What processes can explain how very large populations are able to converge on the use of a particular word or grammatical construction without global coordination? Answering this question helps to understand why new language constructs usually propagate along an S-shaped curve with a rather sudden transition towards global agreement. It also helps to analyze and design new technologies that support or orchestrate self-organizing communication systems, such as recent social tagging systems for the web. The article introduces and studies a microscopic model of communicating autonomous agents performing language games without any central control. We show that the system undergoes a disorder/order transition, going trough a sharp symmetry breaking process to reach a shared set of conventions. Before the transition, the system builds up non-trivial scale-invariant correlations, for instance in the distribution of competing synonyms, which display a Zipf-like law. These correlations make the system ready for the transition towards shared conventions, which, observed on the time-scale of collective behaviors, becomes sharper and sharper with system size. This surprising result not only explains why human language can scale up to very large populations but also suggests ways to optimize artificial semiotic dynamics.

An exact "branch by branch" calculation of the diffusional flux is proposed for partially absorbed random walks on arbitrary tree structures. In the particular case of symmetric trees, an explicit analytical expression is found which is valid whatever the size of the tree. Its application to the respiratory phenomena in pulmonary acini gives an analytical description of the crossover regime governing the human lung efficiency.

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In the mammalian lung acini, O(2) diffuses into quasi-static air toward the alveolar membrane, where the gas exchange with blood takes place. The O(2) flux is then influenced by the O(2) diffusivity, the membrane permeability, and the acinus geometric complexity. This phenomenon has been recently studied in an abstract geometric model of the acinus, the Hilbert acinus (Sapoval B, Filoche M, and Weibel ER, Proc Natl Acad Sci USA 99: 10411, 2002). This is extended here to a more realistic geometry originated from the morphological model of Kitaoka et al. (Kitaoka K, Tamura S, and Takaki R, J Appl Physiol 88: 2260-2268, 2000). Two-dimensional numerical simulations of the steady-state diffusion equation with mixed boundary conditions are used to quantify the process. The alveolar O(2) concentration, or partial pressure, and the O(2) flux are computed and show that diffusional screening exists at rest. These results confirm that smaller acini are more efficient, as suggested for the Hilbert acini.

The possibility to renormalize random walks is used to study numerically the oxygen diffusion and permeation in the acinus, the diffusion cell terminating the mammalian airway tree. This is done in a 3D tree structure which can be studied from its topology only. The method is applied to the human acinus real morphology as studied by Haefeli-Bleuer and Weibel in order to compute the respiratory efficiency of the human lung. It provides the first quantitative evidence of the role of diffusion screening in real 3D mammalian respiration. The net result of this study is that, at rest, the efficiency of the human acinus is only of order 33%. Application of these results to CO2 clearance provides for the first time a theoretical support to the empirical relation between the O2 and CO2 partial pressures in blood.

We study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of x(c), the value of the avalanche exponent tau, and the asymptotic distribution of minimal fitnesses.

We study here the Bak-Sneppen model, a prototype model for the study of self-organized criticality. In this model several species interact and undergo extinction with a power-law distribution of activity bursts. Species are defined through their "fitness" whose distribution in the system is uniform above a certain threshold. Run time statistics is introduced for the analysis of the dynamics in order to explain the peculiar properties of the model. This approach based on conditional probability theory, takes into account the correlations due to memory effects. In this way, we may compute analytically the value of the fitness threshold with the desired precision. This represents a substantial improvement with respect to the traditional mean field approach.

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