The first section of this technical appendix details the order of operations within the model, the second the method of network construction and parameterization, and the third the methodology by which results given in the paper were derived. The fourth section details additional analysis of the role of the updating rate, λ, absent a complex network. The fifth section does the same for core beh...

Failure diagnosis in large and complex systems is a critical and challenging task. In the realm of model based diagnosis on discrete event systems, computing a failure diagnosis means computing the set of system behaviours that could explain observations. Depending on the diagnosed system, such behaviours can be numerous, so that a problem of representing them is induced. The paper discusses ab...

We introduce a solvable model of randomly growing systems consisted of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analyzed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in wide fields can be derived from this basic physical model. Statistical data of growth r...

Abstract: Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we de...

tris(3-bromo-acetylacetonato) chromium(iii) as an inert and very stable complex with a good leaving group was synthesized using as-prepared cr(acetylacetonate)3. highly ordered nanoporous silica (lus-1), with some great features, was functionalized with 3-aminopropyltriethoxysilane. then the as-prepared product was modified with tris(3-bromo-acetylacetonato) chromium(iii) under mild reaction co...

A systematic method for approximating the complex-order Laplacian operator by realizable integer-order transfer functions is presented in this work. The realization performed a simple structure where only one active element used. Thanks to employment of impedances, both integrators and differentiators can be readily implemented same core simply interchanging associated impedance locations. vali...