Session X43: Statistical Mechanics of Social Systems

Microscopic to Macroscopic Dynamical Models of Sociality

To help them survive, social animals, such as humans, need to share knowledge and responsibilities with other members of the species. The larger their social network, the bigger the pool of knowledge available to them. Since time is a limited resource, a way of optimising its use is meeting amongst individuals whilst fulfilling other necessities. In this sense it is useful to know how many, and how often, early humans could meet during a given period of time whilst performing other necessary tasks, such as food gathering. Using a simplified model of these dynamics, which comprehend encounter and memory, we aim at producing a lower-bound to the number of meetings hunter-gatherers could have during a year. We compare the stochastic agent-based model to its mean-field approximation and explore some of the features necessary for the difference between low population dynamics and its continuum limit. We observe an emergent property that could have an inference in the layered structure seen in each person's social organisation. This could give some insight into hunter-gatherer's lives and the development of the social layered structure we have today.   

Impact of Bursty Communication Patterns on Naming Game Competitions.

The currently dominant model of opinion spread dynamics chooses speakers randomly, giving rise to an exponentially distributed wait time between speaking events. Many studies, however, suggest that a more appropriate distribution would be a power law since it captures the bursty nature of communication\footnote{J. Candia, M. Gonzalez, P. Wang et al., J. Phys. A, 41 22 (2008).}$^,$\footnote{J. Iribarren, E. Moro, PRL. 103, 038702 (2009).}$^,$\footnote{P. Van Mieghem, R. van de Bovenkamp, PRL 110, 108701 (2013).}$^,$\footnote{A. Vazquez, B. Racz, A. Lukacs et al., PRL 98, 158702 (2007).}$^,$\footnote{M. Karsai et al. PRE 83, 025102(R) (2011).}. Here we study how adjusting the wait times for agents to speak to fit various distributions affects the dynamics of the naming game. Specifically, we show that by creating a system with competition between two groups (each with a different wait time distribution but the same mean), the symmetry of the system is broken and in the infinite system the 'burstier' community always wins. In contrast, when this burstiness is studied in the voter model, the symmetry breaking does not occur. Lastly, we show that burstiness in the naming game with committed agents shifts downwards the critical population required for consensus.   

Comparison of human mobility patterns in different settings

The development of location tracking technologies and big-data analysis capacities makes it possible to understand human mobility patterns at the global level through the analysis of huge datasets made available by open-data communities. Working with millions of empirical world-wide GPS trajectories, we examine users' mobility patterns in urban, rural and intermediate scenarios. Similar scaling properties are found in the analysis of several quantities, including end-to-end distance, radius of gyration, mean-squared displacement, and fixed-interval step-length. The impact of cities is elucidated by comparing mobility patterns in major cities worldwide.   

Effects of long-range interactions in the one-dimensional Sznajd model

The Sznajd model is a one-dimensional, binary, voter-like model used to study consensus in systems where information flows outward from like-minded agent pairs. Here, we introduce long-range interactions to the Sznajd model, quantified by the parameter p in analogy with the dynamic and static small-world rewiring parameter (p$\to $1 is the mean-field limit, p$\to $0 is the 1-D limit). We use Monte Carlo simulations and finite-size scaling analyses to characterize the exit probability for p$\ne $0, finding a step function that depends on two p-dependent exponents. By examining the p$\to $0 limit of these exponents, we comment on the functional form of the exit probability in one dimension, which has been an open question. We complement this limiting approach (letting p$\to $0, which offers considerable computational speedup over the pure p$=$0 case) by also simulating the p$=$0 case via a parallel algorithm. This investigation also probes the dependence of consensus time and system magnetization on p.   

