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PubMedDate not supplied

Graph valence shells as molecular descriptors.

We have introduced a new simple structural descriptor for molecules that is based on the count of the valence shells for vertices in molecular graphs. The construction of the new descriptor is illustrated on 2,3-dimethylhexane and is reported for the 18 octane isomers. The relationship of the new descriptor to the path numbers of a graph is discussed. It can be seen that the path counts and the count of valence of neighbor shells are related for paths of length two (and shells of range two). There is no appreciable correlation between the count of the longer paths and the count of the corresponding neighbor valence shells at larger separations. Use of the neighbor valence shells as molecular descriptors is illustrated on the boiling point, the entropy, and the density of octanes. An intriguing situation is observed for regressions involving considered properties of n-octane isomers C8H18 in that the paths of length two, three, and four and the shells of the range two, three, and four give identical multivariate regression statistics. An explanation for this somewhat unusual aspect of MRA (multiple regression analysis) is offered.

Journal Article↗

PubMedDate not supplied

Automation of protein 2D proton NMR assignment by means of fuzzy mathematics and graph theory.

The novel methodology for protein 2D NMR assignment presented in this paper is based upon protein spin coupling graph theory analysis, fuzzy graph pattern recognition, and tree searching. The method required to formalize the whole assignment procedure into a logical system which can be properly processed by computer software is also discussed. Solutions for peak overlaps, spin coupling network overlaps, and details related to the automated assignment of BPTI are reported as well.

Algorithms↗

PubMedDate not supplied

A new graph descriptor for molecules containing cycles. Application as screening criterion for searching molecular structures within large databases of organic compounds.

The search of molecular structures inside a large database of chemical compounds is a critical step for many computer programs used in several domains of chemistry. During the last years, the size of many chemical databases has dramatically increased, hence in the meantime, search engines needed to be more and more powerful. The speed and the efficiency of screening processes of the chemical compounds are thus essential. Looking forward for algorithms dedicated to structure and substructure search, we have developed a new graph descriptor for structures containing cycles in order to find efficient indexation and classification criteria of molecular structures. This graph descriptor can be used as a screening criteria for structure and substructure search in large databases of organic compounds.

Journal Article↗

PubMed1990

Computational techniques for vertex partitioning of graphs.

A powerful vertex-partitioning algorithm is developed and applied for vertex partitioning of graphs of chemical and spectroscopic interest. The codes developed on the basis of these algorithms are tested and compared for performance with other methods based on the Morgan algorithm and the principal eigenvector algorithm based on the Givens-Householder method. The newly developed algorithm and codes appear to be more powerful than the Morgan and the principal eigenvector algorithms for vertex partitioning of graphs.

Chemistry, Physical↗

PubMedDate not supplied

Modeling boiling points of cycloalkanes by means of iterated line graph sequences.

A class of models for predicting boiling points of cycloalkanes is put forward, based on iterated line graphs L(i), i = 1, 2,., of the molecular graph G = L(0). Let m(i) be the number of edges of L(i), i = 0, 1, 2,. The models analyzed are of the form a(0)m(i)()(0) + a(1)m(i)(1) + a(2)m(i)(2) +. + a(k)m(ik) + b. Our optimal QSPR formulas contain m(0), m(1), m(2), m(3), and/or m(4) but never m(5) and m(6). Their precision is as good as or better than the approximations recently reported by Rücker and Rücker (J. Chem. Inf. Comput. Sci. 1999, 39, 788-802).

Journal Article↗

PubMedDate not supplied

Prediction of aquatic toxicity: use of optimization of correlation weights of local graph invariants.

Quantitative structure-activity relationships (QSARs) were developed for three sets of toxicity data. Chemicals in each set represented a number of narcoses and electrophilic mechanisms of toxic action. A series of quantitative structure-toxicity models correlating toxic potency with a number of optimization of correlation weights of local graph invariants were developed. In the case of the toxicity of a heterogeneous set of benzene derivatives to Tetrahymena pyriformis, the QSARs were based on the Descriptor of Correlation Weights (DCW) using atoms and extended connectivity (EC) graph invariants. The model [log (IGC(50)(-1)) = 0.0813 DCW(a(k),(3)EC(k)) + 2.636; n = 157, r(2) = 0.883, s = 0.27, F = 1170, Pr > F = 0.0001] based on third-order EC of 89 descriptors was observed to be best for the benzene data. However, fits for these data of > 0.800 were achieved ECs with as few as 23 variables. The relationship between the toxicity predicted by this model and experimental toxicity values for the test set [obs. log(IGC(50)(-1))) = 0.991 (pred. (log(IGC(50)(-1))) - 0.012; n = 60, r(2) = 0.863, s = 0.28, F = 372, Pr > F = 0.0001] is excellent. The utility of the approach was demonstrated by the model [log (IGC(50)(-1)) = 0.1744(DCW (a(k), (2)EC) - 3.505; n = 39, r(2) = 0.900, s = 0.35, F = 333, Pr > F = 0.0001] for the toxicity data for T. pyriformis exposed to halo-substituted aliphatic compounds and the model [log (IC(50)(-1)) = 0.1699(DCW (a(k), (2)EC)) - 2.610; n = 66, r(2) = 0.901, s = 0.31, F = 583, Pr > F = 0.0001] for the Vibrio fischeri toxicity data.

