Abstract

A pulse-coupled neural network was implemented, for the first time to our knowledge, in a hybrid electro-optical laboratory demonstration system. Dynamic coherent traveling-wave patterns were observed that repeated their spatial patterns at each locality with a period that depended on the local input pattern and strength. Coherence and periodicity were maintained far beyond the physical limits of the linking receptive fields, suggesting a new mechanism for information transmission in a network with limited local connectivity. With no linking, the output became chaotic because the relative phases increased linearly in time.

© 1993 Optical Society of America

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  1. R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
    [CrossRef]
  2. P. W. Dicke, “Simulation dynamischer merkmalskop-plungen in einem neuronalen netzwerkmodell,” inaugural dissertation (Department of Biophysics, Philipps University, Marburg, Germany, 1992).
  3. R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).
  4. A. S. French, R. B. Stein, IEEE Trans. Bio-Med. Electron. BME-17, 248 (1970).
    [CrossRef]
  5. J. L. Johnson, “Phase and frequency locking in a pulse-coupled neural model,” presented at the Third International Seminar on Digital Image Processing in Medicine, Remote Sensing and Visualization of Information, Riga, Latvia, April 21–25, 1992.
  6. See, for example,S. Grossberg, D. Somers, Neural Networks 4, 453 (1991).
    [CrossRef]
  7. A. V. Holden, M. Markus, H. G. Othmer, eds., Nonlinear Wave Processes in Excitable Media (Plenum, London, to be published).
  8. A. B. Medvinsky, A. V. Panfilov, A. M. Pertsov, in Self-Organization, Autowaves and Structures Far From Equilibrium, V. I. Krinsky, ed. (Springer-Verlag, Berlin, 1984), pp. 195–199.
    [CrossRef]
  9. G. Häusler, in Parallel Processing in Neural Systems and Computers, R. Eckmiller, G. Hartmann, G. Hauske, eds. (North-Holland, Amsterdam, 1990), pp. 533–538.

1991 (1)

See, for example,S. Grossberg, D. Somers, Neural Networks 4, 453 (1991).
[CrossRef]

1990 (1)

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

1988 (1)

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

1970 (1)

A. S. French, R. B. Stein, IEEE Trans. Bio-Med. Electron. BME-17, 248 (1970).
[CrossRef]

Arndt, M.

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

Bauer, R.

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Brosch, M.

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Dicke, P.

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

Dicke, P. W.

P. W. Dicke, “Simulation dynamischer merkmalskop-plungen in einem neuronalen netzwerkmodell,” inaugural dissertation (Department of Biophysics, Philipps University, Marburg, Germany, 1992).

Eckhorn, R.

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

French, A. S.

A. S. French, R. B. Stein, IEEE Trans. Bio-Med. Electron. BME-17, 248 (1970).
[CrossRef]

Grossberg, S.

See, for example,S. Grossberg, D. Somers, Neural Networks 4, 453 (1991).
[CrossRef]

Häusler, G.

G. Häusler, in Parallel Processing in Neural Systems and Computers, R. Eckmiller, G. Hartmann, G. Hauske, eds. (North-Holland, Amsterdam, 1990), pp. 533–538.

Johnson, J. L.

J. L. Johnson, “Phase and frequency locking in a pulse-coupled neural model,” presented at the Third International Seminar on Digital Image Processing in Medicine, Remote Sensing and Visualization of Information, Riga, Latvia, April 21–25, 1992.

Jordan, W.

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Kruse, W.

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Medvinsky, A. B.

A. B. Medvinsky, A. V. Panfilov, A. M. Pertsov, in Self-Organization, Autowaves and Structures Far From Equilibrium, V. I. Krinsky, ed. (Springer-Verlag, Berlin, 1984), pp. 195–199.
[CrossRef]

Munk, M.

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Panfilov, A. V.

