Analytical results for the Sznajd model of opinion formation

The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed $1/n$ dependence in the distribution of votes in Brazilian elections is provided.Comment: 10 pages 5 figure

Loop expansion around the Bethe-Peierls approximation for lattice models

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetisation and correlation function.Comment: 8 page

Multi-market minority game: breaking the symmetry of choice

Generalization of the minority game to more than one market is considered. At each time step every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of utility then market occupancies become inhomogeneous with preference given to this market where the fluctuation occured first. There exists a critical size of agent population above which agents on bigger market behave collectively. In this regime there always exists a history of decisions for which all agents on a bigger market react identically.Comment: 15 pages, 12 figures, Accepted to 'Advances in Complex Systems

Statistical properties of stock order books: empirical results and models

We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most interesting features concern (i) the statistics of incoming limit order prices, which follows a power-law around the current price with a diverging mean; and (ii) the humped shape of the average order book, which can be quantitatively reproduced using a `zero intelligence' numerical model, and qualitatively predicted using a simple approximation.Comment: Revised version, 10 pages, 4 .eps figures. to appear in Quantitative Financ

Van Kampen's expansion approach in an opinion formation model

We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that there is a nonzero probability of a spontaneous change of opinion (A->I, B->I). From the master equation, and via van Kampen's Omega-expansion approach, we have obtained the "macroscopic" evolution equation, as well as the Fokker-Planck equation governing the fluctuations around the deterministic behavior. Within the same approach, we have also obtained information about the typical relaxation behavior of small perturbations.Comment: 17 pages, 6 figures, submited to Europ.Phys.J.

A Unified Framework for the Pareto Law and Matthew Effect using Scale-Free Networks

We investigate the accumulated wealth distribution by adopting evolutionary games taking place on scale-free networks. The system self-organizes to a critical Pareto distribution (1897) of wealth $P(m)\sim m^{-(v+1)}$ with $1.6 < v <2.0$ (which is in agreement with that of U.S. or Japan). Particularly, the agent's personal wealth is proportional to its number of contacts (connectivity), and this leads to the phenomenon that the rich gets richer and the poor gets relatively poorer, which is consistent with the Matthew Effect present in society, economy, science and so on. Though our model is simple, it provides a good representation of cooperation and profit accumulation behavior in economy, and it combines the network theory with econophysics.Comment: 5 pages, 8 figure

Collective Behavior of Asperities in Dry Friction at Small Velocities

We investigate a simple model of dry friction based on extremal dynamics of asperities. At small velocities, correlations develop between the asperities, whose range becomes infinite in the limit of infinitely slow driving, where the system is self-organized critical. This collective phenomenon leads to effective aging of the asperities and results in velocity dependence of the friction force in the form $F\sim 1- \exp(-1/v)$.Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.

Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically-relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.Comment: 4 pages, 2 figures, 2 column revtex format, to be submitted to PRL 1; reference added and minor rewording of the first paragraph; Title change and major reorganization (but no result changes) in response to referee comments; to be published in PR

Effect of a columnar defect on the shape of slow-combustion fronts

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough excess driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a non-zero excess driving in agreement with the simulated behavior of the ASEP model.Comment: 7 pages, 7 figure

Cracking Piles of Brittle Grains

A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various morphologies, depending on the degree of randomness in the packing and on the ductility of the grains. The external force necessary to continue the cracking process is constant in wide range of values of the fraction of already cracked grains. If the grains are very brittle, the force fluctuations become periodic in early stages of cracking. Distribution of cracking avalanches obeys a power law with exponent $\tau = 2.4 \pm 0.1$.Comment: RevTeX, 6 pages, 7 postscript figures, submitted to Phys. Rev.