Let G be a connected complex reductive group acting on a smooth algebraic variety X. Then the cotangent bundle T ∗ X on X carries a canonical symplectic structure, and the G-action induces a moment map Φ : T ∗ X → g . Consider the Hamiltonian vector fields attached to functions of the form f ◦ Φ with f ∈ C[g]. In this paper we study the asymptotic behavior of the associated flow (a so-called in...

This is an introduction to the special issue titled “Collective behavior and evolutionary games” that is in the making at Chaos, Solitons & Fractals. The term collective behavior covers many different phenomena in nature and society. From bird flocks and fish swarms to social movements and herding effects [1–5], it is the lack of a central planner that makes the spontaneous emergence of sometim...

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. Numerical simulations of large systems indicate that, at variance with the Kuramoto model, (i) the macroscopic dynamics stays irregular and (ii) the m...

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-neuro...

With the rapid expansion of the Internet and WWW, the problem of analyzing social media data has received an increasing amount of attention in the past decade. The boom in social media platforms offers many possibilities to study human collective behavior and interactions on an unprecedented scale. In the past, much work has been done on the problem of learning from networked data with homogene...

Collective behavior emerging out of self-organization is one of the most striking properties of an animal group. Typically, it is hypothesized that each individual in an animal group tends to align its direction of motion with those of its neighbors. Most previous models for collective behavior assume an explicit alignment rule, by which an agent matches its velocity with that of neighbors in a...

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agent...

Swarm robotics is a new approach to the coordination of multirobot systems which consist of a number of simple physical robots [1]. It is supposed that a desired collective behavior emerges from the interaction between the robots and the interaction of robots with the environment. This approach emerged in the field of artificial swarm intelligence as well as the biological study of insects, ant...

This paper utilizes survey data on labor union coverage at the firm level to examine union-nonunion differences in investment activity among 706 U.S. companies during the 1970s. Consistent with a model of union rent seeking, firm-level collective bargaining is associated with significantly lower physical capital and R&D investment, even following extensive control for firm and industry characte...

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 ...