Information transfer and behavioural inertia in starling flocks

Minimal work protocols for inertial particles in nonharmonic traps

Progress in miniaturized technology allows us to control physical systems at nanoscale with remarkable precision. Experimental advancements have sparked interest in control problems in stochastic thermodynamics, typically concerning a time-dependent potential applied to a nanoparticle to reach a target stationary state in a given time with minimal energy cost. We study this problem for a particle subject to thermal fluctuations in a regime that takes into account the effects of inertia, and, building on the results of a previous work, we provide a numerical method to find optimal controls even for non-Gaussian initial and final conditions, corresponding to nonharmonic confinements. Although we focus on a regime where the driving time is long compared to the characteristic relaxation times of the dynamics, the control protocol and the time-dependent position distribution are qualitatively different from the corresponding overdamped limit: in particular, a symmetry of the boundary conditions, which is preserved in the absence of inertia, turns out to be broken in the underdamped regime. We also show that the momentum mean tends to a constant value along the trajectory, except close to the boundary, while the evolution of the position mean and of the second moments is highly nontrivial. Our results also support that the lower bound on the optimal entropy production computed from the overdamped case is tight in the adiabatic limit.

Reynolds rules in swarm fly behavior based on KAN transformer tracking method

The analysis of complex flight patterns and collective behaviors in swarming insects has emerged as a significant focus across biological and computational fields. Tracking these insects, like fruit fly, presents persistent challenges due to their rapid motion patterns and frequent occlusions in densely populated environments. To address these challenges, we propose a tracking method using particle filter framework combined with a Kolmogorov-Arnold Network (KAN)-Transformer model to extract the global features and fine-grained features of the trajectory. Additionally, manually annotated ground truth datasets are established to enable thorough assessment of tracking methods. Experimental results demonstrate the effectiveness and robustness of our proposed tracking method. Analysis of tracked trajectories revealed the Reynolds rules of flocking behavior.

The 2025 motile active matter roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Finding emergence in data by maximizing effective information

Quantifying emergence and modeling emergent dynamics in a data-driven manner for complex dynamical systems is challenging due to the fact that emergent behaviors cannot be directly captured by micro-level observational data. Thus, it is crucial to develop a framework to identify emergent phenomena and capture emergent dynamics at the macro-level using available data. Inspired by the theory of causal emergence (CE), this paper introduces a machine learning framework to learn macro-dynamics in an emergent latent space and quantify the degree of CE. The framework maximizes effective information, resulting in a macro-dynamics model with enhanced causal effects. Experimental results on simulated and real data demonstrate the effectiveness of the proposed framework. It quantifies degrees of CE effectively under various conditions and reveals distinct influences of different noise types. It can learn a one-dimensional coarse-grained macro-state from functional magnetic resonance imaging data to represent complex neural activities during movie clip viewing. Furthermore, improved generalization to different test environments is observed across all simulation data.

Collective dynamics of pulse-coupled swarmalators

Collective motion in nature, from the murmurations of starlings to firefly flashes, showcases a remarkable level of self-organization. Swarmalator models are an emerging paradigm for describing collective behavior of oscillators which sync and swarm. Traditionally, most studies have focused on the self-organizing dynamics of swarmalators with continuous coupling. However, a key aspect of many biological systems, pulsed interactions, remains unexplored within the framework of swarmalators. In this paper, we analyze the collective behavior of pulse-coupled swarmalators with different characteristics of pulse and phase response curves. We report several collective states facilitated by the pulsatile interactions including bump state, active bump state, partial synchronized state, radial wave state, and death state. The stationary nature of spatial and phase dynamics characterizes the death state. Further, we provide an analytical estimate for the threshold coupling strength for the death state's existence by analyzing the minimal model's dynamics with two coupled swarmalators.

Body orientation change of neighbors leads to scale-free correlation in collective motion

Collective motion, such as milling, flocking, and collective turning, is a common and captivating phenomenon in nature, which arises in a group of many self-propelled individuals using local interaction mechanisms. Recently, vision-based mechanisms, which establish the relationship between visual inputs and motion decisions, have been applied to model and better understand the emergence of collective motion. However, previous studies often characterize the visual input as a transient Boolean-like sensory stream, which makes it challenging to capture the salient movements of neighbors. This further hinders the onset of the collective response in vision-based mechanisms and increases demands on visual sensing devices in robotic swarms. An explicit and context-related visual cue serving as the sensory input for decision-making in vision-based mechanisms is still lacking. Here, we hypothesize that body orientation change (BOC) is a significant visual cue characterizing the motion salience of neighbors, facilitating the emergence of the collective response. To test our hypothesis, we reveal the significant role of BOC during collective U-turn behaviors in fish schools by reconstructing scenes from the view of individual fish. We find that an individual with the larger BOC often takes on the leading role during U-turns. To further explore this empirical finding, we build a pairwise interaction mechanism on the basis of the BOC. Then, we conduct experiments of collective spin and collective turn with a real-time physics simulator to investigate the dynamics of information transfer in BOC-based interaction and further validate its effectiveness on 50 real miniature swarm robots. The experimental results show that BOC-based interaction not only facilitates the directional information transfer within the group but also leads to scale-free correlation within the swarm. Our study highlights the practicability of interaction governed by the neighbor's body orientation change in swarm robotics and the effect of scale-free correlation in enhancing collective response.

