Evidence of a robust universality class in the critical behavior of self-propelled agents: metric versus topological interactions

Banded phases in topological flocks

Flocking phase transitions arise in many aligning active soft matter systems, and an interesting question concerns the role of "topological" vs. "metric" interactions on these transitions. While recent theoretical work suggests that the order-disorder transition in these polar aligning models is universally first order, numerical studies have suggested that topological models may instead have a continuous transition. Some recent simulations have found that some variations of topologically interacting flocking agents have a discontinuous transition, but unambiguous observations of phase coexistence using common Voronoi-based alignment remains elusive. In this work, we use a custom GPU-accelerated simulation package to perform million-particle-scale simulations of a Voronoi-Vicsek model in which alignment interactions stem from an XY-like Hamiltonian. By accessing such large systems on appropriately long time scales and in the time-continuous limit, we are able to show a regime of stable phase coexistence between the ordered and disordered phases, confirming the discontinuous nature of this transition in the thermodynamic limit.

Inverse modeling of time-delayed interactions via the dynamic-entropy formalism

Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically measured equal-time correlation functions. Focusing on collective motion of active units, this constraint is reasonable when the interaction timescale is much faster than that of the interacting units, as in starling flocks, yet it fails in a number of counterexamples, as in leukocyte coordination (where signaling proteins diffuse among two cells). Here, we relax this assumption and develop a path integral approach to maximum-entropy framework, which includes delay in signaling. Our method is able to infer the strength of couplings and fields, but also the time required by the couplings to completely transfer information among the units. We demonstrate the validity of our approach providing excellent results on synthetic datasets of non-Markovian trajectories generated by the Heisenberg-Kuramoto and Vicsek models equipped with delayed interactions. As a proof of concept, we also apply the method to experiments on dendritic migration, where matching equal-time correlations results in a significant information loss.

Learning self-driven collective dynamics with graph networks

Despite decades of theoretical research, the nature of the self-driven collective motion remains indigestible and controversial, while the phase transition process of its dynamic is a major research issue. Recent methods propose to infer the phase transition process from various artificially extracted features using machine learning. In this thesis, we propose a new order parameter by using machine learning to quantify the synchronization degree of the self-driven collective system from the perspective of the number of clusters. Furthermore, we construct a powerful model based on the graph network to determine the long-term evolution of the self-driven collective system from the initial position of the particles, without any manual features. Results show that this method has strong predictive power, and is suitable for various noises. Our method can provide reference for the research of other physical systems with local interactions.

Phase transitions in biology: from bird flocks to population dynamics

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Scale-Free Dynamics in Animal Groups and Brain Networks

Collective phenomena fascinate by the emergence of order in systems composed of a myriad of small entities. They are ubiquitous in nature and can be found over a vast range of scales in physical and biological systems. Their key feature is the seemingly effortless emergence of adaptive collective behavior that cannot be trivially explained by the properties of the system's individual components. This perspective focuses on recent insights into the similarities of correlations for two apparently disparate phenomena: flocking in animal groups and neuronal ensemble activity in the brain. We first will summarize findings on the spontaneous organization in bird flocks and macro-scale human brain activity utilizing correlation functions and insights from critical dynamics. We then will discuss recent experimental findings that apply these approaches to the collective response of neurons to visual and motor processing, i.e., to local perturbations of neuronal networks at the meso- and microscale. We show how scale-free correlation functions capture the collective organization of neuronal avalanches in evoked neuronal populations in nonhuman primates and between neurons during visual processing in rodents. These experimental findings suggest that the coherent collective neural activity observed at scales much larger than the length of the direct neuronal interactions is demonstrative of a phase transition and we discuss the experimental support for either discontinuous or continuous phase transitions. We conclude that at or near a phase-transition neuronal information can propagate in the brain with similar efficiency as proposed to occur in the collective adaptive response observed in some animal groups.

Collective motion patterns of self-propelled agents with both velocity alignment and aggregation interactions

We combine the velocity alignment and aggregation mechanisms to study the collective motion of active agents in noisy circumstances. The agents are located on a two-dimensional square plane, and the proportion of velocity alignment and aggregation interactions are, respectively, set to be k and 1-k. In the case of k=1 our model is similar to the classical Vicsek model, while it degenerates to the view angle model for k=0. By tuning the intensity of the external noise η and the proportional coefficient k, and carrying out extensive numerical simulations, we find that the system can exhibit diverse dynamic patterns widely observed in real biological systems. By means of finite-size scaling analysis, we confirm that the presence of the aggregation interaction affects not only the position of the critical noise η_{c} (beyond which the agents display disordered motion) but also the type of the phase transition of the collective motion. In particular, under a weak external noise environment, the transition from disordered to ordered state by increasing k (i.e., by decreasing the proportion of aggregation interaction) is found to be of first order. Besides, for moderate external noise, we also find the existence of the optimal proportion of the aggregation interaction for the system to achieve the highest degree of order. Our results highlights the important role of the aggregation interaction in the collective motion and may have promising potential applications in natural self-propelled particles and artificial multiagent systems.

Synchronization of multi-agent systems with metric-topological interactions

A hybrid multi-agent systems model integrating the advantages of both metric interaction and topological interaction rules, called the metric-topological model, is developed. This model describes planar motions of mobile agents, where each agent can interact with all the agents within a circle of a constant radius, and can furthermore interact with some distant agents to reach a pre-assigned number of neighbors, if needed. Some sufficient conditions imposed only on system parameters and agent initial states are presented, which ensure achieving synchronization of the whole group of agents. It reveals the intrinsic relationships among the interaction range, the speed, the initial heading, and the density of the group. Moreover, robustness against variations of interaction range, density, and speed are investigated by comparing the motion patterns and performances of the hybrid metric-topological interaction model with the conventional metric-only and topological-only interaction models. Practically in all cases, the hybrid metric-topological interaction model has the best performance in the sense of achieving highest frequency of synchronization, fastest convergent rate, and smallest heading difference.