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.

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.

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.

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.

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.

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.

Non-optimal perceptual decision in human navigation.

We highlight that optimal cue combination does not represent a general principle of cue interaction during navigation, extending Rahnev & Denison's (R&D) summary of nonoptimal perceptual decisions to the navigation domain. However, we argue that the term "suboptimality" does not capture the way visual and nonvisual cues interact in navigational decisions.

Rotational error in path integration: encoding and execution errors in angle reproduction.

Path integration is fundamental to human navigation. When a navigator leaves home on a complex outbound path, they are able to keep track of their approximate position and orientation and return to their starting location on a direct homebound path. However, there are several sources of error during path integration. Previous research has focused almost exclusively on encoding error-the error in registering the outbound path in memory. Here, we also consider execution error-the error in the response, such as turning and walking a homebound trajectory. In two experiments conducted in ambulatory virtual environments, we examined the contribution of execution error to the rotational component of path integration using angle reproduction tasks. In the reproduction tasks, participants rotated once and then rotated again to face the original direction, either reproducing the initial turn or turning through the supplementary angle. One outstanding difficulty in disentangling encoding and execution error during a typical angle reproduction task is that as the encoding angle increases, so does the required response angle. In Experiment 1, we dissociated these two variables by asking participants to report each encoding angle using two different responses: by turning to walk on a path parallel to the initial facing direction in the same (reproduction) or opposite (supplementary angle) direction. In Experiment 2, participants reported the encoding angle by turning both rightward and leftward onto a path parallel to the initial facing direction, over a larger range of angles. The results suggest that execution error, not encoding error, is the predominant source of error in angular path integration. These findings also imply that the path integrator uses an intrinsic (action-scaled) rather than an extrinsic (objective) metric.

Durability of Silicone Airway Stents in the Management of Benign Central Airway Obstruction.

PURPOSE: The literature is devoid of a comprehensive analysis of silicone airway stenting for benign central airway obstruction (BCAO). With the largest series in the literature to date, we aim to demonstrate the safety profile, pattern of re-intervention, and duration of silicone airway stents. METHODS: An institutional database was used to identify patients with BCAO who underwent rigid bronchoscopy with dilation and silicone stent placement between 2002 and 2015 at Rush University Medical Center. RESULTS: During the study period, 243 stents were utilized in 63 patients with BCAO. Pure tracheal stenosis was encountered in 71% (45/63), pure tracheomalacia in 11% (7/63), and a hybrid of both in 17% (11/63). Median freedom from re-intervention was 104 (IQR 167) days. Most common indications for re-intervention include mucus accumulation (60%; 131/220), migration (28%; 62/220), and intubation (8%; 18/220). The most common diameters of stent placed were 12 mm (94/220) and 14 mm (96/220). The most common lengths utilized were 30 mm (60/220) and 40 mm (77/220). Duration was not effected by stent size when placed for discrete stenosis. However, 14 mm stents outperformed 12 mm when tracheomalacia was present (157 vs. 37 days; p = 0.005). Patients with a hybrid stenosis fared better when longer stents were used (60 mm stents outlasted 40 mm stents 173 vs. 56 days; p = 0.05). CONCLUSION: Rigid bronchoscopy with silicone airway stenting is a safe and effective option for the management of benign central airway obstruction. Our results highlight several strategies to improve stent duration.

Intercepting a moving target: On-line or model-based control?

When walking to intercept a moving target, people take an interception path that appears to anticipate the target's trajectory. According to the constant bearing strategy, the observer holds the bearing direction of the target constant based on current visual information, consistent with on-line control. Alternatively, the interception path might be based on an internal model of the target's motion, known as model-based control. To investigate these two accounts, participants walked to intercept a moving target in a virtual environment. We degraded the target's visibility by blurring the target to varying degrees in the midst of a trial, in order to influence its perceived speed and position. Reduced levels of visibility progressively impaired interception accuracy and precision; total occlusion impaired performance most and yielded nonadaptive heading adjustments. Thus, performance strongly depended on current visual information and deteriorated qualitatively when it was withdrawn. The results imply that locomotor interception is normally guided by current information rather than an internal model of target motion, consistent with on-line control.

Number of Ribs Resected is Associated with Respiratory Complications Following Lobectomy with en bloc Chest Wall Resection.

