Session H12: Statistical and Nonlinear Physics of Social Systems

Patterns of inequality: Dynamics of income distribution in USA and global energy consumption distribution

Applying the principle of entropy maximization, we argued that the distribution of money in a closed economic system should be exponential [1], see also recent review [2]. In this talk, we show that income distribution in USA is exponential for the majority of population (about 97\%). However, the high-income tail follows a power law and is highly dynamical, i.e., out of equilibrium. The fraction of income going to the tail swelled to 20\% of all income in 2000 and 2006 at the peaks of speculative bubbles followed by spectacular crashes. Next, we analyze the global distribution of energy consumption per capita among different countries. In the first approximation, it is reasonably well captured by the exponential function. Comparing the data for 1990 and 2005, we observe that the distribution is getting closer to the exponential, presumably as a result of globalization of the world economy.\\[4pt] [1] A.~A.~Dragulescu and V.~M.~Yakovenko, \textit{Eur.~Phys.~J.~B} {\bf 17}, 723 (2000). \newline [2] V.~M.~Yakovenko and J.~B.~Rosser, to appear in \textit{Rev.~Mod.~Phys.} (2009), arXiv:0905.1518.   

Allocation of Wealth and Emergence of Inequality

Though socioeconomic inequality has always been a classic subject of study in sociology and finance, it has caught the attention of many physicists in the last decade. The application of kinetic theory of gases to study the emergence of wealth distributions continues to develop itself as a new field of applications of statistical physics. The challenge for physicists is to identify basic microscopic interactions among individuals, namely trading and investment, which rule the macroscopic statistics of the system of individuals as a whole. Several models have been elaborated and certain microscopic parameters were identified as vital for the existence of statistically different wealth distributions. We present a model which considers different savings propensities, stochastic nature of trades and investments, and explore specific choices of micro-trading parameters which produce qualitatively different wealth distributions like those of the United States and Australia.   

The market behavior and performance of different strategy evaluation schemes

We observe the performances of three strategy evaluation schemes, which are the history-dependent wealth game, the trend-opposing minority game, and the trend-following majority game in a stock market where the price is exogenously determined. The price is either directly adopted from the real stock market indices or generated with the Markov chain of order $\le 2$. Each scheme's success is quantified by average wealth accumulated by the traders equipped with the scheme. The wealth game, as it learns from the history, generally shows good performance unless the market is highly unpredictable. The majority game is relatively successful in a trendy market dominated by long periods of sustained price increasing or decreasing. On the other hand, the minority game is suitable for a market with persistent zig-zag price patterns. These observations agree with our intuition and support the viability of the wealth game as a strategy evaluation scheme in typical markets.   

Modeling of First-Passage Processes in Financial Markets

In this talk, we attempt to make a microscopic modeling the first-passage process (or the first-exit process) of the BUND future by minority game with market history. We find that the first-passage process of the minority game with appropriate history length generates the same properties as the BTP future (the middle and long term Italian Government bonds with fixed interest rates), namely, both first-passage time distributions have a crossover at some specific time scale as is the case for the Mittag-Leffler function. We also provide a macroscopic (or a phenomenological) modeling of the first-passage process of the BTP future and show analytically that the first-passage time distribution of a simplest mixture of the normal compound Poisson processes does not have such a crossover.   

Habituation and 1/f Noise

We present a model to explain the psychophysical phenomena of habituation using methods from non-equilibrium statistical physics and complex network theory. Habituation is a ubiquitous and extremely simple from of learning through which animals, including humans; learn to disregard stimuli that are no longer novel, thereby allowing them to attend to new stimuli.Herein we present a statistical habituation model (SHM) based on a generalization of linear response theory and discrete events using renewal theory. The SHM introduces a theory of the effective synaptic weight connecting two neuron networks, with the synaptic weight being described by a time series with inverse power-law statistics. The statistics determine the distribution of time intervals between events, which in a complex neuronal network leads to neuronal avalanches, see e.g., Beggs and Plenz (J. Neurosci 23, 11167, 2003). The SHM establishes that the fundamental mechanism producing habituation in its myriad of forms is the 1/f-nose that is generically produced in individual neurons and in complex neuronal networks. Both simple harmonic and more complicated stimuli are shown to habituate (decay) as inverse power laws with indices determined by the power-law index of the effective synaptic statistical distribution. This is the first theory that directly relates the psychophysical phenomenon of habituation to the dynamics of the brain.   

Critical behavior of epidemic spreading in dynamic small world networks

Dynamic small-world (DSW) contact networks model populations that have fixed short range links but time varying stochastic long range links between individuals, such as in mobile populations. The measure of mobility is given by a parameter p that is directly analogous to the rewiring parameter in standard small-world networks. This study investigates the relative effects of vaccinations and avoidance of infected individuals in a susceptible-infected-recovered (SIR) epidemic model on a DSW network. We derive (1) the critical mobility required for an outbreak to occur as a function of the disease's infectivity, recovery rate, avoidance rate, and vaccination rate and (2) an expression to calculate the amount of vaccination and/or avoidance necessary to prevent the disease-free to endemic transition. Agreement between these calculated points and numerical simulation is excellent. We then show via finite size scaling that the transition is indeed a continuous phase transition and find the associated critical exponent. From this and other scaling relations at the critical point we can comment on the model's potential universality.   