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback-Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

Layer-by-layer unsupervised clustering of statistically relevant fluctuations in noisy time-series data of complex dynamical systems

Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.

Generic Coupling between Internal States and Activity Leads to Activation Fronts and Criticality in Active Systems

To understand the onset of collective motion, we investigate active systems where particles switch on and off their self-propulsion. We prove that even when the only possible transition is off→on, an active two-state system behaves as an effective three-state (inactive/passive) system that exhibits a sharp phase transition in 1D, and critical behavior in 2D, with scale-invariant activity avalanches. The obtained results show how criticality can naturally emerge in active systems, providing insight into the way collectives distribute, process, and respond to local environmental cues.

Leaderless consensus decision-making determines cooperative transport direction in weaver ants

Animal groups need to achieve and maintain consensus to minimize conflict among individuals and prevent group fragmentation. An excellent example of a consensus challenge is cooperative transport, where multiple individuals cooperate to move a large item together. This behaviour, regularly displayed by ants and humans only, requires individuals to agree on which direction to move in. Unlike humans, ants cannot use verbal communication but most likely rely on private information and/or mechanical forces sensed through the carried item to coordinate their behaviour. Here, we investigated how groups of weaver ants achieve consensus during cooperative transport using a tethered-object protocol, where ants had to transport a prey item that was tethered in place with a thin string. This protocol allows the decoupling of the movement of informed ants from that of uninformed individuals. We showed that weaver ants pool together the opinions of all group members to increase their navigational accuracy. We confirmed this result using a symmetry-breaking task, in which we challenged ants with navigating an open-ended corridor. Weaver ants are the first reported ant species to use a 'wisdom-of-the-crowd' strategy for cooperative transport, demonstrating that consensus mechanisms may differ according to the ecology of each species.

Self-aligning active agents with inertia and active torque

We extend the study of the inertial effects on the two-dimensional dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational dynamics to the translational one, produces unexpected and nontrivial dynamics, already at the deterministic level. Examining first the motion of a free particle, we contrast the role of inertia depending on the sign of the self-aligning torque. When positive, inertia does not alter the steady-state linear motion of an a-chiral self-propelled particle. On the contrary, for a negative self-aligning torque, inertia leads to the destabilization of the linear motion into a spontaneously broken chiral symmetry orbiting dynamics. Adding an active torque, or bias, to the angular dynamics, the bifurcation becomes imperfect in favor of the chiral orientation selected by the bias. In the case of a positive self-alignment, the interplay of the active torque and inertia leads to the emergence, out of a saddle-node bifurcation, of solutions which coexist with the simply biased linear motion. In the context of a free particle, the rotational inertia leaves unchanged the families of steady-state solutions but sets their stability properties. The situation is radically different when considering the case of a collision with a wall, where a very singular oscillating dynamics takes place which can only be captured if both translational and rotational inertia are present.

Inertial spin model of flocking with position-dependent forces

We propose an extension to the inertial spin model (ISM) of flocking and swarming. The model has been introduced to explain certain dynamic features of swarming (second sound, a lower than expected dynamic critical exponent) while preserving the mechanism for onset of order provided by the Vicsek model. The inertial spin model (ISM) has only been formulated with an imitation ("ferromagnetic") interaction between velocities. Here we show how to add position-dependent forces in the model, which allows to consider effects such as cohesion, excluded volume, confinement, and perturbation with external position-dependent field, and thus study this model without periodic boundary conditions. We study numerically a single particle with an harmonic confining field and compare it to a Brownian harmonic oscillator and to a harmonically confined active Browinian particle, finding qualitatively different behavior in the three cases.

Perception of motion salience shapes the emergence of collective motions

Despite the profound implications of self-organization in animal groups for collective behaviors, understanding the fundamental principles and applying them to swarm robotics remains incomplete. Here we propose a heuristic measure of perception of motion salience (MS) to quantify relative motion changes of neighbors from first-person view. Leveraging three large bird-flocking datasets, we explore how this perception of MS relates to the structure of leader-follower (LF) relations, and further perform an individual-level correlation analysis between past perception of MS and future change rate of velocity consensus. We observe prevalence of the positive correlations in real flocks, which demonstrates that individuals will accelerate the convergence of velocity with neighbors who have higher MS. This empirical finding motivates us to introduce the concept of adaptive MS-based (AMS) interaction in swarm model. Finally, we implement AMS in a swarm of ~102 miniature robots. Swarm experiments show the significant advantage of AMS in enhancing self-organization of the swarm for smooth evacuations from confined environments.

