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arXiv2008

Parameter Evaluation of a Simple Mean-Field Model of Social Interaction

The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical and phenomenological point of view. We propose a parameter evaluation procedure and test it by fitting our model against three families of data coming from different cases: the estimated interaction parameters are found to have similar positive values establishing a quantitative confirmation of the peer imitation behavior found in social psychology. Moreover all the values of the interaction parameters belong to the phase transition regime suggesting its possible role in the study of social systems.

physics.soc-ph↗
arXiv2008

Generalization of the model of conflict between two armed groups

The conflicts between armed groups often go on for years. The classical model of such conflicts accounts for the number of participants and for the technology level of the equipment of the groups. Below we extend this model in order to account for events that are present for limited time. As examples we discuss three kinds of such events: inclusion of reserves, presence of epidemics and use of non-conventional weapons. We show that if such events are not handled properly by the leaders of the groups the corresponding group can lose the conflict.

physics.soc-ph↗
arXiv2009

Statistical Characterizers of Transport in a Communication Network

We identify the statistical characterizers of congestion and decongestion for message transport in model communication lattices. These turn out to be the travel time distributions, which are Gaussian in the congested phase, and log-normal in the decongested phase. Our results are demonstrated for two dimensional lattices, such the Waxman graph, and for lattices with local clustering and geographic separations, gradient connections, as well as for a 1-d ring lattice with random assortative connections. The behavior of the distribution identifies the congested and decongested phase correctly for these distinct network topologies and decongestion strategies. The waiting time distributions of the systems also show identical signatures of the congested and decongested phases.

physics.soc-ph↗
arXiv2010

Social Aggregation as a Cooperative Game

A new approach for the description of phenomena of social aggregation is suggested. On the basis of psychological concepts (as for instance social norms and cultural coordinates), we deduce a general mechanism for the social aggregation in which different clusters of individuals can merge according to the cooperation among the agents. In their turn, the agents can cooperate or defect according to the clusters distribution inside the system. The fitness of an individual increases with the size of its cluster, but decreases with the work the individual had to do in order to join it. In order to test the reliability of such new approach, we introduce a couple of simple toy models with the features illustrated above. We see, from this preliminary study, how the cooperation is the most convenient strategy only in presence of very large clusters, while on the other hand it is not necessary to have one hundred percent of cooperators for reaching a totally ordered configuration with only one megacluster filling the whole system.

physics.soc-ph↗
arXiv2008

Trust! Why it Has Been Lost and How to Regain It

This essay suggests that a proper assessment of the presently unfolding financial crisis, and its cure, requires going back at least to the late 1990s, accounting for the cumulative effect of the ITC, real-estate and financial derivative bubbles. We focus on the deep loss of trust, not only in Wall Street, but more importantly in Main Street, and how to recover it on the short and long terms. A multi-disciplinary approach is needed to deal with the nonlinear complex systems of the present world, in order to develop a culture of fairness, and of upside opportunities associated with a risky world.

q-fin.GN↗
arXiv2009

Predator-Prey Model for Stock Market Fluctuations

We present a dynamical model for the price evolution of financial assets. The model is based in a two level structure. In the first stage one finds an agent-based model that describes the present state of the investors' beliefs, perspectives or strategies. The dynamics is inspired by a model for describing predator-prey population evolution: agents change their mind through self- or mutual interaction, and the decision is adopted on a random basis, with no direct influence of the price itself. One of the most appealing properties of such a system is the presence of large oscillations in the number of agents sharing the same perspective, what may be linked with the existence of bullish and bearish periods in financial markets. In the second stage one has the pricing mechanism, which will be driven by the relative population in the different investors' groups. The price equation will depend on the specific nature of the species, and thus it may change from one market to the other: we will firstly present a simple model of excess demand, and subsequently consider a more elaborate liquidity model. The outcomes of both models are analysed and compared.

q-fin.TR↗
arXiv2008

Serial correlation and heterogeneous volatility in financial markets: beyond the LeBaron effect

We study the relation between serial correlation of financial returns and volatility at intraday level for the S&P500 stock index. At daily and weekly level, serial correlation and volatility are known to be negatively correlated (LeBaron effect). While confirming that the LeBaron effect holds also at intraday level, we go beyond it and, complementing the efficient market hyphotesis (for returns) with the heterogenous market hyphotesis (for volatility), we test the impact of unexpected volatility, defined as the part of volatility which cannot be forecasted, on the presence of serial correlations in the time series. We show that unexpected volatility is instead positively correlated with intraday serial correlation.

