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**11 - 14**of**14**### Agent Models of Supply Network Dynamics - Analysis, Design, and Operation

, 2001

"... : Real-world industrial supply networks are highly complex structures made up of a multitude of competing individual companies. Today's structures span the whole planet and link processes over a timeline what measures in months. In this article we focus on one of the most complex networks, the su ..."

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: Real-world industrial supply networks are highly complex structures made up of a multitude of competing individual companies. Today's structures span the whole planet and link processes over a timeline what measures in months. In this article we focus on one of the most complex networks, the supply in the automotive industry. The observed dynamics emerge from the physical and virtual interactions of the individual components of the supply network. The complexity of the net makes an analytic description of the system-level behavior infeasible. Instead, we have to resort to models of the individual dynamics that are then explored in simulation experiments. In this article we compare two modeling approaches -- equation-based and agent-based modeling -- and we report on two research projects at ERIM's Center for Electronic Commerce that applied agent-based modeling in the analysis of simple supply structures. Simulation of system dynamics is a central element in supply network management research. Agent-based models of real-world supply chains can be build by domain experts that do not have to be versed in information technology (IT). Using these models, a quantitative evaluation of the impact of parameters and strategies in the supply network design can show the financial advantage of the introduction of supply network management. The bulk of this article reports on a simulation exercise at the DaimlerChrysler Corporation that identified a potential win-win situation for all partners along the supply chain if a new forecast policy is adopted. 2 Chapter # 1.

### Cellular Neural Networks and Least Squares for partial differential problems parallel solving

, 2009

"... This paper shows how Cellular Neural Networks (CNN) can be harnessed into solving partial differential problems through an adaptation of the Least Squares Finite Elements Method. As CNNs can be implemented on distributed parallel architectures, this method allows the distribution of a resource deman ..."

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This paper shows how Cellular Neural Networks (CNN) can be harnessed into solving partial differential problems through an adaptation of the Least Squares Finite Elements Method. As CNNs can be implemented on distributed parallel architectures, this method allows the distribution of a resource demanding differential problem over a computer network.

### Cellular Computing and Least Squares for partial differential problems parallel solving

, 2009

"... This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures, this method allows the distribution of a resource demanding dif ..."

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This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures, this method allows the distribution of a resource demanding differential problem over a computer network.

### Analog computation with dynamical systems

"... A b s t r a c t Physical systems exhibit various levels of complexity: their long term dynamics may converge to fixed points or exhibit complex chaotic behavior. This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are n ..."

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A b s t r a c t Physical systems exhibit various levels of complexity: their long term dynamics may converge to fixed points or exhibit complex chaotic behavior. This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems, discrete or continuous in time, on the basis of an intrinsic time scale of the system. Dissipative dynamical systems are classified into the computational complexity classes Pd, Co-RPd, NPd and EXP,t, corresponding to their standard counterparts, according to the complexity of their long term behavior. The complexity of chaotic attractors relative to regular ones leads to the conjecture Pa:fi NPj. Continuous time flows have been proven useful in solving various practical problems. Our theory provides the tools for an algorithmic analysis of such flows. As an example we analyze the