Dynamics on modular networks with heterogeneous correlations
Abstract
We develop a new ensemble of modular random graphs in which degreedegree correlations can be different in each module, and the intermodule connections are defined by the joint degreedegree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the wellknown configuration model and LancichinettiFortunatoRadicchi networks) by allowing a heterogeneous distribution of degreedegree correlations across modules, which is important for the consideration of nonidentical interacting networks.
 Authors:
 MACSI, Department of Mathematics and Statistics, University of Limerick (Ireland)
 (United Kingdom)
 Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)
 Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina, Chapel Hill, North Carolina 275993250 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 22250790
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONFIGURATION; CORRELATIONS; DIAGRAMS; GRAPH THEORY; RANDOMNESS
Citation Formats
Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 275993216, and Gleeson, James P.. Dynamics on modular networks with heterogeneous correlations. United States: N. p., 2014.
Web. doi:10.1063/1.4869983.
Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 275993216, & Gleeson, James P.. Dynamics on modular networks with heterogeneous correlations. United States. doi:10.1063/1.4869983.
Melnik, Sergey, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Porter, Mason A., CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, Mucha, Peter J., Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 275993216, and Gleeson, James P.. Sun .
"Dynamics on modular networks with heterogeneous correlations". United States.
doi:10.1063/1.4869983.
@article{osti_22250790,
title = {Dynamics on modular networks with heterogeneous correlations},
author = {Melnik, Sergey and Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP and Porter, Mason A. and CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP and Mucha, Peter J. and Institute for Advanced Materials, Nanoscience and Technology, University of North Carolina, Chapel Hill, North Carolina 275993216 and Gleeson, James P.},
abstractNote = {We develop a new ensemble of modular random graphs in which degreedegree correlations can be different in each module, and the intermodule connections are defined by the joint degreedegree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the wellknown configuration model and LancichinettiFortunatoRadicchi networks) by allowing a heterogeneous distribution of degreedegree correlations across modules, which is important for the consideration of nonidentical interacting networks.},
doi = {10.1063/1.4869983},
journal = {Chaos (Woodbury, N. Y.)},
number = 2,
volume = 24,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}

Estimating onedimensional models from frequencydomain electromagnetic data using modular neural networks
An artificial neural network interpretation system is being used to interpret data from a frequencydomain electromagnetic (EM) geophysical system in near real time. The interpretation system integrates 45 separate networks in a data visualization shell. The networks produce interpretations at three different transmitterreceiver (TxRx) separations for halfspace and layeredearth interpretations. Modular neural networks (MNN`s) were found to be the only paradigm that could successfully perform the layeredearth interpretations. An MNN with 16 inputs, five local experts, each with seven hidden processing elements, and three outputs was trained on 4795 patterns for 200 epochs. For twolayer models with a resistivity contrastmore » 
Integrated analysis of multiple data sources reveals modular structure of biological networks
It has been a challenging task to integrate highthroughput data into investigations of the systematic and dynamic organization of biological networks. Here, we presented a simple hierarchical clustering algorithm that goes a long way to achieve this aim. Our method effectively reveals the modular structure of the yeast proteinprotein interaction network and distinguishes protein complexes from functional modules by integrating highthroughput proteinprotein interaction data with the added subcellular localization and expression profile data. Furthermore, we take advantage of the detected modules to provide a reliably functional context for the uncharacterized components within modules. On the other hand, the integration ofmore » 
Managerworkerbased model for the parallelization of Quantum Monte Carlo on heterogeneous and homogeneous networks.
A managerworkerbased parallelization algorithm for Quantum Monte Carlo (QMCMW) is presented and compared with the pure iterative parallelization algorithm, which is in common use. The new managerworker algorithm performs automatic load balancing, allowing it to perform near the theoretical maximal speed even on heterogeneous parallel computers. Furthermore, the new algorithm performs as well as the pure iterative algorithm on homogeneous parallel computers. When combined with the dynamic distributable decorrelation algorithm (DDDA) [Feldmann et al., J Comput Chem 28, 2309 (2007)], the new managerworker algorithm allows QMC calculations to be terminated at a prespecified level of convergence rather than upon amore »