Skip to main content

2016 | OriginalPaper | Buchkapitel

Asymmetries in Synaptic Connections and the Nonlinear Fokker-Planck Formalism

verfasst von : Roseli S. Wedemann, Angel R. Plastino

Erschienen in: Artificial Neural Networks and Machine Learning – ICANN 2016

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In previous work we have developed illustrative, neurocomputational models to describe mechanisms associated with mental processes. In these efforts, we have considered mental processes in phenomena such as neurosis, creativity, consciousness/unconsciousness, and some characteristics of the psychoses. Memory associativity is a key feature in the theoretical description of these phenomena, and much of our work has focused on modeling this mechanism. In traditional neural network models of memory, the symmetry of synaptic connections is a necessary condition for reaching stationary states. The assumption of symmetric weights seems however to be biologically unrealistic. Efforts to model stationary network states with asymmetric weights are mathematically complex and are usually applied to restricted situations. This has motivated us to explore the possibility of a new approach to the synaptic symmetry problem, based on its analogies with some features of the nonlinear Fokker-Planck formalism.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Vidal de Carvalho, L.A., Quintella Mendes, D., Wedemann, R.S.: Creativity and delusions: the dopaminergic modulation of cortical maps. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003, Part I. LNCS, vol. 2657, pp. 511–520. Springer, Heidelberg (2003)CrossRef Vidal de Carvalho, L.A., Quintella Mendes, D., Wedemann, R.S.: Creativity and delusions: the dopaminergic modulation of cortical maps. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003, Part I. LNCS, vol. 2657, pp. 511–520. Springer, Heidelberg (2003)CrossRef
2.
Zurück zum Zitat Wedemann, R.S., Donangelo, R., Vidal de Carvalho, L.A.: Generalized memory associativity in a network model for the neuroses. Chaos 19(1), 015116 (2009)MathSciNetCrossRef Wedemann, R.S., Donangelo, R., Vidal de Carvalho, L.A.: Generalized memory associativity in a network model for the neuroses. Chaos 19(1), 015116 (2009)MathSciNetCrossRef
3.
Zurück zum Zitat Wedemann, R.S., Vidal de Carvalho, L.A.: Some things psychopathologies can tell us about consciousness. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds.) ICANN 2012, Part I. LNCS, vol. 7552, pp. 379–386. Springer, Heidelberg (2012)CrossRef Wedemann, R.S., Vidal de Carvalho, L.A.: Some things psychopathologies can tell us about consciousness. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds.) ICANN 2012, Part I. LNCS, vol. 7552, pp. 379–386. Springer, Heidelberg (2012)CrossRef
4.
Zurück zum Zitat Freud, S.: Introductory Lectures on Psycho-Analysis, Standard Edition. W. W. Norton and Company, New York, London (1966). First German edition (1917) Freud, S.: Introductory Lectures on Psycho-Analysis, Standard Edition. W. W. Norton and Company, New York, London (1966). First German edition (1917)
5.
Zurück zum Zitat Kandel, E.: Psychiatry, Psychoanalysis, and the New Biology of Mind. American Psychiatric Publishing Inc., Washington, D.C., London (2005) Kandel, E.: Psychiatry, Psychoanalysis, and the New Biology of Mind. American Psychiatric Publishing Inc., Washington, D.C., London (2005)
6.
Zurück zum Zitat Shedler, J.: The efficacy of psychodynamic psychotherapy. Am. Psychol. 65(2), 98–109 (2010)CrossRef Shedler, J.: The efficacy of psychodynamic psychotherapy. Am. Psychol. 65(2), 98–109 (2010)CrossRef
7.
Zurück zum Zitat Cleeremans, A., Timmermans, B., Pasquali, A.: Consciousness and metarepresentation: a computational sketch. Neural Netw. 20, 1032–1039 (2007)CrossRef Cleeremans, A., Timmermans, B., Pasquali, A.: Consciousness and metarepresentation: a computational sketch. Neural Netw. 20, 1032–1039 (2007)CrossRef
8.