Remapping revisited: how the hippocampus represents different spaces

The representation of distinct spaces by hippocampal place cells has been linked to changes in their place fields (the locations in the environment where the place cells discharge strongly), a phenomenon that has been termed 'remapping'. Remapping has been assumed to be accompanied by the reorganization of subsecond cofiring relationships among the place cells, potentially maximizing hippocampal information coding capacity. However, several observations challenge this standard view. For example, place cells exhibit mixed selectivity, encode non-positional variables, can have multiple place fields and exhibit unreliable discharge in fixed environments. Furthermore, recent evidence suggests that, when measured at subsecond timescales, the moment-to-moment cofiring of a pair of cells in one environment is remarkably similar in another environment, despite remapping. Here, I propose that remapping is a misnomer for the changes in place fields across environments and suggest instead that internally organized manifold representations of hippocampal activity are actively registered to different environments to enable navigation, promote memory and organize knowledge.

A robotic falcon induces similar collective escape responses in different bird species

Patterns of collective escape of a bird flock from a predator are fascinating, but difficult to study under natural conditions because neither prey nor predator is under experimental control. We resolved this problem by using an artificial predator (RobotFalcon) resembling a peregrine falcon in morphology and behaviour. We imitated hunts by chasing flocks of corvids, gulls, starlings and lapwings with the RobotFalcon, and compared their patterns of collective escape to those when chased by a conventional drone and, in case of starlings, hunted by wild peregrine falcons. Active pursuit of flocks, rather than only flying nearby by either the RobotFalcon or the drone, made flocks collectively escape more often. The RobotFalcon elicited patterns of collective escape in flocks of all species more often than the drone. Attack altitude did not affect the frequency of collective escape. Starlings escaped collectively equally often when chased by the RobotFalcon or a wild peregrine falcon. Flocks of all species reacted most often by collective turns, second most often by compacting and third by splitting into subflocks. This study demonstrates the potential of an artificial aerial predator for studying the collective escape behaviour of free-living birds, opening exciting avenues in the empirical study of prey-predator interactions.

Dynamical order and many-body correlations in zebrafish show that three is a crowd

Zebrafish constitute a convenient laboratory-based biological system for studying collective behavior. It is possible to interpret a group of zebrafish as a system of interacting agents and to apply methods developed for the analysis of systems of active and even passive particles. Here, we consider the effect of group size. We focus on two- and many-body spatial correlations and dynamical order parameters to investigate the multistate behavior. For geometric reasons, the smallest group of fish which can exhibit this multistate behavior consisting of schooling, milling and swarming is three. We find that states exhibited by groups of three fish are similar to those of much larger groups, indicating that there is nothing more than a gradual change in weighting between the different states as the system size changes. Remarkably, when we consider small groups of fish sampled from a larger group, we find very little difference in the occupancy of the state with respect to isolated groups, nor is there much change in the spatial correlations between the fish. This indicates that fish interact predominantly with their nearest neighbors, perceiving the rest of the group as a fluctuating background. Therefore, the behavior of a crowd of fish is already apparent in groups of three fish.

Environmental impact on visual perception modulates behavioral responses of schooling fish to looming predators

Aggregation in social fishes has evolved to improve safety from predators. The individual interaction mechanisms that govern collective behavior are determined by the sensory systems that translate environmental information into behavior. In dynamic environments, shifts in conditions impede effective visual sensory perception in fish schools, and may induce changes in the collective response. Here, we consider whether environmental conditions that affect visual contrast modulate the collective response of schools to looming predators. By using a virtual environment to simulate four contrast levels, we tested whether the collective state of minnow fish schools was modified in response to a looming optical stimulus. Our results indicate that fish swam slower and were less polarized in lower contrast conditions. Additionally, schooling metrics known to be regulated by non-visual sensory systems tended to correlate better when contrast decreased. Over the course of the escape response, schools remained tightly formed and retained the capability of transferring social information. We propose that when visual perception is compromised, the interaction rules governing collective behavior are likely to be modified to prioritize ancillary sensory information crucial to maximizing chance of escape. Our results imply that multiple sensory systems can integrate to control collective behavior in environments with unreliable visual information.

Optimising peak energy reduction in networks of buildings

Buildings are amongst the world's largest energy consumers and simultaneous peaks in demand from networks of buildings can decrease electricity system stability. Current mitigation measures either entail wasteful supply-side over-specification or complex centralised demand-side control. Hence, a simple schema is developed for decentralised, self-organising building-to-building load coordination that requires very little information exchange and no top-down management-analogous to other complex systems with short range interactions, such as coordination between flocks of birds or synchronisation in fireflies. Numerical and experimental results reveal that a high degree of peak flattening can be achieved using surprisingly small load-coordination networks. The optimum reductions achieved by the simple schema can outperform existing techniques, giving substantial peak-reductions as well as being remarkably robust to changes in other system parameters such as the interaction network topology. This not only demonstrates that significant reductions in network peaks are achievable using remarkably simple control systems but also reveals interesting theoretical results and new insights which will be of great interest to the complexity and network science communities.

Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature

The collective motion observed in living active matter, such as fish schools and bird flocks, is characterized by its dynamic and complex nature, involving various moving states and transitions. By tailoring physical interactions or incorporating information exchange capabilities, inanimate active particles can exhibit similar behavior. However, the lack of synchronous and arbitrary control over individual particles hinders their use as a test system for the study of more intricate collective motions in living species. Herein, a novel optical feedback control system that enables the mimicry of collective motion observed in living objects using active particles is proposed. This system allows for the experimental investigation of the velocity alignment, a seminal model of collective motion (known as the Vicsek model), in a microscale perturbed environment with controllable and realistic conditions. The spontaneous formation of different moving states and dynamic transitions between these states is observed. Additionally, the high robustness of the active-particle group at the critical density under the influence of different perturbations is quantitatively validated. These findings support the effectiveness of velocity alignment in real perturbed environments, thereby providing a versatile platform for fundamental studies on collective motion and the development of innovative swarm microrobotics.

A self-organizing robotic aggregate using solid and liquid-like collective states

Designing robotic systems that can change their physical form factor as well as their compliance to adapt to environmental constraints remains a major conceptual and technical challenge. To address this, we introduce the Granulobot, a modular system that blurs the distinction between soft, modular, and swarm robotics. The system consists of gear-like units that each contain a single actuator such that units can self-assemble into larger, granular aggregates using magnetic coupling. These aggregates can reconfigure dynamically and also split into subsystems that might later recombine. Aggregates can self-organize into collective states with solid- and liquid-like properties, thus displaying widely differing compliance. These states can be perturbed locally via actuators or externally via mechanical feedback from the environment to produce adaptive shape-shifting in a decentralized manner. This, in turn, can generate locomotion strategies adapted to different conditions. Aggregates can move over obstacles without using external sensors or coordinates to maintain a steady gait over different surfaces without electronic communication among units. The modular design highlights a physical, morphological form of control that advances the development of resilient robotic systems with the ability to morph and adapt to different functions and conditions.

Local control for the collective dynamics of self-propelled particles

Utilizing a paradigmatic model for the motion of interacting self-propelled particles, we demonstrate that local accelerations at the level of individual particles can drive transitions between different collective dynamics, leading to a control process. We find that the ability to trigger such transitions is hierarchically distributed among the particles and can form distinctive spatial patterns within the collective. Chaotic dynamics occur during the transitions, which can be attributed to fractal basin boundaries mediating the control process. The particle hierarchies described in this paper offer decentralized capabilities for controlling artificial swarms.

Inertial effect on evasion and pursuit dynamics of prey swarms: the emergence of a favourable mass ratio for the predator-prey arms race

We show, based on a theoretical model, how inertia plays a pivotal role in the survival dynamics of a prey swarm while chased by a predator. With the varying mass of the prey and predator, diverse escape patterns emerge, such as circling, chasing, maneuvering, dividing into subgroups, and merging into a unitary group, similar to the escape trajectories observed in nature. Moreover, we find a transition from non-survival to survival of the prey swarm with increasing predator mass. The transition regime is also sensitive to the variation in prey mass. Further, the analysis of the prey group survival as a function of predator-to-prey mass ratio unveils the existence of three distinct regimes: (i) frequent chase and capture leading to the non-survival of the prey swarm, (ii) an intermediate regime where competition between pursuit and capture occurs, resembling an arms race, and (iii) the survival regime without the capture of prey. Interestingly, our study demonstrates the existence of a favourable predator-prey mass ratio for coexistence of both prey and predator in an ecosystem, which agrees well with the field studies.

SMART-BARN: Scalable multimodal arena for real-time tracking behavior of animals in large numbers

The SMART-BARN (scalable multimodal arena for real-time tracking behavior of animals in large numbers) achieves fast, robust acquisition of movement, behavior, communication, and interactions of animals in groups, within a large (14.7 meters by 6.6 meters by 3.8 meters), three-dimensional environment using multiple information channels. Behavior is measured from a wide range of taxa (insects, birds, mammals, etc.) and body size (from moths to humans) simultaneously. This system integrates multiple, concurrent measurement techniques including submillimeter precision and high-speed (300 hertz) motion capture, acoustic recording and localization, automated behavioral recognition (computer vision), and remote computer-controlled interactive units (e.g., automated feeders and animal-borne devices). The data streams are available in real time allowing highly controlled and behavior-dependent closed-loop experiments, while producing comprehensive datasets for offline analysis. The diverse capabilities of SMART-BARN are demonstrated through three challenging avian case studies, while highlighting its broad applicability to the fine-scale analysis of collective animal behavior across species.

