Abstract
The universal differential and difference equation form an important basis for reified temporal-causal networks and their implementation. In this chapter, a more in depth analysis is presented of the universal differential and difference equation. It is shown how these equations can be derived in a direct manner and they are illustrated by some examples. Due to the existence of these universal difference and differential equation, the class of temporal-causal networks is closed under reification: by them it can be guaranteed that any reification of a temporal-causal network is itself also a temporal-causal network. That means that dedicated modeling and analysis methods for temporal-causal networks can also be applied to reified temporal-causal networks. In particular, it guarantees that reification can be done iteratively in order to obtain multilevel reified network models that are very useful to model multiple orders of adaptation. Moreover, as shown in Chap. 9, the universal difference equation enables that software of a very compact form can be developed, as all reification levels are handled by one computational reified network engine in the same manner. Alternatively, it is shown how the universal difference or differential equation can be used for compilation by multiple substitution for all states, which leads to another form of implementation. The background of these issues is discussed in the current chapter.
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References
Ashby, W.R.: Design for a Brain. Chapman and Hall, London (second extended edition). First edition, 1952 (1960)
Brauer, F., Nohel, J.A.: Qualitative Theory of Ordinary Differential Equations. Benjamin (1969)
Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins Co. (1924), Dover Publications (1956)
Port, R.F., van Gelder, T.: Mind as Motion: Explorations in the Dynamics of Cognition. MIT Press, Cambridge, MA (1995)
Treur, J.: Network-Oriented Modeling: Addressing Complexity of Cognitive, Affective and Social Interactions. Springer Publishers, Berlin (2016)
Treur, J.: Network reification as a unified approach to represent network adaptation principles within a network. In: Proceedings of the 7th International Conference on Natural Computing. Lecture Notes in Computer Science, vol. 11324, pp. 344–358. Springer Publishers, Berlin (2018a)
Treur, J.: Multilevel network reification: representing higher order adaptivity in a network. In: Proceedings of the 7th International Conference on Complex Networks and their Applications, ComplexNetworks’18, vol. 1. Studies in Computational Intelligence, vol. 812, pp. 635–651. Springer, Berlin (2018b)
Treur, J.: The ins and outs of network-oriented modeling: from biological networks and mental networks to social networks and beyond. In: Transactions on Computational Collective Intelligence. Contents of Keynote Lecture at ICCCI’18, vol. 32, pp. 120–139. Springer Publishers, Berlin (2019a)
Treur, J.: Design of a software architecture for multilevel reified temporal-causal networks (2019b). https://doi.org/10.13140/rg.2.2.23492.07045. URL: https://www.researchgate.net/publication/333662169
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Treur, J. (2020). On the Universal Combination Function and the Universal Difference Equation for Reified Temporal-Causal Network Models. In: Network-Oriented Modeling for Adaptive Networks: Designing Higher-Order Adaptive Biological, Mental and Social Network Models. Studies in Systems, Decision and Control, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-030-31445-3_10
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DOI: https://doi.org/10.1007/978-3-030-31445-3_10
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