Coordination number pattern recognition

R. E. Williams, Coordination number-pattern recognition theory of carborane structures, Adv. Incrg. Chem. Radiochem. 18, 67-142 (1976). R. E. Williams, Chap. 2 in G. A. Olah, K. Wade and R. E. Williams (eds.). Electron Deficient Boron and Carbon Clusters, Wiley, New York, 1991, pp. 11-93. 

Coordination Number Pattern Recognition Theory of Carborane Structures Robert E. Williams... 

COORDINATION NUMBER PATTERN RECOGNITION THEORY OF CARBORANE STRUCTURES ... 

This paper subscribes to the third viewpoint, and is based on an empirical approach that involves coordination number pattern recognition (CNPR). It is a simplistic approach, yet it apparently accommodates most if not all carborane and borane structures. For compounds that are still controversial and for compounds that have not yet been discovered or characterized, the CNPR thesis frequently predicts different structures, or at least fewer candidates, than do any of the theoretical treatments. 

This section presents the structure of the boron hybrides and is arranged in accordance with the relationship defined by Wade s Rules and expressed by Williams and Rudolph. Thus for the boranes containing six or more pairs of skeletal bonding electrons, the relationship between the structures of the closo-, nido-, arachno-and hypho-species is described. In cases where the parent borane does not exist, examples from heteroboranes with the correctly predicted structure based on Williams coordination number pattern recognition theory (CNPR) of borane structures will be described 70. Treated separately will be mono- and diborane species and also species with more than 12 boron atoms. Although there have been several reviews on the structures of the boranes in recent years none have used the current approach89. ... 

Non-contact 3D digitizing systems are mostly used in the field of reverse engineering, in which numerical models are reconstructed from clouds of points, as described in the literature [6], They are also used in pattern recognition of machine vision applications, online measurement systems and dimensional control systems. With these systems, the coordinates of a large number of points can be obtained in a few seconds, but they require further treatment as they form discrete images of objects [7]. 

An analytical method can be represented by a point or by a region in a multidimensional "space of procedures". The coordinates correspond to the parameters of the method, like accuracy, time, cost, etc.. Kaiser C4213 applied the information theory.to the estimation of the "informing power" of analytical procedures. Pattern recognition methods have been proposed by Wold et. al. C36, 341, 3433 for an objective evaluation of analytical methods. A data matrix is obtained by the application of me-thods to a number of real samples. Mathematical models were constructed for the clusters describing the methods under consideration. 

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