@article {Cocho2019,
	title = {Rank-frequency distribution of natural languages: A difference of probabilities approach},
	journal = {Physica A: Statistical Mechanics and its Applications},
	volume = {532},
	year = {2019},
	pages = {121795},
	abstract = {In this paper we investigate the time variation of the rank k of words for six Indo-European languages using the Google Books N-gram Dataset. Based on numerical evidence, we regard k as a random variable whose dynamics may be described by a Fokker{\textendash}Planck equation which we solve analytically. For low ranks the distinct languages behave differently, maybe due to the syntax rules, whereas for k>50 the law of large numbers predominates. We analyze the frequency distribution of words using the data and their adjustment in terms of time-dependent probability density distributions. We find small differences between the data and the fits due to conflicting dynamic mechanisms, but the data show a consistent behavior with our general approach. For the lower ranks the behavior of the data changes among languages presumably, again, due to distinct dynamic mechanisms. We discuss a possible origin of these differences and assess the novel features and limitations of our work.},
	keywords = {Fokker{\textendash}Planck equation, Languages, Master equation, Rank dynamics},
	issn = {0378-4371},
	doi = {10.1016/j.physa.2019.121795},
	url = {https://doi.org/10.1016/j.physa.2019.121795},
	author = {Germinal Cocho and Rosal{\'\i}o F. Rodr{\'\i}guez and Sergio S{\'a}nchez and Jorge Flores and Carlos Pineda and Carlos Gershenson}
}
@article {159,
	title = {Requisite Variety, Autopoiesis, and Self-organization},
	journal = {Kybernetes},
	volume = {44},
	year = {2015},
	pages = {866{\textendash}873},
	author = {Carlos Gershenson}
}
@conference {GershensonEtAl2006,
	title = {The Role of Redundancy in the Robustness of Random {Boolean} Networks},
	booktitle = {{Artificial Life X}, Proceedings of the Tenth International Conference on the Simulation and Synthesis of Living Systems.},
	year = {2006},
	pages = {35{\textendash}42},
	publisher = {MIT Press},
	organization = {MIT Press},
	abstract = {Evolution depends on the possibility of successfully exploring fitness landscapes via mutation and recombination. With these search procedures, exploration is difficult in "rugged" fitness landscapes, where small mutations can drastically change functionalities in an organism. Random Boolean networks (RBNs), being general models, can be used to explore theories of how evolution can take place in rugged landscapes; or even change the landscapes. In this paper, we study the effect that redundant nodes have on the robustness of RBNs. Using computer simulations, we have found that the addition of redundant nodes to RBNs increases their robustness. We conjecture that redundancy is a way of "smoothening" fitness landscapes. Therefore, redundancy can facilitate evolutionary searches. However, too much redundancy could reduce the rate of adaptation of an evolutionary process. Our results also provide supporting evidence in favour of Kauffman{\textquoteright}s conjecture (Kauffman, 2000, p.195).},
	url = {http://uk.arxiv.org/abs/nlin.AO/0511018},
	author = {Carlos Gershenson and Stuart A. Kauffman and Ilya Shmulevich},
	editor = {Rocha, L. M. and L. S. Yaeger and M. A. Bedau and D. Floreano and R. L. Goldstone and A. Vespignani}
}
