Models Of Collective Behavior Research Articles

Spatio-temporal correlations in models of collective motion ruled by different dynamical laws

Information transfer is an essential factor in determining the robustness of biological systems with distributed control. The most direct way to study the mechanisms ruling information transfer is to experimentally observe the propagation across the system of a signal triggered by some perturbation. However, this method may be inefficient for experiments in the field, as the possibilities to perturb the system are limited and empirical observations must rely on natural events. An alternative approach is to use spatio-temporal correlations to probe the information transfer mechanism directly from the spontaneous fluctuations of the system, without the need to have an actual propagating signal on record. Here we test this method on models of collective behaviour in their deeply ordered phase by using ground truth data provided by numerical simulations in three dimensions. We compare two models characterized by very different dynamical equations and information transfer mechanisms: the classic Vicsek model, describing an overdamped noninertial dynamics and the inertial spin model, characterized by an underdamped inertial dynamics. By using dynamic finite-size scaling, we show that spatio-temporal correlations are able to distinguish unambiguously the diffusive information transfer mechanism of the Vicsek model from the linear mechanism of the inertial spin model.

Self-organized hydrodynamics with density-dependent velocity

Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is \begin{document} $(ρ v(ρ))'≥q 0$ \end{document} , i.e. a nondecreasing mass flux \begin{document} $ρ v(ρ)$ \end{document} with respect to the density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.

Influencing Busy People in a Social Network.

We identify influential early adopters in a social network, where individuals are resource constrained, to maximize the spread of multiple, costly behaviors. A solution to this problem is especially important for viral marketing. The problem of maximizing influence in a social network is challenging since it is computationally intractable. We make three contributions. First, we propose a new model of collective behavior that incorporates individual intent, knowledge of neighbors actions and resource constraints. Second, we show that the multiple behavior influence maximization is NP-hard. Furthermore, we show that the problem is submodular, implying the existence of a greedy solution that approximates the optimal solution to within a constant. However, since the greedy algorithm is expensive for large networks, we propose efficient heuristics to identify the influential individuals, including heuristics to assign behaviors to the different early adopters. We test our approach on synthetic and real-world topologies with excellent results. We evaluate the effectiveness under three metrics: unique number of participants, total number of active behaviors and network resource utilization. Our heuristics produce 15-51% increase in expected resource utilization over the naïve approach.

On effective temperature in network models of collective behavior.

Collective behavior of self-propelled units is studied analytically within the Vectorial Network Model (VNM), a mean-field approximation of the well-known Vicsek model. We propose a dynamical systems framework to study the stochastic dynamics of the VNM in the presence of general additive noise. We establish that a single parameter, which is a linear function of the circular mean of the noise, controls the macroscopic phase of the system-ordered or disordered. By establishing a fluctuation-dissipation relation, we posit that this parameter can be regarded as an effective temperature of collective behavior. The exact critical temperature is obtained analytically for systems with small connectivity, equivalent to low-density ensembles of self-propelled units. Numerical simulations are conducted to demonstrate the applicability of this new notion of effective temperature to the Vicsek model. The identification of an effective temperature of collective behavior is an important step toward understanding order-disorder phase transitions, informing consistent coarse-graining techniques and explaining the physics underlying the emergence of collective phenomena.

Resilience, tipping, and hydra effects in public health: emergent collective behavior in two agent-based models.

BackgroundCollective health behavior often demonstrates counter-intuitive dynamics, sometimes resisting interventions designed to produce change, or even producing effects that are in the opposite direction than intended by the intervention, e.g. lowering infectivity resulting in increased infections. At other times collective health behavior exhibits sudden large-scale change in response to small interventions or change in the environment, a phenomenon often called “tipping.” I hypothesize that these seemingly very different phenomena can all be explained by the same dynamic, a type of collective resilience.MethodsI compared two simple agent-based models of interactions in networks: a public health behavior game, in which individuals decide whether or not to adopt protective behavior, and a microbial-level game, in which three different strains of bacteria attack each other. I examined the type of networks and other conditions that support a dynamic balance, and determined what changes of conditions will tip the balance.ResultsBoth models show lasting dynamic equilibrium and resilience, resulting from negative feedback that supports oscillating coexistence of diversity under a range of conditions. In the public health game, health protection is followed by free-riding defectors, followed by a rise in infection, in long-lasting cycles. In the microbial game, each of three strains takes turns dominating. In both games, the dynamic balance is tipped by lowering the level of local clustering, changing the level of benefit, or lowering infectivity or attack rate. Lowering infectivity has the surprising effect of increasing the numbers of infected individuals. We see parallel results in the microbial game of three bacterial strains, where lowering one strain’s attack rate (analogous to lowering infectivity) increases the numbers of the restrained attacker, a phenomenon captured by the phrase, “the enemy of my enemy is my friend.”ConclusionsCollective behavior often shows a dynamic balance, resulting from negative feedback, supporting diversity and resisting change. Above certain threshold conditions, the dynamic balance is tipped towards uniformity of behavior. Under a certain range of conditions we see “hydra effects” in which interventions to lower attack rate or infectivity are self-defeating. Simple models of collective behavior can explain these seemingly disparate dynamics.Electronic supplementary materialThe online version of this article (doi:10.1186/s12889-016-2938-8) contains supplementary material, which is available to authorized users.

