Journal articles: 'Network Correlations'

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Lary, D. J., M. D. Müller, and H. Y. Mussa. "Using neural networks to describe tracer correlations." Atmospheric Chemistry and Physics 4, no. 1 (January 31, 2004): 143–46. http://dx.doi.org/10.5194/acp-4-143-2004.

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Abstract. Neural networks are ideally suited to describe the spatial and temporal dependence of tracer-tracer correlations. The neural network performs well even in regions where the correlations are less compact and normally a family of correlation curves would be required. For example, the CH4-N2O correlation can be well described using a neural network trained with the latitude, pressure, time of year, and CH4 volume mixing ratio (v.m.r.). In this study a neural network using Quickprop learning and one hidden layer with eight nodes was able to reproduce the CH4-N2O correlation with a correlation coefficient between simulated and training values of 0.9995. Such an accurate representation of tracer-tracer correlations allows more use to be made of long-term datasets to constrain chemical models. Such as the dataset from the Halogen Occultation Experiment (HALOE) which has continuously observed CH4 (but not N2O) from 1991 till the present. The neural network Fortran code used is available for download.

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Lary, D. J., M. D. Müller, and H. Y. Mussa. "Using neural networks to describe tracer correlations." Atmospheric Chemistry and Physics Discussions 3, no. 6 (November 13, 2003): 5711–24. http://dx.doi.org/10.5194/acpd-3-5711-2003.

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Abstract. Neural networks are ideally suited to describe the spatial and temporal dependence of tracer-tracer correlations. The neural network performs well even in regions where the correlations are less compact and normally a family of correlation curves would be required. For example, the CH4-N2O correlation can be well described using a neural 5 network trained with the latitude, pressure, time of year, and CH4 volume mixing ratio (v.m.r.). In this study a neural network using Quickprop learning and one hidden layer with eight nodes was able to reproduce the CH4-N2O correlation with a correlation co-efficient of 0.9995. Such an accurate representation of tracer-tracer correlations allows more use to be made of long-term datasets to constrain chemical models. Such as the 10 dataset from the Halogen Occultation Experiment (HALOE) which has continuously observed CH4 (but not N2O) from 1991 till the present. The neural network Fortran code used is available for download

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Zhao, Li, David C. Alsop, John A. Detre, and Weiying Dai. "Global fluctuations of cerebral blood flow indicate a global brain network independent of systemic factors." Journal of Cerebral Blood Flow & Metabolism 39, no. 2 (August 17, 2017): 302–12. http://dx.doi.org/10.1177/0271678x17726625.

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Global synchronization across specialized brain networks is a common feature of network models and in-vivo electrical measurements. Although the imaging of specialized brain networks with blood oxygenation sensitive resting state functional magnetic resonance imaging (rsfMRI) has enabled detailed study of regional networks, the study of globally correlated fluctuations with rsfMRI is confounded by spurious contributions to the global signal from systemic physiologic factors and other noise sources. Here we use an alternative rsfMRI method, arterial spin labeled perfusion MRI, to characterize global correlations and their relationship to correlations and anti-correlations between regional networks. Global fluctuations that cannot be explained by systemic factors dominate the fluctuations in cerebral blood flow. Power spectra of these fluctuations are band limited to below 0.05 Hz, similar to prior measurements of regional network fluctuations in the brain. Removal of these global fluctuations prior to measurement of regional networks reduces all regional network fluctuation amplitudes to below the global fluctuation amplitude and changes the strength and sign of inter network correlations. Our findings support large amplitude, globally synchronized activity across networks that require a reassessment of regional network amplitude and correlation measures.

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Peron, T. K. D., C. H. Comin, D. R. Amancio, L. da F. Costa, F. A. Rodrigues, and J. Kurths. "Correlations between climate network and relief data." Nonlinear Processes in Geophysics Discussions 1, no. 1 (April 24, 2014): 823–40. http://dx.doi.org/10.5194/npgd-1-823-2014.