PURPOSE: Pulmonary lobectomy with en bloc chest wall resection is a common strategy for treating lung cancers invading the chest wall. We hypothesized a direct relationship exists between number of ribs resected and postoperative respiratory complications. METHODS: An institutional database was queried for patients with non-small cell lung cancer that underwent lobectomy with en bloc chest wall resection between 2003 and 2014. Propensity matching was used to identify a cohort of patients who underwent lobectomy via thoracotomy without chest wall resection. Patients were propensity matched on age, gender, smoking history, FEV1, and DLCO. The relationship between number of ribs resected and postoperative respiratory complications (bronchoscopy, re-intubation, pneumonia, or tracheostomy) was examined. RESULTS: Sixty-eight patients (34 chest wall resections; 34 without chest wall resection) were divided into 3 cohorts: cohort A = 0 ribs resected (n = 34), cohort B = 1-3 ribs resected (n = 24), and cohort C = 4-6 ribs resected (n = 10). Patient demographics were similar between cohorts. The 90-day mortality rate was 2.9 % (2/68) and did not vary between cohorts. On multivariate analysis, having 1-3 ribs resected (OR 19.29, 95 % CI (1.33, 280.72); p = 0.03), 4-6 ribs resected [OR 26.66, (1.48, 481.86); p = 0.03), and a lower DLCO (OR 0.91, (0.84, 0.99); p = 0.02) were associated with postoperative respiratory complications. CONCLUSIONS: In patients undergoing lobectomy with en bloc chest wall resection for non-small cell lung cancer, the number of ribs resected is directly associated with incidence of postoperative respiratory complications.

How you get there from here: interaction of visual landmarks and path integration in human navigation.

How do people combine their sense of direction with their use of visual landmarks during navigation? Cue-integration theory predicts that such cues will be optimally integrated to reduce variability, whereas cue-competition theory predicts that one cue will dominate the response direction. We tested these theories by measuring both accuracy and variability in a homing task while manipulating information about path integration and visual landmarks. We found that the two cues were near-optimally integrated to reduce variability, even when landmarks were shifted up to 90°. Yet the homing direction was dominated by a single cue, which switched from landmarks to path integration when landmark shifts were greater than 90°. These findings suggest that cue integration and cue competition govern different aspects of the homing response: Cues are integrated to reduce response variability but compete to determine the response direction. The results are remarkably similar to data on animal navigation, which implies that visual landmarks reset the orientation, but not the precision, of the path-integration system.

Follow the leader: visual control of speed in pedestrian following.

When people walk together in groups or crowds they must coordinate their walking speed and direction with their neighbors. This paper investigates how a pedestrian visually controls speed when following a leader on a straight path (one-dimensional following). To model the behavioral dynamics of following, participants in Experiment 1 walked behind a confederate who randomly increased or decreased his walking speed. The data were used to test six models of speed control that used the leader's speed, distance, or combinations of both to regulate the follower's acceleration. To test the optical information used to control speed, participants in Experiment 2 walked behind a virtual moving pole, whose visual angle and binocular disparity were independently manipulated. The results indicate the followers match the speed of the leader, and do so using a visual control law that primarily nulls the leader's optical expansion (change in visual angle), with little influence of change in disparity. This finding has direct applications to understanding the coordination among neighbors in human crowds.

A potential mechanism for Gibsonian resonance: behavioral entrainment emerges from local homeostasis in an unsupervised reservoir network.

While the cognitivist school of thought holds that the mind is analogous to a computer, performing logical operations over internal representations, the tradition of ecological psychology contends that organisms can directly "resonate" to information for action and perception without the need for a representational intermediary. The concept of resonance has played an important role in ecological psychology, but it remains a metaphor. Supplying a mechanistic account of resonance requires a non-representational account of central nervous system (CNS) dynamics. Towards this, we present a series of simple models in which a reservoir network with homeostatic nodes is used to control a simple agent embedded in an environment. This network spontaneously produces behaviors that are adaptive in each context, including (1) visually tracking a moving object, (2) substantially above-chance performance in the arcade game Pong, (2) and avoiding walls while controlling a mobile agent. Upon analyzing the dynamics of the networks, we find that behavioral stability can be maintained without the formation of stable or recurring patterns of network activity that could be identified as neural representations. These results may represent a useful step towards a mechanistic grounding of resonance and a view of the CNS that is compatible with ecological psychology.

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.

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.

Do walkers follow their heads? Investigating the role of head rotation in locomotor control.

Eye and head rotations are normally correlated with changes in walking direction; however, it is unknown whether they play a causal role in the control of steering. The objective of the present study was to answer two questions about the role of head rotations in steering control when walking to a goal. First, are head rotations sufficient to elicit a change in walking direction? Second, are head rotations necessary to initiate a change in walking direction or guide steering to a goal? To answer these questions, participants either walked toward a goal located 7 m away or were cued to steer to the left or right by 37°. On a subset of trials, participants were either cued to voluntarily turn their heads to the left or right, or they underwent an involuntary head perturbation via a head-mounted air jet. The results showed that large voluntary head turns (35°) yielded slight path deviations (1°-2°) in the same or opposite direction as the head turn, depending on conditions, which have alternative explanations. Involuntary head rotations did not elicit path deviations despite comparable head rotation magnitudes. In addition, the walking trajectory when turning toward an eccentric goal was the same regardless of head orientation. Steering can thus be decoupled from head rotation during walking. We conclude that head rotations are neither a sufficient nor a necessary component of steering control, because they do not induce a turn and they are not required to initiate a turn or to guide the locomotor trajectory to a goal.