Selection Strategies for Social Influence in the Threshold Model

The ubiquity of online social networks makes the study of social influence extremely significant for its applications to marketing, politics and security. Maximizing the spread of influence by strategically selecting nodes as initiators of a new opinion or trend is a challenging problem. We study the performance of various strategies for selection of large fractions of initiators on a classical social influence model, the Threshold model (TM). 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. The strategies we study are of two kinds: strategies based solely on the initial network structure (Degree-rank, Dominating Sets, PageRank etc.) and strategies that take into account the change of the states of the nodes during the evolution of the cascade, e.g. the greedy algorithm. We find that the performance of these strategies depends largely on both the network structure properties, e.g. the assortativity, and the distribution of the thresholds assigned to the nodes \footnote{Karampourniotis et al., PLOS ONE (in press); arXiv:1506.00986}. We conclude that the optimal strategy needs to combine the network specifics and the model specific parameters to identify the most influential spreaders.   

Pattern Selection and Super-Patterns in Opinion Dynamics

We study pattern formation in the bounded confidence model of opinion dynamics. In this random process, opinion is quantified by a single variable. Two agents may interact and reach a fair compromise, but only if their difference of opinion falls below a fixed threshold. Starting from a uniform distribution of opinions with compact support, a traveling wave forms and it propagates from the domain boundary into the unstable uniform state. Consequently, the system reaches a steady state with isolated clusters that are separated by distance larger than the interaction range. These clusters form a quasi-periodic pattern where the sizes of the clusters and the separations between them are nearly constant. We obtain analytically the average separation between clusters L. Interestingly, there are also very small quasi-periodic modulations in the size of the clusters. The spatial periods of these modulations are a series of integers that follow from the continued-fraction representation of the irrational average separation L.   

Spatially clustered zealots in a two-dimensional voter model

The voter model, solvable in all dimensions in its standard form, has been extensively used to study behavior dynamics by using the tools of statistical mechanics. Recently, much work has been focused on determining the effects of zealots in the voter model, where a zealot is an agent that maintains its opinion (akin to an Ising spin variable) no matter the local environment. Here we investigate the effects of spatially clustered zealots in the standard voter model on a two-dimensional square lattice. The clustering of zealots is quantified by the conditional probability that a zealot of the $+$1 state appears on an adjacent site to a randomly chosen zealot. (All zealots are of the $+$1 state.) We determine the functional forms of the system consensus time with respect to system size, clustering, and zealot density, and compare these findings to previous results that do not include clustering. We also discuss an interesting random walk problem that arises when one attempts to calculate how clustering affects the consensus time for fixed zealot density and system size.   

Highlighting impact: Do editors' selections identify influential papers?

A recent trend in scientific publishing is that journal editors highlight each week a select set among the papers published (usually) in their respective journals. The highlighted papers are deemed of higher quality, importance, or interest than the 'average' paper and feature prominently in the publishers' websites. We perform a citation analysis of the highlighted papers for a number of journals from various publishers in physics. By comparing the performance of highlighted papers relative to (a) typical papers and (b) highly cited papers in their source journals and in other journals in the field, we explore whether, and to what extent, the selection process at the time of publication identifies papers that will turn out to be influential. We discuss the broader implications for research assessment.   

Measuring diversity and coherence using hierarchical APS-PACS classification of sub fields of physics and their impact on citations.

American Physical Society introduced Physics and Astronomy Classification Scheme (PACS) in 1975 to classify different subfields of physics in a hierarchical tree structure. Since 1985, almost all the physical review articles include the PACS code to refer different subfields it belongs to. In this work, we define the notion of diversity of articles and authors based on the PACS codes they are associated with, using Weitzamn diversity index, from 1985-2012. We find that the fraction of authors with high diversity is increasing with time, whereas the fraction of least diversity are decreasing, and moderate diversity authors have higher tendency to switch over to other diversity groups. By measuring the interconnectedness among the PACS codes, we define measures of coherence of papers and authors. The diversity and coherence captures the dimensions of Interdisciplinarity. Based on which we study the correlation between Interdisciplinarity (within sub fields of physics) and citations. We find that the diversity index of articles is correlated with the citations they received in a given time period from their publication year. Articles with lower and higher end of diversity index receive lesser citations than the moderate diversity papers.   

