Graph-based approaches

A considerable improvement over purely graph-based approaches is the analysis of metabolic networks in terms of their stoichiometric matrix. Stoichiometric analysis has a long history in chemical and biochemical sciences [59 62], considerably pre-dating the recent interest in the topology of large-scale cellular networks. In particular, the stoichiometry of a metabolic network is often available, even when detailed information about kinetic parameters or rate equations is lacking. Exploiting the flux balance equation, stoichiometric analysis makes explicit use of the specific structural properties of metabolic networks and allows us to put constraints on the functional capabilities of metabolic networks [61,63 69]. 

Zhang, H., and Kuo, T. (1996), Graph-Based Approach to Disassembly Model for End-Of-life Product Recycling, in Proceedings of the 1996 lEEE/CMPT International Electronic Manufacturing Technology Symposium (Austin, TX), pp. 247—254. 

Because of their clearness, the graph-based approaches are considered as the most suitable form of illustration. A lot of different types were developed ... 

As to the numerical computation of ARR residuals, two possible bond graph based approaches have been presented. One approach suited for online as well as for offline FDI is to use a diagnostic bond graph in which storage elements are in preferred derivative causality in order to be independent of initial conditions that are difficult to be obtained in online FDI. Moreover, sensors are in inverted causality. 

General scheme of building up optimal descriptors with the hydrogen-suppressed graphs based approach can be demonstrated using example of ethyl isopropyl sulhde with the following numbering of atoms ... 

Advantages of the incremental true bond graph-based approach presented in this chapter are that the matrices can be automatically set up in symbolic form from an original bond graph and its associated incremental bond graph by available software. Parameter sensitivities of transfer functions are then obtained by multiplication of matrix entries which can be performed by software in symbolic form. There is no need for symbolic differentiation of transfer functions. The purpose of determining sensitivities of transfer functions in symbolic form is that, in the design of a robust control, it may be useful to know how sensitive transfer functions are with respect to certain parameter uncertainties. 

He, K., lerapetritou, M.G., Androulakis, I.P. A graph-based approach to developing adaptive representations of complex reaction mechanisms. Combust. Flame 155, 585-604 (2008)... 

Kramer, M. A., and Palowitch, B. L., Rule-based approach to fault diagnosis using the signed directed graph, AlChE J. 33(7), 1067-1078 (1987). 

In this chapter, the mathematical formulation of the variable classification problem is stated and some structural properties are discussed in terms of graphical techniques. Different strategies are available for carrying out process-variable classification. Both graph-oriented approaches and matrix-based techniques are briefly analyzed in the context of their usefulness for performing variable categorization. The use of output set assignment procedures for variable classification is described and illustrated. 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

Froehlich, H., Wegner, J.K., Sieker, F. and Zell, A. (2006) Kernel functions for attributed molecular graphs - a new similarity-based approach to ADME prediction in classification and regression. QSAR Combinatorial Science, 25, 317-326. 

A molecular branching index was proposed for acyclic graphs, based on the double invariant approach and called - AA/ branching index. A calculation example [Randic, 1997d Randic, 1998a] for 2-methylpentane is given in Box D-7, where the symbol " p represents a path of length m. 

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