Local terms

Selecting the values of the parameters for the calculations we have in mind a 1 1 aqueous 1 m solution at a room temperature for which the Debye length is 0.3 nm. We assume that the non-local term has the same characteristic length, leading to b=. For the adsorption potential parameter h we select its value so that it has a similar value to the other contributions to the Hamiltonian. To illustrate, a wall potential with h = 1 corresponds to a square well 0.1 nm wide and 3.0 kT high or, conversely, a 3.0 nm wide square well of height 1.0 kT. 

To create our terminology containing both internal terms and external terms we semiautomatically extract terms from available external resources (e.g., MeSH, EMTREE, UniProt). Then we fit the extracted terms to our data structure and preserve the reference to the source system because sometimes terms are very specific to certain databases. We refer to the terms specific to a database as local terms. These local terms are stored in a dedicated data structure, the Metastore. It must be noted that we refer to accession codes and identifiers used in databases such as UniProt, RefSeq, and GO as local terms (see Tables 31.1 and 31.2). 

The example below illustrates the identification of a term, how this identified term is associated with one or more concepts, and how a type is associated with the identified concepts creating the typed entities. The example also shows how the normalized term and local terms are used to drive the UltraLink. 

The list of normalized terms, synonyms and local terms for each concept type (e.g., DISEASES—COMPANIES—TARGETS—PRODUCTS— MODES OF ACTION) in each source, as deemed relevant for the creation of the UltraLink... 

Then with each source in that list to get the local term(s) related to the concept type that is bound to the normalized term. 

The UltraLink component then generates a list of value pairs with the form (SOURCE, LOCAL TERM) using the information extracted from the Metastore. It should be noted that an UltraLink is only generated if the data source contains information about the term under consideration. 

For each of the generated value pairs (SOURCE, LOCAL TERM) an UltraLink can now be created and the substitution rules can be applied. To construct the contextual menu, the UltraLink component will fetch the title to display in the Web Interface as well as the URL to link to from the Metastore. It will then apply a set of substitution rules such as, for example ... 

Replace the value of the entity to UltraLink by the local term. 

Example on Tumor Necrosis Factor Alpha. The term tumor necrosis factor alpha can be readily identified from text. The GetLinks method fetches the local terms associated with the normalized term for the various sources from the Metastore. The local terms are then used for pointing to the original records and linking to specific applications (Table 31.5). 

In order to reduce the complexity of the problem, several approximation schemes have been developed. In the BGK model, the collision integral is replaced by a simple local term ensuring that the well-known Maxwell distribution is reached at thermal equilibrium [16]. The linearization method assumes that the phase space distribution is given by a small perturbation h on top of a (local) Maxwell distribu-tion/o (see, e.g., [17, 18]) ... 

Thus, these orbitals can be used to represent exactly any property of the system in localized terms. The NAOs divide naturally into a leading high-occupancy set (the natural minimal basis ) and a residual low-occupancy set (the natural Rydberg basis ), where the occupancies of the latter orbitals are usually quite negligible for chemical purposes. Thus, even if the underlying variational basis set is of high dimensionality (6-311++G for the applications of this book), a perturbative analysis couched in NAO terms has the simplicity of an elementary minimal-basis treatment without appreciable loss of chemical accuracy. 

The Xa multiple scattering method generates approximate singledeterminant wavefunctions, in which the non-local exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. The orbitals are solutions of the one-electron differential equation (in atomic units)... 

Due to the localization terms entering the localized representation, an extra computational work is necessary. It represents only a small fraction of the total computing time, in a given order, because the number of indices to be summed up are always less in the localization terms than in the canonical ones. 

D. The Atom-plus-Ligand Local-Term Approximation... 

To avoid the confusion to which this topic is prone we should define a local-term approximation which gives the total shielding a(A) of the nucleus A in terms of the shielding due to electronic circulations on A and on its directly bonded neighbors (ligands) L, i.e.. 

The atom-plus-ligand local-term approximation has been justified a posteriori for 30) and 57) shielding, since certain expected relationships of chemical shifts, such as additivity of substituent effects, were found to be absent for the observed shifts, but were fulfilled for i.e., after correction for the atom-plus-ligand diamagnetic term. Some examples are given in the following sections. 

The corresponding periodic correlation of F shifts (39) is more extensive and informative. This and the corresponding plot for proton shielding (38) have been constructed using absolute values of the molecular shielding terms, avoiding the hazards of local-term approximations. Discussion of these periodicities is postponed to Section V. 

Notice that the integrand of (22) does not depend only, as all the other terms of (22), on the positional coordinate R of the ij)k(R)- One says that (22) is a non-local term, and this fact considerably complicates calculations unless approximations are performed to make it local (so to reduce (20) to the form of the Hamiltonian (11)). 

For the non-local term E c, defined in (22), Kohn and Sham ° suggested afunctional similar to that of the Thomas-Fermi theory. In this way, Eq. (20) is completely reduced to functionals of n(R) and then to a local form. 

Normally, for pharmaceuticals, the requirement is <1 iS/cm, but this depends on the local terms of reference. 

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