DRG with error propagation

Pepiot-Desjardins and Pitsch (2005, 2008) noticed that Eq. (7.7) does not distinguish between reactions that create or destroy species i and suggested an alternative definition  

The operator (.) selects only the positive terms in the summation, and the operator (.) selects only the negative terms and makes them positive. Equation (7.10) calculates the ratio of the sum of the rates belonging to the pair of species (i, j) to the total rate of formation or destruction of species i. Note that aU forward and backward rates must be considered separately as a single reaction when using the connection weights (7.10), or else partial equilibrium reactions could result in artificially low connection weights. 

Pepiot-Desjardins and Pitsch (2008) made further extensions to DRG by incorporating error propagation, called DRG with error propagation (DRGEP). In this method the assumption that aU coupled species are equally important in the mechanism is lost, and errors are damped as they propagate alcnig the graph from the initially selected important species. The importance index is therefore calculated as 

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This procedure will not be discussed further here, but the DRG methodology has proven to be easy to implement and to fully automate. Hence, it has become very popular to use for reduction of larger mechanisms. In its simplest form DRG has however proved to have some limitations. These have been addressed in extended versions of the procedure. This includes DRG with error propagation (DRGEP) (Pepiot-Desjardins Pitsch, 2008), DRG aided sensitivity analysis (DRGASA) (Zheng et al., 2007) and DRGEP and sensitivity analysis (Niemeyer et al., 2010). The reader is referred to these works for further discussion. 

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