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MOLecular Structure GENeration with MOLGEN, new features and future developments
 Fresenius J. Anal. Chem
, 1997
"... MOLGEN is a computer program system which is designed for generating molecular graphs fast, redundancy free and exhaustively. In the present paper we describe its basic features, new features of the current release MOLGEN 3.5, and future developments which provide considerable improvements and ex ..."
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MOLGEN is a computer program system which is designed for generating molecular graphs fast, redundancy free and exhaustively. In the present paper we describe its basic features, new features of the current release MOLGEN 3.5, and future developments which provide considerable improvements and extensions. 1 Introduction MOLGEN [17] is a generator for molecular graphs (=connectivity isomers or constitutional formulae) allowing to generate all isomers that correspond to a given molecular formula and (optional) further conditions like prescribed and forbidden substructures, ring sizes etc. The input consists of ffl the empirical formula, together with ffl an optional list of macroatoms, which means prescribed substructures that must not overlap, ffl an optional goodlist, that consists of prescribed substructures which may overlap, ffl an optional badlist, containing forbidden substructures, ffl an optional interval for the minimal and maximal size of rings, ffl an optional num...
Interpretation of Quantitative StructureProperty and –Activity
"... The potential utility of data reduction methods (e.g. principal component analysis) for the analysis of matrices assembled from the related properties of large sets of compounds is discussed by reference to results obtained from solvent polarity scales, ongoing work on solubilities and sweetness pro ..."
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Cited by 4 (2 self)
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The potential utility of data reduction methods (e.g. principal component analysis) for the analysis of matrices assembled from the related properties of large sets of compounds is discussed by reference to results obtained from solvent polarity scales, ongoing work on solubilities and sweetness properties, and proposed general treatments of toxicities and gas chromatographic retention indices.
Philosophy of Mathematical Chemistry: A Personal Perspective
 HYLE International Journal for Philosophy of Chemistry
"... Abstract: This article discusses the nature of mathematical chemistry, discrete mathematical chemistry in particular. Molecules and macromolecules can be represented by model objects using methods of discrete mathematics, e.g., graphs and matrices. Mathematical formalisms are further applied on the ..."
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Abstract: This article discusses the nature of mathematical chemistry, discrete mathematical chemistry in particular. Molecules and macromolecules can be represented by model objects using methods of discrete mathematics, e.g., graphs and matrices. Mathematical formalisms are further applied on the model objects to distill various quantitative characteristics. The end product of such an exercise can be a better understanding of chemistry, the development of quantitative scales for qualitative notions of chemistry, or an illumination of the structural basis of chemical and biological properties. The aforementioned aspects of mathematical chemistry are discussed based on my own practitioner’s perspective.
Limit Laws for the Randić Index of Random Binary Tree Models
, 2006
"... Abstract. We investigate the Randić index of random binary trees under two standard probability models: the one induced by random permutations and the Catalan (uniform). In both cases the mean and variance are computed by recurrence methods and shown to be asymptotically linear in the size of the tr ..."
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Abstract. We investigate the Randić index of random binary trees under two standard probability models: the one induced by random permutations and the Catalan (uniform). In both cases the mean and variance are computed by recurrence methods and shown to be asymptotically linear in the size of the tree. The recursive nature of binary search trees lends itself in a natural way to application of the contraction method, by which a limit distribution (for a suitably normalized version of the index) is shown to be Gaussian. The Randić index (suitably normalized) is also shown to be normally distributed in binary Catalan trees, but the methodology we use for this derivation is singularity analysis of formal generating functions.
Intrinsic Dimensionality of Chemical Space: Characterization and Applications
, 2015
"... One popular method for the representation and characterization of chemical structure is through the use of their computed mathematical descriptors. Such descriptors, often called molecular descriptors, quantify different aspects of molecular structure, viz., size, shape, branching, cyclicity, bondin ..."
