Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization.

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

Relative rate of expansion controls speed in one-dimensional pedestrian following.

Patterns of crowd behavior are believed to result from local interactions between pedestrians. Many studies have investigated the local rules of interaction, such as steering, avoiding, and alignment, but how pedestrians control their walking speed when following another remains unsettled. Most pedestrian models assume the physical speed and distance of others as input. The present study compares such "omniscient" models with "visual" models based on optical variables. We experimentally tested eight speed control models from the pedestrian- and car-following literature. Walking participants were asked to follow a leader (a moving pole) in a virtual environment, while the leader's speed was perturbed during the trial. In Experiment 1, the leader's initial distance was varied. Each model was fit to the data and compared. The results showed that visual models based on optical expansion (\(\dot{\theta }\)) had the smallest root mean square error in speed across conditions, whereas other models exhibited increased error at longer distances. In Experiment 2, the leader's size (pole diameter) was varied. A model based on the relative rate of expansion (\(\dot{\theta }/\theta \)) performed better than the expansion rate model (\(\dot{\theta }\)), because it is less sensitive to leader size. Together, the results imply that pedestrians directly control their walking speed in one-dimensional following using relative rate of expansion, rather than the distal speed and distance of the leader.

Is the neighborhood of interaction in human crowds metric, topological, or visual?

Global patterns of collective motion in bird flocks, fish schools, and human crowds are thought to emerge from local interactions within a neighborhood of interaction, the zone in which an individual is influenced by their neighbors. Both metric and topological neighborhoods have been reported in animal groups, but this question has not been addressed for human crowds. The answer has important implications for modeling crowd behavior and predicting crowd disasters such as jams, crushes, and stampedes. In a metric neighborhood, an individual is influenced by all neighbors within a fixed radius, whereas in a topological neighborhood, an individual is influenced by a fixed number of nearest neighbors, regardless of their physical distance. A recently proposed alternative is a visual neighborhood, in which an individual is influenced by the optical motions of all visible neighbors. We test these hypotheses experimentally by asking participants to walk in real and virtual crowds and manipulating the crowd's density. Our results rule out a topological neighborhood, are approximated by a metric neighborhood, but are best explained by a visual neighborhood that has elements of both. We conclude that the neighborhood of interaction in human crowds follows naturally from the laws of optics and suggest that previously observed "topological" and "metric" interactions might be a consequence of the visual neighborhood.

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of 'stripe' formation in human data.

When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows.

The visual coupling between neighbours explains local interactions underlying human 'flocking'.

Patterns of collective motion in bird flocks, fish schools and human crowds are believed to emerge from local interactions between individuals. Most 'flocking' models attribute these local interactions to hypothetical rules or metaphorical forces and assume an omniscient third-person view of the positions and velocities of all individuals in space. We develop a visual model of collective motion in human crowds based on the visual coupling that governs pedestrian interactions from a first-person embedded viewpoint. Specifically, humans control their walking speed and direction by cancelling the average angular velocity and optical expansion/contraction of their neighbours, weighted by visibility (1 - occlusion). We test the model by simulating data from experiments with virtual crowds and real human 'swarms'. The visual model outperforms our previous omniscient model and explains basic properties of interaction: 'repulsion' forces reduce to cancelling optical expansion, 'attraction' forces to cancelling optical contraction and 'alignment' to cancelling the combination of expansion/contraction and angular velocity. Moreover, the neighbourhood of interaction follows from Euclid's Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar perceptual principles may apply to collective motion in other species.

Bumblebees display characteristics of active vision during robust obstacle avoidance flight.

Insects are remarkable flyers and capable of navigating through highly cluttered environments. We tracked the head and thorax of bumblebees freely flying in a tunnel containing vertically oriented obstacles to uncover the sensorimotor strategies used for obstacle detection and collision avoidance. Bumblebees presented all the characteristics of active vision during flight by stabilizing their head relative to the external environment and maintained close alignment between their gaze and flightpath. Head stabilization increased motion contrast of nearby features against the background to enable obstacle detection. As bees approached obstacles, they appeared to modulate avoidance responses based on the relative retinal expansion velocity (RREV) of obstacles and their maximum evasion acceleration was linearly related to RREVmax. Finally, bees prevented collisions through rapid roll manoeuvres implemented by their thorax. Overall, the combination of visuo-motor strategies of bumblebees highlights elegant solutions developed by insects for visually guided flight through cluttered environments.

A day at the beach: Does visually perceived distance depend on the energetic cost of walking?

