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Search: id:A065247
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| A065247 |
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Imperfect formal neural networks with n components. |
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+0
3
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| 0, 0, 60, 15652352, 18446731528483929840, 1461501637330902918203677267647731623106580665344, 3940200619639447921227904010014361380507973
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of {0,1}^n to {0,1}^n vector-vector maps of which at least one component is not a formal neuron, i.e. some are not 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 WS 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)=A057156(n)-A000609(n)^n=A057156(n)-A065246(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; the remaining 2^(2*4)-14^2 = 256-196 = 60 = a(2) functions are synthesized from both neurons and non-neurons. For n = 3, 104 = A000609(3) formal neurons and 152 non-neurons gives (2^24)-A065246(3) = 15652352 = a(4) nets with at least one linearly non separable component.
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CROSSREFS
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Cf. A000609, A065246, A065248, A064436.
Sequence in context: A003795 A003921 A003928 this_sequence A058930 A132096 A051322
Adjacent sequences: A065244 A065245 A065246 this_sequence A065248 A065249 A065250
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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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