Phase transitions and complex systems: <i>Simple, nonlinear models capture complex systems at the edge of chaos</i>

The emergence of a complex language is one of the fundamental events of human evolution, and several remarkable features suggest the presence of fundamental principles of organization. These principles seem to be common to all languages. The best known is the so-called Zipf's law, which states that the frequency of a word decays as a (universal) power law of its rank. The possible origins of this law have been controversial, and its meaningfulness is still an open question. In this article, the early hypothesis of Zipf of a principle of least effort for explaining the law is shown to be sound. Simultaneous minimization in the effort of both hearer and speaker is formalized with a simple optimization process operating on a binary matrix of signal-object associations. Zipf's law is found in the transition between referentially useless systems and indexical reference systems. Our finding strongly suggests that Zipf's law is a hallmark of symbolic reference and not a meaningless feature. The implications for the evolution of language are discussed. We explain how language evolution can take advantage of a communicative phase transition. Beyond their specific differences, all known human languages exhibit two fully developed distinguishing traits with regard to animal communication systems: syntax (1) and symbolic reference (2). Trying to explain the complexity gap between humans and other species, different authors have adopted different views from gradual evolution (3) to non-Darwinian positions (4). Arguments are often qualitative in nature and sometimes ad hoc. Only recently mathematical models have explicitly addressed these questions (5, 6).It seems reasonable to assume that our human ancestors started off with a communication system capable of rudimentary referential signaling, which subsequently evolved into a system with a massive lexicon supported by a recursive system that could combine entries in the lexicon into an infinite variety of meaningful utterances (7). In contrast, nonhuman repertoires of signals are generally small (8, 9). We aim to provide new theoretical insights to the absence of intermediate stages between animal communication and language (9).Here we adopt the view that the design features of a communication system are the result of interaction between the constraints of the system and demands of the job required (7). More precisely, we will understand the demands of a task such as providing easy-to-decode messages for the receiver. Our system will be constrained by the limitations of a sender trying to code such an easy-to-decode message.Many authors have pointed out that tradeoffs of utility concerning hearer and speaker needs to appear at many levels. As for the phonological level, speakers want to minimize articulatory effort and hence encourage brevity and phonological reduction. Hearers want to minimize the effort of understanding and hence desire explicitness and clarity (3, 10). Regarding the lexical level (10, 11), the effort for the hearer has to do with determining what the word...

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“…3C). As it occurs with other complex systems (16), the presence of a phase transition is associated with the emergence of power laws (17).…”

Section: Resultsmentioning

confidence: 99%

Least effort and the origins of scaling in human language

Cancho

Solé²

2003

Proc. Natl. Acad. Sci. U.S.A.

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404

206

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“…This is in contrast to changes at higher θ d values where on average the decrease is less than twofold for every 0.1 increment in θ d . These results suggest a phase transition-defined as a significant change of state when parameter values cross a certain threshold (Solé et al 1996)-occurring in the vicinity of θ d = 0, where the qualitative behavior of the system undergoes a significant alteration. Considered a signature of complex networks (Castellano et al 2000;Holme and Newman 2006), in our case the phase transition is the change from a very sparse network with an average network density of 0.12 % for nonzero values of θ d to a relatively dense network with an average density of 29.4 % when…”

Section: Aggregate Social Capitalmentioning

confidence: 80%

Churning, power laws, and inequality in a spatial agent-based model of social networks

Cho

Mansury

2016

Ann Reg Sci

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Amidst many previous network models lacking a spatial dimension, this paper proposes a dynamic agent-based model of social network formation that explicitly considers space. We find that varying the dynamics of agent interaction causes the emergence of differential degree distributions as well as nonlinear dynamics in social and spatial inequalities. The scale-free property of degree connectivity vanishes when tie formation dominates tie dissolution, with power laws re-emerging when tie dissolution is of equal strength or stronger than tie formation. Furthermore, we find a nonlinear relationship between network density and agent inequality in social resources. In particular, multiple phase transitions occur where the relationship is positive in one phase but negative in another. This suggests that, contrary to intuition, higher connectivity can have an adverse distributional impact by benefiting the already privileged. Critically, we find a tradeoff between agent inequality and spatial inequality where the geographic concentration of social resources accompanies a more equal distribution of connectivity. Finally, the disadvantage of agents with limited spatial reach is exacerbated as network density increases. Our results thus highlight the importance of distinguishing between social and spatial inequality in policymaking.

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“…The simplest model that accounted for this phenomenon included two types of chemicals, indicated by D and L and corresponding to the two forms [36,37]. They can react with an additional molecule A following the set of reactions [17,18,22,23] where two alternative stable states r 1 ¼ 0, 1 are possible, both accessible from r 1 ¼ 1/2 through an amplification phenomenon. This can be seen using the so-called potential function V b (r 1 ) defined from…”

Section: Synthetic Prebiotic Chemistrymentioning

confidence: 99%

Synthetic transitions: towards a new synthesis

Solé

2016

Phil. Trans. R. Soc. B

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One contribution of 13 to a theme issue 'The major synthetic evolutionary transitions'. The evolution of life in our biosphere has been marked by several major innovations. Such major complexity shifts include the origin of cells, genetic codes or multicellularity to the emergence of non-genetic information, language or even consciousness. Understanding the nature and conditions for their rise and success is a major challenge for evolutionary biology. Along with data analysis, phylogenetic studies and dedicated experimental work, theoretical and computational studies are an essential part of this exploration. With the rise of synthetic biology, evolutionary robotics, artificial life and advanced simulations, novel perspectives to these problems have led to a rather interesting scenario, where not only the major transitions can be studied or even reproduced, but even new ones might be potentially identified. In both cases, transitions can be understood in terms of phase transitions, as defined in physics. Such mapping (if correct) would help in defining a general framework to establish a theory of major transitions, both natural and artificial. Here, we review some advances made at the crossroads between statistical physics, artificial life, synthetic biology and evolutionary robotics.This article is part of the themed issue 'The major synthetic evolutionary transitions'.

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Phase transitions and complex systems: Simple, nonlinear models capture complex systems at the edge of chaos

Cited by 107 publications

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Least effort and the origins of scaling in human language

Least effort and the origins of scaling in human language

Churning, power laws, and inequality in a spatial agent-based model of social networks

Synthetic transitions: towards a new synthesis

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