Session Y11: Statistical Mechanics of Social Systems

Transition between different search patterns in human online search behavior

We investigate the human online search behavior by analyzing data sets from different search engines. Based on the comparison of the results from several click-through data-sets collected in different years, we observe a transition of the search pattern from a L\'{e}vy-flight-like behavior to a Brownian-motion-type behavior as the search engine algorithms improve. This result is consistent with findings in animal foraging processes. A more detailed analysis shows that the human search patterns are more complex than simple L\'{e}vy flights or Brownian motions. Notable differences between the behaviors of different individuals can be observed in many quantities.   

Social consensus and tipping points with opinion inertia

When opinions, behaviors or ideas diffuse within a population, some are invariably more sticky than others. The stickier the opinion, the greater an individual's inertia to replace it with an alternative. Here we study the effect of stickiness of opinions in a two-opinion model, where individuals change their opinion only after a certain number of consecutive encounters with the alternative opinion.\footnote{C. Doyle \textit{et al}, preprint arXiv:1411.1723} We focus on the scenario where initially a minority of the population adopts an opinion that is as sticky or stickier than that of the majority, and investigate how the critical size of the initial minority required to tip the entire population over to its opinion, depends on the stickiness of the minority opinion. We analyze this scenario for a complete-graph topology through simulations, and through a semi- analytical approach which yields an upper bound for the critical minority size. We present analogous simulation results for the case of the Erdos-Renyi random network. Finally, we investigate the coarsening properties of sticky opinion spreading on two- dimensional lattices, and show that the presence of stickiness gives rise to an effective surface tension that causes the coarsening behavior to become curvature-driven.   

A Universal Power Law Governing Pedestrian Interactions

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.   

Finite size scaling analysis on Nagel-Schreckenberg model for traffic flow

The traffic flow problem as a many-particle non-equilibrium system has caught the interest of physicists for decades. Understanding the traffic flow properties and though obtaining the ability to control the transition from the free-flow phase to the jammed phase plays a critical role in the future world of urging self-driven cars technology. We have studied phase transitions in one-lane traffic flow through the mean velocity, distributions of car spacing, dynamic susceptibility and jam persistence -as candidates for an order parameter- using the Nagel-Schreckenberg model to simulate traffic flow. The length dependent transition has been observed for a range of maximum velocities greater than a certain value. Finite size scaling analysis indicates power-law scaling of these quantities at the onset of the jammed phase.   

Tabletop Traffic Jams: Modeling Traffic Jams using Self Propelled Particles

We model behavior of traffic using Self Propelled Particles (SPPs). Granular rods with asymmetric mass distribution confined to move in a circular channel on a vibrated substrate and interact with each other through inelastic collision serve as our model vehicle. Motion of a single vehicle is observed to be composed of 2 parts, a linear velocity in the direction of lighter end of particle and a non-Gaussian random velocity. We find that the collective mean speed of the SPPs is constant over a wide range of line densities before decreasing rapidly as the maximum packing is approached indicating the spontaneous formation of Phantom jams. This decrease in speed is observed to be far greater than any small differences in the mean drift speed of individual SPPs , and occurs as the collision frequency between SPPs increase exponentially with line density. However the random velocity component of SPPs remain super-diffusive over entire range of line densities. While the collective motion at low densities is characterized by caravan following behind the slowest particle leading to clustering, at higher densities we see formation of jamming waves travelling in direction opposite to that of motion of particles.   

Dynamics of influence and social balance in spatially-embedded regular and random networks

Structural balance - the tendency of social relationship triads to prefer specific states of polarity - can be a fundamental driver of beliefs, behavior, and attitudes on social networks. Here we study how structural balance affects deradicalization in an otherwise polarized population of leftists and rightists constituting the nodes of a low-dimensional social network. Specifically, assuming an externally moderating influence that converts leftists or rightists to centrists with probability $p$, we study the critical value $p = p_c$, below which the presence of metastable mixed population states exponentially delay the achievement of centrist consensus. Above the critical value, centrist consensus is the only fixed point. Complementing our previously shown results for complete graphs, we present results for the process on low-dimensional networks, and show that the low-dimensional embedding of the underlying network significantly affects the critical value of probability $p$. Intriguingly, on low-dimensional networks, the critical value $p_c$ can show non-monotonicity as the dimensionality of the network is varied. We conclude by analyzing the scaling behavior of temporal variation of unbalanced triad density in the network for different low-dimensional network topologies.   

Self-organization of divided hierarchy

There are two types of extreme form of hierarchy, one is the plutonomy where small fraction of winners and losers and many people in the middle class appear and the other a divided hierarchy where half of population become winners and the remaining half become losers. We study the emergence of the divided hierarchy in a model society which consists of bellicose individuals who always try to fight and fight with the strongest neighbor and pacific individuals who always try not to fight and when necessary fight with the weakest neighbor. In our model society, (1) individuals make random walk on a square lattice, (2) when two individuals encounter they fight each other and (3) the winner deprives wealth from the loser. By a Monte Carlo simulation, we show that there are two transitions when the population density is increased; one is a transition from the egalitarian society to a hierarchical society I where winners, losers and middle classes coexist and the other is a transition from the hierarchical society I to a hierarchical society II where winners and losers exist but no middle classes exist, that is the divided hierarchy. We also show that clusters consisting mostly of bellicose individuals appear in the hierarchical society I.   

