Conclusions
A study of the proposed mathematical model of the mechanism of operative memory indicates that formation of circulating excitations is accounted for by short-term trace effects of synaptic transmission, well known in neurophysiology (posttetanic potentiation, temporary facilitation, and path formation). These results give added support to the recirculation theory, which maintains that fixation and storage of incoming information occurs via a stream of nervous impulses circulating in closed chains. The circulation of a stream, in turn, leads to stable morphological or chemical alterations in the structure of the synaptic apparatus, which constitutes the basis of long-term memory.
Similar content being viewed by others
Literature Cited
P. S. Kuznetsov and Yu. I. Petunin, “A study of random walk in neuronal networks and mathematical modeling of certain neurophysiological processes,” in: Statistical Electrophysiology. Proceedings of a Symposium on Statistical Electrophysiology [in Russian], Vilnius (1968), pp. 315–324.
P. S. Kuznetsov, B. S. Mityagin, and Yu. I. Petunin, “Cyclicity of the final portion of random walk on a multigraph,” Proceedings of the Sixth Winter Institute on Mathematical Programming and Related Problems [in Russian], Moscow (1975), pp. 21–34.
Ju. I. Petunin, “Mathematical modeling of synaptic transmission; neuronal models of memory,” Proc. of the First International Conference on Mathematical Modeling, St. Louis, U.S.A., No. 1, Aug. 29–Sept. (1977), pp. 34–45.
S. Ochs, Elements of Neurophysiology, Wiley (1965).
E. D. Adrian, The Basis of Sensation, Norton, New York (1928).
E. D. Adrian, “The electrical activity of the mammalian olfactory bulb,” Electroencephalogr. Clin. Neurophysiol., No. 2, 377–388 (1950).
B. H. Matthews, “The response of a single and organ,” J. Physiol., No. 71, 64–110 (1931).
H. K. Hartline, H. G. Wagner, and E. F. MacNichol, “The peripheral origin of nervous activity in the visual system,” Cold Spring Harbor Symp. Quant. Biol., No. 17, 125–141 (1952).
R. Galambos and H. Davis, “The response of single auditory-nerve fibers to acoustic stimulation,” J. Neurophysiol., No. 6, 39–58 (1943).
A. B. Kogan, “Probabilistic-statistical principles of neuronal organization of the brain functional systems,” Dokl. Akad. Nauk SSSR,154, No. 5, 1231–1233 (1964).
A. B. Kogan, Yu. I. Petunin, and O. G. Chorayan, “A study of the impulse activity of neurons by methods of the theory of stochastic processes,” Biofizika,11, No. 5, 887–893 (1966).
Information Concept and Biological Systems [Russian translation], Mir, Moscow (1966).
J. Eccles, Physiology of Synapses, Springer-Verlag (1973).
Problems of Bionics [in Russian], Nauka, Moscow (1967).
W. R. Russel, Brain. Memory. Learning: A Neurologist's View, Clarendon Press, Oxford (1959).
C. P. Duncan, “The retroactive effect of electroshock on learning,” J. Comp. Physiol., No. 42, 32–44 (1949).
R. W. Gerard, “The fixation of experience,” in: CIOMS Symposium on Brain Mechanisms and Learning, J. F. Delafresnaye, A. Fessard, and J. Konorski, eds., Blackwell Scientific Publishers, Oxford (1961), pp. 21–35.
R. E. Ransmeier and R. W. Gerard, “Effects of temperature, convulsion, and metabolic factors on rodent memory and E.E.G.,” Am. J. Physiol., No. 179, 663–664 (1954).
M. Verzeano, Fifth International Congress on EEG and Clinical Neurophysiology, Rome, Italy, Sept. (1961), pp. 7–13.
M. Verzeano and K. Negishi, “Neuronal activity in wakefulness and in sleep,” in: Nature of Sleep: Ciba Found. Symp. Little, Brown, and Co., Boston (1961), p. 108.
A. B. Kogan and O. G. Chorayan, “Features of the evolution of functional organization of the central nervous system,” Rev. Roum. Biol. Ser. Zool.,11, No. 2, 117–121 (1966).
F. Morel, “Storage of information in nervous systems,” in: Information Concept and Biological Systems [Russian translation], Mir, Moscow (1966), pp. 179–214.
A. Fessard, “Role of Neuronal networks in sensory information transmission,” in: Theory of Communication in Sensory Systems [Russian translation], Mir, Moscow (1964), pp. 81–99.
D. O. Hebb, The Organization of Behavior, Wiley, New York (1949).
R. Couteaux, “Principaux critéres morphologiques et cytochimiques utilisables aujourd'hu pour définir les divers types de synapses,” Actual. Neurophysiol., Ser. 3, 145–173 (1961).
E. G. Gray, “Axo-somatic and axo-dendritic synapses of the cerebral cortex: An electron microscope study,” J. Anat., No. 93, 420–433 (1959).
L. H. Hamlyn, “The structure of the mossy fibre endings in the hippocampus of the rabbit,” J. Anat., No. 96, 112–120 (1962).
V. V. Chavchanidze, N. D. Sergienko, and R. G. Gachechiladze, “Trace processes in the central nervous system,” Abstract of paper presented at the Republican Conference on Technical Cybernetics [in Russian], Tbilisi (1964).
N. V. Antakova, I. K. Malinovskaya, and M. Yu. Ul'yanov, “Change in the synaptic apparatus of neuronal network in the frog spinal cord as a result of experimental action,” Abstract of paper presented at the All-Union Symposium on Applied Mathematics and Cybernetics [in Russian], Gorkii (1967).
F. Harary, Graph Theory, Addison-Wesley, Reading, Massachusetts (1969).
B. Katz, Nerve, Muscle, and Synapse, McGraw-Hill, New York (1966).
F. Rosenblatt, Principles of Neurodynamics [Russian translation], Mir, Moscow (1965).
W. K. Taylor, “Electrical simulation of some nervous system functional activities,” in: Proceedings of the Third London Symposium on Information Theory, Butterworths, London (1955), pp. 140–153.
W. Penfield and L. Roberts, Speech and Brain-Mechanisms, Princeton University, Princeton, New Jersey (1959).
T. A. Mering, Features of Closure of Conditioned-Reflex Association [Russian translation], Meditsina, Moscow (1967).
W. Feller, An Introduction to Probability Theory and Its Application, 3rd edn., Wiley, New York (1968).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
G. Somjen, Sensory Coding in Mammalian Nervous System, Appleton-Century-Croft, New York (1972).
S. Kuffler and J. Nicholls, From Neuron to Brain [Russian translation], Mir, Moscow (1979).
T. N. Grechenenko, Neurophysiological Mechanisms of Memory [in Russian], Nauka, Moscow (1979).
Additional information
Translated from Kibernetika, No. 2, pp. 119–129, March–April, 1981.
Rights and permissions
About this article
Cite this article
Min'ko, A.A., Petunin, Y.I. Mathematical modeling of short-term memory. Cybern Syst Anal 17, 287–298 (1981). https://doi.org/10.1007/BF01069647
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01069647