Compact and ordered swarms of unmanned aerial vehicles in cluttered environments

The globally coordinated motion produced by the classical swarm model is typically generated by simple local interactions at the individual level. Despite the success of these models in interpretation, they cannot guarantee compact and ordered collective motion when applied to the cooperation of unmanned aerial vehicle (UAV) swarms in cluttered environments. Inspired by the behavioral characteristics of biological swarms, a distributed self-organized Reynolds (SOR) swarm model of UAVs is proposed. In this model, a social term is designed to keep the swarm in a collision-free, compact, and ordered collective motion, an obstacle avoidance term is introduced to make the UAV avoid obstacles with a smooth trajectory, and a migration term is added to make the UAV fly in a desired direction. All the behavioral rules for agent interactions are designed with as simple a potential function as possible. And the genetic algorithm is used to optimize the parameters of the model. To evaluate the collective performance, we introduce different metrics such as (a) order, (b) safety, (c) inter-agent distance error, (d) speed range. Through the comparative simulation with the current advanced bio-inspired compact and Vasarhelyi swarm models, the proposed approach can guide the UAV swarm to pass through the dense obstacle environment in a safe and ordered manner as a compact group, and has adaptability to different obstacle densities.

Characterization of lab-based swarms of Anopheles gambiae mosquitoes using 3D-video tracking

Mosquito copulation is a crucial determinant of its capacity to transmit malaria-causing Plasmodium parasites as well as underpinning several highly-anticipated vector control methodologies such as gene drive and sterile insect technique. For the anopheline mosquitoes responsible for African malaria transmission, mating takes place within crepuscular male swarms which females enter solely to mate. However, the mechanisms that regulate swarm structure or that govern mate choice remain opaque. We used 3D-video tracking approaches and computer vision algorithms developed for the study of other complex biological systems to document swarming behavior of a lab-adapted Anopheles gambiae line in a lab-based setting. By reconstructing trajectories of individual mosquitoes lasting up to 15.88 s, in swarms containing upwards of 200 participants, we documented swarm-like behavior in both males and females. In single sex swarms, encounters between individuals were fleeting (< 0.75 s). By contrast, in mixed swarms, we were able to detect 79 'brief encounters' (> 0.75 s; < 2.5 s) and 17 longer-lived encounters (> 2.5 s). We also documented several examples of apparent male-male mating competition. These findings represent the first steps towards a more detailed and quantitative description of swarming and courtship behavior in one of the most important vectors of malaria.

Anomalous Self-Organization in Active Piles

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity's strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak-Tang-Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

Swarming Transition in Super-Diffusive Self-Propelled Particles

A super-diffusive Vicsek model is introduced in this paper that incorporates Levy flights with exponent α. The inclusion of this feature leads to an increase in the fluctuations of the order parameter, ultimately resulting in the disorder phase becoming more dominant as α increases. The study finds that for α values close to two, the order-disorder transition is of the first order, while for small enough values of α, it shows degrees of similarities with the second-order phase transitions. The article formulates a mean field theory based on the growth of the swarmed clusters that accounts for the decrease in the transition point as α increases. The simulation results show that the order parameter exponent β, correlation length exponent ν, and susceptibility exponent γ remain constant when α is altered, satisfying a hyperscaling relation. The same happens for the mass fractal dimension, information dimension, and correlation dimension when α is far from two. The study reveals that the fractal dimension of the external perimeter of connected self-similar clusters conforms to the fractal dimension of Fortuin-Kasteleyn clusters of the two-dimensional Q=2 Potts (Ising) model. The critical exponents linked to the distribution function of global observables vary when α changes.

Long-Range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions

We study a two-dimensional, nonreciprocal XY model, where each spin interacts only with its nearest neighbors in a certain angle around its current orientation, i.e., its "vision cone." Using energetic arguments and Monte Carlo simulations, we show that a true long-range ordered phase emerges. A necessary ingredient is a configuration-dependent bond dilution entailed by the vision cones. Strikingly, defects propagate in a directional manner, thereby breaking the parity and time-reversal symmetry of the spin dynamics. This is detectable by a nonzero entropy production rate.

Directional speakers as a tool for animal vocal communication studies

Audio playbacks are a common experimental tool in vocal communication research. However, low directionality of sound makes it hard to control the audience exposed to the stimuli. Parametric speakers offer a solution for transmitting directional audible signals by using ultrasonic carrier waves. The targeted transmission of vocal signals offers exciting opportunities for testing the diffusion of information in animal groups and mechanisms for resolving informational ambiguities. We have field tested the quality and directionality of a commercial parametric speaker, Soundlazer SL-01. Additionally, we assessed its usability for performing playback experiments by comparing behavioural responses of free-ranging meerkats (Suricata suricatta) with calls transmitted from conventional and parametric speakers. Our results show that the tested parametric speaker is highly directional. However, the acoustic structure of meerkat calls was strongly affected and low frequencies were not reliably reproduced by the parametric speaker. The playback trials elicited weakened behavioural responses probably due to the partial distortion of the signal but also indicating the potential importance of social facilitation for initiating mobbing events in meerkats. We conclude that parametric speakers can be useful tools for directed transmission of animals calls but after a careful assessment of signal fidelity.

