Abstract Although belief propagation is a useful inference tool in several network-based contexts given its speed, its precision deteriorates when encountering loops. Generalized belief propagation (GBP) was introduced around two decades ago to mitigate this issue. However, it did not become widely used since it did not provide an explicit algorithm applicable to any network. This only changed recently, with the introduction of the first explicit and general version of GBP for networks, the Cantwell–Newman (CN)-method, which remained until now the only algorithm with such properties. Here, we provide a family of algorithms with these characteristics. We begin by considering the case where the network only has short loops. In this scenario, we improve on the CN-method by developing a algorithm with optimal time complexity, the NIB-method. We then consider networks that also have long loops. In this context, we show that the NIB-method provides advantages compared to the CN-method: it is faster for the networks where the CN-method is expected to work well, and it is applicable to more networks, i.e. highly dense networks. In general, both the CN-method and the family algorithms introduced here become non-equivalent approximations, and they can provide different levels of accuracy when applied to the same network, as we show numerically using two artificial networks. This discrepancy can have important practical implications, as we discuss in the context of decoding and error correction.
Structured environments organize active-particle currents by coupling propulsion and orientational dynamics to geometry. Translationally periodic ratchets can produce a rotation-frequency-dependent drift across equivalent unit cells, but the locked position remains spatially degenerate. In this paper, we show that a radially periodic landscape removes this degeneracy through self-referential feedback that weakens with orbital radius. Trajectories initialized within finite capture basins converge to preferred phase-locked radii, and the resulting locked orbits exhibit a chirality-odd transverse mobility under a weak radial force. Depinned trajectories instead organize into near-integer winding branches whose normalized mean drift approaches the associated branch label. The second harmonic of the radial potential reshapes the radial barriers and changes which branches are reached from a prescribed initial state. Near a locking boundary, an effective angular potential describes noise-activated phase slips and their first-passage statistics. The full radial dynamics shows how repeated slips accumulate into radial spreading. With short-range repulsion, the radial-well structure remains visible as the particles redistribute outward. Together, these results establish a geometric route for organizing frequency-dependent transport in patterned, substrate-confined active matter and may guide the design of chiral microrobotic and granular-roller systems.
Accurate prediction of pedestrian flow at critical subway nodes (e.g. gates, escalators, staircases) prone to bottlenecks is fundamental to assessing collective dynamics (e.g. crowd crush risk). However, large peak and off-peak contrasts, spatial interdependencies, and heterogeneous node capacities undermine the predictive performance of single-expert models. To address such complexity, we propose a hybrid sequence- and graph-based Mixture of Experts approach, ResGAT-BX, comprising i) a Graph Attention Network to model spatial dependencies and ii) Bidirectional GRU and extended long short-term memory experts to capture temporal variability, thereby improving adaptability across conditions. Using ResGAT-BX predictions, we quantify node-level risk via crowd-gathering density, duration, and throughput fluctuation amplitude. Experiments on a real-world Qingdao subway dataset demonstrate i) ResGAT-BX's robustness via parameter-sensitivity analyses and ii) ResGAT-BX's consistently superior performance over state-of-the-art baselines for both direct flow volume prediction and derived crowd crush risk anticipation across multiple metrics and regimes, including peak surges and off-peak fluctuations. The dataset used in this study has been publicly released on GitHub: https://github.com/niupeng111/Node-Pedestrian-Flow-Dataset.
This paper develops a mean-field framework for modelling opinion polarization and correlated opinion alignment in online communities, with particular attention to the structural conditions under which misinformation-prone environments arise. Rather than tracking the propagation of specific false content, the framework identifies the interaction regimes in which a platform's aggregation mechanism becomes structurally unable to recover an accurate global opinion signal, which is the condition under which misinformation becomes consequential. We consider a population divided into interacting groups, where individuals hold binary opinions and influence one another through a coupling matrix that captures both within-community and cross-community interactions. Using ideas from statistical mechanics, the model describes collective opinion formation through an energy-based formulation and an associated Gibbs measure. We study the behaviour of the system in the limit of large populations and analyse the resulting community-level opinion margins. Optimal aggregation weights are derived by minimizing the expected discrepancy between the true global opinion and its approximation based on community-level signals. The analysis identifies three regimes of behaviour: weak coupling, the critical regime, and strong coupling, each leading to different macroscopic outcomes. In the weak-coupling regime, opinions are only weakly correlated, and the optimal weights are uniquely determined by a linear system involving the correlation structure. In the strong-coupling regime, the system exhibits either collective alignment or complete polarization, and the optimal weights are no longer uniquely defined. We also distinguish between cooperative and antagonistic interaction structures and show how they lead to consensus formation, echo chambers, or polarized states. These results show how the strength and sign of inter-community coupling determine whether platforms converge toward consensus, fragment into echo chambers, or become irreducibly polarized, and how the resulting aggregation breakdown, in turn, creates the structural conditions under which misinformation thrives.
We introduce a class of multispecies exclusion processes in which each species follows its own intra-species interaction mechanism. In contrast to previously studied integrable multispecies models-such as the multispecies TASEP, where the intra-species interaction rule is identical across all species-our framework allows the intra-species rule to vary across species, while inter-species interactions obey a long-range swap rule. We prove that Bethe ansatz integrability is preserved in the binary regime, where each species follows either TASEP-type or drop-push-type dynamics, by establishing the Yang-Baxter structure of the associated scattering matrices. Furthermore, we identify nontrivial families of species compositions through a continuous interpolation between these dynamics that remain integrable, and extend the model to include bidirectional motion. These results show that Bethe ansatz integrability extends to a broad class of multispecies systems with species-dependent interaction mechanisms, providing a framework for deriving exact transition probabilities and analyzing nonequilibrium dynamics.