It takes less effort to walk from here to the Tiki Hut on the brick walkway than on the sandy beach. Does that influence how far away the Tiki Hut looks? The energetic cost of walking on dry sand is twice that of walking on firm ground (Lejeune et al., 1998). If perceived distance depends on the energetic cost or anticipated effort of walking (Proffitt, 2006), then the distance of a target viewed over sand should appear much greater than one viewed over brick. If perceived distance is specified by optical information (e.g., declination angle from the horizon; Ooi et al., 2001), then the distances should appear similar. Participants (N = 13) viewed a target at a distance of 5, 7, 9, or 11 m over sand or brick and then blind-walked an equivalent distance on the same or different terrain. First, we observed no main effect of walked terrain; walked distances on sand and brick were the same (p = 0.46), indicating that locomotion was calibrated to each substrate. Second, responses were actually greater after viewing over brick than over sand (p < 0.001), opposite to the prediction of the energetic hypothesis. This unexpected overshooting can be explained by the slight incline of the brick walkway, which partially raises the visually perceived eye level (VPEL) and increases the target distance specified by the declination angle. The result is thus consistent with the information hypothesis. We conclude that visually perceived egocentric distance depends on optical information and not on the anticipated energetic cost of walking.

Exit choice during evacuation is influenced by both the size and proportion of the egressing crowd.

It is unclear how building occupants take information from the social and built environment into account when choosing an egress route during emergency evacuation. Conflicting tendencies have been previously reported: to follow the crowd, to avoid congestion, and to avoid unknown egress routes alone. We hypothesize that these tendencies depend on an interaction between social influence and the affordances (opportunities for egress) of the built environment. In three virtual reality (VR) experiments (each N = 15), we investigated how social influence interacts with the affordances of available exits to determine exit choice. Participants were immersed in a crowd of virtual humans walking to the left or right exit, and were asked to walk to one of the exits. Experiment 1 tested the role of social influence by manipulating both the proportion of the crowd walking toward one exit (Crowd Proportion of 0 to 100%, in 10% increments) and the absolute number of virtual humans going to the exit (Crowd Size of 10 or 20). Experiment 2 tested the role of affordances by introducing two visible exit doors (1m width) in a closed room, and following the same protocol. Experiment 3 tested larger exit doors (3m width) that afford rapid egress for more people. In the small crowd, participants were increasingly likely to follow the majority as its proportion increased. In the large crowd, however, participants tended to avoid the more crowded exit if the doors were narrow (Experiment 2), but not if the doors were wide (Experiment 3). Participants tended to follow a 100% majority in all experiments, thereby avoiding going to an exit alone. We propose that the dynamics of exit choice can be understood in terms of competition between alternative egress routes: the attraction of an exit increases with the proportion of the crowd moving toward it, becoming dominant at 100%, but decreases with the absolute number in the crowd moving toward it, relative to the exit's affordance for egress.

Information Is Where You Find It: Perception as an Ecologically Well-Posed Problem.

Texts on visual perception typically begin with the following premise: Vision is an ill-posed problem, and perception is underdetermined by the available information. If this were really the case, however, it is hard to see how vision could ever get off the ground. James Gibson's signal contribution was his hypothesis that for every perceivable property of the environment, however subtle, there must be a higher order variable of information, however complex, that specifies it-if only we are clever enough to find them. Such variables are informative about behaviorally relevant properties within the physical and ecological constraints of a species' niche. Sensory ecology is replete with instructive examples, including weakly electric fish, the narwal's tusk, and insect flight control. In particular, I elaborate the case of passing through gaps. Optic flow is sufficient to control locomotion around obstacles and through openings. The affordances of the environment, such as gap passability, are specified by action-scaled information. Logically ill-posed problems may thus, on closer inspection, be ecologically well-posed.

Robust weighted averaging accounts for recruitment into collective motion in human crowds.