A. B. Medvinsky, A. V. Panfilov, A. M. Pertsov, in Self-Organization, Autowaves and Structures Far From Equilibrium, V. I. Krinsky, ed. (Springer-Verlag, Berlin, 1984), pp. 195–199.
[CrossRef]

Pertsov, A. M.

A. B. Medvinsky, A. V. Panfilov, A. M. Pertsov, in Self-Organization, Autowaves and Structures Far From Equilibrium, V. I. Krinsky, ed. (Springer-Verlag, Berlin, 1984), pp. 195–199.
[CrossRef]

Reitboeck, H. J.

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

Somers, D.

See, for example,S. Grossberg, D. Somers, Neural Networks 4, 453 (1991).
[CrossRef]

Stein, R. B.

A. S. French, R. B. Stein, IEEE Trans. Bio-Med. Electron. BME-17, 248 (1970).
[CrossRef]

IEEE Trans. Bio-Med. Electron. (1)

A. S. French, R. B. Stein, IEEE Trans. Bio-Med. Electron. BME-17, 248 (1970).
[CrossRef]

Invest. Ophthalmol. Vis. Sci. (1)

R. Eckhorn, R. Bauer, M. Brosch, W. Jordan, W. Kruse, M. Munk, Invest. Ophthalmol. Vis. Sci. 29, 331 (1988).

Neural Comput. (1)

R. Eckhorn, H. J. Reitboeck, M. Arndt, P. Dicke, Neural Comput. 2, 293 (1990).
[CrossRef]

Neural Networks (1)

See, for example,S. Grossberg, D. Somers, Neural Networks 4, 453 (1991).
[CrossRef]

Other (5)

A. V. Holden, M. Markus, H. G. Othmer, eds., Nonlinear Wave Processes in Excitable Media (Plenum, London, to be published).

A. B. Medvinsky, A. V. Panfilov, A. M. Pertsov, in Self-Organization, Autowaves and Structures Far From Equilibrium, V. I. Krinsky, ed. (Springer-Verlag, Berlin, 1984), pp. 195–199.
[CrossRef]

G. Häusler, in Parallel Processing in Neural Systems and Computers, R. Eckmiller, G. Hartmann, G. Hauske, eds. (North-Holland, Amsterdam, 1990), pp. 533–538.

P. W. Dicke, “Simulation dynamischer merkmalskop-plungen in einem neuronalen netzwerkmodell,” inaugural dissertation (Department of Biophysics, Philipps University, Marburg, Germany, 1992).

J. L. Johnson, “Phase and frequency locking in a pulse-coupled neural model,” presented at the Third International Seminar on Digital Image Processing in Medicine, Remote Sensing and Visualization of Information, Riga, Latvia, April 21–25, 1992.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the model neuron. All inputs to boxes with asterisks have leaky-integrator connections. Those for the linking input have short time constants; those for the feeding input have long time constants. The linking field modulates the feeding field to produce the total internal activity. The step function and variable threshold θ compose the pulse generator.

Fig. 2
Fig. 2

Electro-optical laboratory demonstration system. A defocused SLM provides the linking modulation of the input image to form the internal activity U as the CCD camera input. A computer and a frame grabber provide the step function and the threshold decay loop. Each processing cycle took approximately 10 s.

Fig. 3
Fig. 3

Dynamic periodic traveling waves. (a)–(e) Pulse output images (512 × 512, 8 bits) of processing cycles 82, 83, 84, 85, and 86, respectively. (f) Shows the sum of cycles 1–86 and recovers the original input image of a square (lower left-hand quadrant) and a bright spot (lower right-hand quadrant) on a light background.

Equations (6)

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θ ˙ j = - α θ j + K Y j ,
Y j = Step ( U j - θ j ) ,
U j = F j ( 1 + β L j ) ,
L j = Y Spatial ,
L ( x , y , t + 1 ) = Y ( k x + R u , k y + R v , t ) × Step ( 1 - u 2 + v 2 ) d u d v ,
R = h D 2 P ,             k = P - h P .

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