Hierarchical Approaches

Valcarcel, M. Tuque de Castro, M. D. A Hierarchical Approach to Analytical Chemistry, Trends Anal. Chem., 1995,14, 242-250. Further details on evaluating analytical methods may be found in Wilson, A. L. The Performance-Characteristics of Analytical Methods, Part l-Talanta, 1970, 17, 21-29 Part ll-Talanta, 1970, 17, 31M4 Part lll-Talanta, 1973, 20, 725-732 Part IV-Talanta, 1974,21, 1109-1121. 

In order to address these challenges, a hierarchical approach may be adopted. This approach focuses on the big picture first, then adds details to promising solutions. Therefore, preliminary screening ought to be conducted first to identify overall reaction alternatives that meet process requirements in terms of desired product, cost effectiveness, environmental acceptability, and thermodynamic feasibility. At this stage, minimum details are to be invoked. The problem of synthesizing environmentally acceptable reactions EARs has been introduced by Crabtree and El-Halwagi (1994) and can be stated as follows ... 

On a smaller scale, a facility manager may rely on participatory management techniques, such as quality circles or task teams, or may pursue a more traditionally hierarchical approach. Similarly, a division may display entirely different management styles in several different function areas the sales organization may be highly structured, while research and development is more collegial and informal. 

Atchison, G.J., Sandheinrich, M.B., and Bryan, M.D. (1996). Effects of environmental stressors on interspecific interactions of aquatic animals. In M.C. Newman and C.H. Jagoe (Eds.), Quantitative Ecotoxicology A Hierarchical Approach. Lewis, Chelsea, Ml. 

Together, these decomposition approaches argue for combining functional, goal, and structural perspectives of the plant, as needed, in constructing interpretation systems. With any of these hierarchical approaches, each node in the hierarchy can be construed to define a localized interpreter. 

The U.S. EPA recommends an integrated, hierarchical approach for managing municipal solid waste that includes12... 

Fig. 12.1. Hierarchical approach decomposition into strategic planning, scheduling and execution.

The hierarchical approach was developed in the early days of computer-aided planning and can be visualized by a pyramid (Fig. 12.1). It was the right solution to the challenges of the restricted capability of computer systems at that time that required a decomposition of problems to reduce their size. 

Air pollution control methods, 26 667-729 gaseous emissions control, 26 678-694 hierarchical approach in, 26 675-678 measurement of air pollution, 26 672-675... 

A hierarchical approach. In Quantitative Structure-Activity Relationship (QSAR) Models of Mutagens and Carcinogens, Benigni, R., Ed., CRC Press, Boca Raton, FL, 2003, pp. 207-234. 

Basak, S. C. and Mills, D. Quantitative structure-property relationships (QSPRs) for the estimation of vapor pressure A hierarchical approach using mathematical structural descriptors. J. Chem. Inf. Comput. Sci. 2001, 41, 692-701. 

Fielder, R.J., Gaunt, I.F., Rhodes, C., Sullivan, F.M. and Swanston, D.W. (1987). A hierarchical approach to the assessment of dermal and ocular irritancy a report by the British Toxicological Society working party on irritancy. Human Toxicol. 6 269-278. 

Implement hierarchical approaches, along with professional judgment, and reference to other cases, to account for uncertainty in the estimation of distribution parameters. 

Figure 1.2 Comparison of parallel and hierarchical screening strategies.ln the parallel screen the first three assays are run in parallel followed by a manual decision to reduce the candidate compounds down for the subsequent set of three assays. The use of real-time data QC steps and feedback in the hierarchical approach supports the filtering out of failed compounds prior to submission to the next assay. Both strategies...

Ganapathy, S. Carlier, C. Randolph, T. W. O Brien, J. A. Influence of Local Structural Correlations on Free-Radical Reactions in Supercritical Fluids A Hierarchical Approach, Ind. Eng. Chem. Res. 1996, 35, 19-27. 

Basically the perturbative techniques can be grouped into two classes time-local (TL) and time-nonlocal (TNL) techniques, based on the Nakajima-Zwanzig or the Hashitsume-Shibata-Takahashi identity, respectively. Within the TL methods the QME of the relevant system depends only on the actual state of the system, whereas within the TNL methods the QME also depends on the past evolution of the system. This chapter concentrates on the TL formalism but also shows comparisons between TL and TNL QMEs. An important way how to go beyond second-order in perturbation theory is the so-called hierarchical approach by Tanimura, Kubo, Shao, Yan and others [18-26], The hierarchical method originally developed by Tanimura and Kubo [18] (see also the review in Ref. [26]) is based on the path integral technique for treating a reduced system coupled to a thermal bath of harmonic oscillators. Most interestingly, Ishizaki and Tanimura [27] recently showed that for a quadratic potential the second-order TL approximation coincides with the exact result. Numerically a hint in this direction was already visible in simulations for individual and coupled damped harmonic oscillators [28]. 

Using a numerical decomposition of the spectral density which describes the coupling of the system to the environment allows one to develop TL and TNL non-Markovian QMEs. Using the hierarchical approach the results can be extended from second-order perturbation theory to higher orders to be able to study the convergence properties of the different approaches. As shown in the example for bosonic baths, the TL formalism shows numerically almost converged results. Actually, this numerical finding has been analytically proven... 

The hierarchical approach to the traceability of pH measurements and pH reference materials is consistent with the agreed approach to traceability for metrology in chemistry [23]. Uncertainties stated for the primary method and for all subsequent measurements permit the uncertainties for all steps to be linked to the primary reference material. 

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