Phase transitions in least-effort communications

oliver — Tue, 16 Nov 2010 05:31:13 +0000

Our new paper Phase transitions in least-effort communications has been published in J. Stat. Mech. In this work, we critically examine a model that attempts to explain the emergence of power laws (e.g., Zipf’s law) in human language. The model is based on the principle of least effort in communications—specifically, the overall effort is balanced between the speaker effort and listener effort, with some trade-off. It has been shown that an information-theoretic interpretation of this principle is sufficiently rich to explain the emergence of Zipf’s law in the vicinity of the transition between referentially useless systems (one signal for all referable objects) and indexical reference systems (one signal per object). The phase transition is defined in the space of communication accuracy (information content) expressed in terms of the trade-off parameter. Our study explicitly solves the continuous optimization problem, subsuming a recent, more specific result obtained within a discrete space. The obtained results contrast Zipf’s law found by heuristic search (that attained only local minima) in the vicinity of the transition between referentially useless systems and indexical reference systems, with an inverse-factorial (sub-logarithmic) law found at the transition that corresponds to global minima. The inverse-factorial law is observed to be the most representative frequency distribution among optimal solutions.

Origins of Scaling in Genetic Code

oliver — Mon, 21 Sep 2009 12:02:56 +0000

The principle of least effort in communications has been shown, by Ferrer i Cancho and Solé, to explain emergence of power laws (e.g., Zipf’s law) in human languages. In our new paper, Origins of Scaling in Genetic Code (O. Obst, D. Polani, M. Prokopenko), published on ECAL 2009, we apply the principle and the information-theoretic model of Ferrer i Cancho and Solé to genetic coding. The application of the principle is achieved via equating the ambiguity of signals used by “speakers” with codon usage, on the one hand, and the effort of “hearers” with needs of amino acid translation mechanics, on the other hand. The re-interpreted model captures the case of the typical (vertical) gene transfer, and confirms that Zipf’s law can be found in the transition between referentially useless systems (i.e., ambiguous genetic coding) and indexical reference systems (i.e., zero-redundancy genetic coding). As with linguistic symbols, arranging genetic codes according to Zipf’s law is observed to be the optimal solution for maximising the referential power under the effort constraints. Thus, the model identifies the origins of scaling in genetic coding — via a trade-off between codon usage and needs of amino acid translation. Furthermore, the paper extends Ferrer i Cancho Solé model to multiple inputs, reaching out toward the case of horizontal gene transfer (HGT) where multiple contributors may share the same genetic coding. Importantly, the extended model also leads to a sharp transition between referentially useless systems (ambiguous HGT) and indexical reference systems (zero-redundancy HGT). Zipf’s law is also observed to be the optimal solution in the HGT case.

genetic code, evolution, language, zipf’s law, horizontal gene transfer

oliver.obst.eu » coding

Phase transitions in least-effort communications

Origins of Scaling in Genetic Code