Abstract Memory, interaction, and environmental feedback are central mechanisms by which living active matter generates collective organization. We introduce a scalable hybrid particle--field framework for chemotactic populations in which each run-and-tumble particle carries an internal memory variable, interacts through regularized short- and long-range forces, and consumes a diffusive nutrient field. Recent treatments of chemotaxis with a resolved internal state eliminate that state by coarse-graining, while particle--field solvers for chemotaxis carry no pairwise interaction to accelerate; here the internal variable is retained by every particle and the nonlocal interaction is evaluated with controlled error. Compactly supported interactions are computed exactly by cell lists and nonlocal forces by Barnes--Hut traversal, reducing the dominant cost from $O(N^2)$ to approximately $O(N\log N)$, while the consumed field is advanced by an unconditionally positive splitting. We establish finite-particle regularity, $N$-independent estimates for the particle-generated nutrient source, exactness of the cell-list force, a local Barnes--Hut monopole error bound, and a formal kinetic limit on the position--direction--memory phase space. Numerical experiments verify cell-list force evaluation to machine precision, a measured global traversal error of $2.7$--$4.5\%$, first-order time and second-order grid convergence, empirical $N^{-1/2}$ fluctuation scaling of the empirical density, and force-evaluation benchmarks to $N=10^6$. Sweeping the uptake strength at fixed attraction suppresses aggregation by a factor of fourteen: consumption-driven chemotaxis with an external source is self-limiting, a field-mediated effect that a prescribed nutrient landscape cannot produce. The method provides a reproducible computational route for studying emergent regimes in complex living matter.
Real-world network data often suffer from noise, biases, and missing data in edge weights, all of which can undermine the reliability of downstream network analyses. Standard noise filtering approaches, whether treating individual edges one-by-one or assuming a uniform global noise level, are suboptimal because, in practice, both signal and noise can be heterogeneous and correlated across multiple edges. To address this challenge, we introduce the Network Wiener Filter (NetWF), a principled method for collective edge-level noise filtering that jointly leverages network structure and explicit noise characteristics. It is capable of reducing noise in observed edge weights as well as inferring missing edge weights. It applies broadly across network types and scales efficiently to large empirical systems, as we demonstrate using real-world network data from two distinct settings. We envision the NetWF as a new foundation for error-aware network analysis.
Early warning indicators (EWIs) have been developed in an attempt to forewarn of approaching tipping points. In the case of bifurcation-induced tipping (Ashwin et al 2025 Proc. R. Soc. A 481 20250405), the most commonly used EWIs are related to the phenomenon of ‘Critical Slowing Down (CSD)’, which involves an increase in the variance and autocorrelation of a state variable prior to the bifurcation (Scheffer et al 2009 Nature 461 53–59). CSD can provide useful early warning in systems which remain close to a quasi-equilibrium state as they approach the bifurcation (Dakos et al 2008 Technical Report ). Under these circumstances, fluctuations reveal the declining stability of the steady state. However, CSD is far less reliable in a strongly forced system where the control variable is changing quickly compared to the characteristic timescale of the system. In such strongly forced systems, it is possible to temporarily overshoot the bifurcation, without causing tipping (Ritchie et al 2021 Nature 592 517–523). However, currently there is no robust way of determining when a strongly forced system has passed the bifurcation. Here we develop a more reliable EWI for strongly forced systems, by looking instead at the fluctuations about a reconstructed quasi-equilibrium state. The variance of the reconstructed quasi-equilibrium state blows-up as the bifurcation point is approached, such that the inverse of the variance goes to zero at the bifurcation. We show that our new EWI, which we call ‘Increased Variance of Quasi-equilibrium’, is able to forewarn of a critical point being crossed in both weakly and strongly forced systems.
Stochastic oscillations can emerge in two-population models as a consequence of endogenous finite-size fluctuations. Here, we investigate how the introduction of a third fluctuating species, representing an additional interacting population, affects the stochastic dynamics of a prototypical model of neuronal interactions. Our results show that the presence of this additional species can substantially modify the collective behavior of the neuronal populations. When the characteristic sizes of the neuronal populations and the third species are of the same order, the latter modifies the characteristic frequency of the noise-induced quasi-cycles and can ultimately suppress their emergence. Conversely, when the neuronal populations are more abundant than the characteristic size of the third species, the latter enhances the effective noise acting on the neuronal populations, thereby amplifying their stochastic fluctuations. These results demonstrate that an additional population can qualitatively alter noise-induced collective dynamics, either modulating or suppressing coherent stochastic oscillations or enhancing the strength of demographic fluctuations. More generally, our findings point to the importance of accounting for intermediate stochastic populations when modeling interacting noisy oscillators and provide a framework for investigating how additional sources of fluctuations affect collective dynamics and synchronization beyond the classical Kuramoto setting.
Oscillatory dynamics are ubiquitous in driven systems, but in real-world environments their regularity is often perturbed by time-dependent and stochastic inputs. Elevator systems provide a representative example of a nonautonomous oscillatory system under such external modulation. In this study, we analyze long-term measurements of two elevators operating in a multipurpose building. We developed a measurement system that records the elevator position and direction of motion over time and examined their relative dynamics using spatial-distance, correlation-based, and phase-based measures. The observed behavior varies across weekdays, weekends, and different parts of the observation period, reflecting nonstationary external driving associated with changing demand conditions. Although the motion shows mild variations in period and amplitude, the relative dynamics exhibit weak and intermittent coordination rather than a single persistent synchronized mode. These results suggest that real-world elevator systems can display nontrivial synchronization-like behavior under time-varying and noisy forcing, even far from the idealized conditions assumed in simple oscillator models.
