Nearest-neighbor model

The nearest-neighbor (NN) approach relates the property of a query compound, Yq, to the properties of k nearest-neighbor (kNN) compounds selected from a database. The general model is 

The kNN compounds used to estimate the query property are those k database compounds that exhibit the greatest similarity to the query compound. Basak and Grunwald [42] and Basak et al. [47] use the mean of the kNN property values 

The ANN approach has also been applied to compound classification. For example, Drefahl [48] has discussed the ANN approach to discriminate chlorinated organics with respect to their volatility from aqueous solutions. Varmuza [49] has described ANN classification as a standard method in pattern recognition and provides references to its use in spectra interpretation. 

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Clearly, proximity and orientation play a role in enzyme catalysis, but there is a problem with each of the above comparisons. In both cases, it is impossible to separate true proximity and orientation effects from the effects of entropy loss when molecules are brought together (described the Section 16.4). The actual rate accelerations afforded by proximity and orientation effects in Figures 16.14 and 16.15, respectively, are much smaller than the values given in these figures. Simple theories based on probability and nearest-neighbor models, for example, predict that proximity effects may actually provide rate increases of only 5- to 10-fold. For any real case of enzymatic catalysis, it is nonetheless important to remember that proximity and orientation effects are significant. 

The tfee nearest-neighbor model developed above is used to classih four unknowQsamples. Based on majority vote, the predicted classes are unknown 1 = D, u own 2 = A, unknown 3 = D, and unknown 4 A. 

Equation (13) contains the first two in the hierarchy of mean relaxation frequencies <1/t>jt, The matrix, Table IV permits the evaluation of further such quantities and thus of the set kt, k of rate constants from relaxation data. Equation (13) and its continuation is entirely general for the nearest-neighbor model under consideration and describes the initial... 

For the disordered (A2) phases, rjeq = 0, Eq. 17.19 is satisfied automatically, and equilibrium tie-lines are present if W < 0 and T < Tcrit = W/k, as illustrated in Fig. 17.5. In the nearest-neighbor model, ordered B2 solutions can appear at any uniform composition Xb Nonzero equilibrium structural order parameters appear only if W > 0 at temperatures T satisfying... 

Nearest-neighbor models fragment constants Properties of k similar compounds... 

Fig. n.n. The sp d TB model with the cation-anion and anion-anion interactions ([75], solid line) compared with the sp s TB nearest neighbor model ([76], dashed line), the EMA model (dotted line) and the experimental data points CdS (o) [77], (A) [78], ( ) [79],... 

Johnson K. L., Contact Mechanics, Cambridge University Press, Cambridge England, 1985. Johnson R. A., Analytic Nearest-Neighbor Model for fee Metals, Phys. Rev. B37, 3924 (1988). Johnson W. C. and Cahn J. W., Elastically Induced Shape Bifurcations of Inclusions, Acta Metall. 32, 1925 (1984). 

The intra- and interchain interactions can be schematically summarized in Figure 4. From a simplistic nearest-neighbor model, there is one intrachain interaction, and three interchain interactions arising between two acceptors (A), /aa, two metallocenium cations (D), /dd, or between a cation and acceptor, /da- These interactions can have different magnitudes and either be ferromagnetic (/>0) or antiferromagnetic coupling (/<0). The... 

This result differs only slightly from the expression for derived from the nearest-neighbor model, that is. Equation 5.16. In view of the many extra assumptions to be made and, hence, the additional uncertainties introduced, the approximation is not really improved by including interaction with neighboring molecules beyond the nearest ones. 

The peculiarity of this method is the potential to include any number of conformational states in the mathematical process. Cooperative effects can also be taken into account by calculations with a nearest-neighbor model. 

Transitions in other kinds of system can also be treated by the nearest-neighbor model. One example is the magnetization of metals. 

Real magnets are three-dimensional. The importance of the one-dimensional Ising model is that it illustrates the principles of the nearest-neighbor model and that it can be solved exactly. For the three-dimensional Ising model, no... 

Kierzek R., Caruthers, M. H., Longfellow, C. E., Swinton, D., Turner, D. H., and Freier, S. M. (1986) Polymer supported RNA synthesis and its application to test the nearest-neighbor model for duplex stability. Biochemistry 25,7840-7846. 

Next we consider the heat of mixing using a simple nearest neighbor model. Let m a be the nearest neighbor binding energy per atom for pure A, Mbb for pure B, and Mab for an A atom next to a B atom. For mole fraction x of B atoms, the probability of atom B next to atom A is X and the total energy for the A atoms is... 

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