Information theory INDEX

James, C. A., Weininger, D., Delaney, J. Daylight Theory Manual, Daylight Chemical Information Systems, Mission Viejo, CA, USA, http //www.daylight.com/ dayhtml/doc/theory/index.html. 

Chen B. Wornell G. W. (2001). Quantization index modulation A class of provably good methods for digital watermarking and information embedding. IEEE Trans, on Information Theory, 47 (4), 1423-1443. 

On the basis of graph theory and information theory, Bertz [30] has proposed, in the past few years, the first general index of molecular complexity (T ), so introducing a quantitative concept of "molecular complexity" which may be applied to synthetic analysis. 

One of the most widely used indexes of community structure has been species diversity. Many measures for diversity are used, from such elementary forms as species number to measures based on information theory. A decrease in species diversity is usually taken as an indication of stress or impact upon a particular ecosystem. Diversity indexes, however, hide the dynamic nature of the system and the effects of island biogeography and seasonal state. As demonstrated in microcosm experiments, diversity is often insensitive to toxicant impacts. 

The Bertz index incorporates skeletal complexity by representing the molecular structure as a graph (a skeletal molecular graph that represents all nonhydrogen atoms) that will have properties that are expressed as so-called graph theoretical invariants. Bertz uses information theory to incorporate the effects of symmetry, and also accounts for molecular size and the presence of heteroatoms in his general index of complexity. 

Barone, R. Petitjean, M. Baralotto, C. Piras, P Chanon, M. Information theory description of synthetic strategies A new similarity index. 2003, 16, 9. 

The entropy index as defined in equation 18.36 is potentially very useful in the fundamental evaluation of any separation processes, not just in solid-liquid separation. Besides the Russian references ", Ogawa et al. derived the same entropy index (but using mass fractions rather than volumetric ones) from information theory and proposed its use for the evaluation of any separation process. 

The use of entropy in particle technology is not restricted to evaluations of separation efficiency. A unit-less definition of entropy virtually identical with that in equation 18.6 but in terms of probability of events, as used in information theory and proposed by Shannon , has been applied in geology to histograms and cumulative curves by Sharp and Fan to define a sorting index for particle size analysis. Sharp applied the information entropy to... 

The Wiener index [86] can be expressed in terms of the distance matrix [87] and equals the half-sum of all distance matrix entries. Randi(5 [88] and Kier and Hall indices of order 0-3 [89] are calculated from coordination numbers of atoms or from values of atomic connectivity. The Kier shape index (order 1-3) [90] depends on the number of skeletal atoms, molecular branching, and the ratio of the atomic radius and the radius of the carbon atom in the sp hybridization state. The Kier flexibility index [90] is derived from the Kier shape index. The Balaban index depends on the row sums of the entries of the distance matrix and the cyclomatic number [92,93]. The information content index and its derivatives (order 0-2) are based on the Shannon information theory [95]. Modifications of the information content index are structural information content, complementary information content, and bond information content [96],... 

Keywords Information theory Mutual information Information integration Dynamical cluster index Dynamical system Boolean networks... 

The polynomial (1.5) which I called cycle index is, if H is the symmetric group, equal to the principal character of H in representation theory. Professor Schur informed me that the cycle index of an arbitrary permutation group being really a subgroup of a symmetric group is of importance for the representation of this symmetric group. We will, however, not expand on the relationship between representation theory and our subject. 

In the "general index of complexity" (C ) proposed by Bertz, besides the number of connections, symmetry is also taken into account. Such an index, that incorporates concepts from the "graph theory" and the "theory of information" [7] is defined as ... 

Note that the number of diffraction peaks decreases with time as the droplet diameter decreases, and the number density of peaks is very nearly proportional to the droplet size. The intensity of the scattered light also decreases with size. The resolution of the photodiode array is not adequate to resolve the fine structure that is seen in Fig. 21, but comparison of the phase functions shown in Fig. 22 with Mie theory indicates that the size can be determined to within 1% without taking into account the fine structure. In this case, however, the results are not very sensitive to refractive index. Some information is lost as the price of rapid data acquisition. 

Global hardness. The partial charge concept helps the chemist to visualize within a molecule or a network, how the electronic density changes as a function of the spatial location of the various atomic constituents. Another useful information for chemical reactivity would be to visualize where the electronic chemical potential variation should be the largest or the lowest. Such a parameter is called a frontier index and may be defined in density-functional theory as f = dQHOMO/LUMO N (16). Point-charge approximation of this relation shows that each atom of a chemical compound should have a frontier index fj such that (17) ... 

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