Phase transitions in least-effort communications

Prokopenko, Mikhail; Ay, Nihat; Obst, Oliver; Polani, Daniel

doi:10.1088/1742-5468/2010/11/p11025

Cited by 31 publications

(70 citation statements)

References 15 publications

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“…This problem has been addressed by explicitly introducing efficiency measures E (such as average path length) along with cost constraints C (such as number of connections of a given graph) [25][26][27]. A similar example in another field models languages as a network of associations between objects and words, and considers language evolution through a least effort process [28][29][30]. Here, the cost-efficiency conflict is mapped onto coding/decoding efforts for users of an economic (while ambiguous) language.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions in Pareto optimal complex networks

Seoane

Solé

2015

Phys. Rev. E

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The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem, finding phase transitions of different kinds. Distinct phases are associated with different arrangements of the connections, but the need of drastic topological changes does not determine the presence or the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.

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Section: Introductionmentioning

confidence: 99%

Phase transitions in Pareto optimal complex networks

Seoane

Solé

2015

Phys. Rev. E

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“…The importance of this work, which we revisit here, is that it introduced a framework of language games to explain Zipf's law which influenced many subsequent works [6][7][8][9] and contributed to the current interest in modeling different aspects of language dynamics [11].…”

Section: Introductionmentioning

confidence: 99%

Analysis of an information-theoretic model for communication

Dickman¹,

Moloney²,

Altmann³

2012

J. Stat. Mech.

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We study the cost-minimization problem posed by Ferrer i Cancho and Solé in their model of communication that aimed at explaining the origin of Zipf's law [PNAS 100, 788 (2003)].Direct analysis shows that the minimum cost is min{λ, 1 − λ}, where λ determines the relative weights of speaker's and hearer's costs in the total, as shown in several previous works using different approaches. The nature and multiplicity of the minimizing solution changes discontinuously at λ = 1/2, being qualitatively different for λ < 1/2, λ > 1/2, and λ = 1/2. Zipf's law is found only in a vanishing fraction of the minimum-cost solutions at λ = 1/2 and therefore is not explained by this model. Imposing the further condition of equal costs yields distributions substantially closer to Zipf's law, but significant differences persist. We also investigate the solutions reached by the previously used minimization algorithm and find that they correctly recover global minimum states at the transition.

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“…8,9 Other known explanations involve, e.g., multiplicative processes, 30,31 games, 32 and information theoretic arguments. [33][34][35][36] In this paper, we will focus on a certain corollary of the Zipf-Mandelbrot law, namely a relationship between the length of the text and the number of different words therein. This relationship is usually called Herdan's or Heaps' law in the English literature.…”

Section: A Zipf's and Herdan's Lawsmentioning

confidence: 99%

Excess entropy in natural language: Present state and perspectives

Dębowski

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We review recent progress in understanding the meaning of mutual information in natural language. Let us define words in a text as strings that occur sufficiently often. In a few previous papers, we have shown that a power-law distribution for so defined words (a.k.a. Herdan's law) is obeyed if there is a similar power-law growth of (algorithmic) mutual information between adjacent portions of texts of increasing length. Moreover, the power-law growth of information holds if texts describe a complicated infinite (algorithmically) random object in a highly repetitive way, according to an analogous power-law distribution. The described object may be immutable (like a mathematical or physical constant) or may evolve slowly in time (like cultural heritage). Here, we reflect on the respective mathematical results in a less technical way. We also discuss feasibility of deciding to what extent these results apply to the actual human communication.

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Phase transitions in least-effort communications

Cited by 31 publications

References 15 publications

Phase transitions in Pareto optimal complex networks

Phase transitions in Pareto optimal complex networks

Analysis of an information-theoretic model for communication

Excess entropy in natural language: Present state and perspectives

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