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Copy-mutate processes for growth of bipartite networks: an application to
cultural evolution
Osame Kinouchi, Antônio Carlos Roque
Adriano de Jesus Holanda (FFCLRP-USP)
Rosa Wanda Diez Garcia (FMRP)
Pedro Zambianchi (Faculdade Bandeirantes)
Why culinary?
• Physicists like to explain and model interesting statistical patterns (power laws)
• New application of complex networks ideas
• Database relatively easy to construct
• Analogy to biological evolution: growth network algorithm
• Similar to other humans, physicists like to eat
Why cookbooks?
• Recipes = cultural replicators (memes)
• Recipes in standard algorithmic form
• Cookbooks provide judicious (non-random) selection of recipes
Ingredients and RecipesBipartite network
Recipes
Ingredients
Cultural invariance
Temporal invariance
Complementary Cumulative
Distribution
72.1)(:pdf kkp
Recipe degree distribution
Copy-mutate model
Fitness selection
fi
fj
Substitute if fj > fi
Fitness fi interval [0,1]
Ingredient pool
Recipe with K ingredients
Model results
)/exp()( 0rrrA
CrF
Founder Effect
Founder Effect (II)
Fitness functions
fitnessculinary )(
1)(
fitness recipe1
fitness ingredient
)(
1
1
tR
k
k
K
i
ki
k
i
FtR
tF
fK
F
f
Slow dynamics
1F(t) = c t-
Conclusions
• Bipartite network of ingredients and recipes is scale free with non-trivial exponent 1.7 (out of range of generalized Yule process)
• Rank-frequency plot can be fitted by Darwinian copy-mutate process with ingredient fitness
• Model suggests presence of “founder effect” and slow (glassy) dynamics in cultural evolution
Acknowledgments: CNPq
Rank Entropy
)(ln)( rfrfSr
Rank Entropy