Individual heterogeneity generates 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 typically 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 can drive explosive network behavior and 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 cannot be ignored.Comment: 6 pages, 4 figure

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 population's 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

Atypical viral dynamics from transport through popular places

The flux of visitors through popular places undoubtedly influences viral spreading -- from H1N1 and Zika viruses spreading through physical spaces such as airports, to rumors and ideas spreading though online spaces such as chatrooms and social media. However there is a lack of understanding of the types of viral dynamics that can result. Here we present a minimal dynamical model which focuses on the time-dependent interplay between the {\em mobility through} and the {\em occupancy of} such spaces. Our generic model permits analytic analysis while producing a rich diversity of infection profiles in terms of their shapes, durations, and intensities. The general features of these theoretical profiles compare well to real-world data of recent social contagion phenomena.Comment: 14 pages, 16 figure

Anomalous Contagion and Renormalization in Dynamical Networks with Nodal Mobility

The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on average, underlying nodal mobility can dramatically distort outbreak profiles. Highly nonlinear dynamical regimes emerge in which increasing mobility either amplifies or suppresses outbreak severity. Predicted profiles mimic recent outbreaks of real-space contagion (social unrest) and online contagion (pro-ISIS support). We show that this nodal mobility can be renormalized in a precise way for a particular class of dynamical networks

Multi-Species Cohesion: Humans, machinery, AI and beyond

What large-scale cohesive behaviors -- desirable or dangerous -- can suddenly emerge from systems with interacting humans, machinery and software including AI? When will they emerge? How will they evolve and be controlled? Here we offer some answers to these urgent questions by introducing an aggregation model that accounts for entities' inter- and intra-species diversities. It yields a novel multi-dimensional 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 related real-world systems, e.g. Hamas-Hezbollah online support, human-machine team interactions, AI-determined topic coherence. A key takeaway is that good and bad 'surprises' will appear increasingly quickly as humans-machinery-AI etc. mix more -- but the theory offers a rigorous approach for understanding and controlling this

Shockwaves and turbulence 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 shockwave-like solutions explain how, why and when such activity rises from 'out-of-nowhere', and show how it can be delayed, re-shaped 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.Comment: Feedback welcome to [email protected]

Nonequilibrium Quantum Systems: Divergence between Global and Local Descriptions

Even photosynthesis—the most basic natural phenomenon underlying life on Earth—involves the nontrivial processing of excitations at the pico- and femtosecond scales during light-harvesting. The desire to understand such natural phenomena, as well as interpret the output from ultrafast experimental probes, creates an urgent need for accurate quantitative theories of open quantum systems. However it is unclear how best to generalize the well-established assumptions of an isolated system, particularly under nonequilibrium conditions. Here we compare two popular approaches: a description in terms of a direct product of the states of each individual system (i.e., a local approach) versus the use of new states resulting from diagonalizing the whole Hamiltonian (i.e., a global approach). The main difference lies in finding suitable operators to derive the Lindbladian and hence the master equation. We show that their equivalence fails when the system is open, in particular under the experimentally ubiquitous condition of a temperature gradient. By solving for the steady state populations and calculating the heat flux as a test observable, we uncover stark differences between the formulations. This divergence highlights the need to establish rigorous ranges of applicability for such methods in modeling nanoscale transfer phenomena—including during the light-harvesting process in photosynthesis