By Subhash C. Basak, Visit Amazon's Guillermo Restrepo Page, search results, Learn about Author Central, Guillermo Restrepo, , Jose L. Villaveces

Advances in Mathematical Chemistry and Applications highlights the hot growth within the rising self-discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have introduced jointly 27 chapters written via sixty eight the world over well known specialists in those volumes.

Each quantity contains a smart integration of mathematical and chemical suggestions and covers quite a few purposes within the box of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology.

Volume 2 explores deeper the subjects brought in quantity 1, with quite a few extra subject matters equivalent to topological techniques for classifying fullerene isomers; chemical response networks; discrimination of small molecules utilizing topological molecular descriptors; GRANCH equipment for the mathematical characterization of DNA, RNA and protein sequences; linear regression tools and Bayesian concepts; in silico toxicity prediction equipment; drug layout; integration of bioinformatics and structures biology, molecular docking, and molecular dynamics; metalloenzyme types; protein folding versions; molecular periodicity; generalized topologies and their functions; and lots of more.

    • Brings jointly either the theoretical and sensible points of the basic techniques of mathematical chemistry
    • Covers purposes in numerous fields similar to drug discovery, defense of human in addition to ecological healthiness, chemoinformatics, bioinformatics, toxicoinformatics, and computational biology, to call only a few
    • About 1/2 the ebook focuses totally on present paintings, new functions, and rising techniques for the mathematical characterization of crucial features of molecular constitution, whereas the opposite part describes functions of structural method of new drug discovery, digital screening, protein folding, predictive toxicology, DNA constitution, and structures biology

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    Example text

    Chemical properties thus emerge by mapping experimental reactions into abstract reaction types (Fig. (3)), which involves a transformation of an empirical reaction network into a reduced representation of the same kind, where the transformation preserves the essential logical structure of the original network. Category theory allows formalising this intuition by giving necessary and sufficient conditions for stating that a transformation between reaction networks is ‘structure-preserving’. Elements of Category Theory The essential identity of mathematical objects is not determined by what the object ‘is by itself’, but by what it ‘is related to’.

    The core of the formalism of category theory is the generalization of these different criteria of structurepreserving transformation by means of the concept of morphisms in a category. Definition 1 (Category). A category collection of morphisms such that consists of a collection of objects and a i). For each ∈ there exist a unique object Dom( ) ∈ called the domain of f and a unique object Cod( ) ∈ called the codomain of . A morphism f with Dom( ) = and Cod( ) = is noted as ∶ → . ii). For each , , ∈ , ∶ → , and ∶ → , there exists a unique morphism ∘ ∶ → in called the composite of and .

    Suitably defined closure operators on a substance set capture this idea, by adding to the closure of a subset of substances all those substances that are ‘as similar to elements of S as elements of S are among themselves’. The first two properties of closure operators are indispensable to follow this idea faithfully. Indeed, if we were to remove property i), a substance in could be dissimilar to elements of when considered in the context of , which is absurd; and if we remove property ii), we could have cl( ) ⊈ cl( ) for ⊆ , so that there exists at least one ∈ cl( ) ∖ cl( ), that is, a substance that is at the same time similar and not similar to those of , which is absurd as well.

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