Meta-structural properties in collective behaviours

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this contribution, we consider Collective Behaviours as coherent sequences of spatial configurations adopted by agents interacting through corresponding different structures over time. The approach relates to the one adopted time ago when introducing the concept of multiple systems arising when each composing element can play simultaneously or sequentially different roles. In this case, each element simultaneously or sequentially belongs to different systems. Multiple structures over time and their sequences are considered as meta-structures establishing coherent sequences of different systems. They are intended as coherent when acquiring emergent properties. Such coherence is considered here as being represented by the values adopted by suitable mesoscopic variables and their properties, i.e. meta-structural properties, allowing the researcher to (a) recognise a phenomenon as emergent, (b) induce emergence of collective behaviour in populations of elements collectively interacting, (c) act on collective emergent phenomena with the purpose to change, regulate and maintain acquired properties and (d) merge different collective emergent phenomena. We introduce a formal tool, i.e. the mesoscopic general vector to represent the adoption, over time, of mesoscopic properties by collectively interacting elements. We mention future experimental lines of activities, future lines of research and possible applications. 1. Introduction In this paper, we present a research project aiming at introducing and experimenting a new semi-classical approach (Minati 2008, 2009) to model coherence as related to the emergence of acquired properties in processes of collective behaviour. The approach is to be considered as a semi-classical one because of two main reasons. On one hand, it may be considered as classical since it is based on considering possible to separate, distinguish and measure components establishing phenomena of collective behaviour, non-valid assumption, for instance, when dealing with quantum approaches. Furthermore, interactions are considered to be …