Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Field Computation in Natural and Artificial Intelligence

  • Bruce J. MacLennan
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30440-3_199

Definition of the Subject

field may be defined as a spatially continuous distribution of continuous quantity. The term is intended to include physical fields, such as electromagnetic fields and potential fields, but also patterns of electrical activity over macroscopic regions of neural cortex. Fields include two‐dimensional representations of information, such as optical images and their continuous Fourier transforms, and one‐dimensional images, such as audio signals and their spectra, but, as will be explained below, fields are not limited to two or three dimensions. A field transformation is a mathematical operation or function that operates on one or more fields in parallel yielding one or more fields as results. Since, from a mathematical standpoint, fields are defined over a continuous domain, field transformations operate with continuous parallelism. Some examples of field transformations are point-wise summation and multiplication of fields, Fourier and wavelet transforms,...

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Primary Literature

  1. 1.
    Adamatzky A (2001) Computing in nonlinear media and automata collectives. Institute of Physics Publishing, BristolzbMATHGoogle Scholar
  2. 2.
    Adamatzky A, De Lacy Costello B, Asai T (2005) Reaction‐diffusion computers. Elsevier, AmsterdamGoogle Scholar
  3. 3.
    Anderson JA (1995) An introduction to neural networks. MIT Press, CambridgezbMATHGoogle Scholar
  4. 4.
    Anderson RA (1995) Coordinate transformations and motor planning in posterior parietal cortex. In: Gazzaniga MS (ed) The cognitive neurosciences. MIT Press, Cambridge, pp 519–32Google Scholar
  5. 5.
    Bar-Yam Y (1997) Dynamics of complex systems. Perseus Books, ReadingzbMATHGoogle Scholar
  6. 6.
    Bizzi E, Mussa-Ivaldi FA (1995) Toward a neurobiology of coordinate transformation. In: Gazzaniga MS (ed) The cognitive neurosciences. MIT Press, Cambridge, pp 495–506Google Scholar
  7. 7.
    Bohm D, Hiley BJ (1993) The undivided universe: an ontological interpretation of quantum theory. Routledge, New YorkGoogle Scholar
  8. 8.
    Bonabeau E, Dorigo M, Theraulaz G (1999) Swarm intelligence: from natural to artificial systems. Santa Fe Institute Studies in the Sciences of Complexity. Oxford University Press, New YorkGoogle Scholar
  9. 9.
    Brachman G, Narici L (1966) Functional analysis. Academic Press, New YorkGoogle Scholar
  10. 10.
    Camazine S, Deneubourg J-L, Franks NR, Sneyd G, Theraulaz J, Bonabeau E (2001) Self‐organization in biological systems. Princeton University Press, PrincetonGoogle Scholar
  11. 11.
    Changeux J-P (1985) Neuronal man: the biology of mind. Oxford University Press, Oxford, tr. by L. GareyGoogle Scholar
  12. 12.
    Daubechies I, Grossman A, Meyer Y (1986) Painless non‐orthogonal expansions. J Math Phys 27:1271–1283MathSciNetADSzbMATHGoogle Scholar
  13. 13.
    Daugman JG (1993) An information‐theoretic view of analog representation in striate cortex. In: Schwartz EL (ed) Computational neuroscience. MIT Press, Cambridge, pp 403–423Google Scholar
  14. 14.
    Davies JA (2005) Mechanisms of morphogensis. Elsevier, AmsterdamGoogle Scholar
  15. 15.
    Deneubourg JL (1977) Application de l'ordre par fluctuation à la description de certaines étapes de la construction du nid chez les termites. Insectes Sociaux 24:117–130Google Scholar
  16. 16.
    Dirac PAM (1958) The principles of quantum mechanics, 4th edn. Oxford University Press, OxfordzbMATHGoogle Scholar
  17. 17.
    Droulez J, Berthoz A (1991) The concept of dynamic memory in sensorimotor control. In: Humphrey DR, Freund H-J (eds) Motor control: concepts and issues. Wiley, New York, pp 137–161Google Scholar
  18. 18.
    Droulez J, Berthoz A (1991) A neural network model of sensoritopic maps with predictive short-term memory properties. Proc Natl Acad Sci USA 88:9653–9657ADSGoogle Scholar
  19. 19.
    Feldman JA, Ballard DH (1982) Connectionist models and their properties. Cogn Sci 6(3):205–254Google Scholar
  20. 20.
    Gabor D (1946) Theory of communication. J Inst Electr Eng 93(III):429–457Google Scholar
  21. 21.
    Georgopoulos AP (1995) Motor cortex and cognitive processing. In: The Cognitive Neurosciences. MIT Press, Cambridge, pp 507–517Google Scholar
  22. 22.
    Goodman SJ, Anderson RA (1989) Microstimulation of a neural‐network model for visually guided saccades. J Cogn Neurosci 1:317–326Google Scholar
  23. 23.
