creators_name: Wakeling, Joseph creators_id: JWakeling type: preprint datestamp: 2003-09-19 lastmod: 2011-03-11 08:55:20 metadata_visibility: show title: Order-disorder transition in the Chialvo-Bak `minibrain' controlled by network geometry subjects: neuro-mod subjects: comp-sci-neural-nets full_text_status: public keywords: Phase transitions; Neural networks; Neuroscience note: Published in Physica A 325 (2003) 561-569. abstract: We examine a simple biologically-motivated neural network, the three-layer version of the Chialvo-Bak `minibrain' [Neurosci. 90 (1999) 1137], and present numerical results which indicate that a non-equilibrium phase transition between ordered and disordered phases occurs subject to the tuning of a control parameter. Scale-free behaviour is observed at the critical point. Notably, the transition here is due solely to network geometry and not any noise factor. The phase of the network is thus a design parameter which can be tuned. The phases are determined by differing levels of interference between active paths in the network and the consequent accidental destruction of good paths. date: 2003-07 date_type: published refereed: TRUE referencetext: [1] S. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, Oxford, 1993. [2] E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning Ways For Your Mathematical Plays, A. K. Peters, Ltd., 2001. [3] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59 (1987) 381. [4] P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. A 38 (1998) 364. [5] P. Bak, K. Sneppen, Phys. Rev. Lett. 71 (1993) 4083. [6] P. Bak, How Nature Works: The Science of Self-Organized Criticality, Oxford University Press, Oxford, 1997. [7] D. O. Hebb, The Organization of Behaviour, Wiley, New York, 1949. [8] A. G. Barto, Hum. Neurobiol. 4 (1985) 229. [9] A. G. Barto, M. I. Jordan, Proc. IEEE Int. Conf. on Neural Networks 2 (1987) 629. [10] P. Mazzoni, R. A. Andersen, M. I. Jordan, Proc. Natl. Acad. Sci. USA 88 (1991) 4433. [11] P. Alstrom, D. Stassinopoulos, Phys. Rev. E 51 (1995) 5027. [12] D. Stassinopoulos, P. Bak, Phys. Rev. E 51 (1995) 5033. [13] D. R. Chialvo, P. Bak, Neurosci. 90 (1999) 1137. [14] P. Bak, D. R. Chialvo, Phys. Rev. E 63 (2001) 031912. [15] J. Wakeling, P. Bak, Phys. Rev. E 64 (2001) 051920. [16] T. Kohonen, Self-Organizing Maps, Springer-Verlag, Berlin, 2001. [17] J. J. Hopfield, Proc. Natl. Acad. Sci. USA 79 (1982) 2554. [18] D. J. Amit, H. Gutfreund, H. Sompolinsky, Phys. Rev. Lett. 55 (1985) 1530. [19] E. Gardner, J. Phys. A 20 (1987) 3453. [20] H. Sompolinsky, N. Tishby, H. S. Seung, Phys. Rev. Lett. 65 (1990) 1683. [21] E. Barkai, D. Hansel, H. Sompolinsky, Phys. Rev. A 45 (1992) 4146. [22] H. S. Seung, H. Sompolinsky, N. Tishby, Phys. Rev. A 45 (1992) 6056. [23] T. L. H. Watkin, A. Rau, M. Biehl, Rev. Mod. Phys. 65 (1993) 499. [24] J. A. Flanagan, Phys. Rev. E 63 (2001) 036130. [25] G. Parisi, J. Phys. A 19 (1986) L617. [26] J. Z. Young, Proc. Royal Soc. London B 163 (1965) 285. [27] R. M. Fitzsimonds, H. J. Song, M. M. Poo, Nature 388 (1997) 439. [28] J. S. Albus, Brains, Behaviour and Robotics, BYTE Books, McGraw-Hill, Peterborough, NH, 1981. [29] G. M. Edelman, Neural Darwinism: The Theory of Neuronal Group Selection, Basic Books, New York, 1987. [30] T. Araujo, R. Vilela Mendes, Complex Syst. 12 (2000) 357. citation: Wakeling, Joseph (2003) Order-disorder transition in the Chialvo-Bak `minibrain' controlled by network geometry. [Preprint] document_url: http://cogprints.org/3152/1/phase-mb-physa_final.pdf document_url: http://cogprints.org/3152/2/phase-mb-physa_final.ps