Zurück zum Zitat Taylor, J.G., Villa, A.E.P.: The “Conscious I”: a neuroheuristic approach to the mind. In: Baltimore, D., Dulbecco, R., Francois, J., Levi-Montalcini, R. (eds.) Frontiers of Life, pp. 349–368. Academic Press (2001) Taylor, J.G., Villa, A.E.P.: The “Conscious I”: a neuroheuristic approach to the mind. In: Baltimore, D., Dulbecco, R., Francois, J., Levi-Montalcini, R. (eds.) Frontiers of Life, pp. 349–368. Academic Press (2001)
9.
Zurück zum Zitat Taylor, J.G.: A neural model of the loss of self in schizophrenia. Schizophrenia Bull. 37(6), 1229–1247 (2011)CrossRef Taylor, J.G.: A neural model of the loss of self in schizophrenia. Schizophrenia Bull. 37(6), 1229–1247 (2011)CrossRef
10.
Zurück zum Zitat Hertz, J.A., Krogh, A., Palmer, R.G. (eds.): Introduction to the Theory of Neural Computation. Lecture Notes, vol. 1. Perseus Books, Cambridge (1991) Hertz, J.A., Krogh, A., Palmer, R.G. (eds.): Introduction to the Theory of Neural Computation. Lecture Notes, vol. 1. Perseus Books, Cambridge (1991)
11.
Zurück zum Zitat Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983)MathSciNetCrossRefMATH Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983)MathSciNetCrossRefMATH
12.
Zurück zum Zitat Tsallis, C., Stariolo, D.A.: Generalized simulated annealing. Phys. A 233, 395–406 (1996)CrossRef Tsallis, C., Stariolo, D.A.: Generalized simulated annealing. Phys. A 233, 395–406 (1996)CrossRef
13.
Zurück zum Zitat Parisi, G.: Asymmetric neural networks and the process of learning. J. Phys. A Math. Gen. 19, L675–L680 (1986)MathSciNetCrossRef Parisi, G.: Asymmetric neural networks and the process of learning. J. Phys. A Math. Gen. 19, L675–L680 (1986)MathSciNetCrossRef
14.
Zurück zum Zitat Xu, Z.B., Hu, G.Q., Kwong, C.P.: Asymmetric hopfield-type networks: theory and applications. Neural Netw. 9(3), 483–501 (1996)CrossRef Xu, Z.B., Hu, G.Q., Kwong, C.P.: Asymmetric hopfield-type networks: theory and applications. Neural Netw. 9(3), 483–501 (1996)CrossRef
15.
Zurück zum Zitat Hopfield, J.J.: Neurons with graded responses have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. U.S.A. 81, 3088–3092 (1988)CrossRef Hopfield, J.J.: Neurons with graded responses have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. U.S.A. 81, 3088–3092 (1988)CrossRef
16.
Zurück zum Zitat Ribeiro, M.S., Nobre, F., Curado, E.M.F.: Classes of N-dimensional nonlinear Fokker-Planck equations associated to Tsallis entropy. Entropy 13, 1928–1944 (2011)MathSciNetCrossRefMATH Ribeiro, M.S., Nobre, F., Curado, E.M.F.: Classes of N-dimensional nonlinear Fokker-Planck equations associated to Tsallis entropy. Entropy 13, 1928–1944 (2011)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Plastino, A.R., Plastino, A.: Non-extensive statistical mechanics and generalized Fokker-Planck equation. Phys. A 222, 347–354 (1995)MathSciNetCrossRef Plastino, A.R., Plastino, A.: Non-extensive statistical mechanics and generalized Fokker-Planck equation. Phys. A 222, 347–354 (1995)MathSciNetCrossRef
18.
Zurück zum Zitat Tsallis, C., Buckman, D.J.: Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E 54(3), R2197–R2200 (1996)CrossRef Tsallis, C., Buckman, D.J.: Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E 54(3), R2197–R2200 (1996)CrossRef
19.
Zurück zum Zitat Franck, T.D.: Nonlinear Fokker-Planck Equations: Fundamentals and Applications. Springer, Heidelberg (2005) Franck, T.D.: Nonlinear Fokker-Planck Equations: Fundamentals and Applications. Springer, Heidelberg (2005)
20.
Zurück zum Zitat Tsallis, C.: Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World. Springer, New York (2009)MATH Tsallis, C.: Introduction to Nonextensive Statistical Mechanics. Approaching a Complex World. Springer, New York (2009)MATH
Metadaten
Titel
Asymmetries in Synaptic Connections and the Nonlinear Fokker-Planck Formalism
verfasst von
Roseli S. Wedemann
Angel R. Plastino
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-44778-0_3

Premium Partner