q-fin.ST↗
arXiv2008

Computational modelling of evolution: ecosystems and language

Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many units that might reproduce, diffuse, mutate, die, or in some cases for example communicate. These processes might be of some adaptive value, they influence each other and occur on various time scales. That is why such systems are so difficult to study. In this paper we briefly review some computational approaches, as well as our contributions, to the evolution of ecosystems and language. We start from Lotka-Volterra equations and the modelling of simple two-species prey-predator systems. Such systems are canonical example for studying oscillatory behaviour in competitive populations. Then we describe various approaches to study long-term evolution of multi-species ecosystems. We emphasize the need to use models that take into account both ecological and evolutionary processes. Finally, we address the problem of the emergence and development of language. It is becoming more and more evident that any theory of language origin and development must be consistent with darwinian principles of evolution. Consequently, a number of techniques developed for modelling evolution of complex ecosystems are being applied to the problem of language. We briefly review some of these approaches.

q-bio.PE↗
arXiv2010

A Bayesian Framework for Opinion Updates

Opinion Dynamics lacks a theoretical basis. In this article, I propose to use a decision-theoretic framework, based on the updating of subjective probabilities, as that basis. We will see we get a basic tool for a better understanding of the interaction between the agents in Opinion Dynamics problems and for creating new models. I will review the few existing applications of Bayesian update rules to both discrete and continuous opinion problems and show that several traditional models can be obtained as special cases or approximations from these Bayesian models. The empirical basis and useful properties of the framework will be discussed and examples of how the framework can be used to describe different problems given.

physics.soc-ph↗
arXiv2009

TI-games I: An Exploration of Type Indeterminacy In Strategic Decision-Making

The Type Indeterminacy model is a theoretical framework that formalizes the constructive preference perspective suggested by Kahneman and Tversky. In this paper we explore an extention of the TI-model from simple to strategic decision-making. A 2X2 game is investigated. We first show that in a one-shot simultaneaous move setting the TI-model is equivalent to a standard incomplete information model. We then let the game be preceded by a cheap-talk promise exchange game. We show in an example that in the TI-model the promise stage can have impact on next following behavior when the standard classical model predicts no impact whatsoever. The TI approach differs from other behavioral approaches in identifying the source of the effect of cheap-talk promises in the intrinsic indeterminacy of the players' type.

physics.soc-ph↗
arXiv2008

The Science Impact of Astronomy PhD Granting Departments in the United States

The scientific impact of the research of 36 astronomy PhD granting departments is measured and ranked here. Because of the complex nature of Universities, this study looks at the Universities in two ways; first analyzing the impact of the published work over a 10 year period of the Department which grants the PhD and; second, looking at the impact of the published work as a whole including Laboratories, Centers, and Facilities. The Universities considered in the study are drawn from the 1992 NRC study on Programs of Research, Doctorate in Astrophysics and Astronomy with three Universities added. Johns Hopkins, Michigan State, and Northwestern all host substantial astronomical research within their Departments of Physics and Astronomy and so are included here. The first method of measuring impact concentrates on tenured and tenured track faculty, with the top quartile being 1. Caltech, 2. UC Santa Cruz, 3. Princeton, 4. Harvard, 5. U Colorado, Boulder, 6. SUNY, Stony Brook, 7. Johns Hopkins, 8. Penn State, and 9. U Michigan, Ann Arbor. The second method additionally includes "soft money" scientists in research and adjunct faculty positions, with the top quartile being 1. UC Santa Cruz, 2. Princeton, 3. Johns Hopkins 4. Penn State, 5. SUNY Stony Brook, 6. U Michigan, Ann Arbor, 7. New Mexico State, 8. UMass, Amherst, and 9. U Virginia. Both methods reveal important aspects of Universities, representing both the depth and the breadth of the science available at the University. Finally, a comparison is made of the total articles published in the 10 year period, both from the departments alone and from the larger universities. Three Universities have both impact index in the top quartile, and have more than 1000 publications in a decade; UC at Santa Cruz, Princeton, and Johns Hopkins.

physics.soc-ph↗
arXiv2008

Evolution of the personal income distribution in the USA: High incomes

The personal income distribution (PID) above the Pareto threshold is studied and modeled. A microeconomic model is proposed to simulate the PID and its evolution below and above the Pareto income threshold. The model balances processes of income production and dissipation for any person above 15 years of age. The model accurately predicts the observed dependence of the number of people reaching the Pareto threshold on work experience and the functional dependence of the relationship on the per capita real GDP growth for the period from 1994 to 2002. Predictions of the income distribution depending on age are given for past and future. In future, relatively less rich people are observed in the younger age groups and the peak of the relative number shifts to older ages with time. The effect of the power law distribution extending itself to very high incomes is speculated to be the cause of low performance of socialist countries.

