Activity multidimensional

Berezhkovskii A M and Zitzerman V Yu 1990 Activated rate processes in a multidimensional case Physica A 166 585-621... 

Berezhkovskii A M and Zitserman V Yu 1991 Activated rate processes in the multidimensional case. Consideration of recrossings in the multidimensional Kramers problem with anisotropic friction Chem. Phys. 157 141-55... 

Berezhkovskii A M and Zitserman V Yu 1992 Multidimensional activated rate processes with slowly relaxing mode Physica A 187 519-50... 

Hershkovitz E and Poliak E 1997 Multidimensional generalization of the PGH turnover theory for activated rate processes J. Chem. Phys. 106 7678... 

Large data sets such as screening data or results obtained by combinatorial experiments are made up of a large number of data records. Hence a data record may represent a chemical reaction or substance, for example its corresponding variables will define the corresponding reaction conditions or biological activities. Depending on the dimensionality or data type of the information, one-, two-, multidimensional, or specific data types can be identified. 

Discriminant emalysis is a supervised learning technique which uses classified dependent data. Here, the dependent data (y values) are not on a continuous scale but are divided into distinct classes. There are often just two classes (e.g. active/inactive soluble/not soluble yes/no), but more than two is also possible (e.g. high/medium/low 1/2/3/4). The simplest situation involves two variables and two classes, and the aim is to find a straight line that best separates the data into its classes (Figure 12.37). With more than two variables, the line becomes a hyperplane in the multidimensional variable space. Discriminant analysis is characterised by a discriminant function, which in the particular case of hnear discriminant analysis (the most popular variant) is written as a linear combination of the independent variables ... 

Tseng SY, Dustin ML (2002) T-cell activation a multidimensional signaling network. Curr. Opin. Cell Biol 14 575-580... 

The semiempirical nature of the methods used to construct multidimensional potential energy surfaces makes the quantitative validity of the results questionable. Hence the present state of the theoretical calculation of activation energies is unsatisfactory. 

Limited protein stability often hampers successful structure elucidation by X-ray crystallography and/or NMR spectroscopy. Relaxation properties are usually improved at elevated temperatures, and multidimensional NMR experiments require sample lifetimes to extend over several days to weeks in order to acquire all the necessary data. In addition, the activity of contaminating proteases that are sometimes present in purified samples can be significant at the experimental temperatures. Therefore, the stability of a target protein can be a concern, in particular for expensive isotope-labeled proteins. 

On the other hand, factor analysis involves other manipulations of the eigen vectors and aims to gain insight into the structure of a multidimensional data set. The use of this technique was first proposed in biological structure-activity relationship (i. e., SAR) and illustrated with an analysis of the activities of 21 di-phenylaminopropanol derivatives in 11 biological tests [116-119, 289]. This method has been more commonly used to determine the intrinsic dimensionality of certain experimentally determined chemical properties which are the number of fundamental factors required to account for the variance. One of the best FA techniques is the Q-mode, which is based on grouping a multivariate data set based on the data structure defined by the similarity between samples [1, 313-316]. It is devoted exclusively to the interpretation of the inter-object relationships in a data set, rather than to the inter-variable (or covariance) relationships explored with R-mode factor analysis. The measure of similarity used is the cosine theta matrix, i. e., the matrix whose elements are the cosine of the angles between all sample pairs [1,313-316]. 

The solution structure of the 87-residue cytochrome cg from the thermophilic cyanobacterium Synechococcus elongatus (optimal temperature for photosynthetic activity = 57 °C) was determined by multidimensional NMR spectroscopy and molecular dynamics calculations and exhibited the overall topology of class I c cytochromes with four a-helices and a small antiparallel /1-sheet near Met58, one of the axial haem ligands. ... 

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