Mathematical models of neurone interaction

Some properties of neurons are discussed which must be considered in formulating models of their interaction. Among these are characteristics of nerve membranes. Under certain weak conditions on the parameters a neural element may behave as a logical element. With other values of the parameters the behavior can be approximated by a continuous model in which only an average output rate is taken into account as a function of the input. This latter approach is stressed here. Applications to a number of psychological problems are mentioned. Among these are a mechanism for response to curvature in movement, enhancement effects, flicker phenomena, discrimination, and detection of real and apparent movement.

[1]  A. Rapoport.  “Ignition” phenomena in random nets , 1952 .

[2]  A. Rapoport,et al.  A statistical approach to the theory of the central nervous system. , 1948, The Bulletin of mathematical biophysics.

[3]  P M MILNER,et al.  The cell assembly: Mark II. , 1957, Psychological review.

[4]  R. L. Beurle.  Properties of a mass of cells capable of regenerating pulses , 1956, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[5]  H. D. Landahl,et al.  Outline of a matrix calculus for neural nets , 1946 .

[6]  W. Rall.  Theory of Physiological Properties of Dendrites , 1962, Annals of the New York Academy of Sciences.

[7]  W. Reichardt.  Autokorrelations-Auswertung als Funktionsprinzip des Zentralnervensystems , 1957 .

[8]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[9]  H. Grundfest,et al.  Electrical inexcitability of synapses and some consequences in the central nervous system. , 1957, Physiological reviews.

[10]  W. Pitts,et al.  A Statistical Consequence of the Logical Calculus of Nervous Nets , 1943 .

[11]  J. Eccles,et al.  The inhibitory suppression of reflex discharges from motoneurones , 1955, The Journal of physiology.

[12]  Maximo Valentinuzzi,et al.  A mathematical interpretation of motor reactions to fixed and moving stimulation of the eye , 1959 .

[13]  B. Katz,et al.  The effect of inhibitory nerve impulses on a crustacean muscle fibre , 1953, The Journal of physiology.

[14]  H. Landahl.  On the interpretation of the effect of area on the critical flicker frequency , 1957 .

[15]  H. D. Landahl.  A note on mathematical models for the interaction of neural elements , 1961 .

[16]  W. Pitts,et al.  How we know universals; the perception of auditory and visual forms. , 1947, The Bulletin of mathematical biophysics.