Self-similar community structure in a network of human interactions.

We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.

A fuzzy ARTMAP based on quantitative structure-property relationships (QSPRs) for predicting aqueous solubility of organic compounds.

Quantitative structure-property relationships (QSPRs) for estimating aqueous solubility of organic compounds at 25 degrees C were developed based on a fuzzy ARTMAP and a back-propagation neural networks using a heterogeneous set of 515 organic compounds. A set of molecular descriptors, developed from PM3 semiempirical MO-theory and topological descriptors (first-, second-, third-, and fourth-order molecular connectivity indices), were used as input parameters to the neural networks. Quantum chemical input descriptors included average polarizability, dipole moment, resonance energy, exchange energy, electron-nuclear attraction energy, and nuclear-nuclear (core-core) repulsion energy. The fuzzy ARTMAP/QSPR correlated aqueous solubility (S, mol/L) for a range of -11.62 to 4.31 logS with average absolute errors of 0.02 and 0.14 logS units for the overall and validation data sets, respectively. The optimal 11-13-1 back-propagation/QSPR model was less accurate, for the same solubility range, and exhibited larger average absolute errors of 0.29 and 0.28 logS units for the overall and validation sets, respectively. The fuzzy ARTMAP-based QSPR approach was shown to be superior to other back-propagation and multiple linear regression/QSPR models for aqueous solubility of organic compounds.

Neural network based quantitative structural property relations (QSPRs) for predicting boiling points of aliphatic hydrocarbons

Quantitative structural property relations (QSPRs) for boiling points of aliphatic hydrocarbons were derived using a back-propagation neural network and a modified Fuzzy ARTMAP architecture. With the back-propagation model, the selected molecular descriptors were capable of distinguishing between diastereomers. The QSPRs were obtained from four valance molecular connectivity indices (1chiv,2chiv,3chiv,4chiv), a second-order Kappa shape index (2kappa), dipole moment, and molecular weight. The inclusion of dipole moment proved to be particularly useful for distinguishing between cis and trans isomers. A back-propagation 7-4-1 architecture predicted boiling points for the test, validation, and overall data sets of alkanes with average absolute errors of 0.37% (1.65 K), 0.42% (1.73 K), and 0.37% (1.54 K), respectively. The error for the test and overall data sets decreased to 0.19% (0.81 K) and 0.31% (1.30 K), respectively, using the modified Fuzzy ARTMAP network. A back-propagation alkene model, with a 7-10-1 architecture, yielded predictions with average absolute errors for the test, validation, and overall data sets of 1.96% (6.79 K), 1.83% (6.45 K), and 1.25% (4.42 K), respectively. Fuzzy ARTMAP reduced the errors for the test and overall data sets to 0.19% (0.73 K) and 0.25% (0.95 K), respectively. The back-propagation composite model for aliphatic hydrocarbons, with a 7-9- architecture, yielded boiling points with average absolute errors for the test, validation, and overall set of 1.74% (6.09 K), 1.25% (4.68 K), and 1.37% (4.85 K), respectively. The error for the test and overall data sets using the Fuzzy ARTMAP composite model decreased to 0.84% (1.15 K) and 0.35% (1.35 K), respectively. Performance of the QSPRs, developed from a simple set of molecular descriptors, displayed accuracy well within the range of expected experimental errors and of better accuracy than other regression analysis and neural network-based boiling points QSPRs previously reported in the literature.

Identification of coherent structures in turbulent shear flows with a fuzzy artmap neural network.

An implementation of a Fuzzy Artmap neural network is used to detect and to identify (recognise) structures (patterns) embedded in the velocity field of a turbulent wake behind a circular cylinder. The net is trained to recognise both clockwise and anticlockwise eddies present in the u and v velocity fields at 420 diameters downstream of the cylinder that generates the wake, using a pre-processed part of the recorded velocity data. The phase relationship that exists between the angles of the velocity vectors of an eddy pattern is used to reduce the number of classes contained in the data, before the start of the training procedure. The net was made stricter by increasing the vigilance parameter within the interval [0.90, 0.95] and a set of net-weights were obtained for each value. Full data files were scanned with the net classifying patterns according to their phase characteristics. The net classifies about 27% of the recorded signals as eddy motions, with the strictest vigilance parameter and without the need to impose external initial templates. Spanwise distances (homogeneous direction of the flow) within the centres of the eddies identified suggest that they form pairs of counter-rotating vortices (double rollers). The number of patterns selected with Fuzzy Artmap is lower than that reported for template matching because the net classifies eddies according to the recirculating pattern present at the core or central region, while template matching extends the region over which correlation between data and template is performed. In both cases, the topology of educed patterns is in agreement.