Canonical Sectors and Evolution of Firms in the US Stock Markets

In this work, we show how unsupervised machine learning can provide a more objective and comprehensive broad-level sector decomposition of stocks. Classification of companies into sectors of the economy is important for macroeconomic analysis, and for investments into the sector-specific financial indices and exchange traded funds (ETFs). Historically, these major industrial classification systems and financial indices have been based on expert opinion and developed manually. Our method, in contrast, produces an emergent low-dimensional structure in the space of historical stock price returns. This emergent structure automatically identifies ``canonical sectors'' in the market, and assigns every stock a participation weight into these sectors. Furthermore, by analyzing data from different periods, we show how these weights for listed firms have evolved over time.   

Lead-lag relationships between stock and market risk within linear response theory

We study historical correlations and lead-lag relationships between individual stock risks (standard deviation of daily stock returns) and market risk (standard deviation of daily returns of a market-representative portfolio) in the US stock market. We consider the cross-correlation functions averaged over stocks, using historical stock prices from the Standard {\&} Poor's 500 index for 1994-2013. The observed historical dynamics suggests that the dependence between the risks was almost linear during the US stock market downturn of 2002 and after the US housing bubble in 2007, remaining at that level until 2013. Moreover, the averaged cross-correlation function often had an asymmetric shape with respect to zero lag in the periods of high correlation. We develop the analysis by the application of the linear response formalism to study underlying causal relations. The calculated response functions suggest the presence of characteristic regimes near financial crashes, when individual stock risks affect market risk and vice versa.   

Modeling Long-term Behavior of Stock Market Prices Using Differential Equations

Due to incomplete information available in the market and uncertainties associated with the price determination process, the stock prices fluctuate randomly during a short period of time. In the long run, however, certain economic factors, such as the interest rate, the inflation rate, and the company's revenue growth rate, will cause a gradual shift in the stock price. Thus, in this paper, a differential equation model has been constructed in order to study the effects of these factors on the stock prices. The model obtained accurately describes the general trends in the AAPL and XOM stock price changes over the last ten years.   

Social inequalities in probabilistic labor markets

We discuss social inequalities in labor markets for university graduates in Japan by using the Gini and k-indices [1] . Feature vectors which specify the abilities of candidates (students) are built-into the probabilistic labor market model [2]. Here we systematically examine what kind of selection processes (strategies) by companies according to the weighted feature vector of each candidate could induce what type of inequalities in the number of informal acceptances leading to a large mismatch between students and companies. \\[4pt] [1] J. Inoue, A. Ghosh, A. Chatterjee and B. K. Chakrabarti, arXiv:1406.2874\\[0pt] [2] H. Chen and J. Inoue, Evolutionary and Institutional Economics Review, Vol. 10, No. 1, pp. 55-80 (2013)   

Cascades in the Threshold Model for varying system sizes

A classical model in opinion dynamics is the Threshold Model (TM) aiming to model the spread of a new opinion based on the social drive of peer pressure. Under the TM a node adopts a new opinion only when the fraction of its first neighbors possessing that opinion exceeds a pre-assigned threshold. Cascades in the TM depend on multiple parameters, such as the number and selection strategy of the initially active nodes (initiators), and the threshold distribution of the nodes. For a uniform threshold in the network there is a critical fraction of initiators for which a transition from small to large cascades occurs, which for ER graphs is largerly independent of the system size \footnote {Singh P et al. 2013 Sci. Rep. 3 2330}. Here, we study the spread contribution of each newly assigned initiator under the TM for different initiator selection strategies for synthetic graphs of various sizes. We observe that for ER graphs when large cascades occur, the spread contribution of the added initiator on the transition point is independent of the system size, while the contribution of the rest of the initiators converges to zero at infinite system size. This property is used for the identification of large transitions for various threshold distributions.   

Collective behavior in the evolution of scientific research interests

Scientific research is strongly associated with the researchers' interests in particular areas or disciplines. On one hand, the stable research interest enables one to gain the expertise by repetitive practices specialized in a certain field. On the other hand, occasional change on the area of interest may reinvigorate one's research. To date, we lack a quantitative understanding on the likelihood of the research interest change, the consequent impact and the internal mechanism of this dynamical process. Here we analyze the publication records of over 14,000 scientists and quantitatively measure their research interest transitions. Our result shows that the fraction of scientists drops exponentially with the extent of transition, indicating that most scientists keep their interests quite stable. While it is rare, those who change demonstrate a higher-than-average chance to increase the productivity and impact. We propose a theoretical model that reproduces not only the observations in interest evolution but also the patterns of publication activities, allowing us to probe the short-term benefits of exploitation on the established field and the long-term returns of exploration on the new lines of inquiry.   

Median Citation Index vs Journal Impact Factor

The Journal Impact Factor is an arithmetic mean: It is the average number of citations, in a year, to a journal's articles that were published the previous two years. But for the vast majority of scholarly journals, the distribution of these citations is skewed (non-symmetric). We argue that a more representative member of the skewed distribution of citations is its median, not the mean. We thus introduce the Median Citation Index (MCI) and compare it to the journal Impact Factor (JIF) as a potentially more suitable choice of the ``center'' of the distribution, or its typical value. Unlike the JIF, the MCI is far less sensitive to outlier (very highly cited) papers or to gaming, and does not lend itself to the hype of calculating it to three decimal digits.