Environmental Path-Entropy and Collective Motion

Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a "bottom-up" principle: individuals reorient to maximize their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (coaligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects, and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the postdecision orientations and (ii) "cognitive" noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further.

Dynamics of collective motion across time and species

Most studies of collective animal behaviour rely on short-term observations, and comparisons of collective behaviour across different species and contexts are rare. We therefore have a limited understanding of intra- and interspecific variation in collective behaviour over time, which is crucial if we are to understand the ecological and evolutionary processes that shape collective behaviour. Here, we study the collective motion of four species: shoals of stickleback fish (Gasterosteus aculeatus), flocks of homing pigeons (Columba livia), a herd of goats (Capra aegagrus hircus) and a troop of chacma baboons (Papio ursinus). First, we describe how local patterns (inter-neighbour distances and positions), and group patterns (group shape, speed and polarization) during collective motion differ across each system. Based on these, we place data from each species within a 'swarm space', affording comparisons and generating predictions about the collective motion across species and contexts. We encourage researchers to add their own data to update the 'swarm space' for future comparative work. Second, we investigate intraspecific variation in collective motion over time and provide guidance for researchers on when observations made over different time scales can result in confident inferences regarding species collective motion. This article is part of a discussion meeting issue 'Collective behaviour through time'.

A multi-scale review of the dynamics of collective behaviour: from rapid responses to ontogeny and evolution

Collective behaviours, such as flocking in birds or decision making by bee colonies, are some of the most intriguing behavioural phenomena in the animal kingdom. The study of collective behaviour focuses on the interactions between individuals within groups, which typically occur over close ranges and short timescales, and how these interactions drive larger scale properties such as group size, information transfer within groups and group-level decision making. To date, however, most studies have focused on snapshots, typically studying collective behaviour over short timescales up to minutes or hours. However, being a biological trait, much longer timescales are important in animal collective behaviour, particularly how individuals change over their lifetime (the domain of developmental biology) and how individuals change from one generation to the next (the domain of evolutionary biology). Here, we give an overview of collective behaviour across timescales from the short to the long, illustrating how a full understanding of this behaviour in animals requires much more research attention on its developmental and evolutionary biology. Our review forms the prologue of this special issue, which addresses and pushes forward understanding the development and evolution of collective behaviour, encouraging a new direction for collective behaviour research. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Directional switches in network-organized swarming systems with delay

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Low-distortion information propagation with noise suppression in swarm networks

A method for low-distortion (low-dissipation, low-dispersion) information propagation in swarm-type networks with suppression of high-frequency noise is presented. Information propagation in current neighbor-based networks, where each agent seeks to achieve a consensus with its neighbors, is diffusion-like, dissipative, and dispersive and does not reflect the wave-like (superfluidic) behavior seen in nature. However, pure wave-like neighbor-based networks have two challenges: i) It requires additional communication for sharing information about time derivatives and ii) it can lead to information decoherence through noise at high frequencies. The main contribution of this work is to show that delayed self-reinforcement (DSR) by the agents using prior information (e.g., using short-term memory) can lead to the wave-like information propagation at low-frequencies as seen in nature without the need for additional information sharing between the agents. Moreover, it is shown that the DSR can be designed to enable suppression of high-frequency noise transmission while limiting the dissipation and dispersion of (lower-frequency) information content leading to similar (cohesive) behavior of agents. In addition to explaining noise-suppressed wave-like information transfer in natural systems, the result impacts the design of noise-suppressing cohesive algorithms for engineered networks.

Stochasticity may generate coherent motion in bird flocks

Murmurations along with other forms of flocking have come to epitomize collective animal movements. Most studies into these stunning aerial displays have aimed to understand how coherent motion may emerge from simple behavioral rules and behavioral correlations. These studies may now need revision because recently it has been shown that flocking birds, like swarming insects, behave on the average as if they are trapped in elastic potential wells. Here I show, somewhat paradoxically, how coherent motion can be generated by variations in the intensity of multiplicative noise which causes the shape of a potential well to change, thereby shifting the positions and strengths of centres of attraction. Each bird, irrespective of its position in the flock will respond in a similar way to such changes, giving the impression that the flock behaves as one, and typically resulting in scale-free correlations. I thereby show how correlations can be an emergent property of noisy, confining potential wells. I also show how such wells can lead to high density borders, a characteristic of flocks, and I show how they can account for the complex patterns of collective escape patterns of starling flocks under predation. I suggest swarming and flocking do not constitute two distinctly different kinds of collective behavior but rather that insects are residing in relatively stable potential wells whilst birds are residing in unstable potential wells. It is shown how, dependent upon individual perceptual capabilities, bird flocks can be poised at criticality.

