Neighbour principle

Zheng, W. and Tropsha, A. (2000) Novel variable selection quantitative structure-property relationship approach based on the k-neaiest-neighbour principle. J. Chem. Inf. Comput. Sci. 40 185-194. 

Everyone carries a legal dnty of care, established as the neighbour principle . In The Donoghne case (1932) it was said that neighbonr means anyone so closely and directly affected by someone s act or omission that they ought reasonably to have been considered. This duty seeks to ensure that a person takes reasonable care in a situation in which loss or injnry to someone else could be anticipated. It is nniversally recognised that teachers owe a duty of care to pupils and any harm would need to arise from a failure in that duty (see also Chapter 1). This is the concept of negligence— sometimes described as carelessness. 

When considering whether or not a duty of reasonable care was owed courts will always seek to identify an established relationship between the claimant and the duty holder. Relationships that have been established by judicial precedent include employer/employee, doctor/ patient and teacher/pupil. For claims relating to the duty of reasonable care the landmark case that established the neighbour principle was the case of Donoghue v. Stevenson (1932). 

During the case. Lord Aitken made the following statement regarding the manufacturer, which is now known as the neighbour principle ... 

In principle, these fomuilae may be used to convert results obtained at one state point into averages appropriate to a neighbouring state point. For any canonical ensemble average... 

The above statements are valid for monomolecular layers only. In the case of polymer films with layer thickness into the p-range, as are usually produced by electropolymerization, account must also be taken of the fact that the charge transport is dependent on both the electron exchange reactions between neighbouring oxidized and reduced sites and the flux of counterions in keeping with the principle of electroneutrality Although the molecular mechanisms of these processes... 

N t,r) is a predefined neighbourhood function in which r represents the distance in the map between the considered unit and the winning unit. Different neighbourhood functions can be used. The principle is always that units closer to the winning unit are adapted most. Some common functions are shown in Fig. 44.23. Due to this aspect of the learning procedure, the connectivity (i.e. the number of neighbours for each unit) of the network has an influence on its performance. Networks with a different number of neighbours for the units are shown in Fig. 44.22. 

However, according to Hyde and Andersson (1989), for instance, the validity extension of this principle is difficult to evaluate. As time passes, crystallographers are able to solve more and more complex crystal structures, and these tend to have low symmetry. The symmetry principle could be restated by observing that a crystal structure has the highest symmetry compatible with the efficient use of space and the specific requirements of chemical bonding between nearest neighbours. 

The discussion of the defects in FeO has so far been only structural. Now we turn our attention to the balancing of the charges within the crystal. In principle the compensation for the iron deficiency can be made either by oxidation of some Fe(II) ions or by reduction of some oxide anions. It is energetically more favourable to oxidise Fe(II). For each Fe vacancy, two Fe cations must be oxidised to Fe ". In the overwhelming majority of cases, defect creation involves changes in the cation oxidation state. In the case of metal excess in simple compounds, we would usually expect to find that neighbouring cation(s) would be reduced. 

The photoelectron wave-vector k is evaluated using = 2m(E — E ) where E is the energy of the X-ray photon, , a reference energy and m, the mass of the electron. x(k) is multiplied by k"(n = 2 or 3 usually) to magnify the faint EXAFS at large k (Lytle et al, 1975) /c"x(k) is Fourier transformed to yield the RSF, < (R). In the model compound, the first peak at a distance Rj represents the distance to the nearest-neighbour shell and may be compared to R[, the known distance. We can then define a as (R — Rj), which represents the experimentally determined phase correction. In principle, 2a should be equal to the theoretically estimated k-dependent part of /k), viz. if the identity of the scatterer environment has been correctly assumed. It must be emphasized that wherever scatterer identities are obscure (e.g. in several covalently bonded and disordered systems) use of a (and not j) is advisable. Further, the k-dependence of < /k) introduces an intrinsic limitation to its quantitative accuracy. 

The principle of maximum symmetry requires that the crystal structure adopted by a given compound be the most symmetric that can satisfy the chemical constraints. We therefore expect to find high-symmetry environments around atoms wherever possible, but such environments are subject to constraints such as the relationship between site symmetry and multiplicity (eqn (10.2)) and the constraint that each atom will inherit certain symmetries from its bonded neighbours. The problems that arise when we try to match the symmetry that is inherent in the bond graph with the symmetry allowed by the different space groups are discussed in Section 11.2.2.4. 

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