Skip to main content
Log in

Activity in cortical-like neural systems: Short-range effects and attention phenomena

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The kinetic model of cortical-like neural systems is amplified with elements related to a gross lamination in three parts of the basic system. A reduced version of the model, aiming to study only short-range, random aspects of activity propagation, was subjected to an intensive computational experimentation, and the results are briefly presented. The comparison of these results with those of a previous paper, in which aspects related mainly to long-distance effects were described, suggested the possibility of extending the model by considering new features related to phenomena of attention. The results of experimentations with the whole model revealed the possibility of laying the bases for a description of the cognitive activity in a neural frame.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Abeles, M. 1987. Personal communication.

  • Adey, W. R. 1966. Neurophysiological correlates of information transaction and storage in brain tissue. InProgress in Physiological Psychology. Vol. 1, E. Stellar and J. M. Sprague (eds), pp. 1–43. New York: Academic Press.

    Google Scholar 

  • Amari, S. 1971. Characteristics of randomly connected threshold-element network and network systems.Proc. IEEE 59, 35–47.

    Article  MathSciNet  Google Scholar 

  • Amari, S. 1974. A method of statistical neurodynamics.Kybernetik 14, 201–215.

    MATH  MathSciNet  Google Scholar 

  • Andersen, P. 1975. Organization of Hippocampal neurons and their interconnections. InThe Hippocampus, Vol. 1, R. L. Isaacson and K. H. Pribram (eds), pp. 155–175. New York: Plenum Press.

    Google Scholar 

  • Angel, E. and R. Bellman. 1972.Dynamic Programming and Partial Differential Equations. New York: Academic Press.

    MATH  Google Scholar 

  • Berridge, M. 1986. Second messenger dualism in neuromodulation and memory.Nature 323, 294–295.

    Article  Google Scholar 

  • Beurle, R. L. 1956. Properties of a mass of cells capable of regenerating pulses.Phil. Trans. R. Soc. 240A, 55–94.

    Google Scholar 

  • Bures, J., O. Buresova and V. I. Koroleva, 1983. Spreading depression, epilepsy and memory. InNeurophysiological Mechanisms of Epilepsy, V. M. Okujava (ed.), pp. 120–130. Tiblisi: Metsnierba.

    Google Scholar 

  • Dale, N., S. Schacher and E. R. Kandel. 1988. Long-term facilitation in Aplysia involves increase in transmitter release.Science 239, 282–285.

    Google Scholar 

  • Dragunov, M. and H. A. Roberson. 1987. Kindling stimulation induces c-fos protein(s) in granule cells of the rat dentate gyrus.Nature 329, 441–442.

    Article  Google Scholar 

  • Eccles, J. C. 1978. An instruction-selection hypothesis of cerebral learning. InCerebral Correlates of Conscious Experience, P. Buser and A. Rougeul-Buser (eds), pp. 155–175. Amsterdam: Elsevier/North-Holland.

    Google Scholar 

  • Eccles, J. C. 1984. The cerebral neocortex: a theory of its operation. InCerebral Cortex, Vol. 2, E. G. Jones and A. Peters (eds) pp. 1–36. New York: Plenum Press.

    Google Scholar 

  • Fedelman, M. L. 1984. Morphology of the neocortical pyramidal neurons. InCerebral Cortex, Vol. 1, E. G. Jones and A. Peters (eds), pp. 123–200. New York: Plenum Press.

    Google Scholar 

  • Fisher, B. 1973. A neuron field theory: mathematical approach to the problem of large number of interacting nerve cells.Bull. math. Biol. 35, 345–357.

    Article  Google Scholar 

  • Freeman, W. J. 1975.Mass Action in the Nervous System. New York: Academic Press.

    Google Scholar 

  • Freeman, W. J. 1978. Spatial properties of an EEG even in the olfactory bulb and cortex.Electroenceph. clin. Neurophysiol. 44, 586–605.

    Article  Google Scholar 

  • Friedland, R. P., T. F. Budinger, W. J. Jagust, E. Koss, S. Derenzo, R. H. Huesman and Y. Yano. 1985. Positron tomography and the differential diagnosis and pathophysiology of Alzheimer's disease. InSenile Dementia of the Alzheimer Type, J. Traber and W. H. Gispen (eds), pp. 124–133. Berlin: Springer.

    Google Scholar 

  • Goelet, P., V. F. Castellucci, S. Schacher and E. Kandel. 1986. The long and the short of long term memory—a molecular framework.Nature 322, 419–422.

    Article  Google Scholar 

  • Gorelova, N. A. and J. Bures. 1983. Spiral waves of spreading depression in the isolated chicken retina.J. Neurobiol. 14, 353–363.

    Article  Google Scholar 

  • Griffith, J. A. 1963. A field theory of neural nets: I. Derivation of fields equation.Bull. math. Biophys. 25, 111–120.

    MATH  MathSciNet  Google Scholar 

  • Hernandez-Péon, R. 1961. Reticular mechanism of sensory control. InSensory Communication, W. Rosenblith (ed.), pp. 497–520. New York: MIT-Wiley.

    Google Scholar 

  • Hopfield, J. J. 1982. Neural networks and physical systems with emergent collective computational abilities.Proc. natl. Acad. Sci. U.S.A. 79, 2554–2558.

    Article  MathSciNet  Google Scholar 

  • Hopfield, J. J. 1984. Neurons with graded response have collective computational abilities properties like those of two-state neurons.Proc. natl. Acad. Sci. U.S.A. 81, 3088–3092.