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Functional duality in group criticality via ambiguous interactions

Critical phenomena are wildly observed in living systems. If the system is at criticality, it can quickly transfer information and achieve optimal response to external stimuli. Especially, animal collective behavior has numerous critical properties, which are related to other research regions, such as the brain system. Although the critical phenomena influencing collective behavior have been extensively studied, two important aspects require clarification. First, these critical phenomena never occur on a single scale but are instead nested from the micro- to macro-levels (e.g., from a Lévy walk to scale-free correlation). Second, the functional role of group criticality is unclear. To elucidate these aspects, the ambiguous interaction model is constructed in this study; this model has a common framework and is a natural extension of previous representative models (such as the Boids and Vicsek models). We demonstrate that our model can explain the nested criticality of collective behavior across several scales (considering scale-free correlation, super diffusion, Lévy walks, and 1/f fluctuation for relative velocities). Our model can also explain the relationship between scale-free correlation and group turns. To examine this relation, we propose a new method, applying partial information decomposition (PID) to two scale-free induced subgroups. Using PID, we construct information flows between two scale-free induced subgroups and find that coupling of the group morphology (i.e., the velocity distributions) and its fluctuation power (i.e., the fluctuation distributions) likely enable rapid group turning. Thus, the flock morphology may help its internal fluctuation convert to dynamic behavior. Our result sheds new light on the role of group morphology, which is relatively unheeded, retaining the importance of fluctuation dynamics in group criticality.

Pulsed Interaction Signals as a Route to Biological Pattern Formation

We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.

Bouncing dynamics of inertial self-propelled particles reveals directional asymmetry

This study aims to examine experimental conditions in which active particles are forced by their surroundings to move forward and backward in a continuous oscillatory manner. The experimental design is based on using a vibrating self-propelled toyrobot called hexbug, which is placed inside a narrow channel closed on one end by a rigid moving wall. Using the end-wall velocity as a controlling factor, the main forward mode of the hexbug movement can be turned to mostly rearward mode. We investigate the bouncing hexbug motion on both experimental and theoretical grounds. The Brownian model of active particles with inertia is employed in the theoretical framework. The model itself uses a pulsed Langevin equation in order to simulate abrupt changes in velocity that mimic hexbug propulsion in the moments when its legs make contact with the base plate. Significant directional asymmetry is caused by the legs bending backward. We demonstrate that the simulation successfully reproduces the experimental characteristics of hexbug motion after regressing the spatial and temporal statistical characteristics, especially when directional asymmetry is under consideration.

Spontaneous vortex formation by microswimmers with retarded attractions

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.

Circular motion subject to external alignment under active driving: Nonlinear dynamics and the circle map

Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather bent or circular trajectories. We here address self-propelled or actively driven objects that move in discrete steps and additionally tend to migrate towards a certain direction by discrete angular adjustment. Overreaction in the angular alignment is possible. This competition implies pronounced nonlinear dynamics including period doubling and chaotic behavior in a broad parameter regime. Such behavior directly affects the appearance of the trajectories. Furthermore, we address collective motion and effects of spatial self-concentration.

Experimental identification of individual insect visual tracking delays in free flight and their effects on visual swarm patterns

Insects are model systems for swarming robotic agents, yet engineered descriptions do not fully explain the mechanisms by which they provide onboard sensing and feedback to support such motions; in particular, the exact value and population distribution of visuomotor processing delays are not yet quantified, nor the effect of such delays on a visually-interconnected swarm. This study measures untethered insects performing a solo in-flight visual tracking task and applies system identification techniques to build an experimentally-consistent model of the visual tracking behaviors, and then integrates the measured experimental delay and its variation into a visually interconnected swarm model to develop theoretical and simulated solutions and stability limits. The experimental techniques include the development of a moving visual stimulus and real-time multi camera based tracking system called VISIONS (Visual Input System Identification from Outputs of Naturalistic Swarms) providing the capability to recognize and simultaneously track both a visual stimulus (input) and an insect at a frame rate of 60-120 Hz. A frequency domain analysis of honeybee tracking trajectories is conducted via fast Fourier and Chirp Z transforms, identifying a coherent linear region and its model structure. The model output is compared in time and frequency domain simulations. The experimentally measured delays are then related to probability density functions, and both the measured delays and their distribution are incorporated as inter-agent interaction delays in a second order swarming dynamics model. Linear stability and bifurcation analysis on the long range asymptotic behavior is used to identify delay distributions leading to a family of solutions with stable and unstable swarm center of mass (barycenter) locations. Numerical simulations are used to verify these results with both continuous and measured distributions. The results of this experiment quantify a model structure and temporal lag (transport delay) in the closed loop dynamics, and show that this delay varies across 50 individuals from 5-110ms, with an average delay of 22ms and a standard deviation of 40ms. When analyzed within the swarm model, the measured delays support a diversity of solutions and indicate an unstable barycenter.

Signal propagation and linear response in the delay Vicsek model

Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that (1) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (2) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (3) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; and (4) the linear response breaks down when orientation conservation is broken.

