Spontaneous scale-free structure of spike flow graphs in recurrent neural networks

Neural Networks

Volumn 21, Issue 10, 2008, Pages 1530-1536

  Piȩkniewski, Filip ^a   Schreiber, Tomasz ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

Scale free graph; Stochastic neural network; Winner take all dynamics

Indexed keywords

CHARGE TRANSFER; DYNAMICS; GRAPH THEORY; IMAGE CLASSIFICATION; IMAGE SEGMENTATION; ION EXCHANGE; MASS TRANSFER; NAVIGATION SYSTEMS; RECURRENT NEURAL NETWORKS; STOCHASTIC MODELS; VEGETATION;

BOLTZMANN MACHINES; GAUSSIAN WEIGHTS; NATURAL ENERGIES; NEURAL MODELS; NEURAL NETWORK MODELS; NEURONAL MODELS; NUMERICAL EVIDENCES; POWER LAWS; SCALE BEHAVIORS; SCALE-FREE; SCALE-FREE GRAPH; SELF ORGANIZATIONS; SPIKE FLOWS; SPIKING NEURAL NETWORKS; STOCHASTIC DYNAMICS; STOCHASTIC NEURAL NETWORK; TRACTABLE MODELS; WINNER TAKE ALLS; WINNER-TAKE-ALL DYNAMICS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; ENERGY; MATHEMATICAL MODEL; NERVE CELL; NORMAL DISTRIBUTION; PRIORITY JOURNAL; STOCHASTIC MODEL; TEMPERATURE;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; NEURAL NETWORKS (COMPUTER); STOCHASTIC PROCESSES;

EID: 56949101943     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2008.06.011     Document Type: Article

References (18)

1. Aarts E., and Korst J. Simulated annealing and Boltzmann machines: A stochastic approach to combinatorial optimization and neural computing (1989), John Wiley & Sons, Inc., New York, NY, USA
2. Albert R., and Barabási A.-L. Statistical mechanics of complex networks. Reviews of Modern Physics 74 January (2002) 47-97
3. Albert R., Jeong H., and Barabási A.-L. Diameter of the world-wide web. Science 401 September (1999) 130-131
4. Amaral L.A., Scala A., Barthelemy M., and Stanley H.E. Classes of small-world networks. Proceedings of National Academy of Sciences of the United States of America 97 21 (2000) 11149-11152. http://dx.doi.org/10.1073/pnas.200327197 URL: http://dx.doi.org/10.1073/pnas.200327197
5. Barabási A.-L., and Albert R. Emergence of scaling in random networks. Science 286 October (1999) 509-512
6. Barabási A.-L., Jeong H., Néda Z., Ravasz E., Schubert A., and Vicsek T. Evolution of the social network of scientific collaborations. Physica A 311 4 (2002) 590-614
7. i Cancho R.F., and Solé R.V. The small-world of human language. Proceedings of the Royal Society of London B 268 1482 (2001) 2261-2265
8. Izhikevich E.M. Simple model of spiking neurons. IEEE Transactions on Neural Networks 14 (2003) 1569-1572. http://www.nsi.edu/users/izhikevich/publications/spikes.pdf URL: http://www.nsi.edu/users/izhikevich/publications/spikes.pdf
9. Jeong H., Tombor B., Albert R., Oltvai Z.N., and Barabási A.-L. The large-scale organization of metabolic networks. Nature 407 6804 (2000) 651-653
10. Koch C., and Laurent G. Complexity and the nervous system. Science 284 5411 (1999) 96-98. http://www.sciencemag.org/cgi/content/abstract/284/5411/96 URL: http://www.sciencemag.org/cgi/content/abstract/284/5411/96
11. Montoya J.M., and V. R.V.S. Small world patterns in food webs. Journal of Theoretical Biology 214 3 (2002) 405-412
12. Perotti J.I., Tamarit F.A., and Cannas S.A. A scale-free neural network for modelling neurogenesis. Physica A Statistical Mechanics and its Applications 371 Nov. (2006) 71-75
13. Piekniewski F. Emergence of scale-free graphs in dynamical spiking neural networks. Proc. IEEE international joint conference on neural networks (2007), IEEE Press, Orlando, Florida, USA 755-759
14. Piekniewski, F., & Schreiber, T. (2007). Emergence of scale-free spike flow graphs in recurrent neural networks. In: Proc. IEEE symposium series in computational intelligence - foundations of computational intelligence (pp. 357-362)
15. Redner S. How popular is your paper? An empirical study of the citation distribution. European Physical Journal B 4 2 (1998) 131-134
16. Resnick S.I. Extreme values, regular variation, and point processes. Springer series in operations research and financial engineering (1987), Springer-Verlag New York, Inc., Secaucus, NJ, USA
17. Stauffer D., Aharony A., da Fontoura Costa L., and Adler J. Efficient hopfield pattern recognition on a scale-free neural network. The European Physical Journal B 32 (2003) 395-399
18. Talagrand M. Spin glasses: A challenge for mathematicians, cavity and mean field models. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Vol. 46 (2003), Springer-Verlag New York, Inc., Secaucus, NJ, USA