Animals↗

PubMedDate not supplied

Immanants and immanantal polynomials of chemical graphs.

The much-studied determinant and characteristic polynomial and the less well-known permanent and permanental polynomial are special cases of a large class of objects, the immanants and immanantal polynomials. These have received some attention in the mathematical literature, but very little has appeared on their applications to chemical graphs. The present study focuses on these and also generalizes the acyclic or matching polynomial to an equally large class of acyclic immanantal polynomials, generalizes the Sachs theorem to immanantal polynomials, and sets forth relationships between the immanants and other graph properties, namely, Kekulé structure count, number of Hamiltonian cycles, Clar covering polynomial, and Hosoya sextet polynomial.

Journal Article↗

PubMedDate not supplied

A graph-based genetic algorithm and its application to the multiobjective evolution of median molecules.

In this paper we propose a novel graph-based genetic algorithm for the evolution of novel molecular graphs from a predefined set of elements or molecular fragments with an external objective function. A brief overview of existing genetic algorithm approaches in molecular design is provided followed by a description of our approach. The paper continues to suggest a novel application of this program to the multiobjective evolution of median molecules that are structurally representative of a set of objective molecules. We conclude with a summary of our initial results along with a discussion of a variety of improvements and applications of our approach.

Algorithms↗

PubMedDate not supplied

Random walks and chemical graph theory.

Simple random walks probabilistically grown step by step on a graph are distinguished from walk enumerations and associated equipoise random walks. Substructure characteristics and graph invariants correspondingly defined for the two types of random walks are then also distinct, though there often are analogous relations. It is noted that the connectivity index as well as some resistance-distance-related invariants make natural appearances among the invariants defined from the simple random walks.

Journal Article↗

PubMedDate not supplied

Representation of the molecular topology of cyclical structures by means of cycle graphs. 3. Hierarchical model of screening of chemical databases.

The increase in the size and complexity of chemical databases necessitates the proposal and development of efficient methods of classification and recovery of information, which supposes proposal of a model of classification of database records and the use of a compatible model of screening for inspection of clusters and recovery of the molecules that satisfy the search criterion. The cycle graphs model based on consideration of all the cycles and chains (and equivalent cycles and chains) present in the molecular structure has been proven appropriate for classification of chemical databases, giving rise to a generation of different classification levels depending on the structural elements (cycles and chains) that are considered. In this paper we propose a screening model, compatible with the cycle graphs model, based on a hierarchy of levels of abstraction. The set of molecules that satisfies a screening model (or selection criterion) diminishes as we advance in the hierarchy of levels of the model, which allows filtering of records and, therefore, an increase in the efficiency of the screening process. In the following work of this series we describe and validate the screening tool developed.

Journal Article↗

PubMed2000

Walk counts, labyrinthicity, and complexity of acyclic and cyclic graphs and molecules

It is demonstrated how the complexity of a (molecular) graph can be quantified in terms of the walk counts, extremely easily obtained graph invariants that depend on size, branching, cyclicity, and edge and vertex weights (unsaturation, heteroatoms). The influence of symmetry is easily accounted for. The term labyrinthicity is proposed for what is measured by walk counts alone, neglecting symmetry. The total walk count and recently advanced measures of labyrinthicity or complexity are compared with respect to the ordering of structures and to the computational effort required to obtain numerical values.

Journal Article↗

PubMed2004

QSPR modeling the aqueous solubility of alcohols by optimization of correlation weights of local graph invariants.

Optimization of correlation weights of local graph invariants is an approach to model molecular properties and/or activities of chemical or/and biological interest. The essence of the approach may be described by means of three main steps: first, a descriptor which is a function of the weights of local graph invariants must be defined by the suitable choice among the different possibilities from the pool of molecular descriptors; second, correlation weights values which produce as large as possible correlation coefficient value between the selected property values and the descriptor data under consideration are calculated by Monte Carlo optimization procedure (the correlation coefficient is used as the quality objective function); third, a relationship such as property = C0 + C1 descriptor has to be calculated and validated with structures of some training set resorting to the standard least square method. We obtain quite satisfactory results using this calculation procedure to model the aqueous solubility of alcohols whose statistical characteristics are: n = 30, r = 0.9843, s = 0.176, F = 870 (Training Set); n = 33, r = 0.9965, s = 0.0902, F = 4456 (Test Set); n = 63, r = 0.9931, s = 0.121, F = 4379 (complete set of alcohol molecules).

