Combinatorial matrices

Diudea (1996a, 1996b Diudea et al., 2006) introduced two combinatorial matrices, the distance-delta matrix CM and the distance-path matrix CM, whose entries are based on the elements of the related vertex-distance matrix D  

The distance-delta matrix gives a descriptor related to the non-Wiener part of the hyper-Wiener index, while the distance-path matrix allows direct computation of the hyper-Wiener index (Diudea, 1996a, 1996b). It should also be noted that there is the following relationship between the elements of the three matrices based on the shortest graph-distances D, CM, and CM  

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Combinatorial Matrices. There are a number of combinatorial matrices... 

Characteristic polynomial of combinatorial matrices as well as —> spectral indices were proposed as molecular descriptors for QSAR problems [Ivanciuc, Diudea et al, 1998]. 

Combinatorial matrices, denoted by Mb, are defined in terms of the binomial coefficient of the elements of a graph-theoretical matrix M. Each entry U-j of the combinatorial matrix is calculated as the following [Diudea, 1996a] ... 

The most common combinatorial matrices are derived from the distance matrix and detour matrix these are the distance-path matrix, detour-path matrix, delta matrix, and... 

The reciprocal combinatorial matrices, the reciprocal distance-delta matrix CM- and the reciprocal distance-path matrix CM, are matrices whose entries are... 

The reciprocal combinatorial matrices and CM- of T2 (see Figure 2.19) and G, (see strnctnre A in Fignre 2.1), based on the corresponding combinatorial matrices, given above, are as follows ... 

The detour-path matrix, denoted as Ap, is a —> combinatorial matrix analogously defined as the —> distance-path matrix Dp it is a square symmetric matrix Ax A whose off-diagonal entry i-j is the count of all paths of any length m (1 < m < A j) that are included within the longest path from vertex V to vertex Vj (Ay) [Diudea, 1996a]. The diagonal entries are zero. 

The detour-delta matrix, denoted as A, is another combinatorial matrix derived as the difference between the detour-path matrix Ap and the detour matrix A [Janezic, Milicevic... 

The delta matrix or distance-delta matrix or vertex distance-delta matrix, denoted as Da, is another combinatorial matrix defined as the difference between the distance-path matrix Dp and the distance matrix D [Diudea, 1996a Diudea, Katona et al, 1997 Ivanduc, Diudea et al, 1998] ... 

Input code, programmed in Perl, to generate a combinatorial matrix of products from compounds selected in a focused bbrary (see Note 14). 

Generate an optimum 10 X 10 combinatorial matrix for similarity search products. If using the Perl script described in the Subheading 2.2., use the command (see Note 26) ... 

The element [Da] counts the number of internal paths (larger than unity) included in the shortest paths between vertices v and vj the element [Dp] y counts all internal paths included in the shortest paths between vertices v,- and vj in a graph, The matrix Dp allows the direct computation of the hyper-Wiener index, whereas the matrix D gives an index related to the non-Wiener part of the hyper-Wiener index. Obviously, D = Dp - D, From the matrix D(31) we obtain the combinatorial matrix Dp(31) ... 

On-line SPE-LC-ISP-MS/MS (with run times of 1-3 min) is widely used in pharmaceutical, clinical, and combinatorial chemistry, as well as in environmental monitoring, whenever rapid target MS analysis in a complex matrix is required. Thermally assisted... 

In a study conducted by Szardenings et various combinatorial libraries of DPKs scaffolds were created to design and evaluate the activity of DPKs as inhibitors of the matrix metalloproteinases, namely, collegenase-1 and gelatinase B. This study created structure-activity relationships (SAR) for side chains attached to a DPK core structure. These enzymes are therapeutic targets with indications in the treatment of cancer, arthritis, autoimmunity, and cardiovascular disease. 

Defines a combinatorial library called oxazolidines formed by the matrix of products from the combination of the listed dimensions... 

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