Anticipation Induces Polarized Collective Motion in Attraction Based Models

Moving animal groups are prime examples of natural complex systems. In most models of such systems each individual updates its heading based on the current positions and headings of its neighbors. However, recently, a number of models where the heading update instead is based on the future anticipated positions/headings of the neighbors have been published. Collectively these studies have established that including anticipation may have drastically different effects in different models. In particular, anticipation inhibits polarization in alignment-based models and in one alignment-free model, but promotes polarization in another alignment-free model. Indicating that our understanding of how anticipation affects the behavior of alignment-free models is incomplete. Given that attraction is a component of many alignment-free models we include anticipation in an attraction only model here to investigate. We establish that anticipation induces polarized collective motion and inhibits swarming and milling in combination with attraction alone. We also show that anticipation orients milling groups when attraction is sufficiently strong, but not otherwise. Finally, we derive an explicit heading update formula for this model with anticipation that allows for a simple heuristic explanation of its polarization inducing capacity. Due to the biological plausibility of both attraction and anticipation we believe that utilizing these components to explain collective motion in animal groups may be advantageous in some cases

Bistability and Switching Behavior in Moving Animal Groups

Moving animal groups such as schools of fish and flocks of birds frequently switch between different group structures. Standard models of collective motion have been used successfully to explain how stable groups form via local interactions between individuals, but they are typically unable to produce groups that exhibit spontaneous switching. We are only aware of one model, constructed for barred flagtail fish that are known to rely on alignment and attraction to organize their collective motion, that has been shown to generate this type of behavior in 2D (or 3D). Interestingly, another species of fish, golden shiners, do exhibit switching but have been shown to use attraction and repulsion, not alignment, to coordinate themselves in schools. Suggesting that switching may be explained by attraction and repulsion alone, without an alignment interaction. Here we introduce a model based on attraction and repulsion only and show that groups exhibiting switching similar to that observed in experiments with golden shiners emerges. We also establish that switching occur in two boundary-free extensions of the model. Our work suggests that the bistability and switching behavior observed in golden shiners and other moving animal groups may be explained via attractive and repulsive interactions alone

Solving the shepherding problem: heuristics for herding autonomous, interacting agents.

Herding of sheep by dogs is a powerful example of one individual causing many unwilling individuals to move in the same direction. Similar phenomena are central to crowd control, cleaning the environment and other engineering problems. Despite single dogs solving this 'shepherding problem' every day, it remains unknown which algorithm they employ or whether a general algorithm exists for shepherding. Here, we demonstrate such an algorithm, based on adaptive switching between collecting the agents when they are too dispersed and driving them once they are aggregated. Our algorithm reproduces key features of empirical data collected from sheep-dog interactions and suggests new ways in which robots can be designed to influence movements of living and artificial agents

Crowd Control

In July 2017 Hackney Wick became playground and laboratory for a series of collective experiments and exhibits delving into the complex interactions between individuals, groups and their environments. Connecting visual, digital and performance art practices with contemporary scientific research, law and urban design, Crowd Control explored the mechanisms of collective behaviour through observation, simulation and experimentation. Crowd Control was commissioned by Arebyte as part of their 2017 Arts Council England funded programme on ‘systems of control

Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection

Inference of interaction rules of animals moving in groups usually relies on an analysis of large scale system behaviour. Models are tuned through repeated simulation until they match the observed behaviour. More recent work has used the fine scale motions of animals to validate and fit the rules of interaction of animals in groups. Here, we use a Bayesian methodology to compare a variety of models to the collective motion of glass prawns (Paratya australiensis). We show that these exhibit a stereotypical ‘phase transition’, whereby an increase in density leads to the onset of collective motion in one direction. We fit models to this data, which range from: a mean-field model where all prawns interact globally; to a spatial Markovian model where prawns are self-propelled particles influenced only by the current positions and directions of their neighbours; up to non-Markovian models where prawns have ‘memory’ of previous interactions, integrating their experiences over time when deciding to change behaviour. We show that the mean-field model fits the large scale behaviour of the system, but does not capture fine scale rules of interaction, which are primarily mediated by physical contact. Conversely, the Markovian self-propelled particle model captures the fine scale rules of interaction but fails to reproduce global dynamics. The most sophisticated model, the non-Markovian model, provides a good match to the data at both the fine scale and in terms of reproducing global dynamics. We conclude that prawns' movements are influenced by not just the current direction of nearby conspecifics, but also those encountered in the recent past. Given the simplicity of prawns as a study system our research suggests that self-propelled particle models of collective motion should, if they are to be realistic at multiple biological scales, include memory of previous interactions and other non-Markovian effects

