By Gregoire Nicolis
Complexity is rising as a post-Newtonian paradigm for forthcoming a wide physique of phenomena of shock on the crossroads of actual, engineering, environmental, existence and human sciences from a unifying perspective. This e-book outlines the rules of contemporary complexity study because it arose from the cross-fertilization of principles and instruments from nonlinear technological know-how, statistical physics and numerical simulation. it's proven how those advancements result in an realizing, either qualitative and quantitative, of the advanced structures encountered in nature and in daily event and, conversely, how normal complexity acts as a resource of thought for development on the primary point.
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Extra resources for Foundations of complex systems: nonlinear dynamics, statistical physics, information and prediction
Each block of these partitions is thus represented as a whole by one state of variable vj or one instance of support Ii' i- When an observation of attribute a; is made at some support instance, the observed attribute assumes a particular appearance from set Aj • This appearance is a member of exactly one block of the partition Ai / OJ . It is assigned by OJ to a particular state of variable Vj. It is thu s assumed that each observation permits us to recognize that block of A j / O J to which the actual appearance belongs, even though it does not allow us to identify the individual appearance itself.
A prob lem situation whose solution is known is simulated on the computer. A relevant Introduction 21 methodological tool under investigation (usually one designed for a problem of a nondeductive nature) is used to solve the problem. The result obtained is then compared with the known solution. This is repeated a sufficient number of times for different problem situations of the investigated class with the aim of determining useful characteristics of the methodological tool involved. Such characteristics are very important for users of the various methodological tools, as they allow them to properly interpret the results obtained and make appropriate decisions.
One such counterintuitive trap lies in the assumption, often taken for granted, that properties of overall systems can be reconstructed from knowledge of corresponding properties associated with their subsy stems. For instance, it has often been assumed in multidisciplinary societal projects that the whole system is understood when we understand its economic, legal, political, ecological, and other relevant subsystems. Such an assumption is unfortunately warranted only rarely and, even if it is warranted, its validity depends on the chosen subsystems.