Percolation in anisotropic, hyperbolic and small-world lattices and in explosive growth

Percolation on a large variety of systems is discussed. A variety of lattices where exact and approximate solutions of the criticality condition, including anisotropic systems, are considered. Also, hyperbolic systems, such as the heptagonal lattice, are studied with respect to a crossing criterion for percolation to hold. Hierarchical small-world ``Hanoi" lattices and randomized versions are considered as well. Finally, the effects of biased cluster growth by the ``Achlioptas" process, and the resulting explosive cluster growth, are considered. The overall picture shows the richness and complexity of percolation processes, and the existence of many open problems.   

Stability and complexity of small random linear systems

We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.   

Modeling Insurgent Network Structure and Dynamics

We present a methodology for mapping insurgent network structure based on their public rhetoric. Indicators of cooperative links between insurgent groups at both the leadership and rank-and-file levels are used, such as joint policy statements or joint operations claims. In addition, a targeting policy measure is constructed on the basis of insurgent targeting claims. Network diagrams which integrate these measures of insurgent cooperation and ideology are generated for different periods of the Iraqi and Afghan insurgencies. The network diagrams exhibit meaningful changes which track the evolution of the strategic environment faced by insurgent groups. Correlations between targeting policy and network structure indicate that insurgent targeting claims are aimed at establishing a group identity among the spectrum of rank-and-file insurgency supporters. A dynamical systems model of insurgent alliance formation and factionalism is presented which evolves the relationship between insurgent group dyads as a function of their ideological differences and their current relationships. The ability of the model to qualitatively and quantitatively capture insurgent network dynamics observed in the data is discussed.   

Community Structure in Time-Dependent Networks

I examine community structure in time-dependent networks. I draw examples from financial and political networks, showing how the dynamics of community composition, node roles within communities, and modularity can be used to shed insight into the recent credit crisis and political realignments.   

Adapting and Vibration: Empirical Evidence from Human Subjects Experiments

We report a vibration-like social phenomenon (mass behavior of human subjects) in the experiments of experimental economics. vibration is a long existed concept and a widely existed phenomenon in natural and in social phenomena. Usually, the causal of social phenomena is unclear, but recently developed experimental economics studies in laboratory make it possible. During a game in a laboratory experiment, the human subjects are interacting with each other by the strategies of the game, and as a phenomena, the society is keeping evolution. In strategy space, the variables as velocity, accelerant and speed of the subjects can be measured from the detail records of the human subjects from the experiments. Data from the human subjects experiments, which are from Public Goods Game (Chen and Tang, Journal Political Economics, 1998), $2\times 2$ Games (Hyndman, et al, Experimental Economics, 2009) and Prisoners' Dilemma (Duffy and Ochs, Game and Economics behavior, 2009), is implicitly analysis, and harmonic-vibration-like phenomena is shown. This might be helpful to understand the dynamical proceeding of the adaption of a society of human subjects.   

Fat-tail vs. critical random matrix ensembles

Recently, we reported a family of novel fat-tail random matrix ensembles characterized by a parameter $\lambda$ in ``Rotationally invariant family of Levy like random matrix ensembles'', J. Phys. A: Math. Theor. 42, 152001 (2009). It was shown that i) the eigenvalue densities of the ensembles exhibit a power law distribution, the exponent of which depends on the parameter $\lambda $, and ii) the two-level correlation of the ensembles is qualitatively different from that of the Gaussian or the critical ensembles. Here we investigate the Levy-like ensembles in comparison with the critical ensembles, corresponding to $\lambda \quad \to $ 1, particularly in the vicinity of $\lambda $ =1. The study shows that the Levy-like ensembles exhibit characteristics similar to the critical ensembles in terms of the anomalous two-level correlations, i.e. the ghost peak, and the form factor (power spectrum). We discuss these results in the context of well known properties of the critical ensembles, e.g., spontaneous symmetry breaking, multi-fractality as well as in relation to the systems showing 1/f$^{\alpha}$ noise.   

The basic properties of the fractional exclusion statistics

I derive the general conditions that have to be satisfied by the fractional exclusion statistics (FES) parameters in any (macroscopic) FES system. These conditions are obtained using a very simple and intuitive model and define how the FES parameters change at the redefinitions of the particle species in the system. Further, I introduce an ansatz for the FES parameters, which satisfies the general conditions. I check the ansatz for a few well-known models of interacting particle systems, and I calculate the thermodynamics of systems described by these models.   

Use of asymmetric cells in percolation theory

The use of renormalization cells to obtain percolation thresholds and critical exponents for site and bond occupancy is a well-known technique. Herewith we consider bond percolation with two variations to this technique. On one side, we extend the analysis so as to include asymmetric percolation cells on top of the usual symmetric cells giving more points to the scaling analyses. On the other hand, we consider the inflection point of the percolation curve as an indicator for the transition in addition to the usual renormalization analysis. Results show good accuracy comparing well and even better than some reported parameters in the literature. The presentation will go over two dimensions for the sake of simplicity but some early results in three dimensions will be also reported towards the end of the presentation. The implications of these treatments in the field of magnetic phase transitions are also considered.