Concept maps definition

At the end of each chapter, you will find several study aids that complete the chapter. Chapter Reviews provide a summary and Concept Maps show the connections between important topics. The Key Terms, which are in boldface type within the chapter, are listed with their definitions. Understanding the Concepts, a set of questions that use art and models, helps you visualize concepts. Additional Questions and Problems and Challenge Problems provide additional exercises to test your understanding of the topics in the chapter. The problems are paired, which means that each of the odd-numbered problems is matched to the following even-numbered problem. The answers to all the Study Checks, as well as the answers to all the odd-numbered problems are provided at the end of the chapter. If the answers provided match your answers, you most likely understand the topic if not, you need to study the section again. 

Before using concept mapping as activity it is needed to familiarise students with the operational definitions of terms applied, such as concept, label, node, linking relationship, proposition, cross-link. In general, the procedure for constructing new concept maps can be described in terms of four (partly overlapping) phases ... 

These pharmacophore techniques are different in format from the traditional pharmacophore definitions. They can not be easily visualized and mapped to the molecular structures rather, they are encoded as keys or topological/topographical descriptors. Nonetheless, they capture the same idea as the classic pharmacophore concept. Furthermore, this formalism is quite useful in building quantitative predictive models that can be used to classify and predict biological activities. 

In this chapter we will consider definitions of metabolism the biochemistry-physiology continuum. The concept of metabolic pathways and their organization and control of metabolism are likened to a road map involving flow of substrates but with mechanisms to accelerate or slow down pathways or to direct substrates through alternative routes. 

From the definition of covering symmetry which basically rests on the concept of the isometric mapping of a point set onto itself, it is evident that the operators PG map the distance set dkk d) onto itself by intransitive permutations ... 

Clearly we can define these concepts using just the T-action. Let T be any group acting as automorphisms of a group F. The maps / T - F satisfying f at) =/(crossed homomorphisms (they are homomorphisms when the action is trivial). The ones cohomologous to/are those of the form cf (o)[a(c)Y1 for some fixed c in F this is the definition that matches up with ours for G(S), and one can easily check that it is an equivalence relation in general. The set of equivalence classes is denoted // (T, F). 

The inverse mapping from the c space to the c space is equally important as the forward mapping, not only because it provides a link between the lumped species and the original species, but because its existence is a necessary and sufficient condition for exact lumping. For a reduced system hstandard definition of an inverse will not apply. Therefore, we use the concept of a generalized inverse. The generalized inverse of an m X n matrix A satisfies the following criteria ... 

Additionally, a new construct for modeling alternative subgraphs [180] is realized. This is a powerful construct to specify multiple alternative correspondence structures in one rule. For example, there are different options to map a process stream to a pipe which contains different types of valves in different order. All these alternatives can be now specified within one rule. Concepts for the parametrization of integration rules will be defined. Parameters can be set at runtime as well as at rule definition time. Figure 7.19 shows an example of a rule with a runtime parameter in combination with a set-valued pattern A column in the simulation model is mapped to a column in the flowsheet, which has a number of column trays each having a port. The parameter n controls the number of trays, that are added to the column it is provided by the user at runtime. Up to now, the parametrization works with attributes occurring in a rule whose values can be retrieved at runtime without user interaction. 

The specification super-operator is common in quantum chemical emd physical literature for linear mappings of Fock-space operators. It is very helpful to transfer this concept to the extended states A, B) and define the application of super-operators by the action on the operators A and B. We will see later how this definition helps for a compeict notation of iterated equations of motion and perturbation expansions. In certain cases, however, the action of a super-operator is fully equivalent to the action of an operator in the Hilbert space Y. The alternative concept of Y-space operators allows to introduce approximations by finite basis set representations of operators in a well-defined and lucid way. 

This concept was adopted by pedologists and identifies these soils as subaqueous soils, which are permanently flooded soils that occur immediately below a water depth of <2.5 m. These soils have been mapped in an estuarine environment (Demas et al., 1996 Demas and Rabenhorst, 1999). The Natural Resource Conservation Service has amended the definition of soil to include sediments under as much as 2.5 m water (Soil Survey Staff, 1999). The justification used for including sediments of shallow water environments is that these sediments undergo soil-forming processes and are capable of supporting rooted plants, and meet the definition of soil according to the criteria defined in Soil Taxonomy. 

While the concept of a protein catalog undoubtedly existed, at least in the minds of some people, prior to the coining of the term proteome, the realization that protein-protein interactions were a dominant feature of proteome function was certainly considerably less clear. However, such is the case and the second part of the definition requires a detailed knowledge of all of these recognitive events, both stable and transient. The elucidation of these interactions and the underlying networks that they describe have been termed cell-mapping proteomics (Blackstock Weir, 1999). This in fact has been a quite productive area of proteomic research, as described below. 

In this Section we intentionally pass over the discussion concerning the objectivity of concepts that disclose the core of phenomena. This is a matter of special description (see, e.g. [61,62]). Nevertheless, let us bring the definition that seems to be more attractive concerning the objectivity of variables of a dynamic system. Target variables imply a minimum set of used characteristics with maximum imiversality, hence for a maximum range of mapping the system behavior. 

By definition, a mixed quantum-classical method treats the various degrees of freedom (DoF) of a system on a different djmamical footing, e.g. quantum mechanics for the electronic DoF and classical mechanics for the nuclear DoF. As was discussed above, some of the problems with these methods are related to inconsistencies inherent in this mixed quantum-classical ansatz. To avoid these problems, recently a conceptually different way to incorporate quantum mechanical DoF into a semiclassical or quasiclassical theory has been proposed, the so-called mapping approach. " In this formulation, the problem of a classical treatment of discrete DoF such as electronic states is bypassed by transforming the discrete quantum variables to continuous variables. In this section we briefly introduce the general concept of the mapping approach and discuss the quasiclassical implementation of this method as well as applications to the three models introduced above. The semiclassical version of the mapping approach is discussed in Sec. 7. 

The conunon knowledge refers to industry standards and generally accepted supply chain management concepts. The common knowledge facilitates established mappings between concept definitions in repositories maintained by individual supply chain units, thus leading to easier establishment of the common repository used by the supply chain configuration system. 

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