q-fin.GN↗
arXiv2008

Modeling the evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005

The evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005 is analyzed and modeled. There are several versions of personal income distribution (PID) provided by the US Census Bureau (US CB) for this period with various levels of resolution. Effectively, these PIDs result in different Gini coefficients due to the differences between discrete and continuous representations. When all persons of 15 years of age and over are included in the PIDs, Gini coefficient drops from 0.64 in 1947 to 0.54 in 1990. This effect is observed due to a significant decrease in the portion of people without income. For the PIDs not including persons without income, Gini coefficient is varying around 0.51 between 1960 and 2005 with standard deviation of 0.004, i.e. is in fact constant. This Gini coefficient is practically independent on the portion of population included in the PIDs according to any revision of income definitions. The driving force of the model describing the evolution of individual incomes (microeconomic level) and their aggregate value (macroeconomic level) is the change in nominal GDP per capita. The model accurately predicts the evolution of Gini coefficient for the PIDs for people with income. The model gives practically unchanged (normalized) PIDs and Gini coefficient between 1947 and 2005. The empirical Gini curves converge to the predicted one when the number of people without income decreases. Asymptotically, the empirical curves should collapse to the theoretical one when all the working age population obtains an appropriate definition of income. Therefore the model Gini coefficient potentially better describes true behavior of inequality in the USA because the definitions of income used by the US Census Bureau apparently fail to describe true income distribution.

q-fin.GN↗
arXiv2008

Exact prediction of S&P 500 returns

A linear link between S&P 500 return and the change rate of the number of nine-year-olds in the USA has been found. The return is represented by a sum of monthly returns during previous twelve months. The change rate of the specific age population is represented by moving averages. The period between January 1990 and December 2003 is described by monthly population intercensal estimates as provided by the US Census Bureau. Four years before 1990 are described using the estimates of the number of 17 year-olds shifted 8 years back. The prediction of S&P 500 returns for the months after 2003, including those beyond 2007, are obtained using the number of 3 year-olds between 1990 and 2003 shifted by 6 years ahead and quarterly estimates of real GDP per capita. A prediction is available for the period beyond 2007. There are two sharp drops in the predicted returns - in 2007 and 2009, and one strong rally in 2008. Equivalently, S&P 500 index should drop in 2007 and 2009 to the level observed one year before. Potential link between S&P 500 returns and 9-year-old population is tested for cointegration. The Engle-Granger and Johansen tests demonstrate the presence of a long-term equilibrium (cointegrating) relation between these variables. This makes valid standard statistical estimates. Correlation between the predicted and observed indices, including RMS difference, linear regression, and VAR demonstrate good prediction accuracy at two-year horizon, when the prediction uses 7-year-olds instead of 9-year-olds. The RMS difference between the observed and predicted returns for the period between 1992 and 2003 is only 0.09 with standard deviation of the observed series for the same period of 0.12 and the naive (random walk) RMS deference of 0.18.

q-fin.ST↗
arXiv2008

On the dynamics of Social Balance on general networks (with an application to XOR-SAT)

We study nondeterministic and probabilistic versions of a discrete dynamical system (due to T. Antal, P. L. Krapivsky, and S. Redner) inspired by Heider's social balance theory. We investigate the convergence time of this dynamics on several classes of graphs. Our contributions include: 1. We point out the connection between the triad dynamics and a generalization of annihilating walks to hypergraphs. In particular, this connection allows us to completely characterize the recurrent states in graphs where each edge belongs to at most two triangles. 2. We also solve the case of hypergraphs that do not contain edges consisting of one or two vertices. 3. We show that on the so-called "triadic cycle" graph, the convergence time is linear. 4. We obtain a cubic upper bound on the convergence time on 2-regular triadic simplexes G. This bound can be further improved to a quantity that depends on the Cheeger constant of G. In particular this provides some rigorous counterparts to previous experimental observations. We also point out an application to the analysis of the random walk algorithm on certain instances of the 3-XOR-SAT problem.

cs.DM↗
arXiv2008

Modelling the average income dependence on work experience

The average and median income dependence on work experience and time is analyzed and modeled for the USA. The original data set providing the mean and median income estimates in 10 year long intervals spans a long time period of almost 35 years ? from 1967 to 2003. A microeconomic model linking personal income, population age structure and GDP per capita is used to predict the mean income values in various age groups and their relative evolution in time. Also modeled is the value of work experience where the mean income growth ends and it starts to drop exponentially with increasing age. This work experience increases through time as the square root of the per capita GDP growth. Prediction for the following 20 years is given for each age group considering potential per capita growth rate of 1.6%. The USA mean income dependence on work experience for 1987 coincides with that for 2002 in the UK ? the years when per capita GDP were equal in the countries.

q-fin.GN↗
arXiv2008

Modelling real GDP per capita in the USA: cointegration test

A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.

q-fin.GN↗