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A065246
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Formal neural networks with n components.
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3
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1, 4, 196, 1124864, 12545225621776, 7565068551396549351877632, 11519413104737198429297238164593057431690816, 3940200619639447921227904010014361380507973927046544666794829340424572177149721061141426654884915640806627990306816
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OFFSET
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0,2
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COMMENTS
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Number of {0,1}^n to {0,1}^n vector-vector maps of which all components are formal neurons (=threshold gates).
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REFERENCES
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Labos E. (1996): Long Cycles and Special Categories of Formal Neuronal Networks. Acta Biologica Hungarica, 47: 261-272.
Labos E. and Sette M. (1995): Long Cycle Generation by McCulloch-Pitts Networks(MCP-Nets) with Dense and Sparse Weight Matrices. Proc. of BPTM, McCulloch Memorial Conference [eds:Moreno-Diaz R. and Mira-Mira J., pp. 350-359.], MIT Press, Cambridge,MA,USA.
McCulloch, W. S. and Pitts W. (1943): A Logical Calculus Immanent in Nervous Activity. Bull. Math. Biophys. 5:115-133.
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LINKS
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FORMULA
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EXAMPLE
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For n=2 the 14 threshold gates determine 14*14=196 neural nets each built purely from threshold gates. For n=3, 104=A000609(3) formal neurons gives 104^3=a(3) networks, all component functions of which are linearly separable {0,1}^3 -> {0,1} vector-scalar functions.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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