The $-game

We propose a payoff function extending Minority Games (MG) that captures the competition between agents to make money. In contrast with previous MG, the best strategies are not always targeting the minority but are shifting opportunistically between the minority and the majority. The emergent properties of the price dynamics and of the wealth of agents are strikingly different from those found in MG. As the memory of agents is increased, we find a phase transition between a self-sustained speculative phase in which a “stubborn majority” of agents effectively collaborate to arbitrage a market-maker for their mutual benefit and a phase where the market-maker always arbitrages the agents. A subset of agents exhibit a sustained non-equilibrium risk-return profile. Received 5 June 2002 / Received in final form 21 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sornette@unice.fr RID="b" ID="b"CNRS UMR7536 RID="c" ID="c"CNRS UMR6622     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Modelling collective opinion formation by means of active Brownian particles

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical “social” temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems. Received 26 November 1999     

Confinement of columnar diblock copolymers: Simulations, theory and applications

The inherent nanoscale morphologies of self-organizing diblock copolymer melts are now being investigated for a variety of technological applications. To obtain global, well-oriented, regular patterns requires suitably confining and aligning the melt between two flat plates. Here we consider such confinement for an asymmetrical diblock melt, which forms columns of the minority phase in a matrix of the majority phase. We investigate this system with a combination of numerical simulations and strong segregation theory and make suggestions as to when perpendicular orientation should prevail over parallel orientation of the columns. Received 22 May 2001 and Received in final form 14 February 2002     

Rules extraction in short memory time series using genetic algorithms

Data mining is performed using genetic algorithm on artificially generated time series data with short memory. The extraction of rules from a training set and the subsequent testing of these rules provide a basis for the predictions on the test set. The artificial time series are generated using the inverse whitening transformation, and the correlation function has an exponential form with given time constant indicative of short memory. A vector quantization technique is employed to classify the daily rate of return of this artificial time series into four categories. A simple genetic algorithm based on a fixed format of rules is introduced to do the forecasting. Comparing to the benchmark tests with random walk and random guess, genetic algorithms yield substantially better prediction rates, between 50% to 60%. This is an improvement compared with the 47% for random walk prediction and 25% for random guessing method. Received 29 August 2000     

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call “topological”. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested. Received 9 August 2002 / Received in final form 7 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: slanina@fzu.cz     

QCD at high baryon density in a random matrix model

A high-density diquark phase seems to be a generic feature of QCD. If so it should also be reproduced by random matrix models. We discuss a specific one in which the random matrix elements of the Dirac operator are supplemented by a finite chemical potential and by non-random elements which model the formation of instanton-anti-instanton molecules. Comparing our results to those found in a previous investigation by Vanderheyden and Jackson we find additional support for our starting assumption, namely that the existence of a high-density diquark phase is common to all QCD-like model. Received: 20 February 2001 / Accepted: 24 April 2001     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Aging and non-linear glassy dynamics in a mean field model

The mean field approach of glassy dynamics successfully describes systems which are out-of-equilibrium in their low temperature phase. In some cases an aging behaviour is found, with no stationary regime ever reached. In the presence of dissipative forces however, the dynamics is indeed stationary, but still out-of-equilibrium, as inferred by a significant violation of the fluctuation dissipation theorem. The mean field dynamics of a particle in a random but short-range correlated environment, offers the opportunity of observing both the aging and driven stationary regimes. Using a geometrical approach previously introduced by the author, we study here the relation between these two situations, in the pure relaxational limit, i.e. the zero temperature case. In the stationary regime, the velocity (v)-force (F) characteristics is a power law v∼F ⁴, while the characteristic times scale like powers of v, in agreement with an early proposal by Horner. The cross-over between the aging, linear-response regime and the non-linear stationary regime is smooth, and we propose a parametrization of the correlation functions valid in both cases, by means of an “effective time”. We conclude that aging and non-linear response are dual manifestations of a single out-of-equilibrium state, which might be a generic situation. Received 7 May 2000 and Received in final form 22 August 2000     

Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Received 31 January 2001 and Received in final form 26 June 2001     

The Nambu–Jona–Lasinio model of light nuclei

The Nambu–Jona–Lasinio model of the deuteron suggested by Nambu and Jona–Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron–proton collective excitation, i.e. a Cooper np–pair, induced by a phenomenological local four–nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one–nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon–loop anomalies which are completely determined by one–nucleon loop diagrams. The dominance of contributions of nucleon–loop anomalies to effective Lagrangians of low–energy nuclear interactions is justified in the large N _C expansion, where N _C is the number of quark colours. Received: 10 March 2000     

