Graph-based structure analyses

Graph-based structure analyses had not been used for the specific objective of encoding relative shape. There was the frequent inference that indexes derived from these methods encode shape information, although none had been conceived with this specific objective in mind. It is from the graph of a molecule that we have derived the kappa indexes with the objective of encoding relative shape. 

Marburger, A. Westfechtel, B. (2010). Graph-based structural analysis for telecommunication systems, Graph transformations and model-driven engineering, Vol. 5765 of Lecture Notes in Computer Science, Springer-Verlag, pp. 363-392. 

In this chapter the classification of measurements and unmeasured variables of chemical processes is discussed. After the statement of the problem, variable categorization is posed in terms of a structural analysis of the flowsheet. Then graph-and matrix-based strategies are briefly described and discussed. Illustratives examples of application are included. 

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]. 

Step 1. Performance of data structure analysis on real study data (untransformed and transformed) to reveal hidden structure, patterns, and relationships in the data set. This involves data visualization (graphing and fitting) and exploratory modeling (e.g., tree-based modeling). 

Bond Graph-based Analysis of Structural Observability... 

HIV-1 potencies of the two groups of reverse transcriptase inhibitors whose base structure is shown in Fig. 8 and hsted in Table 13, commonly known as TIBO and HEPT derivatives. The activities are measured by the concentration of compound required to achieve 50% protection for MT-4 cells against the virus for modeling reasons it is expressed as log(10 C5o). In the present analysis, both types of graphs based on HFG and GAO are used, including the Morgan-extended connectivities °ECfc, EC, and EC introduced previously. The flexible variable is deflned as ... 

When performing quantitative analysis of a graph based process language we choose structural semantic rules such that they impose the minimum semantic interpretation necessary to determine the control flow of a model. In the case of a BPMN BPD, it adds no more semantic interpretation than implied by the standard (Object Management Group 2011a). In the case of BPMN, when we have imposed restrictions they have been made only for simplicity and are discussed at length in previous work (Herbert Sharp 2012). 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

It is to be noted that the QSPR/QSAR analysis of nanosubstances based on elucidation of molecular structure by the molecular graph is ambiguous due to a large number of atoms involved in these molecular systems. Under such circumstances the chiral vector can be used as elucidation of structure of the carbon nanotubes (Toropov et al., 2007c). The SMILES-like representation information for nanomaterials is also able to provide reasonable good predictive models (Toropov and Leszczynski, 2006a). 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

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