Untangling Performance from Success

Fame, popularity and celebrity status, frequently used tokens of success, are often loosely related to, or even divorced from professional performance. This dichotomy is partly rooted in the difficulty to distinguish performance, an individual measure that captures the actions of a performer, from success, a collective measure that captures a community's reactions to these actions. Yet, finding the relationship between the two measures is essential for all areas that aim to objectively reward excellence, from science to business. Here we quantify the relationship between performance and success by focusing on tennis, an individual sport where the two quantities can be independently measured. We show that a predictive model, relying only on a tennis player's performance in tournaments, can accurately predict an athlete's popularity, both during a player's active years and after retirement. Hence the model establishes a direct link between performance and momentary popularity. The agreement between the performance-driven and observed popularity suggests that in most areas of human achievement exceptional visibility may be rooted in detectable performance measures.   

A simple model for research interest evolution patterns

Sir Isaac Newton supposedly remarked that in his scientific career he was like ``\ldots a boy playing on the sea-shore \ldots finding a smoother pebble or a prettier shell than ordinary". His remarkable modesty and famous understatement motivate us to seek regularities in how scientists shift their research focus as the career develops. Indeed, despite intensive investigations on how microscopic factors, such as incentives and risks, would influence a scientist's choice of research agenda, little is known on the macroscopic patterns in the research interest change undertaken by individual scientists throughout their careers. Here we make use of over 14,000 authors' publication records in physics. By quantifying statistical characteristics in the interest evolution, we model scientific research as a random walk, which reproduces patterns in individuals’ careers observed empirically. Despite myriad of factors that shape and influence individual choices of research subjects, we identified regularities in this dynamical process that are well captured by a simple statistical model. The results advance our understanding of scientists' behaviors during their careers and open up avenues for future studies in the science of science.   

Development of kink jams in traffic flow

Near the threshold of absolute stability of uniform, steady traffic flow, car-following models can often be reduced to a modified Korteweg-deVries (mKdV) equation plus small corrections. The mKdV equation has a continuous family of hyperbolic-kink solutions describing boundaries between regions of different traffic densities, i.e. the edges of traffic jams. A solvability calculation picks out the one member of this family which is consistent with the correction terms; this is usually labelled the ``selected'' kink. This identification is problematic, however, since it must be the downstream boundary condition that determines which kink solution is realized. We display a two-parameter family of mKdV solutions which has the kink solutions as one limit and uniform flow as another, and show how the correction terms can lead to kinks developing from initially near-uniform traffic. We then clarify the meaning of the usual solvability calcuation and of the ``selected'' kink.   

A Langevin model for low density pedestrian dynamics

The dynamics of pedestrian crowds shares deep connections with statistical physics and fluid dynamics. Reaching a quantitative understanding, not only of the average behaviours but also of the statistics of (rare) fluctuations would have major impact, for instance, on the design and safety of civil infrastructures. A key feature of pedestrian dynamics is its strong intrinsic variability, that we can already observe at the single individual level. In this work we aim at a quantitative characterisation of this statistical variability by studying individual fluctuations. We consider experimental observations of low-density pedestrian flows in a corridor within a building at Eindhoven University of Technology. Few hundreds of thousands of pedestrian trajectories with high space and time resolutions have been collected via a Microsoft Kinect 3D-range sensor and automatic head tracking techniques. From these observations we model pedestrians as active Brownian particles by means of a generalised Langevin equation. With this model we can quantitatively reproduce the observed dynamics including the statistics of ordinary pedestrian fluctuations and of rarer U-turn events. Low density, pair-wise interactions between pedestrians are also discussed.   

A Hierarchy of Multi-Lane Driven Diffusive Systems with Unfair Resource Availability

We present a model system for objects which have the ability to move along columns with the availability of a low entropy resource which is provided abundantly to a first column. The “unused” part of this resource is available to objects in neighbouring consecutive columns. This forms a hierarchy of multi-lane driven diffusive systems, which displays interesting dynamics. We present results from Monte Carlo simulations of the system.