Chemicals hyperspace

The concept of property space, which was coined to quanhtahvely describe the phenomena in social sciences [11, 12], has found many appUcahons in computational chemistry to characterize chemical space, i.e. the range in structure and properhes covered by a large collechon of different compounds [13]. The usual methods to approach a quantitahve descriphon of chemical space is first to calculate a number of molecular descriptors for each compound and then to use multivariate analyses such as principal component analysis (PCA) to build a multidimensional hyperspace where each compound is characterized by a single set of coordinates. 

For a complete picture, however, some critical remarks have to be added. For medium-sized molecules, the obviously successful combination of theoretical prediction and experimental verification rather should be considered as an individually tailored interplay, which is based on numerous assumptions i.e. so-called chemical intuition. Tobeginwith, any hypersurface design confined to a few selected coordinates will only cover the aspects introduced thereby. Even several independent cuts through the (3n-6) dimensional hyperspace cannot unravel the complexity of a molecule in a specific molecular state. And although semiempirical methods - especially MNDO (10)- are not only fast but to quite an extent also reliable, their numerical accuracy should not be overstressed. Thus semiempirical hypersurfaces might better be considered as supplying trends in essential features, which can be compared to and correlated with measurement data to add the numerical accuracy, and, in return, to test and to substantiate all underlying assumptions. 

For such applications of classical optimization theory, the data on energy and gradients are so computationally expensive that only the most efficient optimization methods can be considered, no matter how elaborate. The number of quantum chemical wave function calculations must absolutely be minimized for overall efficiency. The computational cost of an update algorithm is always negligible in this context. Data from successive iterative steps should be saved, then used to reduce the total number of steps. Any algorithm dependent on line searches in the parameter hyperspace should be avoided. 

Thousands of chemical compounds have been identified in oils and fats, although only a few hundred are used in authentication. This means that each object (food sample) may have a unique position in an abstract n-dimensional hyperspace. A concept that is difficult to interpret by analysts as a data matrix exceeding three features already poses a problem. The art of extracting chemically relevant information from data produced in chemical experiments by means of statistical and mathematical tools is called chemometrics. It is an indirect approach to the study of the effects of multivariate factors (or variables) and hidden patterns in complex sets of data. Chemometrics is routinely used for (a) exploring patterns of association in data, and (b) preparing and using multivariate classification models. The arrival of chemometrics techniques has allowed the quantitative as well as qualitative analysis of multivariate data and, in consequence, it has allowed the analysis and modelling of many different types of experiments. 

As an example I cite our early searches on the chemical structure properties indole and ethyiamine and the medical use properties sympathomimetic and parasympathomimetic 8). These searches revealed two sets ot intersecting hyperspace axes. One ot these intersections contains compounds with ethyiamine structures (Property A in Table IV) which have the medical use property sympathomimetic the other cluster indicates organic ammonium ions... 

R. A. Dammkoehler, S. F. Karasek, E. F. B. Shands, and G. R. Marshall, Constrained Search of Conformational Hyperspace Segmentation and Parallelism, Abstr. 204th ACS National Meeting, American Chemical Society, Washington, DC, 1992. 

A theoretical dimensionality of the hyperspace of independent chemical sensor features has been estimated to be 1021 (Fig. 21.1) and includes the permutations of varying sensing materials, transducer principles, and modes of operation for each sensor/transducer combination.13 As shown in the present book, all types of sensing materials have been explored with combinatorial technologies, which demonstrates the desire of the sensing community for the accelerated development of sensing materials using newly introduced research tools. 

T. , Transducer Modu at on. Matenals transducers+ + . + Geometries Parameters Parameter j Shapes Multiple Modulation Parameters Hyperspace of Chemical Sensor Features... 

Fig. 21.1 Hyperspace of chemical sensor features with about 1021 independent features. Reprinted with permission from Gopel et al.1 Copyright 1998 Elsevier...

Dalby A, J G Nourse, W D Hounshell, A K I Gushurst, D L Grier, B A Leland and J Laufer 1992 Descriphon of Several Chermcal Structure File Formats Used by Computer Programs Developed at Molecular Design Lirmted journal of Chemical Information and Computer Science 32 244-255 Dammkoehler R A, S F Karasek, E F B Shands and G R Marshall 1989. Constrained Search of Conformational Hyperspace Journal of Computer-Aided Molecular Design 3 3-21. 

Now a series of chemometric methods have been used in SAR. Generally speaking, different chemometric methods are suitable for different cases for each kind of these methods has its own advantages and disadvantages, and the best approach should be the combination of several chemometric techniques that complement each other, as that we have discussed in chapter one. So it is helpful to introduce briefly the different chemometric methods widely used in SAR. Here chemical pattern recognition methods will be specially emphasized since different projections can provide plentiful information from different projection maps from the hyperspaces. In SAR practice, some chemical pattern recognition methods are often used as complementary methods in the application of SVM. 

Because both medical use and chemical structure are associated in the same computer file, they form a hyperspace. The nonparametric nature of this hyperspace was discussed in a... 

We have described in the preceeding section four different cuts through the hyperspace of medical uses and their frequency in the Merak Index data base. By "cut" we refer by analogy to a projection of the hyperspace onto one or more recognizable orthogonal Cartesian axes. In this section we will discuss what we have learned from these four cuts. We will also approach, but certainly not exhaust, the association of this hyperspace (the effect space) with the hyperspace containing the chemical structure of compounds having these uses (the structure space). 

The same reasoning which suggests this possibility of extrapolation also leads to the conclusion that it is this particular cut through the medical use hyperspace which leads into associations with the chemical structure hyperspace. 

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