Collective Behaviour

Participants

Cédric Sueur
Paul Bourgine
Stella Marc-Zwecker
Nicolas Rivier
Hervé Wozniak
Pierre Collet Computer Science, Stochastic Optimization

Keywords

interactions, self-organization, coherence, stability, dynamics, microlevel, mesolevels, macrolevel, graphs, hypergraphs, networks, hypernetworks, parcimony principle

Introduction

From molecules to galaxies, we observe some entities (atom, cell, individual or star) that interact together by attraction and/or repulsion and from these local interactions emerge a global structure, organised and complex, having its own characteristics and displaying mesolevels of organization.

According to the different forces impacting the interactions between entities, the global structure/system can be more or less cohesive (spatial) and/or stable (temporal). Coherence is defined as the correlation within and between different dimensions (and at different spatio-temporal scales).

The different systems can also be connected together by some entities, at the micro and/or at the mesolevel. These entities allows some exchanges between the different systems (matter between galaxies, information or genes between groups). These exchanges of genes or new matters (new atoms) give new properties to one or both of the systems.

Interactions between the different systems and the methodologies measuring them bring about several issues, such as how to define these systems as specific entities (animal group, galaxy, etc.). Some entities make the connection between two systems, or systems are fusing or are fissioning. However, we do not know when the two entities become one or one splits into two or more.

Objects

From stars to clusters to galaxies to clusters of galaxies

From individuals to groups to societies

From cells to organs to organisms

From atoms to molecules to supermolecules

Challenges:

When fusing, stars into galaxies can be see like birds or fishes into flocks or schools. Three rules can be designed: alignment, maximum distance (cohesion, to avoid separation) and miminal distance (to avoid collision). Other self-organizing rules were found in animals, for example in ants colonies to find the best food source or in primates groups to move collectively. The rules that are applied at this level seem to be the same than the ones that are applied at the neural networks (such as the diffusion model allowing optimal decisions) or at the molecular level (with amplification effect, snow-ball effect or feedback loop). It may be interesting to study and find, by using either a top-down and a bottom-up approach, the rules underlying all these collective behaviours at the basis of complex systems (molecules, organisms, animal groups, ecosystems and galaxies). According to the Parcimony principle, we should find at the microlevel some rules simple and similar between different systems both at the mesolevel and at the macrolevel and conclude about the universality of collective behaviours and decision rules, whatever the nature of the complex system and of its entities.
Definition of coherence (spatio-temporal integrity), stability (temporal, ESS) and cohesion (spatial, diffusion, fission-fusion dynamics, segregation) of the different complex systems defined here. Stars may display some spatial segregation with large and old stars at the center of a core as it is found in primates with top-ranking individuals in the middle of the group and low-ranking ones at the group periphery.
Common methodology (diffusion models, common algorithms, graphs and dynamics thereon) and bridging the gap between all disciplines (from physics to biology to ecology and astrophysics; i.e. knowledge about each discipline and between each discipline)
New methods of simulation avoiding or controlling numerical diffusion
Studying mesolevels. Most studies are done at the microlevel and macrolevel, but not on the intermediate levels. The mesolevel may be better defined by using hypergraphs and hypernetworks. We need to express phenomenogically the generic micro, generic meso and collective macro dynamics and to identify the constraints.

Self-organization and parcimony or rules

Coherence of complex systems

Common methodology and linking disciplines

New methods of simulation avoiding numerical diffusion

Study of mesolevels