Quantitative nearest neighbors

Recently, a quantitative lateral interaction model for desorption kinetics has been suggested (103). It is based on a statistical derivation of a kinetic equation for the associative desorption of a heteronuclear diatomic molecule, taking into account lateral interactions between nearest-neighbor adatoms in the adsorbed layer. Thereby a link between structural and kinetic studies of chemisorption has been suggested. 

Zheng W, Tropsha A. Novel variable selection quantitative structure-property relationship approach based on the k-nearest-neighbor principle. J Chem Inf Comput Sci 2000 40(l) 185-94. 

Shen, M., Letiran, A., Xiao, Y., Golbraikh, A., Kohn, H., Tropsha, A. Quantitative structure-activity relationship analysis of functionalized amino acid anticonvulsant agents using k nearest neighbor and simulated annealing PLS methods./. Med. Chem. 2002, 45, 2811-2823. 

A quantitative approach to placing a confidence on classification is to calculate the proportion of the K nearest neighbors that are members of the respective classes. In the terminology used in this book, this is an attempt to validate... 

Medina-Franco, J. L., Golbraikh, A., Oloff, S., Castillo, R., Tropsha, A. (2005) Quantitative structure-activity relationship analysis of pyridinone HIV-1 reverse transcriptase inhibitors using the nearest neighbor method and QSAR-based database mining. J Comput Aided Mol Des 19, 229-242. 

The presence of radium in biological materials or environmental samples is generally determined by virtue of its radioactivity. Except in the laboratory where radium compounds have been isolated and determined for a certain purpose, determination of radium compounds in biological and environmental samples is relatively rare. As a Group IIA alkaline earth element, radium is similar in its chemical behavior to other members of that group, especially its nearest neighbor, barium. For example, radium tends to precipitate as the sulfate, which is the basis for its isolation for chemical analysis by coprecipitation with barium sulfate. Furthermore, radium associates with calcium in living systems and accumulates in bone. The determination of radium compounds or specific isotopes is usually accomplished by a separation procedure, followed by quantitative analysis of total radium based on its radioactivity. 

Impurity ions in wurtzite lattices are described by the same expressions for P2, and P3c, with a numerically insignificant difference in P3o. These expressions are only quantitatively accurate in the dilute limit, but many of the doped nanocrystals discussed in this chapter fall in this limit. The reader is referred to Ref. 42 for a generalized treatment of the problem. Figure 2(b) plots the probabilities calculated from Eq. 4a-d as a function of impurity concentration. The fraction of dopants having at least one nearest-neighbor dopant is quite high even at moderate impurity concentrations (<5%). Needless to say, whereas purification to ensure size uniformity is possible (size-selective precipitation), no purification method has yet been developed for ensuring uniform dopant concentrations in an ensemble of nanocrystals. 

Supervised learning methods - multivariate analysis of variance and discriminant analysis (MVDA) - k nearest neighbors (kNN) - linear learning machine (LLM) - BAYES classification - soft independent modeling of class analogy (SIMCA) - UNEQ classification Quantitative demarcation of a priori classes, relationships between class properties and variables... 

An even more quantitative application of VB theory can be developed from the realization that the nearest-neighbor VB model as developed, for example, by Pauling [10], can be mapped exactly onto a Heisenberg spin Hamiltonian [17]. The Heisenberg spin Hamiltonian has long been used to study the interaction between magnetic atoms in transition metal compounds and other paramagnetic substances [18], and can be written most simply as... 

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