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Search: id:A065246
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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, 39402006196394479212279040100143613805079739270465446667948293404245721771497210\ 61141426654884915640806627990306816
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OFFSET
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0,2
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COMMENT
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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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FORMULA
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a(n)=A000609(n)^n; for n>1 a(n)<A057156(n).
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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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Cf. A000609, A065247, A065248, A064436.
Sequence in context: A042127 A017546 A144044 this_sequence A156235 A034862 A049656
Adjacent sequences: A065243 A065244 A065245 this_sequence A065247 A065248 A065249
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 26 2001
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