Agent-based models of 'flocking' and 'schooling' have shown that a weighted average of neighbor velocities, with weights that decay gradually with distance, yields emergent collective motion. Weighted averaging thus offers a potential mechanism of self-organization that recruits an increasing, but self-limiting, number of individuals into collective motion. Previously, we identified and modeled such a 'soft metric' neighborhood of interaction in human crowds that decays exponentially to zero at a distance of 4-5m. Here we investigate the limits of weighted averaging in humans and find that it is surprisingly robust: pedestrians align with the mean heading direction in their neighborhood, despite high levels of noise and diverging motions in the crowd, as predicted by the model. In three Virtual Reality experiments, participants were immersed in a crowd of virtual humans in a mobile head-mounted display and were instructed to walk with the crowd. By perturbing the heading (walking direction) of virtual neighbors and measuring the participant's trajectory, we probed the limits of weighted averaging. (1) In the 'Noisy Neighbors' experiment, the neighbor headings were randomized (range 0-90°) about the crowd's mean direction (±10° or ±20°, left or right); (2) in the 'Splitting Crowd' experiment, the crowd split into two groups (heading difference = 10-40°) and the proportion of the crowd in one group was varied (50-84%); (3) in the 'Coherent Subgroup' experiment, a perturbed subgroup varied in its coherence (heading SD = 0-2°) about a mean direction (±10° or ±20°) within a noisy crowd (heading range = 180°), and the proportion of the crowd in the subgroup was varied. In each scenario, the results were predicted by the weighted averaging model, and attraction strength (turning rate) increased with the participant's deviation from the mean heading direction, not with group coherence. However, the results indicate that humans ignore highly discrepant headings (45-90°). These findings reveal that weighted averaging in humans is highly robust and generates a common heading direction that acts as a positive feedback to recruit more individuals into collective motion, in a self-reinforcing cascade. Therefore, this 'soft' metric neighborhood serves as a mechanism of self-organization in human crowds.

Executing the homebound path is a major source of error in homing by path integration.

Path integration-the constant updating of position and orientation in an environment-is an important component of spatial navigation, however, its mechanisms are poorly understood. The aims of this study are (a) to test the encoding-error model of path integration, which focuses solely on encoding as a potential source of error, and (b) to develop a model of path integration that best predicts path integration errors. We tested the encoding-error model by independently measuring participants' encoding errors in distance and angle reproduction tasks, and then using those reproduction errors to predict individual participants' errors in a triangle completion task. We sampled the distribution of encoding errors using Monte Carlo methods to predict the homebound path, and then compared the predictions to observed triangle completion behavior. The correlation between predicted errors and actual errors in the triangle completion task was extremely weak, whereas an alternative model using execution error alone was sufficient to describe the observed errors. A model incorporating both encoding and execution errors best described the triangle completion errors. These results suggest that errors in executing the response may contribute more to overall errors in path integration than do encoding errors, challenging the assumption that errors reflect encoding alone. Errors in triangle completion might not arise from failing to know where you are, but from an inability to get back home. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Bumblebees perceive the spatial layout of their environment in relation to their body size and form to minimize inflight collisions.

Animals that move through complex habitats must frequently contend with obstacles in their path. Humans and other highly cognitive vertebrates avoid collisions by perceiving the relationship between the layout of their surroundings and the properties of their own body profile and action capacity. It is unknown whether insects, which have much smaller brains, possess such abilities. We used bumblebees, which vary widely in body size and regularly forage in dense vegetation, to investigate whether flying insects consider their own size when interacting with their surroundings. Bumblebees trained to fly in a tunnel were sporadically presented with an obstructing wall containing a gap that varied in width. Bees successfully flew through narrow gaps, even those that were much smaller than their wingspans, by first performing lateral scanning (side-to-side flights) to visually assess the aperture. Bees then reoriented their in-flight posture (i.e., yaw or heading angle) while passing through, minimizing their projected frontal width and mitigating collisions; in extreme cases, bees flew entirely sideways through the gap. Both the time that bees spent scanning during their approach and the extent to which they reoriented themselves to pass through the gap were determined not by the absolute size of the gap, but by the size of the gap relative to each bee's own wingspan. Our findings suggest that, similar to humans and other vertebrates, flying bumblebees perceive the affordance of their surroundings relative their body size and form to navigate safely through complex environments.

Nonverbal leadership emergence in walking groups.

The mechanisms underlying the emergence of leadership in multi-agent systems are under investigation in many areas of research where group coordination is involved. Nonverbal leadership has been mostly investigated in the case of animal groups, and only a few works address the problem in human ensembles, e.g. pedestrian walking, group dance. In this paper we study the emergence of leadership in the specific scenario of a small walking group. Our aim is to propose a rigorous mathematical methodology capable of unveiling the mechanisms of leadership emergence in a human group when leader or follower roles are not designated a priori. Two groups of participants were asked to walk together and turn or change speed at self-selected times. Data were analysed using time-dependent cross correlation to infer leader-follower interactions between each pair of group members. The results indicate that leadership emergence is due both to contextual factors, such as an individual's position in the group, and to personal factors, such as an individual's characteristic locomotor behaviour. Our approach can easily be extended to larger groups and other scenarios such as team sports and emergency evacuations.