Attraction Based Models of Collective Motion

Animal groups often exhibit highly coordinated collective motion in a variety of situations. For example, bird flocks, schools of fish, a flock of sheep being herded by a dog and highly efficient traffic on an ant trail. Although these phenomena can be observed every day all over the world our knowledge of what rules the individual's in such groups use is very limited. Questions of this type has been studied using so called self-propelled particle (SPP) models, most of which assume that collective motion arises from individuals aligning with their neighbors. Here we introduce and analyze a SPP-model based on attraction alone. We find that it produces all the typical groups seen in alignment-based models and some novel ones. In particular, a group that exhibits collective motion coupled with non-trivial internal dynamics. Groups that have this property are rarely seen in SPP-models and we show that even when a repulsion term is added to the attraction only model such groups are still present. These findings suggest that an interplay between attraction and repulsion may be the main driving force in real flocks and that the alignment rule may be superfluous. We then proceed to model two different experiments using the SPP-model approach. The first is a shepherding algorithm constructed primarily to model experiments where a sheepdog is herding a flock of sheep. We find that in addition to modeling the specific experimental situation well the algorithm has some properties which may make it useful in more general shepherding situations. The second is a traffic model for leaf-cutting ants bridges. Based on earlier experiments a set of traffic rules for ants on a very narrow bridge had been suggested. We show that these are sufficient to produce the observed traffic dynamics on the narrow bridge. And that when extended to a wider bridge by replacing 'Stop' with 'Turn' the new rules are sufficient to produce several key characteristics of the dynamics on the wide bridge, in particular three-lane formation

Attraction Based Models of Collective Motion

Animal groups often exhibit highly coordinated collective motion in a variety of situations. For example, bird flocks, schools of fish, a flock of sheep being herded by a dog and highly efficient traffic on an ant trail. Although these phenomena can be observed every day all over the world our knowledge of what rules the individual's in such groups use is very limited. Questions of this type has been studied using so called self-propelled particle (SPP) models, most of which assume that collective motion arises from individuals aligning with their neighbors. Here we introduce and analyze a SPP-model based on attraction alone. We find that it produces all the typical groups seen in alignment-based models and some novel ones. In particular, a group that exhibits collective motion coupled with non-trivial internal dynamics. Groups that have this property are rarely seen in SPP-models and we show that even when a repulsion term is added to the attraction only model such groups are still present. These findings suggest that an interplay between attraction and repulsion may be the main driving force in real flocks and that the alignment rule may be superfluous. We then proceed to model two different experiments using the SPP-model approach. The first is a shepherding algorithm constructed primarily to model experiments where a sheepdog is herding a flock of sheep. We find that in addition to modeling the specific experimental situation well the algorithm has some properties which may make it useful in more general shepherding situations. The second is a traffic model for leaf-cutting ants bridges. Based on earlier experiments a set of traffic rules for ants on a very narrow bridge had been suggested. We show that these are sufficient to produce the observed traffic dynamics on the narrow bridge. And that when extended to a wider bridge by replacing 'Stop' with 'Turn' the new rules are sufficient to produce several key characteristics of the dynamics on the wide bridge, in particular three-lane formation

Persistent homology in the cubical setting : theory, implementations and applications

The Theory of persistent homology, as developed by Gunnar Carlsson at Stanford and others, is based on simplicial homology. In this thesis we explore the possibility of basing persistent homology on cubical homology. We managed to achieve this to some extent and have created a working set of prototype procedures able to calculate the persistent homology of a filtered cubical complex in 2D, and in part 3D, with mod 2 coefficients. We also propose a path that should transform our embryo to a set of procedures capable of handling real applications, in e.g. digital image processing, involving large amounts of data. Extensions to arbitrary finite dimension, orientation, spaces with torsion, PID coefficients and more are also included in the plan for the future.Validerat; 20101217 (root