A Class of 3-D Distributed Modular Computing Nets

  • Arminda Moreno-Díaz
  • Gabriel de Blasio
  • Roberto Moreno-Díaz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)


The class of flat triangular and layered nets of simple computing units, which gives rise to Newton and Hermite filters in two dimensions are extended to 3-D by means of two natural discrete ways. First, by means of the so called Pascal Pyramids; and second, by introducing a rectangular grilled “retina”, which leads to a kind of Newton quadrangular pyramids and to 3-D Newton Filters and Nets. Both cases can be extended to the continuous in the form of 2-D Hermite functions and filters of different orders (degree of derivatives). Preliminary results and examples are presented.


Receptive Field Order Zero Output Unit Computing Unit Hermite Function 
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This work has been supported, in part, by Spanish Ministry of Science projects MTM2011-28983-CO3-03 and MTM2014-56949-C3-2-R.


  1. 1.
    Nolte, J.: The Human Brain: An Introduction to its Functional Anatomy. Elsevier Health Sciences Pub. (2008)Google Scholar
  2. 2.
    Moreno-Díaz, R., McCulloch, W.S.: Circularities in nets and the concept of functional matrices. In: Proctor, L. (ed.) Biocibernetics of the Central Nervous System, pp. 145–150. Little & Brown, MA (1969)Google Scholar
  3. 3.
    Lettvin, J.: Warren and Walter. In: McCulloch, R. (ed.) Collected Works of W.S. McCulloch, vol. II, chap. 56, pp. 514–530. Intersystems Pub. (1969)Google Scholar
  4. 4.
  5. 5.
    Moreno-Díaz, Jr., R.: Computación Paralela y Distribuida: Relaciones Estructura-Función en Retinas. Ph.D thesis, Universidad de Las Palmas de Gran Canaria (1993)Google Scholar
  6. 6.
    Moreno-Díaz, A., de Blasio, G., Moreno-Díaz Jr., R.: Distributed, layered and reliable computing nets to represent neuronal receptive fields. Math. Biosci. Eng. 11(2), 343–361 (2014)Google Scholar
  7. 7.
    de Blasio, G., Moreno-Díaz, A., Moreno-Díaz, R.: Eulerian numbers weigths in distributed computing nets. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) Computer Aided Systems Theory. LNCS, pp. 88–94, Springer, Heidelberg (2015)Google Scholar
  8. 8.
    Bondarenko, B.A.: Generalized Pascal triangles and pyramids. The Fibonacci Association Pub. (Translated from Russian by R.C. Bollinger), chapter 1.5 (1993)Google Scholar
  9. 9.
    Brannen, C.: Pascal Triangle and Lisi’s E8 Quantum Numbers (2008).
  10. 10.
    Marr, D.: Vision. Freeman and Company, San Francisco (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Arminda Moreno-Díaz
    • 1
  • Gabriel de Blasio
    • 2
  • Roberto Moreno-Díaz
    • 2
  1. 1.School of Computer ScienceMadrid Technical UniversityMadridSpain
  2. 2.Instituto Universitario de Ciencias Y Tecnologías CibernéticasULPGCLas PalmasSpain

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