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Abstract. In the last few years, the scientific community has witnessed an ongoing trend of using ideas developed in the study of complex networks to analyze climate dynamics. This powerful combination, usually called climate networks, can be used to uncover non-trivial patterns of weather changes along the years. Here we investigate the temperature network of North America region and show that two network characteristics, namely degree and clustering, have markedly differences between the Eastern and Western regions. We show that such differences are a reflection of the presence of a large network community in the western side of the continent. Moreover, we provide evidences that this large community is a consequence of the peculiar characteristics of the western relief of North America.

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Peron, T. K. D., C. H. Comin, D. R. Amancio, L. da F. Costa, F. A. Rodrigues, and J. Kurths. "Correlations between climate network and relief data." Nonlinear Processes in Geophysics 21, no. 6 (November 27, 2014): 1127–32. http://dx.doi.org/10.5194/npg-21-1127-2014.

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Abstract. In the last few years, the scientific community has witnessed an ongoing trend of using ideas developed in the study of complex networks to analyze climate dynamics. This powerful combination, usually called climate networks, can be used to uncover non-trivial patterns of weather changes throughout the years. Here we investigate the temperature network of the North American region and show that two network characteristics, namely degree and clustering, have marked differences between the eastern and western regions. We show that such differences are a reflection of the presence of a large network community on the western side of the continent. Moreover, we provide evidence that this large community is a consequence of the peculiar characteristics of the western relief of North America.

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Daduna, Hans, and Ryszard Szekli. "Correlation formulas for Markovian network processes in a random environment." Advances in Applied Probability 48, no. 1 (March 2016): 176–98. http://dx.doi.org/10.1017/apr.2015.12.

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Abstract We consider Markov processes, which describe, e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit steady-state distribution of product form available in the literature, we note that this steady-state distribution does not provide information about the correlation structure in time and space (over nodes). We study this correlation structure via one-step correlations for the queueing-environment process. Although formulas for absolute values of these correlations are complicated, the differences of correlations of related networks are simple and have a nice structure. We therefore compare two networks in a random environment having the same invariant distribution, and focus on the time behaviour of the processes when in such a network the environment changes or the rules for travelling are perturbed. Evaluating the comparison formulas we compare spectral gaps and asymptotic variances of related processes.

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Jungsbluth, Magnus, Bernd Burghardt, and Alexander K. Hartmann. "Fingerprinting networks: Correlations of local and global network properties." Physica A: Statistical Mechanics and its Applications 381 (July 2007): 444–56. http://dx.doi.org/10.1016/j.physa.2007.03.029.

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Lary, D. J., and H. Y. Mussa. "Using an extended Kalman filter learning algorithm for feed-forward neural networks to describe tracer correlations." Atmospheric Chemistry and Physics Discussions 4, no. 3 (June 30, 2004): 3653–67. http://dx.doi.org/10.5194/acpd-4-3653-2004.

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Abstract. In this study a new extended Kalman filter (EKF) learning algorithm for feed-forward neural networks (FFN) is used. With the EKF approach, the training of the FFN can be seen as state estimation for a non-linear stationary process. The EKF method gives excellent convergence performances provided that there is enough computer core memory and that the machine precision is high. Neural networks are ideally suited to describe the spatial and temporal dependence of tracer-tracer correlations. The neural network performs well even in regions where the correlations are less compact and normally a family of correlation curves would be required. For example, the CH4-N2O correlation can be well described using a neural network trained with the latitude, pressure, time of year, and CH4 volume mixing ratio (v.m.r.). The neural network was able to reproduce the CH4-N2O correlation with a correlation coefficient between simulated and training values of 0.9997. The neural network Fortran code used is available for download.

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Zhang, Zhongzhi, and Shuigeng Zhou. "Correlations in random Apollonian network." Physica A: Statistical Mechanics and its Applications 380 (July 2007): 621–28. http://dx.doi.org/10.1016/j.physa.2007.02.058.