Micro- and macromodels of social networks. I. Theory fundamentals

We consider two approaches to the design and analysis of social networks, namely, macro- and microdescriptions. According to the former approach, the structure of relations in a social network is averaged, and agents' behavior is studied "in the mean." The latter approach takes into account the structural features of the influence graph of agents and their individual decision-making principles. The first and second approaches are compared using the threshold model of collective behavior with a common relative threshold.

Phase Transitions in a Kinetic Flocking Model of Cucker--Smale Type

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered" to an "ordered" state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition.

A Cucker--Smale Model with Noise and Delay

A generalization of the Cucker-Smale model for collective animal behaviour is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modelling: (i) stochasticity (imperfections) of individual behaviour; and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker-Smale model are derived by using a suitable Lyapunov functional. As a byproduct, a new result regarding the asymptotic behaviour of delayed geometric Brownian motion is obtained. In the second part of the paper results of systematic numerical simulations are presented. They not only illustrate the analytical results, but hint at a somehow surprising behaviour of the system - namely, that an introduction of intermediate time delay may facilitate flocking.

Collective Action in Networks: Evidence from the Chilean Student Movement

Hundreds of thousands of students skipped school during the 2011 student movement in Chile to protest and reform educational institutions. Using administrative data on millions of students’ daily school attendance decisions on protest and non-protest days, a large network composed by the lifetime history of classmates, and differential network exposure to the first national protest, this paper tests how networks affect protest behavior. The main finding is that individual participation follows a threshold model of collective behavior: students were influenced by their networks to skip school on protest days only when more than 40 percent of the members of their networks also skipped school. Additional findings show that protest participation imposed significant educational costs on students and helped to shift votes towards non-traditional opposition parties. Taken together, results indicate that networks amplify the effect of protests in non-linear ways with potentially significant consequences for institutional change.

How quantum entanglement in DNA synchronizes double-strand breakage by type II restriction endonucleases

Macroscopic quantum effects in living systems have been studied widely in pursuit of fundamental explanations for biological energy transport and sensing. While it is known that type II endonucleases, the largest class of restriction enzymes, induce DNA double-strand breaks by attacking phosphodiester bonds, the mechanism by which simultaneous cutting is coordinated between the catalytic centers remains unclear. We propose a quantum mechanical model for collective electronic behavior in the DNA helix, where dipole–dipole oscillations are quantized through boundary conditions imposed by the enzyme. Zero-point modes of coherent oscillations would provide the energy required for double-strand breakage. Such quanta may be preserved in the presence of thermal noise by the enzyme׳s displacement of water surrounding the DNA recognition sequence. The enzyme thus serves as a decoherence shield. Palindromic mirror symmetry of the enzyme–DNA complex should conserve parity, because symmetric bond-breaking ceases when the symmetry of the complex is violated or when physiological parameters are perturbed from optima. Persistent correlations in DNA across longer spatial separations—a possible signature of quantum entanglement—may be explained by such a mechanism.

Social density processes regulate the functioning and performance of foraging human teams.

Social density processes impact the activity and order of collective behaviours in a variety of biological systems. Much effort has been devoted to understanding how density of people affects collective human motion in the context of pedestrian flows. However, there is a distinct lack of empirical data investigating the effects of social density on human behaviour in cooperative contexts. Here, we examine the functioning and performance of human teams in a central-place foraging arena using high-resolution GPS data. We show that team functioning (level of coordination) is greatest at intermediate social densities, but contrary to our expectations, increased coordination at intermediate densities did not translate into improved collective foraging performance, and foraging accuracy was equivalent across our density treatments. We suggest that this is likely a consequence of foragers relying upon visual channels (local information) to achieve coordination but relying upon auditory channels (global information) to maximise foraging returns. These findings provide new insights for the development of more sophisticated models of human collective behaviour that consider different networks for communication (e.g. visual and vocal) that have the potential to operate simultaneously in cooperative contexts.