Are avatars treated like human obstacles during aperture crossing in virtual environments?

RESEARCH OBJECTIVE: The current study set out to determine whether individuals walking in a virtual reality environment pass through apertures made of two avatars differently than apertures created by two pole obstacles, as previously observed between pole and human obstacles in real-world environments. METHODS: Eleven healthy young adults wore a head-mounted virtual reality display, walked along a 10 m path and passed through a virtual aperture located 5 m from the starting location. Participants were instructed to avoid colliding with the obstacles when passing through the aperture. The experiment was conducted in a block design, where the aperture was either created by two pole obstacles or by two avatars. In both conditions, the width of the aperture ranged between 1.0-1.8x each participant's shoulder width. RESULTS: Regardless of whether the aperture was created by the virtual poles or the avatars, participants rotated their shoulders for all aperture sizes and results found no significant differences in shoulder rotation angle, onset of rotation, walking speed or velocity at time of crossing between the two types of obstacles. Therefore, it appears that the differences in avoidance behaviours observed in real-world settings between people and pole obstacles is not translated to a virtual reality environment. SIGNIFICANCE: It is possible that during experiments in which the avatars do not move, they do not possess human-like qualities suggested to be responsible for the increased caution used when walking through real human obstacles and instead, are treated as any ordinary obstacle.

Route selection in barrier avoidance.

BACKGROUND: Fajen and Warren's steering dynamics model can reproduce human paths around an extended barrier by adding 'waypoints' at each end - if one waypoint is selected to minimize the global path curvature (Gérin-Lajoie and Warren, 2008). We propose that waypoint selection behaves like a choice between two competing goals, in which the smaller distance (d) and deviation angle (ß) is preferred (Ulrich and Borenstein, 1998). Here we manipulate these two variables to test the determinants of route selection. RESEARCH QUESTION: How does route selection in barrier avoidance depend on the local distance (d) and deviation angle (ß) of each end, and on global path length (P) and curvature (C)? METHODS: Participants (Exp1 N = 19; Exp2 N = 15) walked around a barrier to a visible goal in a virtual environment. Barrier orientation and lateral position were manipulated to vary the difference in distance (Δd) and in deviation angle (Δß) between the left and right ends of the barrier. Left/Right route data were analyzed using a mixed-effects logistic regression model, with Δß, Δd, and observed ΔP and ΔC as predictors. RESULTS: The main effects of Δß and Δd significantly predicted Rightward responses (p < .001), more strongly than ΔP and ΔC (ΔBIC = 29.5). When Δß and Δd agreed, responses were toward the smaller distance and deviation (88% overall); when they conflicted, responses were in between (65% toward smaller ß). The 75% choice threshold for Δß was ±1.65˚, and for Δd was 0.75 m, from the 50% chance level. SIGNIFICANCE: During barrier avoidance, participants select a route that minimizes the local distance (d) and deviation angle (ß) of the waypoint, rather than the global path length (P) or path curvature (C). These findings support the hypothesis that route selection is governed by competing waypoints, instead of comparing planned paths to the final goal.

Probing the invariant structure of spatial knowledge: Support for the cognitive graph hypothesis.

We tested four hypotheses about the structure of spatial knowledge used for navigation: (1) the Euclidean hypothesis, a geometrically consistent map; (2) the Neighborhood hypothesis, adjacency relations between spatial regions, based on visible boundaries; (3) the Cognitive Graph hypothesis, a network of paths between places, labeled with approximate local distances and angles; and (4) the Constancy hypothesis, whatever geometric properties are invariant during learning. In two experiments, different groups of participants learned three virtual hedge mazes, which varied specific geometric properties (Euclidean Control Maze, Elastic Maze with stretching paths, Swap Maze with alternating paths to the same place). Spatial knowledge was then tested using three navigation tasks (metric shortcuts on empty ground plane, neighborhood shortcuts with visible boundaries, route task in corridors). They yielded the following results: (a) Metric shortcuts were insensitive to detectable shifts in target location, inconsistent with the Euclidean hypothesis. (b) Neighborhood shortcuts were constrained by visible boundaries in the Elastic Maze, but not in the Swap Maze, contrary to the Neighborhood and Constancy hypotheses. (c) The route task indicated that a graph of the maze was acquired in all environments, including knowledge of local path lengths. We conclude that primary spatial knowledge is consistent with the Cognitive Graph hypothesis. Neighborhoods are derived from the graph, and local distance and angle information is not embedded in a geometrically consistent map.

Non-Euclidean navigation.