Alcohols↗

PubMed2000

Prognostic value of graph theory-based tissue architecture analysis in carcinomas of the tongue.

Several studies on oral squamous cell carcinomas (OSCC) suggest that the clinical value of traditional histologic grading is limited both by poor reproducibility and by low prognostic impact. However, the prognostic potential of a strictly quantitative and highly reproducible assessment of the tissue architecture in OSCC has not been evaluated. Using image analysis, in 193 cases of T1-2 (Stage I-II) OSCC we retrospectively investigated the prognostic impact of two graph theory-derived structural features: the average Delaunay Edge Length (DEL_av) and the average homogeneity of the Ulam Tree (ELH_av). Both structural features were derived from subgraphs of the Voronoi Diagram. The geometric centers of the cell nuclei were computed, generating a two-dimensional swarm of point-like seeds from which graphs could be constructed. The impact on survival of the computed values of ELH_av and DEL_av was estimated by the method of Kaplan and Meier, with relapse-free survival and overall survival as end-points. The prognostic values of DEL_av and ELH_av as computed for the invasive front, the superficial part of the carcinoma, the total carcinoma, and the normal-appearing oral mucosa were compared. For DEL_av, significant prognostic information was found in the invasive front (p < 0.001). No significant prognostic information was found in superficial part of the carcinoma (p = 0.34), in the carcinoma as a whole (p = 0.35), or in the normal-appearing mucosa (p = 0.27). For ELH_av, significant prognostic information was found in the invasive front (p = 0.01) and, surprisingly, in putatively normal mucosa (p = 0.03). No significant prognostic information was found in superficial parts of the carcinoma (p = 0.34) or in the total carcinoma (p = 0.11). In conclusion, strictly quantitative assessment of tissue architecture in the invasive front of OSCC yields highly prognostic information.

Aged↗

PubMed1997

[Inclination of the Hess-Weiss coordimetric graph. An indirect sign of ocular torsion?].

BACKGROUND: The coordimetric examinations according to Hess-Weiss (HW) and Hess-Lancaster produce the bidimensional graphic demonstration of eye deviations. The horizontal and vertical deviations can be shown easily, whereas cyclotorsion cannot be detected readily. Clinical experience has suggested, however, that there may be an association between rotation of the HW graph and cyclotorsion. The question is, how much can the bidimensional presentation be influenced by the cyclotorsion? METHODS: 48 patients with posttraumatic superior oblique palsy were investigated. The cyclotropia measured at the tangent scale of Harms (dark-red glass method) was compared to the rotation of the HW graph. Patients were divided into 2 groups: 27 unilateral and 21 bilateral palsy. CONCLUSION: The association between the two examination parameters was significant in both patient groups (Group 1 p < 0.01, Group 2 p < 0.05).

Adolescent↗

PubMedDate not supplied

[Percentile graphs in the documentation of acetabular angle in children with hip dysplasia. A tool in the diagnosis and quality control of its treatment].

The acetabular index (AI; Hilgenreiner 1925) has proven to be a reliable parameter for the radiological diagnosis of developmental hip dysplasia (DDH). Age-dependent normal values and ranges of the AI are well documented. These data, however, have so far not been presented graphically in a way which would have made them suitable for patient data documentation on a routine basis (calculation of percentiles, time-axis with log scale, smoothing). We have therefore created graphs meeting these requirements, based on a previous examination of the AI of 719 girls and 428 boys (Tönnis and Brunken 1968). These graphs have meanwhile proven to be a useful and time-saving tool for the diagnosis as well as quality control of the treatment in children with DDH.

Acetabulum↗

PubMed2002

Random graph models of social networks.

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

Humans↗

PubMed1988

Interrelations between random walks on diagrams (graphs) with and without cycles.

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Algorithms↗

PubMed2000

Bounds for cell entries in contingency tables given marginal totals and decomposable graphs.

Upper and lower bounds on cell counts in cross-classifications of nonnegative counts play important roles in a number of practical problems, including statistical disclosure limitation, computer tomography, mass transportation, cell suppression, and data swapping. Some features of the Frechet bounds are well known, intuitive, and regularly used by those working on disclosure limitation methods, especially those for two-dimensional tables. We previously have described a series of results relating these bounds to theory on loglinear models for cross-classified counts. This paper provides the actual theory and proofs for the special case of decomposable loglinear models and their related independence graphs. It also includes an extension linked to the structure of reducible graphs and a discussion of the relevance of other results linked to nongraphical loglinear models.

Journal Article↗