Internal character dictates phase transition dynamics between isolation and cohesive grouping

We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different critical points arising for different character-dependent grouping mechanisms. These critical points move in opposite directions as the populations diversity decreases. Our analytical theory helps explain why a particular class of universality is so common in the real world, despite fundamental differences in the underlying entities. Furthermore, it correctly predicts the non-monotonic temporal variation in connectivity observed recently in one such system.

Transition in the Waiting-Time Distribution of Price-Change Events in a Global Socioeconomic System

The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the deviations in the waiting-time distribution away from one generated by a random process, may help unravel the feedback mechanisms that drive the underlying dynamics. We analyze the waiting-time distributions of high frequency foreign exchange data for the best executable bid-ask prices across all major currencies. We find that the lognormal distribution yields a good overall fit for the waiting-time distribution between currency rate changes if both short and long waiting times are included. If we restrict our study to long waiting-times, each currency pairs distribution is consistent with a power law tail with exponent near to 3.5. However for short waiting times, the overall distribution resembles one generated by an archetypal complex systems model in which boundedly rational agents compete for limited resources. Our findings suggest a gradual transition arises in trading behavior between a fast regime in which traders act in a boundedly rational way, and a slower one in which traders decisions are driven by generic feedback mechanisms across multiple timescales and hence produce similar power-law tails irrespective of currency type.

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.

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.

Computational modeling of collective human behavior: Example of financial markets

We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information but lack local information from their social network, and a model in which the traders form a dynamically evolving social network but lack any decision-making based on global information. We show that a suitable combination of these two models -- in particular, a population of virtual traders with access to both global and local information -- produces results for the price return distribution which are closer to the reported stylized facts. We believe that this type of model can be applied across a wide range of systems in which collective human activity is observed.