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1. Emergent hypernetworks in weakly coupled oscillators

   https://doi.org/10.1038/s41467-022-32282-4  

   Nijholt, Eddie; Ocampo-Espindola, Jorge Luis; Eroglu, Deniz; Kiss, István Z.; Pereira, Tiago (December 2022, Nature Communications)

   Abstract Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence. 

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2. Programmable self-organization of heterogeneous microrobot collectives

   https://doi.org/10.1073/pnas.2221913120  

   Ceron, Steven; Gardi, Gaurav; Petersen, Kirstin; Sitti, Metin (June 2023, Proceedings of the National Academy of Sciences)

   At the microscale, coupled physical interactions between collectives of agents can be exploited to enable self-organization. Past systems typically consist of identical agents; however, heterogeneous agents can exhibit asymmetric pairwise interactions which can be used to generate more diverse patterns of self-organization. Here, we study the effect of size heterogeneity in microrobot collectives composed of circular, magnetic microdisks on a fluid–air interface. Each microrobot spins or oscillates about its center axis in response to an external oscillating magnetic field, in turn producing local magnetic, hydrodynamic, and capillary forces that enable diverse collective behaviors. We demonstrate through physical experiments and simulations that the heterogeneous collective can exploit the differences in microrobot size to enable programmable self-organization, density, morphology, and interaction with external passive objects. Specifically, we can control the level of self-organization by microrobot size, enable organized aggregation, dispersion, and locomotion, change the overall shape of the collective from circular to ellipse, and cage or expel objects. We characterize the fundamental self-organization behavior across a parameter space of magnetic field frequency, relative disk size, and relative populations; we replicate the behavior through a physical model and a swarming coupled oscillator model to show that the dominant effect stems from asymmetric interactions between the different-sized disks. Our work furthers insights into self-organization in heterogeneous microrobot collectives and moves us closer to the goal of applying such collectives to programmable self-assembly and active matter. 

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3. Transition to Collective Motion in Nonreciprocal Active Matter: Coarse Graining Agent-Based Models into Fluctuating Hydrodynamics

   https://doi.org/10.1103/PhysRevX.15.041015  

   Martin, David; Seara, Daniel; Avni, Yael; Fruchart, Michel; Vitelli, Vincenzo (October 2025, Physical Review X)

   Two hallmarks of nonequilibrium systems, from active colloids to animal herds, are agent motility and nonreciprocal interactions. Their interplay creates feedback loops that lead to complex spatiotemporal dynamics crucial to understand and control the nonlinear response of active systems. Here, we introduce a minimal model that captures these two features at the microscopic scale while admitting an exact hydrodynamic theory valid also in the fully nonlinear regime. Using statistical mechanics techniques, we exactly coarse-grain our nonreciprocal microscopic model into a fluctuating hydrodynamics and use dynamical systems insights to analyze the resulting equations. In the absence of motility, we find two transitions to oscillatory phases occurring via distinct mechanisms: a Hopf bifurcation and a saddle node on invariant circle bifurcation. In the presence of motility, this rigorous approach, complemented by numerical simulations, allows us to quantitatively assess the hitherto neglected impact of interspecies nonreciprocity on a paradigmatic transition in active matter: the emergence of collective motion. When nonreciprocity is weak, we show that flocking is accelerated and bands tend to synchronize with a spatial overlap controlled by nonlinearities. When nonreciprocity is strong, flocking is superseded by a chase and rest dynamical phase, where each species alternates between a chasing state, when they propagate, and a resting state, when they stand still. Phenomenological models with linear nonreciprocal couplings fail to predict the chase and rest phase, which illustrates the usefulness of our exact coarse-graining procedure. Finally, we demonstrate how fluctuations in finite systems can be harnessed to characterize microscopic nonreciprocity from macroscopic time-correlation functions, even in phases where nonreciprocal interactions do not affect the thermodynamic steady state. 

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4. A stochastic-statistical residential burglary model with independent Poisson clocks

   https://doi.org/10.1017/S0956792520000029  

   WANG, CHUNTIAN; ZHANG, YUAN; BERTOZZI, ANDREA L.; SHORT, MARTIN B. (January 2020, European Journal of Applied Mathematics)

   Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci. 18 , 1249–1267], a pioneering agent-based statistical model of residential burglary criminal behaviour, with deterministic time steps assumed for arrivals of events in which the residential burglary aggregate pattern formation is quantitatively studied for the first time; (2) the SSRB model (agent-based stochastic-statistical model of residential burglary crime) [Wang, Zhang, Bertozzi & Short (2019) Active Particles , Vol. 2 , Springer Nature Switzerland AG, in press], in which the stochastic component of the model is theoretically analysed by introduction of a Poisson clock with time steps turned into exponentially distributed random variables. To incorporate independence of agents, in this work, five types of Poisson clocks are taken into consideration. Poisson clocks (I), (II) and (III) govern independent agent actions of burglary behaviour, and Poisson clocks (IV) and (V) govern interactions of agents with the environment. All the Poisson clocks are independent. The time increments are independently exponentially distributed, which are more suitable to model individual actions of agents. Applying the method of merging and splitting of Poisson processes, the independent Poisson clocks can be treated as one, making the analysis and simulation similar to the SSRB model. A Martingale formula is derived, which consists of a deterministic and a stochastic component. A scaling property of the Martingale formulation with varying burglar population is found, which provides a theory to the finite size effects . The theory is supported by quantitative numerical simulations using the pattern-formation quantifying statistics. Results presented here will be transformative for both elements of application and analysis of agent-based models for residential burglary or in other domains. 

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5. Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

   https://doi.org/10.1371/journal.pcbi.1009869  

   Wagner, Robert J.; Vernerey, Franck J. (February 2022, PLOS Computational Biology)

   Maini, Philip K. (Ed.)

   Collective living systems regularly achieve cooperative emergent functions that individual organisms could not accomplish alone. The rafts of fire ants (Solenopsis invicta) are often studied in this context for their ability to create aggregated structures comprised entirely of their own bodies, including tether-like protrusions that facilitate exploration of and escape from flooded environments. While similar protrusions are observed in cytoskeletons and cellular aggregates, they are generally dependent on morphogens or external gradients leaving the isolated role of local interactions poorly understood. Here we demonstrate through an ant-inspired, agent-based numerical model how protrusions in ant rafts may emerge spontaneously due to local interactions. The model is comprised of a condensed structural network of agents that represents the monolayer of interconnected worker ants, which floats on the water and gives ant rafts their form. Experimentally, this layer perpetually contracts, which we capture through the pairwise contraction of all neighboring structural agents at a strain rate of d ˙ . On top of the structural layer, we model a dispersed, on-lattice layer of motile agents that represents free ants, which walk on top of the floating network. Experimentally, these self-propelled free ants walk with some mean persistence length and speed that we capture through an ant-inspired phenomenological model. Local interactions occur between neighboring free ants within some radius of detection, R , and the persistence length of freely active agents is tuned through a noise parameter, η as introduced by the Vicsek model. Both R and η where fixed to match the experimental trajectories of free ants. Treadmilling of the raft occurs as agents transition between the structural and free layers in accordance with experimental observations. Ultimately, we demonstrate how phases of exploratory protrusion growth may be induced by increased ant activity as characterized by a dimensionless parameter, A . These results provide an example in which functional morphogenesis of a living system may emerge purely from local interactions at the constituent length scale, thereby providing a source of inspiration for the development of decentralized, autonomous active matter and swarm robotics. 

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