On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks

Theoretical analysis using mathematical models is often used to understand a mechanism of collective motion in a self-propelled system. In the experimental system using camphor disks, several kinds of characteristic motions have been observed due to the interaction of two camphor disks. In this paper, we understand the emergence mechanism of the motions caused by the interaction of two self-propelled bodies by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematical model. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, is chaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due to torus bifurcation.

Dominating lengthscales of zebrafish collective behaviour

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the collective dynamics of fifty zebrafish. We observed the emergence of collective behaviour changing between ordered to randomised, upon adaptation to new environmental conditions. We quantify the spatial and temporal correlation functions of the fish and identify two length scales, the persistence length and the nearest neighbour distance, that capture the essence of the behavioural changes. The ratio of the two length scales correlates robustly with the polarisation of collective motion that we explain with a reductionist model of self–propelled particles with alignment interactions.

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.

Motion pattern-based crowd scene classification using histogram of angular deviations of trajectories

Automated crowd behaviour analysis and monitoring is a challenging task due to the unpredictable nature of the crowd within a particular scene and across different scenes. The prior knowledge of the type of scene under consideration is a crucial mid-level information, which could be utilized to develop robust crowd behaviour analysis systems. In this paper, we propose an approach to automatically detect the type of a crowded scene based on the global motion patterns of the objects within the scene. Three different types of scenes whose global motion pattern characteristics vary from uniform to non-uniform are considered in this work, namely structured, semi-structured, and unstructured scenes, respectively. To capture the global motion pattern characteristics of an input crowd scene, we first extract the motion information in the form of trajectories using a key-point tracker and then compute the average angular orientation feature of each trajectory. This paper utilizes these angular features to introduce a novel feature vector, termed as Histogram of Angular Deviations (HAD), which depicts the distribution of the pair-wise angular deviation values for each trajectory vector. Since angular deviation information is resistant to changes in scene perspectives, we consider it as a key feature for distinguishing the scene types. To evaluate the effectiveness of the proposed HAD-based feature vector in classifying the crowded scenes, we build a crowd scene classification model by training the classical machine learning algorithms on the publicly available Collective Motion Database. The experimental results demonstrate the superior crowd classification performance of the proposed approach as compared to the existing methods. In addition to this, we propose a technique based on quantizing the angular deviation values to reduce the feature dimension and subsequently introduce a novel crowd scene structuredness index to quantify the structuredness of an input crowded scene based on its HAD.

Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.

Formation, collective motion, and merging of macroscopic bacterial aggregates

Chemotactic bacteria form emergent spatial patterns of variable cell density within cultures that are initially spatially uniform. These patterns are the result of chemical gradients that are created from the directed movement and metabolic activity of billions of cells. A recent study on pattern formation in wild bacterial isolates has revealed unique collective behaviors of the bacteria Enterobacter cloacae. As in other bacterial species, Enterobacter cloacae form macroscopic aggregates. Once formed, these bacterial clusters can migrate several millimeters, sometimes resulting in the merging of two or more clusters. To better understand these phenomena, we examine the formation and dynamics of thousands of bacterial clusters that form within a 22 cm square culture dish filled with soft agar over two days. At the macroscale, the aggregates display spatial order at short length scales, and the migration of cell clusters is superdiffusive, with a merging acceleration that is correlated with aggregate size. At the microscale, aggregates are composed of immotile cells surrounded by low density regions of motile cells. The collective movement of the aggregates is the result of an asymmetric flux of bacteria at the boundary. An agent-based model is developed to examine how these phenomena are the result of both chemotactic movement and a change in motility at high cell density. These results identify and characterize a new mechanism for collective bacterial motility driven by a transient, density-dependent change in motility.

Collective Motion of Cells Modeled as Ring Polymers

In this article, we use a coarse-grained model of disjoint semi-flexible ring polymers to investigate computationally the spatiotemporal collective behavior of cell colonies. A ring polymer in this model is...

Label-free Cell Tracking Enables Collective Motion Phenotyping in Epithelial Monolayers

Collective cell migration is an umbrella term for a rich variety of cell behaviors, whose distinct character is essential for biological function, notably for cancer metastasis. One essential feature of collective behavior is the motion of cells relative to their immediate neighbors. We introduce an AI-based pipeline to segment and track cell nuclei from phase contrast images. Nuclei segmentation is based on a U‐Net convolutional neural network trained on images with nucleus staining. Tracking, based on the Crocker-Grier algorithm, quantifies nuclei movement and allows for robust downstream analysis of collective motion. Since the AI algorithm required no new training data, our approach promises to be applicable to and yield new insights for vast libraries of existing collective motion images. In a systematic analysis of a cell line panel with oncogenic mutations, we find that the collective rearrangement metric, D2min, which reflects non-affine motion, shows promise as an indicator of metastatic potential.

Surveying a Swarm: Experimental Techniques to Establish and Examine Bacterial Collective Motion

The survival and successful spread of many bacterial species hinges on their mode of motility. One of the most distinct of these is swarming, a collective form of motility where a dense consortium of bacteria employ flagella to propel themselves across a solid surface. Surface environments pose unique challenges, derived from higher surface friction/tension and insufficient hydration. Bacteria have adapted by deploying an array of mechanisms to overcome these challenges. Beyond allowing bacteria to colonize new terrain in the absence of bulk liquid, swarming also bestows faster speeds and enhanced antibiotic resistance to the collective. These crucial attributes contribute to the dissemination, and in some cases pathogenicity, of an array of bacteria. This mini-review highlights; 1) aspects of swarming motility that differentiates it from other methods of bacterial locomotion. 2) Facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges. 3) The (often difficult) approaches required to cultivate genuine swarmers. 4) The methods available to observe and assess the various facets of this collective motion, as well as the features exhibited by the population as a whole.