Contrarian compulsions produce time dependent flocking of active particles

Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic adjustment of the flock or period doubling in time. This is demonstrated by analyzing a modified Vicsek model of self-propelled particles and its corresponding kinetic equation valid for a large number of particles. We have carried out a stability and bifurcation analysis of the order-disorder transition to spatially uniform stationary or time periodic solutions that are characterized by their complex order parameters. Direct numerical simulations differing from theoretical predictions indicate the formation of spatiotemporal structures. Strikingly, we have found that increasing the usual alignment noise may favor flocking and an optimum noise produces the strongest possible order parameter.Comment: 21 pages, 12 figures, revised versio

A probabilistic weak formulation of mean field games and applications

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed strategies which provide approximate Nash equlibria for finite-player games. Our results are applied to a new class of multi-agent price impact models and a class of flocking models for which we prove existence of equilibria

What have we been looking at? A call for consistency in studies of primate vigilance

Vigilance functions to detect threats. In primates, these threats emerge from both predators and conspecifics, but a host of other social, demographic, and ecological factors have been shown to influence primate vigilance patterns. The primate vigilance literature is thus characterized by considerable variation in findings, with inconsistent or contradictory results reported not only across different species but also within species and populations across studies. Some of this variation could emerge from fundamental differences in the methods employed, making comparisons across species and groups challenging. Furthermore, identifying consistent behavioral markers for the state of vigilance appears to have proved challenging in primates, leading to a range of definitions being developed. Deviation at this level leads directly into concomitant variation at the level of sampling methodologies. As a result, the primate vigilance literature currently presents a diverse series of approaches to exploring subtly different behaviors and phenomena. This review calls for a greater consistency in studying vigilance, with the aim of encouraging future research to follow similar principles leading to more comparable results. Identifying whether an animal is in a vigilant state is challenging for most field researchers; identifying and recording a more general behavior of “looking” should though be more achievable. Experimental approaches could then be employed to understand the compatibility “looking” has with predator detection (and other threats) in individual study systems. The outcome of this approach will allow researchers to understand the key determinants of looking in their study groups and explore threat detection probabilities given an individual or group's relative level of looking

Informative and misinformative interactions in a school of fish

It is generally accepted that, when moving in groups, animals process information to coordinate their motion. Recent studies have begun to apply rigorous methods based on Information Theory to quantify such distributed computation. Following this perspective, we use transfer entropy to quantify dynamic information flows locally in space and time across a school of fish during directional changes around a circular tank, i.e. U-turns. This analysis reveals peaks in information flows during collective U-turns and identifies two different flows: an informative flow (positive transfer entropy) based on fish that have already turned about fish that are turning, and a misinformative flow (negative transfer entropy) based on fish that have not turned yet about fish that are turning. We also reveal that the information flows are related to relative position and alignment between fish, and identify spatial patterns of information and misinformation cascades. This study offers several methodological contributions and we expect further application of these methodologies to reveal intricacies of self-organisation in other animal groups and active matter in general

Quantifying criticality, information dynamics and thermodynamics of collective motion

Active matter consists of self-propelled particles whose interactions give rise to coherent collective motion. Well-known examples include schools of fish, flocks of birds, swarms of insects and herds of ungulates. On the micro-scale, cells, enzymes and bacteria also move collectively as active matter, inspiring engineering of artificial materials and devices. These diverse systems exhibit similar collective behaviours, including gathering, alignment and quick propagation of perturbations, which emerge from relatively simple local interactions. This phenomenon is known as self-organisation and is observed in active matter as well as in many other complex collective phenomena, including urban agglomeration, financial crises, ecosystems dynamics and technological cascading failures. Some open challenges in the study of self-organisation include (a) how the information processing across the collective and over time gives rise to emergent behaviour, (b) how to identify the regimes in which different collective behaviours exist and their phase transitions, and (c) how to quantify the thermodynamics associated with these phenomena. This thesis aims to investigate these topics in the context of active matter, while building a rigorous theoretical framework. Specifically, this thesis provides three main contributions. Firstly, the question of how to formally measure information transfer across the collective is addressed and applied to a real system, i.e., a school of fish. Secondly, general relations between statistical mechanical and thermodynamical quantities are analytically derived and applied to a model of active matter, resulting in the formulation of the concept of “thermodynamic efficiency of computation during collective motion”. This concept is then extended to the domain of urban dynamics. Thirdly, this thesis provides a rigorous quantification of the non-equilibrium entropy production associated with the collective motion of active Brownian particles