The dynamics of multidimensional secession: fixed points and ideological condensation

Multispecies Cohesion: Humans, Machinery, AI, and Beyond

The global chaos caused by the July 19, 2024 technology meltdown highlights the need for a theory of what large-scale cohesive behaviors-dangerous or desirable-could suddenly emerge from future systems of interacting humans, machinery, and software, including artificial intelligence; when they will emerge; and how they will evolve and be controlled. Here, we offer answers by introducing an aggregation model that accounts for the interacting entities' inter- and intraspecies diversities. It yields a novel multidimensional generalization of existing aggregation physics. We derive exact analytic solutions for the time to cohesion and growth of cohesion for two species, and some generalizations for an arbitrary number of species. These solutions reproduce-and offer a microscopic explanation for-an anomalous nonlinear growth feature observed in various current real-world systems. Our theory suggests good and bad "surprises" will appear sooner and more strongly as humans, machinery, artificial intelligence, and so on interact more, but it also offers a rigorous approach for understanding and controlling this.

Nonlinear spreading behavior across multi-platform social media universe

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Shockwavelike Behavior across Social Media

Online communities featuring "anti-X" hate and extremism, somehow thrive online despite moderator pressure. We present a first-principles theory of their dynamics, which accounts for the fact that the online population comprises diverse individuals and evolves in time. The resulting equation represents a novel generalization of nonlinear fluid physics and explains the observed behavior across scales. Its shockwavelike solutions explain how, why, and when such activity rises from "out-of-nowhere," and show how it can be delayed, reshaped, and even prevented by adjusting the online collective chemistry. This theory and findings should also be applicable to anti-X activity in next-generation ecosystems featuring blockchain platforms and Metaverses.

Hidden order across online extremist movements can be disrupted by nudging collective chemistry

Disrupting the emergence and evolution of potentially violent online extremist movements is a crucial challenge. Extremism research has analyzed such movements in detail, focusing on individual- and movement-level characteristics. But are there system-level commonalities in the ways these movements emerge and grow? Here we compare the growth of the Boogaloos, a new and increasingly prominent U.S. extremist movement, to the growth of online support for ISIS, a militant, terrorist organization based in the Middle East that follows a radical version of Islam. We show that the early dynamics of these two online movements follow the same mathematical order despite their stark ideological, geographical, and cultural differences. The evolution of both movements, across scales, follows a single shockwave equation that accounts for heterogeneity in online interactions. These scientific properties suggest specific policies to address online extremism and radicalization. We show how actions by social media platforms could disrupt the onset and 'flatten the curve' of such online extremism by nudging its collective chemistry. Our results provide a system-level understanding of the emergence of extremist movements that yields fresh insight into their evolution and possible interventions to limit their growth.

Emergent dynamics of extremes in a population driven by common information sources and new social media algorithms

We quantify how and when extreme subpopulations emerge in a model society despite everyone having the same information and available resources – and show that counterintuitively these extremes will likely be enhanced over time by new social media algorithms designed to reduce division. We verify our analysis mathematically, and show it reproduces (a) the time-dependent behavior observed in controlled experiments on humans, (b) the findings of a recent study of online behavior by Facebook concerning the impact of ‘soft’ and ‘hard’ news, (c) the observed temporal emergence of extremes in U.S. House of Representatives voting, and (d) the real-time emergence of a division in national opinion during the ongoing peace process in Colombia. We uncover a novel societal tipping point which is a ‘ghost’ of a nearby saddle-node bifurcation from dynamical systems theory, and which provides a novel policy opportunity for preventing extremes from emerging.

Individual heterogeneity generating explosive system network dynamics

Individual heterogeneity is a key characteristic of many real-world systems, from organisms to humans. However, its role in determining the system's collective dynamics is not well understood. Here we study how individual heterogeneity impacts the system network dynamics by comparing linking mechanisms that favor similar or dissimilar individuals. We find that this heterogeneity-based evolution drives an unconventional form of explosive network behavior, and it dictates how a polarized population moves toward consensus. Our model shows good agreement with data from both biological and social science domains. We conclude that individual heterogeneity likely plays a key role in the collective development of real-world networks and communities, and it cannot be ignored.

