résumé L'existence d'une asymétrie bilaterale en général chez des organismes divers n'offre pas de difficulté particulière du point de vue biophysique. Mais les difficultés surgissent quand on tâche de comprendre l'inégalité très prononcée des cas d'asymétrie droite et gauche. Deux possibilités sont discutées dans ce mémoire. L'une repose sur l'asymétrie fondamentale du champs électromagnétique. Cette explication est considérée comme moins probable. Une autre explication qui nous apparaît plus probable, est fondée sur l'asymétrie moléculaire.