    Haykin S (1999) Neural networks: a comprehensive foundation, 2nd edn. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar
  24. 24.
    Heil CE, Walnut DF (1989) Continuous and discrete wavelet transforms. SIAM Rev 31(4):628–666MathSciNetzbMATHGoogle Scholar
  25. 25.
    Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus response. Nature 376:33–36ADSGoogle Scholar
  26. 26.
    Kirchhoff G (1845) Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisförmige. Ann Phys Chemie 140/64(4):497–514ADSGoogle Scholar
  27. 27.
    Knudsen EJ, du Lac S, Esterly SD (1987) Computational maps in the brain. Ann Rev Neurosc 10:41–65Google Scholar
  28. 28.
    Leon SJ (1986) Linear algebra with applications, 2nd edn. Macmillan, New YorkGoogle Scholar
  29. 29.
    Light WA (1992) Ridge functions, sigmoidal functions and neural networks. In: Cheney EW, Chui CK, Schumaker LL (eds) Approximation theory VII. Academic Press, Boston, pp 163–206Google Scholar
  30. 30.
    Lipshitz L, Rubel LA (1987) A differentially algebraic replacment theorem. Proc Am Math Soc 99(2):367–72MathSciNetzbMATHGoogle Scholar
  31. 31.
    Loo CK, Peruš M, Bischof H (2004) Associative memory based image and object recognition by quantum holography. Open Syst Inf Dyn 11(3):277–289Google Scholar
  32. 32.
    MacLennan BJ (1987) Technology‐independent design of neurocomputers: the universal field computer. In: Caudill M, Butler C (eds) Proceedings of the IEEE First International Conference on Neural Networks, vol 3. IEEE Press, Piscataway, pp 39–49Google Scholar
  33. 33.
    MacLennan BJ (1990) Field computation: a theoretical framework for massively parallel analog computation, parts I–IV. Technical Report CS-90-100. Department of Computer Science, University of Tennessee, Knoxville, Available from www.cs.utk.edu/%7Emclennan
  34. 34.
    MacLennan BJ (1991) Gabor representations of spatiotemporal visual images. Technical Report CS-91-144. Department of Computer Science, University of Tennessee, Knoxville, Available from www.cs.utk.edu/%7Emclennan
  35. 35.
    MacLennan BJ (1993) Information processing in the dendritic net. In: Karl HP (ed) Rethinking neural networks: quantum fields and biological data. Lawrence Erlbaum, Hillsdale, pp 161–197Google Scholar
  36. 36.
    MacLennan BJ (1994) Continuous computation and the emergence of the discrete. In: Karl HP (ed) Origins: brain and self-organization. Lawrence Erlbaum, Hillsdale, pp 121–151Google Scholar
  37. 37.
    MacLennan BJ (1994) Image and symbol: continuous computation and the emergence of the discrete. In: Honavar V, Uhr L (eds) Artificial intelligence and neural networks: steps toward principled integration. Academic Press, New York, pp 207–224Google Scholar
  38. 38.
    MacLennan BJ (1995) Continuous formal systems: a unifying model in language and cognition. In: Proc. of the IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems. IEEE Press, Piscataway, pp 161–172Google Scholar
  39. 39.
    MacLennan BJ (1997) Field computation in motor control. In: Morasso PG, Sanguineti V (eds) Self‐organization, computational maps and motor control. Elsevier, Amsterdam, pp 37–73Google Scholar
  40. 40.
    MacLennan BJ (2003) Transcending Turing computability. Minds Mach 13:3–22zbMATHGoogle Scholar
  41. 41.
    MacLennan BJ (2004) Natural computation and non‐Turing models of computation. Theor Comput Sci 317:115–145MathSciNetzbMATHGoogle Scholar
  42. 42.
    Mathematical Society of Japan (1980) Encyclopedic dictionary of mathematics. MIT Press, CambridgeGoogle Scholar
  43. 43.
    McClelland JL, Rumelhart DE, PDP Research Group (1986) Parallel distributed processing: explorations in the microstructure of cognition, vol 2. Psychological and biological models. MIT Press, CambridgeGoogle Scholar
  44. 44.
    McFadden J (2002) Synchronous firing and its influence on the brain's electromagnetic field: evidence for an electromagnetic field theory of consciousness. J Conscious Stud 9(4):23–50MathSciNetGoogle Scholar
  45. 45.
    Miller MI, Roysam B, Smith KR, O'Sullivan JA (1991) Representing and computing regular languages on massively parallel networks. IEEE Trans Neural Netw 2:56–72Google Scholar
  46. 46.
    Mills JW (1996) The continuous retina: Image processing with a single‐sensor artificial neural field network. In: Proc. IEEE Conference on Neural Networks. IEEE Press, PiscatawayGoogle Scholar
  47. 47.
    Mills JW, Himebaugh B, Kopecky B, Parker M, Shue C, Weilemann C (2006) “Empty space” computes: the evolution of an unconventional supercomputer. In: Proc. of the 3rd Conference on Computing Frontiers. ACM Press, New York, pp 115–126Google Scholar
  48. 48.