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One popular method for the representation and characterization of chemical structure is through the use of their computed mathematical descriptors. Such descriptors, often called molecular descriptors, quantify different aspects of molecular structure, viz., size, shape, branching, cyclicity, bonding patterns, etc. Applications of discrete mathematics in the development of molecular descriptors began in the middle of the twentieth century and the trend is going on in an unabated manner even today. While in the 1970s only a few descriptors could be calculated, currently available software can calculate a large number of descriptors for molecules or biomolecules like DNA / RNA, proteins. When p molecular descriptors are calculated for n molecules, the data set can be viewed as n vectors in p dimensions, each chemical being represented as a point in Rp. Because many of the descriptors are strongly correlated, the n points in Rp will lie on a subspace of dimension lower than p. Methods like principal components analysis (PCA) can be used to characterize the intrinsic dimensionality of chemical spaces. Since the early 1980s, Basak et al have carried out PCA of various congeneric and diverse data sets relevant to new drug discovery and predictive toxicology. Principal components (PCs) derived from mathematical chemodescriptors have been used in the formulation of quantitative structureactivity relationships
InformationTheoretic Biodescriptors for Proteomics Maps: Development and Applications in Predictive Toxicology
"... Abstract: This paper describes an approach using information theory to derive a new complexity measure for proteomics maps generated using 2dimensional gel electrophoresis. The maps used in this study were partitioned into 5x5 grids and the total abundance of protein material in each grid was compa ..."
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Abstract: This paper describes an approach using information theory to derive a new complexity measure for proteomics maps generated using 2dimensional gel electrophoresis. The maps used in this study were partitioned into 5x5 grids and the total abundance of protein material in each grid was compared to the total abundance for the entire map. Next, Shannon's relation was applied to characterize the distribution of spots across the proteomics map. Details of the approach are discussed here, including an illustrative example and an example of the calculations for a proteomics map containing 200 spots. Finally, results for the Map Information Content index are presented for a set of five maps calculated using 200 spots, 500 spots, and 1,054 spots. It is hoped that the application of informationtheoretic techniques to characterize the complexity of these maps, thus reducing the amount of information presented to the researcher, will help in the analysis and comparison of maps containing a great deal of information. KeyWords: 2DE gel; biodescriptor; complexity; information theory; map information content; proteomics; proteomics maps 1
Similarity methods in analog selection, property estimation and clustering of diverse chemicals
"... This account summarizes Dr. Subhash Basak’s work in the field of molecular similarity. In particular, it looks at the development and application of quantitative molecular similarity analysis (QMSA) techniques using physicochemical properties, topological indices, and atom pairs as descriptors for d ..."
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This account summarizes Dr. Subhash Basak’s work in the field of molecular similarity. In particular, it looks at the development and application of quantitative molecular similarity analysis (QMSA) techniques using physicochemical properties, topological indices, and atom pairs as descriptors for developing structure or propertybased similarity spaces and the use of a knearest neighbors (kNN) technique to estimate the properties or activities of chemicals within the space. Additionally, the account discusses the novel tailored similarity technique pioneered by Dr. Basak’s research group and discusses the future of molecular similarity analysis
Mathematical Simulations in Combinatorial Chemistry
, 1996
"... A novel technique for chemical synthesis in drug research is combinatorial chemistry, where usually a set of buildingblock molecules is attached to a core structure in all the combinatorially possible ways. The resulting set of compounds (called a library) can then be systematically screened for a ..."
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A novel technique for chemical synthesis in drug research is combinatorial chemistry, where usually a set of buildingblock molecules is attached to a core structure in all the combinatorially possible ways. The resulting set of compounds (called a library) can then be systematically screened for a desired biological activity. In this paper we discuss ways and limits of a mathematical simulation of this procedure. At first, two methods for selecting the buildingblocks from a given structure pool are presented with the objective to obtain only dissilimar library entries. Next an algorithm is described for the exhaustive and redundancyfree generation of a combinatorial library, illustrated by a singlestep and a multicomponent reaction. Finally equations for the enumeration of the library sizes are derived and the limits of the virtual combinatorial chemistry, i.e. purely in computer and without experiment, are discussed. 1