Mathematics awaits: commentary on ''Genetic Programming and Emergence'' by Wolfgang Banzhaf
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- @Article{Altenberg:2014:GPEM,
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author = "Lee Altenberg",
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title = "Mathematics awaits: commentary on ''Genetic
Programming and Emergence'' by Wolfgang Banzhaf",
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journal = "Genetic Programming and Evolvable Machines",
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year = "2014",
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volume = "15",
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number = "1",
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pages = "87--89",
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month = mar,
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keywords = "genetic algorithms, genetic programming, Evolvability,
Robustness, Subtree exchange, Mathematics, Matrix
theory, Lagrange distribution",
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ISSN = "1389-2576",
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DOI = "doi:10.1007/s10710-013-9198-5",
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size = "3 pages",
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abstract = "Banzhaf provides a portal to the subject of emergence,
noting contentious concepts while not getting sucked
into fruitless debate. Banzhaf refutes arguments
against downward causation much as Samuel Johnson kicks
a stone to refute Berkeley by pointing to concrete
examples in genetic programming, such as the growth of
repetitive patterns within programs. Repetitive
patterns are theoretically predicted to emerge from the
evolution of evolvability and robustness under subtree
exchange. Selection and genetic operators are co-equal
creators of these emergent phenomena. GP systems
entirely formal, and thus their emergent phenomena are
essentially mathematical. The emergence of Lagrangian
distributions for tree shapes under subtree exchange,
for example, gives a glimpse of the possibilities for
mathematical understanding of emergence in GP. The
mathematics underlying emergence in genetic programming
should be pursued with vigour.",
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notes = "\cite{Banzhaf:2014:GPEM}",
- }
Genetic Programming entries for
Lee Altenberg
Citations