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Liu, Kuan, Haiyuan Liu, Dongyan Sun, and Lei Zhang. "Network Inference from Gene Expression Data with Distance Correlation and Network Topology Centrality." Algorithms 14, no. 2 (February 15, 2021): 61. http://dx.doi.org/10.3390/a14020061.

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The reconstruction of gene regulatory networks based on gene expression data can effectively uncover regulatory relationships between genes and provide a deeper understanding of biological control processes. Non-linear dependence is a common problem in the regulatory mechanisms of gene regulatory networks. Various methods based on information theory have been developed to infer networks. However, the methods have introduced many redundant regulatory relationships in the network inference process. A recent measurement method called distance correlation has, in many cases, shown strong and computationally efficient non-linear correlations. In this paper, we propose a novel regulatory network inference method called the distance-correlation and network topology centrality network (DCNTC) method. The method is based on and extends the Local Density Measurement of Network Node Centrality (LDCNET) algorithm, which has the same choice of network centrality ranking as the LDCNET algorithm, but uses a simpler and more efficient distance correlation measure of association between genes. In this work, we integrate distance correlation and network topological centrality into the reasoning about the structure of gene regulatory networks. We will select optimal thresholds based on the characteristics of the distribution of each gene pair in relation to distance correlation. Experiments were carried out on four network datasets and their performance was compared.

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Shokri, Alireza Rangriz, Tayfun Babadagli, and Alireza Jafari. "A Critical Analysis of the Relationship Between Statistical- and Fractal-Fracture-Network Characteristics and Effective Fracture-Network Permeability." SPE Reservoir Evaluation & Engineering 19, no. 03 (June 13, 2016): 494–510. http://dx.doi.org/10.2118/181743-pa.

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Summary Estimation of effective fracture-network permeability (EFNP) is an essential part of modeling transport processes in naturally fractured reservoirs. A practical way of doing this is to use correlations that consider the statistical and physical characteristics of the networks. Thus, selection of the proper parameters to be characterized and/or measured that are highly correlative to the network permeability is critical. In this study, we analyzed fractal-based correlations previously developed by Jafari and Babadagli (2011a, 2011b) to clarify the physical relationship among network properties and the correlation parameters. It was shown that the connectivity index is a more-powerful parameter to rely on in permeability estimation, especially at percolation ranges far from the threshold. Also, it was of high interest to inspect the effect of physical parameters of a fracture network on different fractal dimensions as well as their positive/negative correlation with permeability to make a distinction between the mathematical and physical contributions of variables. We explained the earlier observation of Jafari and Babadagli (2009) regarding the method to determine fractal dimensions and their observed differences, which were found to be related to the computational scheme. That is why the box-counting fractal dimension gives the highest correlation compared with other fractal dimensions, especially the sandbox fractal dimension. The conditions of a strong correlation among different fractal dimensions and the scale-dependency of correlations in natural and synthetic patterns were also addressed.

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Tavakoli, Armin, Marc Olivier Renou, Nicolas Gisin, and Nicolas Brunner. "Correlations in star networks: from Bell inequalities to network inequalities." New Journal of Physics 19, no. 7 (July 5, 2017): 073003. http://dx.doi.org/10.1088/1367-2630/aa7673.

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13

Paluš, M., D. Hartman, J. Hlinka, and M. Vejmelka. "Discerning connectivity from dynamics in climate networks." Nonlinear Processes in Geophysics 18, no. 5 (October 24, 2011): 751–63. http://dx.doi.org/10.5194/npg-18-751-2011.

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Abstract. The bias due to dynamical memory (serial correlations) in an association/dependence measure (absolute cross-correlation) is demonstrated in model data and identified in time series of meteorological variables used for construction of climate networks. Accounting for such bias in inferring links of the climate network markedly changes the network topology and allows to observe previously hidden phenomena in climate network evolution.

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14

McFarland, Dennis. "The Effects of Using Partial or Uncorrected Correlation Matrices When Comparing Network and Latent Variable Models." Journal of Intelligence 8, no. 1 (February 15, 2020): 7. http://dx.doi.org/10.3390/jintelligence8010007.

