Zipf's Law : Balancing signal usage cost and communication efficiency

Copyright: © 2015 Salge et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedWe propose a model that explains the reliable emergence of power laws (e.g., Zipf's law) during the development of different human languages. The model incorporates the principle of least effort in communications, minimizing a combination of the information-Theoretic communication inefficiency and direct signal cost. We prove a general relationship, for all optimal languages, between the signal cost distribution and the resulting distribution of signals. Zipf's law then emerges for logarithmic signal cost distributions, which is the cost distribution expected for words constructed from letters or phonemes. Copyright:Peer reviewedFinal Published versio

Optimization models of natural communication

A family of information theoretic models of communication was introduced more than a decade ago to explain the origins of Zipf’s law for word frequencies. The family is a based on a combination of two information theoretic principles: maximization of mutual information between forms and meanings and minimization of form entropy. The family also sheds light on the origins of three other patterns: the principle of contrast; a related vocabulary learning bias; and the meaning-frequency law. Here two important components of the family, namely the information theoretic principles and the energy function that combines them linearly, are reviewed from the perspective of psycholinguistics, language learning, information theory and synergetic linguistics. The minimization of this linear function is linked to the problem of compression of standard information theory and might be tuned by self-organization.Peer ReviewedPostprint (author's final draft

Cooperation and antagonism in information exchange in a growth scenario with two species

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This is a pre-copyedited, author-produced PDF of an article accepted for publication in Journal of Theoretical Biology following peer review. The version of record [Andres Burgos & Daniel Polani, 'Cooperation and antagonism in information exchange in a growth scenario with two species' Journal of Theoretical Biology, Vol 399 (117-133), June 2016] is available on line via doi: http://dx.doi.org/10.1016/j.jtbi.2016.04.006We consider a simple information-theoretic model of communication, in which two species of bacteria have the option of exchanging information about their environment, thereby improving their chances of survival. For this purpose, we model a system consisting of two species whose dynamics in the world are modelled by a bet-hedging strategy. It is well known that such models lend themselves to elegant information-theoretical interpretations by relating their respective long-term growth rate to the information the individual species has about its environment. We are specifically interested in modelling how this dynamics are affected when the species interact cooperatively or in an antagonistic way in a scenario with limited resources. For this purpose, we consider the exchange of environmental information between the two species in the framework of a game. Our results show that a transition from a cooperative to an antagonistic behaviour in a species results as a response to a change in the availability of resources. Species cooperate in abundance of resources, while they behave antagonistically in scarcity.Peer reviewedFinal Accepted Versio

An Ansatz for undecidable computation in RNA-world automata

In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA-world enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show how the enzymatic reactions match the logical operations of the RNA automaton, and describe how biological exploration of the corresponding evolutionary space is facilitated by the efficient arrangement of RNA polymers into a computational structure. A critical theme of the Ansatz is the self-reference in RNA automata configurations which exploits the program-data duality but results in undecidable computation. We describe how undecidable computation is exemplified in the self-referential Liar paradox that places a boundary on a logical system, and by construction, any RNA automata. We argue that an expansion of the evolutionary space for RNA-2PDA automata can be interpreted as a hierarchical resolution of the undecidable computation by a meta-system (akin to Turing's oracle), in a continual process analogous to Turing's ordinal logics and Post's extensible recursively generated logics. On this basis, we put forward the hypothesis that the resolution of undecidable configurations in RNA-world automata represents a mechanism for novelty generation in the evolutionary space, and propose avenues for future investigation of biological automata

Origins of scaling in genetic code

“The original publication is available at www.springerlink.com” Copyright SpringerThe principle of least effort in communications has been shown, by Ferrer i Cancho and Sol´e, to explain emergence of power laws (e.g., Zipf’s law) in human languages. This paper applies the principle and the informationtheoretic model of Ferrer i Cancho and Sol´e 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 – Sol´e 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.Peer reviewe