Equivalent dynamical complexity in a many-body quantum and collective human system

Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10^{-9} - 10^{-4} meters and 10^{-12} - 10^{-6} seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 10^3 - 10^6 meters and 10^4 - 10^8 seconds), (iii) shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv) makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.

Human group formation in online guilds and offline gangs driven by common team dynamic

Quantifying human group dynamics represents a unique challenge. Unlike animals and other biological systems, humans form groups in both real (offline) and virtual (online) spaces -- from potentially dangerous street gangs populated mostly by disaffected male youths, through to the massive global guilds in online role-playing games for which membership currently exceeds tens of millions of people from all possible backgrounds, age-groups and genders. We have compiled and analyzed data for these two seemingly unrelated offline and online human activities, and have uncovered an unexpected quantitative link between them. Although their overall dynamics differ visibly, we find that a common team-based model can accurately reproduce the quantitative features of each simply by adjusting the average tolerance level and attribute range for each population. By contrast, we find no evidence to support a version of the model based on like-seeking-like (i.e. kinship or `homophily).

Anomalously slow attrition times for asymmetric populations with internal group dynamics

The many-body dynamics exhibited by living objects include group formation within a population, and the non-equilibrium process of attrition between two opposing populations due to competition or conflict. We show analytically and numerically that the combination of these two dynamical processes generates an attrition duration T whose nonlinear dependence on population asymmetry x is in stark contrast to standard mass-action theories. A minority population experiences a longer survival time than two equally balanced populations, irrespective of whether the majority population adopts such internal grouping or not. Adding a third population with pre-defined group sizes allows T(x) to be tailored. Our findings compare favorably to real-world observations.

Self-organized global control of carbon emissions

There is much disagreement concerning how best to control global carbon emissions. We explore quantitatively how different control schemes affect the collective emission dynamics of a population of emitting entities. We uncover a complex trade-off which arises between average emissions (affecting the global climate), peak pollution levels (affecting citizens everyday health), industrial efficiency (affecting the nations economy), frequency of institutional intervention (affecting governmental costs), common information (affecting trading behavior) and market volatility (affecting financial stability). Our findings predict that a self-organized free-market approach at the level of a sector, state, country or continent, can provide better control than a top-down regulated scheme in terms of market volatility and monthly pollution peaks.

Relating the microscopic rules in coalescence-fragmentation models to the macroscopic cluster size distributions which emerge

Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalescence and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. More generally, our work elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus on two well-known models whose fragmentation rules lie at opposite extremes setting the models within the broader context of binary coalescence-fragmentation models. Further, we provide a range of generalizations and new analytic results for a well-known model of social group formation [V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett. 85, 5659 (2000)]. We develop analytic perturbation treatment of the original model, and extend the mathematical to the treatment of growing and declining populations.

Common group dynamic drives modern epidemics across social, financial and biological domains

We show that qualitatively different epidemic-like processes from distinct societal domains (finance, social and commercial blockbusters, epidemiology) can be quantitatively understood using the same unifying conceptual framework taking into account the interplay between the timescales of the grouping and fragmentation of social groups together with typical epidemic transmission processes. Different domain-specific empirical infection profiles, featuring multiple resurgences and abnormal decay times, are reproduced simply by varying the timescales for group formation and individual transmission. Our model emphasizes the need to account for the dynamic evolution of multi-connected networks. Our results reveal a new minimally-invasive dynamical method for controlling such outbreaks, help fill a gap in existing epidemiological theory, and offer a new understanding of complex system response functions.

A dynamical network approach to uncovering hidden causality relationships in collective neuron firings

We analyze the synchronous firings of the salamander ganglion cells from the perspective of the complex network viewpoint where the networks links reflect the correlated behavior of firings. We study the time-aggregated properties of the resulting network focusing on its topological features. The behavior of pairwise correlations has been inspected in order to construct an appropriate measure that will serve as a weight of network connection.

Internal network dynamics prolong a losing battle

Fights-to-the-death occur in many natural, medical and commercial settings. Standard mass action theory and conventional wisdom imply that the minority (i.e. smaller) groups survival time decreases as its relative initial size decreases, in the absence of replenishment. Here we show that the opposite actually happens, if the minority group features internal network dynamics. Our analytic theory provides a unified quantitative explanation for a range of previously unexplained data, and predicts how losing battles in a medical or social context might be extended or shortened using third-party intervention.