    Article  Google Scholar 

  • Hubel, D. H. 1967. Effects of the distortion of sensory input on the visual system of kittens.Physiologist 10, 17–45.

    Google Scholar 

  • Hubel, D. H. and T. N. Wiesel. 1972. Laminar and columnar distribution of geniculocortical fibers in the macaque monkey.J. comp. Neurol. 146, 421–450.

    Article  Google Scholar 

  • Hunt, S. P. 1987. Induction of c-fos-like protein in spinal cord neurons following sensory stimulation.Nature 328, 632–634.

    Article  Google Scholar 

  • Ingber, L. 1982. Statistical mechanics of neocortical interactions. I. Basic formulation.Physica 5D, 83–107.

    MathSciNet  Google Scholar 

  • Kornhuber, H. H. 1973. Neural control of input into long term memory: limbic system and amnestic syndrome in man. InMemory and Transfer of Information, H. P. Zippel (ed.), pp. 1–22. New York: Plenum Press.

    Google Scholar 

  • McCulloch, W. S. and W. A. Pitts. 1943. A logical calculus of the ideas imminent in nervous activity.Bull. math. Biophys. 5, 115–133.

    MATH  MathSciNet  Google Scholar 

  • Magoun, H. W. 1965.The Waking Brain (2nd edn.) Springfield, I: Thomas.

    Google Scholar 

  • Milner, B. 1972. Disorders of learning and memory after temporal-lobe lesions in man.Clin. Neurosurg. 19, 421–446.

    MathSciNet  Google Scholar 

  • Moruzzi, G. and H. W. Magoun. 1949. Brain stem reticular formation and activation of EEG.EEG Clin. Neurophysiol. 1, 455–473.

    Google Scholar 

  • Mountcastle, V. B. 1978. An organizing principle for cerebral function: the unit module and the distributed system. InThe Mindful Brain, Edelman and Mountcastle (eds). Cambridge: MIT Press.

    Google Scholar 

  • Pellionisz, A. and R. Llinas 1982. Space-time representation in the brain. The cerebellum as a predictive space-time metric tensor.Neuroscience 7, 2949–2970.

    Article  Google Scholar 

  • Penfield, W. 1969. Epilepsy, neurophysiology, and some brain mechanisms related to consciousness. InBasic Mechanisms of the Epilepsies, H. H. Jasper, A. A. Ward and A. Pope (eds), pp. 791–805. London: Churchill.

    Google Scholar 

  • Penfield, W. and B. Milner. 1958. Memory deficit produced by bilateral lesions in the hippocampal zone.A.M.A. Arch. Neurol. Psychiatry 79, 475–497.

    Google Scholar 

  • Rapoport A. 1952. Ignition phenomena in random nets.Bull. math. Biophys. 14, 35–44.

    MathSciNet  Google Scholar 

  • Sbitnev, V. J. 1975. Transport of spikes in statistical neuron ensembles. Conception of phase transition.Akademia Nauk CCCP 176, 1–24.

    Google Scholar 

  • Sokolov, E. N. 1960. Neuronal models and the orienting reflex. InCNS and Behavior, Vol. 3, M. A. B. Brazier (ed.), pp. 187–276. New York: Macy Found.

    Google Scholar 

  • Sutula, T., He Xiao-Xian, J. Cavazos and G. Scott. 1988. Synaptic reorganization in the Hippocampus induced by abnormal functional activity.Science 239, 1147–1150.

    Google Scholar 

  • Szentagothai, J. 1975. The “module concept” in cerebral cortex architecture.Brain. Res. 95, 475–496.

    Article  Google Scholar 

  • Szentagothai, J. 1983. The modular architectonic principle of neuronic centers.Rev. Physiol. biochem. Pharmacol. 98, 11–61.

    Google Scholar 

  • Thompson, W. J., G. Bicker, J. P. Changeaux, T. L. Ebendal, M. Heisenberg, C. E. Henderson, W. Huttner, E. R. Kandel, J. B. Mallet, G. S. Stent, H. Thoenen and M. Yaniv. 1987. Activity-dependent regulation of gene expression. (Group Report). InThe Neural and Molecular Bases of Learning, J. P. Changeaux and M. Konishi (eds), pp. 13–30. New York: Wiley.

    Google Scholar 

  • Ventriglia, F. 1974. Kinetic approach to neural systems. I.Bull. math. Biol. 36, 534–544.

    Article  Google Scholar 

  • Ventriglia, F. 1988. Computational simulation of cortical-like neural systems.Bull. math. Biol. 50, 143–185.

    Article  MATH  MathSciNet  Google Scholar 

  • Vinogradova, O. S. 1975. Functional organization of the limbic system in the process of registration of information: facts and hypotheses. InThe Hippocampus, Vol. 2, R. L. Isaacson and K. H. Pribram (eds), pp. 3–69. New York: Plenum Press.

    Google Scholar 

  • Wilson, H. R. and J. D. Cowan. 1973. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.Kybernetik 13, 55–80.

    Article  MATH  Google Scholar 

  • Winfree, A. T. and S. H. Strogatz. 1984. Organizing centres for three-dimensional chemical waves.Nature 311, 611–615.

    Article  Google Scholar 

  • Woody, C. D. 1982.Neurons, Learning and Higher Function. Berlin: Springer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ventriglia, F. Activity in cortical-like neural systems: Short-range effects and attention phenomena. Bltn Mathcal Biology 52, 397–429 (1990). https://doi.org/10.1007/BF02458579

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02458579

Keywords

Navigation