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Network models of the WAIS-IV based on regularized partial correlation matrices have been reported to outperform latent variable models based on uncorrected correlation matrices. The present study sought to compare network and latent variable models using both partial and uncorrected correlation matrices with both types of models. The results show that a network model provided better fit to matrices of partial correlations but latent variable models provided better fit to matrices of full correlations. This result is due to the fact that the use of partial correlations removes most of the covariance common to WAIS-IV tests. Modeling should be based on uncorrected correlations since these represent the majority of shared variance between WAIS-IV test scores.

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15

Griniasty, M., M. V. Tsodyks, and Daniel J. Amit. "Conversion of Temporal Correlations Between Stimuli to Spatial Correlations Between Attractors." Neural Computation 5, no. 1 (January 1993): 1–17. http://dx.doi.org/10.1162/neco.1993.5.1.1.

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It is shown that a simple modification of synaptic structures (of the Hopfield type) constructed to produce autoassociative attractors, produces neural networks whose attractors are correlated with several (learned) patterns used in the construction of the matrix. The modification stores in the matrix a fixed sequence of uncorrelated patterns. The network then has correlated attractors, provoked by the uncorrelated stimuli. Thus, the network converts the temporal order (or temporal correlation) expressed by the sequence of patterns, into spatial correlations expressed in the distributions of neural activities in attractors. The model captures phenomena observed in single electrode recordings in performing monkeys by Miyashita et al. The correspondence is as close as to reproduce the fact that given uncorrelated patterns as sequentially learned stimuli, the attractors produced are significantly correlated up to a separation of 5 (five) in the sequence. This number 5 is universal in a range of parameters, and requires essentially no tuning. We then discuss learning scenarios that could lead to this synaptic structure as well as experimental predictions following from it. Finally, we speculate on the cognitive utility of such an arrangement.

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BARTHÉLEMY, MARC, ALAIN BARRAT, and ALESSANDRO VESPIGNANI. "THE ROLE OF GEOGRAPHY AND TRAFFIC IN THE STRUCTURE OF COMPLEX NETWORKS." Advances in Complex Systems 10, no. 01 (March 2007): 5–28. http://dx.doi.org/10.1142/s021952590700091x.

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We report a study of the correlations among topological, weighted and spatial properties of large infrastructure networks. We review the empirical results obtained for the air-transportation infrastructure that motivates a network modeling approach which integrates the various attributes of this network. In particular, we describe a class of models which include a weight-topology coupling and the introduction of geographical attributes during the network evolution. The inclusion of spatial features is able to capture the appearance of non-trivial correlations between the traffic flows, the connectivity pattern and the actual distances of vertices. The anomalous fluctuations in the betweenness-degree correlation function observed in empirical studies are also recovered in the model. The presented results suggest that the interplay between topology, weights and geographical constraints is a key ingredient in order to understand the structure and evolution of many real-world networks.

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SUN, YUANYUAN, KAINING HOU, and YUJIE ZHAO. "A NETWORK MODEL GENERATED FROM THE RECURSIVE GRAPH BASED ON POLYGON." International Journal of Modern Physics C 24, no. 09 (August 18, 2013): 1350062. http://dx.doi.org/10.1142/s0129183113500629.

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The study of network models is one of the most challenging research fields among the studies of complex networks, which have been the hot research topics in recent decades. In this paper, we construct a deterministic network by a mapping method based on a recursive graph, and analyze its topological characteristics, including degree distribution, clustering coefficient, network diameter, average path length and degree correlations. We obtain that this network has the small-world property and positive correlation. The network modeling as we present gives a new perspective on networks, and helps to understand better the evolutions of the real-life systems, making it possible to explore the complexity of complex systems.

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Wang, Yingkui, Di Jin, Katarzyna Musial, and Jianwu Dang. "Community Detection in Social Networks Considering Topic Correlations." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 321–28. http://dx.doi.org/10.1609/aaai.v33i01.3301321.