A basic set of navigation strategies supports navigational tasks ranging from homing to novel detours and shortcuts. To perform these last two tasks, it is generally thought that humans, mammals and perhaps some insects possess Euclidean cognitive maps, constructed on the basis of input from the path integration system. In this article, I review the rationale and behavioral evidence for this metric cognitive map hypothesis, and find it unpersuasive: in practice, there is little evidence for truly novel shortcuts in animals, and human performance is highly unreliable and biased by environmental features. I develop the alternative hypothesis that spatial knowledge is better characterized as a labeled graph: a network of paths between places augmented with local metric information. What distinguishes such a cognitive graph from a metric cognitive map is that this local information is not embedded in a global coordinate system, so spatial knowledge is often geometrically inconsistent. Human path integration appears to be better suited to piecewise measurements of path lengths and turn angles than to building a consistent map. In a series of experiments in immersive virtual reality, we tested human navigation in non-Euclidean environments and found that shortcuts manifest large violations of the metric postulates. The results are contrary to the Euclidean map hypothesis and support the cognitive graph hypothesis. Apparently Euclidean behavior, such as taking novel detours and approximate shortcuts, can be explained by the adaptive use of non-Euclidean strategies.

What color are emergency exit signs? Egress behavior differs from verbal report.

Illuminated emergency exit signs inform building occupants about safe egress routes in emergencies. These exit signs are often found in the presence of other colored signs, which may distract occupants when searching for safe exits. Such distractions can lead to confusing and even harmful outcomes, especially if occupants misinterpret the sign colors, mistaking non-exit signs for exit signs. We studied which colored signs people were most likely to infer were exit signs in a simulated emergency evacuation using virtual reality (VR). Participants were immersed in a virtual room with two doors (left and right), and an illuminated sign with different colored vertical bars above each door. They saw all pairwise combinations of six sign colors across trials. On each trial, a fire alarm sounded, and participants walked to the door that they thought was the exit. We tested two hypotheses: a local exposure hypothesis that color inferences are determined by exit sign colors in the local environment (i.e., red) and a semantic association hypothesis that color inferences are determined by color-concept associations (i.e. green associated with "go" and "safety"). The results challenged the local exposure hypothesis and supported the semantic association hypothesis. Participants predominantly walked toward green signs, even though the exit signs in the local environment-including the building where the experiment took place-were red. However, in a post-experiment survey, most participants reported that exit signs should be red. The results demonstrated a dissociation between the way observers thought they would behave in emergency situations (red = exit) and the way they did behave in simulated emergencies (green = exit). These findings have implications for the design of evacuation systems. Observers, and perhaps designers, do not always anticipate how occupants will behave in emergency situations, which emphasizes the importance of behavioral evaluations for egress safety.

Collective Motion in Human Crowds.

The balletic motion of bird flocks, fish schools, and human crowds is believed to emerge from local interactions between individuals, in a process of self-organization. The key to explaining such collective behavior thus lies in understanding these local interactions. After decades of theoretical modeling, experiments using virtual crowds and analysis of real crowd data are enabling us to decipher the 'rules' governing these interactions. Based on such results, we build a dynamical model of how a pedestrian aligns their motion with that of a neighbor, and how these binary interactions are combined within a neighborhood in a crowd. Computer simulations of the model generate coherent motion at the global level and reproduce individual trajectories at the local level. This approach yields the first experiment-driven, bottom-up model of collective motion, providing a basis for understanding more complex patterns of crowd behavior in both everyday and emergency situations.

Local interactions underlying collective motion in human crowds.

It is commonly believed that global patterns of motion in flocks, schools and crowds emerge from local interactions between individuals, through a process of self-organization. The key to explaining such collective behaviour thus lies in deciphering these local interactions. We take an experiment-driven approach to modelling collective motion in human crowds. Previously, we observed that a pedestrian aligns their velocity vector (speed and heading direction) with that of a neighbour. Here we investigate the neighbourhood of interaction in a crowd: which neighbours influence a pedestrian's behaviour, how this depends on neighbour position, and how the influences of multiple neighbours are combined. In three experiments, a participant walked in a virtual crowd whose speed and heading were manipulated. We find that neighbour influence is linearly combined and decreases with distance, but not with lateral position (eccentricity). We model the neighbourhood as (i) a circularly symmetric region with (ii) a weighted average of neighbours, (iii) a uni-directional influence, and (iv) weights that decay exponentially to zero by 5 m. The model reproduces the experimental data and predicts individual trajectories in observational data on a human 'swarm'. The results yield the first bottom-up model of collective crowd motion.