Computational Models of Social Influence and Collective Behavior

This chapter provides an overview of computational modeling of conformity, group deliberation, and social diffusion processes, with an emphasis on social psychological perspectives rather than the kinds of structural and institutional issues modeled in political science and sociology. The chapter attempts to illustrate the benefits of building maps of "parameter space" as a way to generalize across single studies and to develop out-of-sample new predictions.

Intrinsic fluctuations and driven response of insect swarms.

Animals of all sizes form groups, as acting together can convey advantages over acting alone; thus, collective animal behavior has been identified as a promising template for designing engineered systems. However, models and observations have focused predominantly on characterizing the overall group morphology, and often focus on highly ordered groups such as bird flocks. We instead study a disorganized aggregation (an insect mating swarm), and compare its natural fluctuations with the group-level response to an external stimulus. We quantify the swarm's frequency-dependent linear response and its spectrum of intrinsic fluctuations, and show that the ratio of these two quantities has a simple scaling with frequency. Our results provide a new way of comparing models of collective behavior with experimental data.

Behavioral dynamics of visually-guided heading alignment in pedestrian following

The collective behavior of human crowds is thought to emerge from the local interactions between individual pedestrians, such as the coordination of walking speed and direction (heading). This coordination is guided by visual information about the motion of one’s neighbors. A critical interaction assumed by many models of collective behavior is the alignment of heading with neighbors. Using a behavioral dynamics framework, we simulated experimental data on pairs of pedestrians to formulate a dynamical model of heading alignment. On each trial, a “follower” either walked behind or beside a “leader” for 20m, while the leader made two unpredictable turns. The initial distance and position, turn sequence, magnitude, and timing varied. Head trajectories were recorded with a 16-camera motion capture system. Results show that the follower’s heading direction was closely coordinated with that of the leader (mean cross-correlation r = 0.92, mean delay between pedestrians = 984 ms for behind; r = 0.93, delay = 219 ms for side-by-side). We tested four models against this data to characterize the follower’s change in heading during alignment, using a least-squares criterion. In the simplest model, the follower's angular acceleration is proportional to the sine of the heading difference (mean r = 0.72, gain k = 0.81 for behind; r = 0.70, k = 0.69 for side-by-side); additional terms did not improve fit. An alternative model that incorporates the mean time delays yielded similar gains (mean r = 0.71, k = 1.17 for behind; r = 0.71, k = 1.21 for side-by-side), thus generalizing across different leader-follower positions. The results show heading alignment is controlled by nulling the difference in heading with a neighbor. This provides a cognitively-grounded model of heading alignment that may be generalized to larger-scale crowd dynamics. We are currently investigating the optical variables that control these interactions. Meeting abstract presented at VSS 2015

Anisotropic interactions in a first-order aggregation model

We extend a well studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modelled by limited sensorial perception of individuals, that depends on their current direction of motion. Consequently, the first-order model becomes implicit, and new analytical issues, such as non-uniqueness and jump discontinuities in velocities, are raised. We study the well-posedness of the anisotropic model and discuss its modes of breakdown. To extend solutions beyond breakdown we propose a relaxation system containing a small parameter ε, which can be interpreted as a small amount of inertia or response time. We show that the limit ε → 0 can be used as a jump criterion to select the physically correct velocities. In smooth regimes, the convergence of the relaxation system as ε → 0 is guaranteed by a theorem due to Tikhonov. We illustrate the results with numerical simulations in two dimensions.

A Measurement Method for Speed Distribution of Collective Motion with Optical Flow and Its Applications to School of Fish

We propose a measurement method for the mean speed distribution of collective motions of highly dense groups with optical flow based on our previous work. This measurement is fundamental for ecological investigations and mathematical modeling of collective animal behaviors. Our method is applicable to highly dense homogeneous groups wherein individual movements are approximately uniform locally. To measure speed distributions, we partition a group into regions and estimate mean speeds in each region by extracting only flows that are relevant to collective motions and averaging them over a period of time. We apply our method to schools of sardines to measure a kind of speed distribution called rotation curve (RC). As experiments, we first performed simulations and found that our method can estimate flows and RCs accurately. We then performed experiments with videos of real fish. The RCs estimated by our method and ones by manual tracking were approximately equal. We applied our method to a longer video and confirmed that time series of RCs can be estimated automatically. In addition, we detected noticeable events by two features derived from flows. We also applied our method to a school of anchovies. The results indicate that our method is practically useful.