Consensus formation times in anisotropic societies

We developed a statistical mechanics model to study the emergence of a consensus in societies of adapting, interacting agents constrained by a social rule B. In the mean-field approximation, we find that if the agents' interaction H_{0} is weak, all agents adapt to the social rule B, with which they form a consensus; however, if the interaction is sufficiently strong, a consensus is built against the established status quo. We observed that, after a transient time α_{t}, agents asymptotically approach complete consensus by following a path whereby they neglect their neighbors' opinions on socially neutral issues (i.e., issues for which the society as a whole has no opinion). α_{t} is found to be finite for most values of the interagent interaction H_{0} and temperature T, with the exception of the values H_{0}=1, T→∞, and the region determined by the inequalities β<2 and 2βH_{0}<1+β-sqrt[1+2β-β^{2}], for which consensus, with respect to B, is never reached.

Internal character dictates transition dynamics between isolation and cohesive grouping

We show that accounting for internal character among interacting heterogeneous entities generates rich 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 population's diversity decreases. Our analytical theory may help explain why a particular class of universality is so common in the real world, despite the fundamental differences in the underlying entities. It also correctly predicts the nonmonotonic temporal variation in connectivity observed recently in one such system.

Local-global interaction and the emergence of scale-free networks with community structures

Understanding complex networks in the real world is a nontrivial task. In the study of community structures we normally encounter several examples of these networks, which makes any statistical inferencing a challenging endeavor. Researchers resort to computer-generated networks that resemble networks encountered in the real world as a means to generate many networks with different sizes, while maintaining the real-world characteristics of interest. The generation of networks that resemble the real world turns out in itself to be a complex search problem. We present a new rewiring algorithm for the generation of networks with unique characteristics that combine the scale-free effects and community structures encountered in the real world. The algorithm is inspired by social interactions in the real world, whereby people tend to connect locally while occasionally they connect globally. This local-global coupling turns out to be a powerful characteristics that is required for our proposed rewiring algorithm to generate networks with community structures, power law distributions both in degree and in community size, positive assortative mixing by degree, and the rich-club phenomenon.

Majority rule dynamics in finite dimensions

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.

Error-driven global transition in a competitive population on a network

We show, both analytically and numerically, that erroneous data transmission generates a global transition within a competitive population playing the "Minority Game" on a network. This transition, which resembles a phase transition, is driven by a "temporal symmetry breaking" in the global outcome series. The phase boundary, which is a function of the network connectivity p and the error probability q, is described quantitatively by the crowd-anticrowd theory.

Networking the seceder model: Group formation in social and economic systems

The seceder model illustrates how the desire to be different from the average can lead to formation of groups in a population. We turn the original, agent based, seceder model into a model of network evolution. We find that the structural characteristics of our model closely match empirical social networks. Statistics for the dynamics of group formation are also given. Extensions of the model to networks of companies are also discussed.

Evolutionary minority game wtih multiple options

We propose and study an evolutionary minority game (EMG) in which the agents are allowed to choose among three possible options. Unlike the original EMG where the agents either win or lose one unit of wealth, the present model assigns one unit of wealth to the winners in the least popular option, deducts one unit from the losers in the most popular option, and awards R (-1<R<1) units for those in the third option. Decisions are made based on the information in the most recent outcomes and on the characteristic probabilities of an agent to follow the predictions based on recent outcomes. Depending on R, the population shows a transition from self-segregation in difficult situations (R< R(c) ) in which the agents tend to follow extreme action to cautious or less decisive action for R> R(c), where R(c) (N) is a critical value for optimal performance of the system that drops to zero as the number of agents N increases.