2011
DOI: 10.1007/978-3-642-19167-1_1
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Methods for Approximations of Quantitative Measures in Self-Organizing Systems

Abstract: Abstract. For analyzing properties of complex systems, a mathematical model for these systems is useful. In micro-level modeling a multigraph can be used to describe the connections between objects. The behavior of the objects in the system can be described by (stochastic) automatons. In such a model, quantitative measures can be defined for the analysis of the systems or for the design of new systems. Due to the high complexity, it is usually impossible to calculate the exact values of the measures, so approx… Show more

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Cited by 17 publications
(10 citation statements)
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“…[176] defines self-organization as an increase in statistical complexity, which in turn is defined as the amount of information required to minimally specify the state of the systemʼs causal architecture. As an alternative to entropy, the use of the mean value of random variables has also been proposed [92].…”
Section: Usagementioning
confidence: 99%
“…[176] defines self-organization as an increase in statistical complexity, which in turn is defined as the amount of information required to minimally specify the state of the systemʼs causal architecture. As an alternative to entropy, the use of the mean value of random variables has also been proposed [92].…”
Section: Usagementioning
confidence: 99%
“…Examples for measurement techniques include the following: Shalizi presented an approach that is based on the efficiency of predictions and makes use of approaches known from the domain of information theory [31], a closely related approach has been presented by Prokopenko et al in [32]: In general, both aim at assessing which level (i.e., from micro to macro) is more efficient for predicting the next states. Similarly, Holzer and De Meer compare the information at the system level (i.e., the sum of all edges in a network-based representation) with the information of a lower level (i.e., a single edge in a network-based representation) [33]. As a result, emergence values are high for those systems with many components depending on each other and low for those systems that mostly comprise independent components.…”
Section: State Of the Artmentioning
confidence: 99%
“…For example, Shalizi (2001) defines self-organization as an increase in statistical complexity, which in turn is defined as the amount of information required to minimally specify the state of the system's causal architecture. As an alternative to entropy, the use of the mean value of random variables has also been proposed (Holzer and De Meer, 2011).…”
Section: Usagementioning
confidence: 99%