Language Evolution and Computation Bibliography

We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB) state. Proposed in the context of language competition and emergence, the AB state was associated with bilingualism and synonymy respectively. We show that the two models are equivalent in the mean field approximation, though the differences at the microscopic level have non-trivial consequences. To point them out, we investigate an extension of these dynamics in which confidence/trust is considered, focusing on the case of an underlying fully connected graph, and we show that the consensus-polarization phase transition taking place in the Naming Game is not observed in the AB model. We then consider the interface motion in regular lattices. Qualitatively, both models show the same behavior: a diffusive interface motion in a one-dimensional lattice, and a curvature driven dynamics with diffusing stripe-like metastable states in a two-dimensional one. However, in comparison to the Naming Game, the AB-model dynamics is shown to slow down the diffusion of such configurations.

We propose a Finite-Memory Naming Game (FMNG) model with respect to the bounded rationality of agents or finite resources for information storage in communication systems. We study its dynamics on several kinds of complex networks, including random networks, small-world networks and scale-free networks. We focus on the dynamics of the FMNG affected by the memory restriction as well as the topological properties of the networks. Interestingly, we found that the most important quantity, the convergence time of reaching the consensus, shows some non-monotonic behaviors by varying the average degrees of the networks with the existence of the fastest convergence at some specific average degrees. We also investigate other main quantities, such as the success rate in negotiation, the total number of words in the system and the correlations between agents of full memory and the total number of words, which clearly explain the nontrivial behaviors of the convergence. We provide some analytical results which help better understand the dynamics of the FMNG. We finally report a robust scaling property of the convergence time, which is regardless of the network structure and the memory restriction.

Words in humans follow the so-called Zipf's law. More precisely, the word frequency spectrum follows a power function, whose typical exponent is $\beta \approx 2$, but significant variations are found. We hypothesize that the full range of variation reflects our ability to balance the goal of communication, i.e. maximizing the information transfer and the cost of communication, imposed by the limitations of the human brain. We show that the higher the importance of satisfying the goal of communication, the higher the exponent. Here, assuming that words are used according to their meaning we explain why variation in $\beta$ should be limited to a particular domain. From the one hand, we explain a non-trivial lower bound at about $\beta=1.6$ for communication systems neglecting the goal of the communication. From the other hand, we find a sudden divergence of $\beta$ if a certain critical balance is crossed. At the same time a sharp transition to maximum information transfer and unfortunately, maximum communication cost, is found. Consistently with the upper bound of real exponents, the maximum finite value predicted is about $\beta=2.4$. It is convenient for human language not to cross the transition and remain in a domain where maximum information transfer is high but at a reasonable cost. Therefore, only a particular range of exponents should be found in human speakers. The exponent $\beta$ contains information about the balance between cost and communicative efficiency.

Here we present a new model for Zipf's law in human word frequencies. The model defines the goal and the cost of communication using information theory. The model shows a continuous phase transition from a no communication to a perfect communication phase. Scaling consistent with Zipf's law is found in the boundary between phases. The exponents are consistent with minimizing the entropy of words. The model differs from a previous model [Ferrer i Cancho, SoleProc. Natl. Acad. Sci. USA 100, 788-791 (2003)] in two aspects. First, it assumes that the probability of experiencing a certain stimulus is controlled by the internal structure of the communication system rather than by the probability of experiencing it in the `outside' world, which makes it specially suitable for the speech of schizophrenics. Second, the exponent ? predicted for the frequency versus rank distribution is in a range where ?>1, which may explain that of some schizophrenics and some children, with ?=1.5-1.6. Among the many models for Zipf's law, none explains Zipf's law for that particular range of exponents. In particular, two simplistic models fail to explain that particular range of exponents: intermittent silence and Simon's model. We support that Zipf's law in a communication system may maximize the information transfer under constraints.