    Moore GE (1965) Cramming more components onto integrated circuits. Electronics 38(8):114–117Google Scholar
  49. 49.
    Peruš M (1998) A quantum information-processing “algorithm” based on neural nets. In: Wang P, Georgiou G, Janikow C, Yao Y (eds) Joint conference on information sciences, vol II. Association for Intelligent Machinery, New York, pp 197–200Google Scholar
  50. 50.
    Pockett S (2000) The nature of consciousness: a hypothesis. Writers Club Press, San JoseGoogle Scholar
  51. 51.
    Pour-El MB (1974) Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers). Trans Am Math Soc 199:1–29MathSciNetzbMATHGoogle Scholar
  52. 52.
    Powell MJD (1987) Radial basis functions for multivariable interpolation: a review. In: Algorithms for approximation. Clarendon, New York, pp 143–167Google Scholar
  53. 53.
    Pribram KH (1991) Brain and perception: holonomy and structural in figural processing. Lawrence Erlbaum, HillsdaleGoogle Scholar
  54. 54.
    Pribram KH, Sharafat A, Beekman GJ (1984) Frequency encoding in motor systems. In: Whiting HTA (ed) Human motor actions: Bernstein reassessed. Elsevier, New York, pp 121–156Google Scholar
  55. 55.
    Rubel LA (1985) The brain as an analog computer. J Theor Neurobiol 4:73–81Google Scholar
  56. 56.
    Rubel LA (1988) Some mathematical limitations of the general‐purpose analog computer. Adv Appl Math 9:22–34MathSciNetzbMATHGoogle Scholar
  57. 57.
    Rubel LA (1993) The extended analog computer. Adv Appl Math 14:39–50MathSciNetzbMATHGoogle Scholar
  58. 58.
    Rumelhart DE, McClelland JL, PDP Research Group (1986) Parallel distributed processing: explorations in the microstructure of cognition, vol 1. Foundations. MIT Press, CambridgeGoogle Scholar
  59. 59.
    Sanger TD (1996) Probability density estimation for the interpretation of neural population codes. J Neurophysiol 76:2790–2793Google Scholar
  60. 60.
    Shannon CE (1941) Mathematical theory of the differential analyzer. J Math Phys Mass Inst Tech 20:337–354MathSciNetzbMATHGoogle Scholar
  61. 61.
    Shannon CE (1993) Mathematical theory of the differential analyzer. In: Sloane NJA, Wyner AD (eds) Claude Elwood Shannon: collected papers. IEEE Press, New York, pp 496–513Google Scholar
  62. 62.
    Skinner SR, Behrman EC, Cruz-Cabrera AA, Steck JE (1995) Neural network implementation using self‐lensing media. Appl Opt 34:4129–4135ADSGoogle Scholar
  63. 63.
    Small JS (2001) The analogue alternative: the electronic analogue computer in Britain and the USA, 1930–1975. Routledge, London, New YorkGoogle Scholar
  64. 64.
    Solé R, Goodwin B (2000) Signs of life: how complexity pervades biology. Basic Books, New YorkGoogle Scholar
  65. 65.
    Soroka WW (1954) Analog methods in computation and simulation. McGraw-Hill, New YorkGoogle Scholar
  66. 66.
    Steinbeck O, Tóth A, Showalter K (1995) Navigating complex labyrinths: optimal paths from chemical waves. Science 267:868–871Google Scholar
  67. 67.
    Ting P-Y, Iltis RA (1994) Diffusion network architectures for implementation of Gibbs samplers with applications to assignment problems. IEEE Trans Neural Netw 5:622–638Google Scholar
  68. 68.
    Tõkés S, Orzó L, Ayoub A (2003) Two‐wavelength POAC (programmable opto‐electronic analogic computer) using bacteriorhodopsin as dynamic holographic material. In: Proc. of ECCTD `03 Conference, vol 3. Krakow, pp 97–100Google Scholar
  69. 69.
    Tõkés S, Orzó L, Váró G, Dér A, Ormos P, Roska T (2001) Programmable analogic cellular optical computer using bacteriorhodopsin as analog rewritable image memory. In: Dér A, Keszthelyi L (eds) Bioelectronic applications of photochromic pigments. IOS Press, Amsterdam, pp 54–73Google Scholar
  70. 70.
    Truitt TD, Rogers AE (1960) Basics of analog computers. John F. Rider, New YorkGoogle Scholar
  71. 71.
    Turing AM (1952) The chemical basis of morphogenesis. Philos Trans Royal Soc B 237:37–72ADSGoogle Scholar

Books and Reviews

  1. 72.
    Bachman G, Narici L (1966) Functional analysis. Academic Press, New YorkzbMATHGoogle Scholar
  2. 73.
    Berberian SK (1961) Introduction to Hilbert space. Oxford, New YorkzbMATHGoogle Scholar
  3. 74.
    MacLennan BJ (1991) Field computation: a theoretical framework for massively parallel analog computation, parts I–IV. Technical Report CS-90-100, Dept. of Computer Science, University of Tennessee, Knoxville. Available from http:www.cs.utk.edu/%7Emclennan
  4. 75.
    MacLennan BJ (2008) Foundations of Field Computation. In preparation. Available from http:www.cs.utk.edu/%7Emclennan

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Bruce J. MacLennan
    • 1
  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of TennesseeKnoxvilleUSA