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By Danail D. Bonchev, Dennis Rouvray

The modern clinical strategy is outfitted on reductionism. The wonderful discovering that this paradigm has limits gave upward push to the idea that of complexity. This publication provides the hot technological know-how of complexity through providing assorted innovations from the analyses of quite a lot of actual international platforms (chemical, biochemical, organic, and ecological). in line with numerous techniques starting from mobile automata and dynamic evolutionary networks to topology and data idea, the ebook includes methodologies of sensible significance for assessing platforms complexity and community research in drugs and biology.

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Extra info for Complexity in Chemistry, Biology and Ecology

Example text

7 also the average local complexity (ξav ) increases with the increase of the fullerene size. 7 we have three C40 (# 11 – 13) and two C44 fullerenes (# 15, 16). 40. Thus if one would select instead of 1/2k as the weights for distant neighbors a different scaling, one would nevertheless obtain again the same complexity indices for these two isomers of C40 . These two isomers, however, differ considerably in their symmetry properties: one (# 11) has only three classes of carbon atoms (of multiplicity 24, 12 and 4), while the other (# 12) has ten equivalent classes (four of multiplicity 6, five of multiplicity 3 and a single class for itself).

Diudea, T. S. Balaban, E. C. Kirby and A. Graovac have recently published a study on how to derive single-walled nanotubes from cylindrical surfaces generated from a square net by deleting bonds in order to change squares into hexagons [88]. Their end result is the prediction of metallic or semiconductor behavior of the nanotube in terms of characteristics of the parent square lattice. This study contains further references to papers by Diudea and Kirby on this topic, including ones that allow coding of the nanotube or carbon torus structure [89-92].

On the Complexity of Fullerenes and Nanotubes 27 Hence, we can conclude that the atomic environment described by the first sequence is more complex than that of the second type of carbon atom – and again we arrived at this conclusion without using numerical parameters for characterizing contributions of atoms at different distance from the atom under consideration. It is this non-numerical aspect of comparability of sequences, which leads to partial order of different environments, which makes attractive the use of partial order.

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