Collective Behavior with Endogenous Thresholds

We endogenize the threshold points in Granovetter’s threshold model of collective behavior (Granovetter 1978). We do this in a simple model that combines strategic complementarity and private information in a dynamic setup with endogenous order of moves. Looking at Granovetter’s model in the strategic context allows us to highlight the sensitivity of collective outcomes to the timing of the games and the reversibility of the actions, and to emphasize an extra incentive for people to follow other people: to encourage more people to follow them

Collective behavior of El Farol attendees

Arthur’s paradigm of the El Farol bar for modeling bounded rationality and inductive behavior is undertaken. The memory horizon available to the agents and the selection criteria they utilize for the prediction algorithm are the two essential variables identified to represent the heterogeneity of agent strategies. The latter is enriched by including various rewarding schemes during decision making. Though the external input of comfort level is not explicitly coded in the algorithm pool, it contributes to each agent’s decision process. Playing with the essential variables, one can maneuver the overall outcome between the comfort level and the endogenously identified limiting state. The distribution of algorithm clusters significantly varies for shorter agent memories. This in turn affects the long-term aggregated dynamics of attendances. We observe that a transition occurs in the attendance distribution at the critical memory horizon where the correlations of the attendance deviations take longer time to decay to zero. A larger part of the crowd becomes more comfortable while the rest of the bar-goers still feel the congestion for long memories. Agents’ confidence on their algorithms and the delayed feedback of attendance data increase the overall collectivity of the system behavior

Collective behavior of El Farol attendees

Arthur’s paradigm of the El Farol bar for modeling bounded rationality and inductive behavior is undertaken. The memory horizon available to the agents and the selection criteria they utilize for the prediction algorithm are the two essential variables identified to represent the heterogeneity of agent strategies. The latter is enriched by including various rewarding schemes during decision making. Though the external input of comfort level is not explicitly coded in the algorithm pool, it contributes to each agent’s decision process. Playing with the essential variables, one can maneuver the overall outcome between the comfort level and the endogenously identified limiting state. The distribution of algorithm clusters significantly varies for shorter agent memories. This in turn affects the long-term aggregated dynamics of attendances. We observe that a transition occurs in the attendance distribution at the critical memory horizon where the correlations of the attendance deviations take longer time to decay to zero. A larger part of the crowd becomes more comfortable while the rest of the bar-goers still feel the congestion for long memories. Agents’ confidence on their algorithms and the delayed feedback of attendance data increase the overall collectivity of the system behavior

Collective behavior of light in vacuum

Under the action of light-by-light scattering, light beams show collective behaviors in vacuum. For instance, in the case of two counterpropagating laser beams with specific initial helicity, the polarization of each beam oscillates periodically between the left and right helicity. Furthermore, the amplitudes and the corresponding intensities of each polarization propagate like waves. Such polarization waves might be observationally accessible in future laser experiments, in a physical regime complementary to those explored by particle accelerators.Comment: Version published in Phys. Rev. A. arXiv admin note: text overlap with arXiv:1710.0333

Collective behavior of heterogeneous neural networks

We investigate a network of integrate-and-fire neurons characterized by a distribution of spiking frequencies. Upon increasing the coupling strength, the model exhibits a transition from an asynchronous regime to a nontrivial collective behavior. At variance with the Kuramoto model, (i) the macroscopic dynamics is irregular even in the thermodynamic limit, and (ii) the microscopic (single-neuron) evolution is linearly stable.Comment: 4 pages, 5 figure

Collective behavior of oscillating electric dipoles

The present work reports about the dynamics of a collection of randomly distributed, and randomly oriented, oscillators in 3D space, coupled by an interaction potential falling as $1/r^3$, where r stands for the inter-particle distance. This model schematically represents a collection of identical biomolecules, coherently vibrating at some common frequency, coupled with a $1/r^3$ potential stemming from the electrodynamic interaction between oscillating dipoles. The oscillating dipole moment of each molecule being a direct consequence of its coherent (collective) vibration. By changing the average distance among the molecules, neat and substantial changes in the power spectrum of the time variation of a collective observable are found. As the average intermolecular distance can be varied by changing the concentration of the solvated molecules, and as the collective variable investigated is proportional to the projection of the total dipole moment of the model biomolecules on a coordinate plane, we have found a prospective experimental strategy of spectroscopic kind to check whether the mentioned intermolecular electrodynamic interactions can be strong enough to be detectable, and thus to be of possible relevance to biology.Comment: 20 pages, 4 figure

Evolving collective behavior in an artificial ecology

Collective behavior refers to coordinated group motion, common to many animals. The dynamics of a group can be seen as a distributed model, each “animal” applying the same rule set. This study investigates the use of evolved sensory controllers to produce schooling behavior. A set of artificial creatures “live” in an artificial world with hazards and food. Each creature has a simple artificial neural network brain that controls movement in different situations. A chromosome encodes the network structure and weights, which may be combined using artificial evolution with another chromosome, if a creature should choose to mate. Prey and predators coevolve without an explicit fitness function for schooling to produce sophisticated, nondeterministic, behavior. The work highlights the role of species’ physiology in understanding behavior and the role of the environment in encouraging the development of sensory systems