Abolitionists and the Eloquence of Abuse: Revisiting Status and Rhetoric in Social Movements

Current discussions of contentious performances profitably draw upon a revival of theories of culture, emotion, and performance. Yet status theory and status claims-making continue to be neglected in the mix because of their received associations with classical tension theory and unpopular functionalist models of collective behavior. Because most social movement participants are outsiders to the ‘halls of power,’ their dependence upon the rhetoric of status in cultivating moral influence is much more fundamental than previously acknowledged, although this relation is hinted at in Tilly's notion of contentious performances. Efforts to recover status theory navigate between two major mistakes in past theories of collective behavior: the voluntaristic overemphasis of affective manipulation by charismatic leaders, and the deterministic conflation of status with large reified social structures. The concept of reception fields is proposed to refer to the relational, fluid, social–psychological status dynamics between movement leaders and audiences during contentious performances, in which distinction and rhetoric are mutually constitutive. The article situates eloquence or the emotional energy of protest rhetoric in the dramaturgical performance of status dynamics within the immediate reception field. The utility of this approach to status rhetoric is illustrated with respect to American antislavery abolitionism.

Low frequency scattering from dynamic fish schools based on collective animal behavior modeling

Low frequency acoustic scattering from swim bladder fish is dominated by the monopole resonance response of the bladder. A school scattering model has previously been developed [Feuillade et al., J. Acoust. Soc. Am., 99 (1), 196-208 (1996)] to predict levels of scattering from schools of bladder fish, which includes multiple scattering effects among the fish, and coherent summation of their radiated fields. In order to incorporate these acoustic interactions, the relative locations of the individual fish within the school are required as an input. To provide a realistic description of fluctuating levels of scattering from schools, a self organizing model of group formation in three dimensional space has been developed, based on biological principles of collective animal behavior [Couzin et al., J. Theor. Biol. (2002) 218, 1-11]. In this model, organization within the school is a function of alignment, and repulsive and attractive tendencies based upon the position and orientation of the individual fish. The results of using this model to simulate the fish behavior demonstrate the spatial and temporal dynamics of the fish school, and indicate how these influence the statistical variability of the acoustic scattering response as a function of frequency. (Work supported by ONR Grant N00014-11-1-0161)

Understanding Dynamic Social Grouping Behaviors of Pedestrians

There have been many studies in the literature on social group recognition of crowds of pedestrians. However, most of these studies have approached the problem from a static point of view. A study on the dynamic property of social groups among people over time can provide significant insight into human behaviors and events. Inspired by sociological models of human collective behavior, in this work, we present a framework for characterizing hierarchical social groups based on evolving tracklet interaction network (ETIN) where the tracklets of pedestrians are represented as nodes and the their grouping behaviors are captured by the edges with associated weights. We use non-overlapping snapshots of the interaction network and develop the framework for a unified dynamic group identification and tracklet association. The approach is evaluated quantitatively and qualitatively on videos of pedestrian scenes where manually labeled ground-truth is given. The results of our approach are consistent to human-perceived dynamic social groups of the crowd. The performance analysis of our method shows that the approach is scalable and it provides situational awareness in a real-world scenarios.

Cell density and cell size dynamics during in vitro tissue growth experiments: Implications for mathematical models of collective cell behaviour

We present a detailed experimental data set describing a tissue growth experiment where a population of cells is initially distributed uniformly, at low density, on a two-dimensional substrate, and grows to eventually form a confluent monolayer. Using image processing tools, we provide precise information about temporal changes in the number of cells, the location of cells and the total area occupied by cells. This information shows that the increase in area occupied by the cell population is affected by both the increase in cell number as well as an increase in the average size of the cells. We show that standard approaches to interpret such experiments, where the cell size is typically treated as a constant, can lead to errors. Furthermore we show that a standard, discrete, random walk model of biological cell motility and cell proliferation should not be used to represent our experimental data set since this standard model treats all cells as having a constant size that does not change with time. Instead, we introduce a generalization of the standard model which allows agents in the random walk model to move, proliferate and grow in size, and we show that the data produced by this more general model is consistent with our experimental data set.