Stochastic resonance in a model of opinion formation on small-world networks

We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a “fashion wave”. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed. Received 19 December 2001     

Isomorphous phase transition and orientational freezing in hexagonal mixed crystal C 70(1 - x) C60x. A pseudospin model

A four-state pseudospin model is constructed for the isomorphous phase transition hcp-2↦hcp-1 in pure C₇₀ and in C₇₀-rich mixed crystal C _{70(1 - x)} C_60x. With the specific anisotropic pseudospin interactions adapted to the C₇₀ crystal the model is equivalent to a two-state Ising model in a temperature-dependent field. Replica symmetric state of the model is shown to approach the critical point when the width of distribution of random fields and/or of random bonds increases. The temperature of the phase transition and the phase equilibrium temperature then are practically constant, whereas the experiment shows their strong decrease with x. The main effect of dilution resides in an x-dependence of the model parameters. Dilatometric data on the hexagonal C _{70(1 - x)} C_60x are used to fit these parameters. A metastable disordered phase subsisting below the phase transition is discovered in a range of the model parameters and is shown to be responsible for the macroscopic behaviour of the system. A good agreement with experimental data is obtained for the spontaneous strain and for the x-dependence of the hysteresis. Received 20 April 2001 and Received in final form 26 September 2001     

Growth and addition in a herding model

A model of herding is introduced which is exceptionally simple, incorporating only two phenomena, growth and addition. At each time step either (i) with probability p the system grows through the introduction of a new agent or (ii) with probability q = 1 - p a free agent already in the system is added at random to a group of size k with rate A_k. Two versions of the model, A _k = k and A _k = 1, are solved and in both versions we find two different types of behaviour. When p > 1/2 all the moments of the distribution of group sizes are linear in time for large time and the group distribution is power-law. When p < 1/2 the system runs out of free agents in a finite time. Received 12 February 2002 Published online 9 July 2002     

Ferromagnetic ordering in graphs with arbitrary degree distribution

We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical exponents as a function of the moments of the degree distribution. Two regimes of the degree distribution are of particular interest. In the case of a divergent second moment, the system is ferromagnetic at all temperatures. In the case of a finite second moment and a divergent fourth moment, there is a ferromagnetic transition characterized by non-trivial critical exponents. Finally, if the fourth moment is finite we recover the mean field exponents. These results are analyzed in detail for power-law distributed random graphs. Received 4 April 2002 Published online 19 July 2002     

Low temperature properties of the random field Potts chain

The random field q-states Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q = 2). This is also the expected outcome based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field perturbations (`chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,..., 5. Finally for q = 2 (Ising case) the domain length distribution is studied for correlated random fields. Received 27 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: rieger@lusi-sb.de     

Adsorption of a random heteropolymer with random self-interactions onto an interface

We consider the adsorption of a random heteropolymer onto an interface within the model of Garel et al. [#!gareletal89!#] by taking into account random self-interactions and ternary repulsive interactions between the monomers. Within the replica trick and by using a self-consistent preaveraging procedure we map the adsorption problem onto the problem of binding state of a quantum mechanical Hamiltonian. The analysis of the latter is treated within the variational method based on the 2nd Legendre transform. Our study reveals a complex behaviour of the localization of the heteropolymer. In particular, we predict a reentrant localization transition for moderate values of the asymmetry of the distribution function of the monomer sequences along the heteropolymer. Received 9 October 2001 and Received in final form 27 February 2002 Published online 6 June 2002     

Resonance and composition effects on the Raman scattering from silver-gold alloy clusters

Low-frequency Raman scattering experiments have been performed on thin films consisting of pure gold or gold-silver alloy clusters embedded in alumina matrix. It is clearly shown that the quadrupolar vibrational modes are observed by Raman scattering because of the effect of resonance with the excitation of the electronic surface dipolar plasmon. This is due to the strong coupling between the collective electronic dipolar excitation and the quadrupolar vibrational modes. This effect of resonance does not exist with the core electron excitations. The mixing of the conduction electron dipolar excitation (surface plasmon) with the core electrons leads to the quenching of the resonant Raman scattering. Received 16 November 2000     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar