On the mathematics of emergence

@article{Cucker2007OnTM,
  title={On the mathematics of emergence},
  author={Felipe Cucker and Stephen Smale},
  journal={Japanese Journal of Mathematics},
  year={2007},
  volume={2},
  pages={197-227}
}
Abstract.We describe a setting where convergence to consensus in a population of autonomous agents can be formally addressed and prove some general results establishing conditions under which such convergence occurs. Both continuous and discrete time are considered and a number of particular examples, notably the way in which a population of animals move together, are considered as particular instances of our setting. 
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References

SHOWING 1-10 OF 21 REFERENCES
Modeling Language Evolution
TLDR
This work describes a model for the evolution of the languages used by the agents of a society and proves convergence of these languages to a common one under certain conditions.
Emergent Behavior in Flocks
TLDR
The main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/ 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only.
Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms
TLDR
A model for asynchronous distributed computation is presented and it is shown that natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms retain the desirable convergence properties of their centralized counterparts.
Coordination of groups of mobile autonomous agents using nearest neighbor rules
TLDR
A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Stable flocking of mobile agents part I: dynamic topology
This is the second of a two-part paper, investigating the stability properties of a system of multiple mobile agents with double integrator dynamics. In this second part, we allow the topology of the
Stable flocking of mobile agents, part I: fixed topology
TLDR
This first part generates stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction.
Multi-Vehicle Flocking: Scalability of Cooperative Control Algorithms using Pairwise Potentials
TLDR
Cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles, show critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.
A Nonlocal Continuum Model for Biological Aggregation
TLDR
A continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal is constructed, and energy arguments are used to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit.
Self-organization and selection in the emergence of vocabulary
TLDR
The combination of self-organization and cultural selection provides a plausible explanation for cultural evolution, which progresses with high transmission rate and is observed that as the vocabulary tends to convergence there is a uniform tendency to exhibit a sharp phase transition.
...
1
2
3
...