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At least 397 records · Page 22Linked to original sources

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

Automatic generation of complementary descriptors with molecular graph networks.

We describe a method for the automatic generation of weakly correlated descriptors for molecular data sets. The method can be regarded as a statistical learning procedure that turns the molecular graph, representing the 2D formula of the compound, into an adaptive whole molecule composite descriptor. By translating the molecular graph structure into a dynamical system, the algorithm can compute an output value that is highly sensitive to the molecular topology. This system can be trained by gradient descent techniques, which rely on the efficient calculation of the gradient by back-propagation. We present computational experiments concerning the classification of the Developmental Therapeutics Program AIDS antiviral screen data set on which the performance of the method compares with that of approaches based on substructure comparison.

Algorithms↗

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↗

PubMedDate not supplied

Chirality of toroidal molecular graphs.

Symmetry properties of a class of toroidal molecular graphs, arising as covers of certain bipartite cubic Cayley graphs of dihedral groups, are studied. Although these symmetries make all vertices and all edges indistinguishable, they imply intrinsic chirality.

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↗

PubMed2005

Graph theory for fused cubic clusters of water dodecamer.

The stable structures of the fused cubic water cluster (H2O)12 are examined using graph theoretical techniques and ab initio calculations. The calculations are obtained by scanning the symmetry of digraph structures of hydrogen-bond network spanning 12 oxygen atom vertexes. Using the Pólya theorem the cycle index expressions for 12 vertexes and 20 edges of a cuboid in point-group symmetry D(4h) are developed. A total of 91 energy-allowed fused cubic structures are obtained, which are classified by 8 point-group symmetries: 1 D(2h), 2 S4, 5 C4, 1 D2, 11 C2, 10 C(i), 1 C(s), and 60 C1. An energy level diagram of the structures reveals 14 bands that correspond to 14 unique two-colored graphs derived from the distributions of four free hydrogens of the cluster.

Macromolecular Substances↗

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↗

PubMed2005

Insights into the quaternary association of proteins through structure graphs: a case study of lectins.

The unique three-dimensional structure of both monomeric and oligomeric proteins is encoded in their sequence. The biological functions of proteins are dependent on their tertiary and quaternary structures, and hence it is important to understand the determinants of quaternary association in proteins. Although a large number of investigations have been carried out in this direction, the underlying principles of protein oligomerization are yet to be completely understood. Recently, new insights into this problem have been gained from the analysis of structure graphs of proteins belonging to the legume lectin family. The legume lectins are an interesting family of proteins with very similar tertiary structures but varied quaternary structures. Hence they have become a very good model with which to analyse the role of primary structures in determining the modes of quaternary association. The present review summarizes the results of a legume lectin study as well as those obtained from a similar analysis carried out here on the animal lectins, namely galectins, pentraxins, calnexin, calreticulin and rhesus rotavirus Vp4 sialic-acid-binding domain. The lectin structure graphs have been used to obtain clusters of non-covalently interacting amino acid residues at the intersubunit interfaces. The present study, performed along with traditional sequence alignment methods, has provided the signature sequence motifs for different kinds of quaternary association seen in lectins. Furthermore, the network representation of the lectin oligomers has enabled us to detect the residues which make extensive interactions ('hubs') across the oligomeric interfaces that can be targetted for interface-destabilizing mutations. The present review also provides an overview of the methodology involved in representing oligomeric protein structures as connected networks of amino acid residues. Further, it illustrates the potential of such a representation in elucidating the structural determinants of protein-protein association in general and will be of significance to protein chemists and structural biologists.

Amino Acid Sequence↗

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↗

PubMed1992

Skill acquisition and development: the roles of state-, parameter, and graph dynamics.

The development of motor skills can be portrayed as a dynamical process that involves three types of dynamics: state dynamics, parameter dynamics, and graph dynamics. The time scales associated with each type of dynamics are discussed, and an outline is provided of the role played by each type in the developing organism. In particular, the role of parameter dynamics and graph dynamics in producing qualitative, bifurcational changes in behavior is described. It is concluded that all three types of dynamics are required for a complete description of skill acquisition and development.

Journal Article↗

PubMed1994

Integration of graph theory and quantum chemistry for structure-activity relationships.

The objective of this article is to outline both graph-theoretically based and quantum chemically based structural indices of potential use in quantitative structure activity correlations. We consider graph-theoretical indices such as the connectivity index, topological index, Wiener index and molecular ID indices. Several structural and geometry-dependent indices can be derived from semiempirical and ab initio quantum calculations based on the charge densities, overlap matrices, frontier orbitals, molecular hardness, free valence, density matrices, quantum spectral difference indices, quantum spectral indices and bond matrices. Finally, the use of electrostatic potentials and charge densities for the prediction of reactive sites will be discussed.

Butadienes↗

PubMed2005

Biogeographic interpretation of splits graphs: least squares optimization of branch lengths.

Although most often used to represent phylogenetic uncertainty, network methods are also potentially useful for describing the phylogenetic complexity expected to characterize recent species radiations. One network method with particular advantages in this context is split decomposition. However, in its standard implementation this approach is limited by a conservative criterion for branch length estimation. Here we extend the utility of split decomposition by introducing a least squares optimization technique for correcting branch lengths that may be underestimated by the standard implementation. This optimization of branch lengths is generally expected to improve divergence time estimates calculated from splits graphs. We illustrate the effect of least squares optimization on such estimates using the Australasian Myosotis and the Hawaiian silversword alliance as examples. We also discuss the biogeographic interpretation and limitations of splits graphs.

Boraginaceae↗

PubMed1992

Timing of physiodesis in limb length inequality. The Straight Line Graph applied in 30 patients.

In a prospective study 30 children underwent 33 physiodeses for lower limb length inequality (LLI). Timing of surgery was based on (bi)annual orthoradiographic measurements and skeletal age, and in accordance with Moseley's Straight Line Graph. The mean predicted LLI was 5.2 (3.0-11) cm and the mean LLI at the end of growth was 1.4 (0.0-4.3) cm. In 9 patients final LLI exceeded 1.5 cm, and one of these patients was operated on twice. In total, secondary operations were performed three times. After analysis of the failures it is concluded that the accuracy of the Straight Line Graph is mainly limited by the pattern of skeletal maturation. Recommendations to prevent failures from other causes are given.

Adolescent↗