Does a roosting flock of migratory birds also echelon in high winds?

The organized aerial manoeuvres of birds in “V” and “J” flock echelons have always captivated onlookers and several of these aspects are still a matter of ongoing research. However, we could not find any published evidence or report on echeloning in a roosting flock of birds in high wind conditions. Here, we provide first evidence of an echelon in a roosting flock of the Eurasian oystercatcher (Haematopus ostralegus ostralegus) at the onset of Storm Malik in Scotland on the morning of the 29th of January 2022, under ~ 11 ms−1 winds. This observation opens-up several new research questions on if, how, and why birds position themselves in a flock while roosting in high winds.

Deep learning in light-matter interactions

The deep-learning revolution is providing enticing new opportunities to manipulate and harness light at all scales. By building models of light-matter interactions from large experimental or simulated datasets, deep learning has already improved the design of nanophotonic devices and the acquisition and analysis of experimental data, even in situations where the underlying theory is not sufficiently established or too complex to be of practical use. Beyond these early success stories, deep learning also poses several challenges. Most importantly, deep learning works as a black box, making it difficult to understand and interpret its results and reliability, especially when training on incomplete datasets or dealing with data generated by adversarial approaches. Here, after an overview of how deep learning is currently employed in photonics, we discuss the emerging opportunities and challenges, shining light on how deep learning advances photonics.

Information conduction and convection in noiseless Vicsek flocks

Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse-grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.

Transition in collective motion decision making

Collective decision making in a biological motion group requires fast and robust transmission of information. Typically, directional switching information propagation across the whole group obeys a linear dispersion law. However, conventional dynamic collective motion models, such as the Vicsek model and the Couzin model did not take into account ultrafast directional synchronous motions. In the present paper, a multiparticle model is proposed based on inertial spin self-propel action, which can provide adequate description of such group motion. By considering both spin mechanism and collision avoidance, the proposed self-propelled particle spin model can nicely describe collective motion with fast directional switching. By analyzing the order parameter of the group-velocity synchronization, a mechanism of group decision making is revealed, which is based on the difference between two clusters of divergent leaders, showing a transition from the compromising phase (i.e., following the group average) to the preferred phase (i.e., aligning to a leader cluster). The finding provides new insight to the decision-making process of followers when they face with divergent leaders in group motion.

Selective interaction and its effect on collective motion

Plenty of empirical evidence on biological swarms reveal that interaction between individuals is selective. Each individual’s neighbor is selected based on one or more featured factors. Based on the self-propelled model, we develop a general probability neighbor selection framework to study the effect of four typical featured factors (i.e., distance, bearing, orientation change and bearing change). In this work, two common cases are involved to comprehensively analyze the impact of the four featured factors on the collective motion. One is the flocking, the other is the responsivity to stimulus. The impact of different selection strengths of the featured factors on both cases are investigated. The effect of noise on flocking and different stimulus intensities on responsivity to stimulus are analyzed. This study allows us to get the insight of selective interaction and suggests the potential solution to overcome the trade-off between flocking and responsivity quality.

Marginal speed confinement resolves the conflict between correlation and control in collective behaviour

Speed fluctuations of individual birds in natural flocks are moderate, due to the aerodynamic and biomechanical constraints of flight. Yet the spatial correlations of such fluctuations are scale-free, namely they have a range as wide as the entire group, a property linked to the capacity of the system to collectively respond to external perturbations. Scale-free correlations and moderate fluctuations set conflicting constraints on the mechanism controlling the speed of each agent, as the factors boosting correlation amplify fluctuations, and vice versa. Here, using a statistical field theory approach, we suggest that a marginal speed confinement that ignores small deviations from the natural reference value while ferociously suppressing larger speed fluctuations, is able to reconcile scale-free correlations with biologically acceptable group’s speed. We validate our theoretical predictions by comparing them with field experimental data on starling flocks with group sizes spanning an unprecedented interval of over two orders of magnitude.

Bird flocks are known to adjust the orientation and speed of individual birds giving rise to correlations that extend across very large groups. The authors show that marginal control provides an explanation of scale-free correlations of speed fluctuations in natural bird flocks of any sizes.

Robustness and Flexibility of Neural Function through Dynamical Criticality

In theoretical biology, robustness refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is reflected in not needing to fine-tune basic parameter constants; flexibility refers to the ability of a system to switch functions or behaviors easily and effortlessly. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven more elusive, as well as also elucidating the apparent opposition between what is required mathematically for models to implement either. In this paper we address a number of arguments in theoretical neuroscience showing that both robustness and flexibility can be attained by systems that poise themselves at the onset of a large number of dynamical bifurcations, or dynamical criticality, and how such poising can have a profound influence on integration of information processing and function. Finally, we examine critical map lattices, which are coupled map lattices where the coupling is dynamically critical in the sense of having purely imaginary eigenvalues. We show that these map lattices provide an explicit connection between dynamical criticality in the sense we have used and "edge of chaos" criticality.