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Network contents including node contents and edge contents can be utilized for community detection in social networks. Thus, the topic of each community can be extracted as its semantic information. A plethora of models integrating topic model and network topologies have been proposed. However, a key problem has not been resolved that is the semantic division of a community. Since the definition of community is based on topology, a community might involve several topics. To ach

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Wang, Xiaolin, Liyuan Yu, and Hanqing Yang. "Correlations between Geometric Properties and Permeability of 2D Fracture Networks." Advances in Civil Engineering 2021 (January 25, 2021): 1–7. http://dx.doi.org/10.1155/2021/6645238.

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The equivalent permeability of fractured rock masses plays an important role in understanding the fluid flow and solute transport properties in underground engineering, yet the effective predictive models have not been proposed. This study established mathematical expressions to link permeability of 2D fracture networks to the geometric properties of fractured rock masses, including number density of fracture lines, total length of fractures per square meter, and fractal dimensions of fracture network structures and intersections. The results show that the equivalent permeability has power law relationships with the geometric properties of fracture networks. The fractal dimensions that can be easily obtained from an engineering site can be used to predict the permeability of a rock fracture network. When the fractal dimensions of fracture network structures and intersections exceed the critical values, the effect of randomness of fracture locations is negligible. The equivalent permeability of a fracture network increases with the increment of fracture density and/or fractal dimensions proportionally.

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Lee, Youjin, Cencheng Shen, Carey E. Priebe, and Joshua T. Vogelstein. "Network dependence testing via diffusion maps and distance-based correlations." Biometrika 106, no. 4 (September 30, 2019): 857–73. http://dx.doi.org/10.1093/biomet/asz045.

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Summary Deciphering the associations between network connectivity and nodal attributes is one of the core problems in network science. The dependency structure and high dimensionality of networks pose unique challenges to traditional dependency tests in terms of theoretical guarantees and empirical performance. We propose an approach to test network dependence via diffusion maps and distance-based correlations. We prove that the new method yields a consistent test statistic under mild distributional assumptions on the graph structure, and demonstrate that it is able to efficiently identify the most informative graph embedding with respect to the diffusion time. The methodology is illustrated on both simulated and real data.

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Zhang, Lele, Callum Stuart, Samithree Rajapaksha, Gentry White, and Timothy Garoni. "Study of Cross-Correlations in Traffic Networks with Applications to Perimeter Control." Transportation Research Record: Journal of the Transportation Research Board 2623, no. 1 (January 2017): 108–16. http://dx.doi.org/10.3141/2623-12.

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A cross-correlation is proposed between network-aggregated density and flow as a natural indicator of traffic phases for two-dimensional road networks. An online estimator of the cross-correlation was studied with the use of empirical data. The result suggests that the measure can be used to identify traffic phases. To understand better the behavior of the true statistical cross-correlation, generic networks were simulated. With homogeneously distributed densities, the simulations suggested that the cross-correlation monotonically decreases with the growth of the mean density and vanishes when the network is at capacity. As a consequence, for such networks, the phase can be identified from a single point on the curve of the cross-correlation versus mean density. A case study of cross-correlation–based perimeter-control strategies was performed, with gate traffic flowing into the network when the cross-correlation was below a (negative) threshold to improve network flows. The simulation results suggest that even with anisotropic traffic demand, the cross-correlation–based control strategy can improve network performance, specifically traffic flow and density heterogeneity.

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Pries, A. R., T. W. Secomb, and P. Gaehtgens. "Structure and hemodynamics of microvascular networks: heterogeneity and correlations." American Journal of Physiology-Heart and Circulatory Physiology 269, no. 5 (November 1, 1995): H1713—H1722. http://dx.doi.org/10.1152/ajpheart.1995.269.5.h1713.

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The objective of this study was to quantify the heterogeneity of topological, morphological, and hemodynamic parameters in microvascular networks and to identify functionally relevant correlations among these parameters. Seven networks in the rat mesentery (383-913 vessel segments per network) were examined, and measurements were made of segment generation, diameter, length, and hematocrit in all segments (n = 3,129) and of flow velocity (only in 3 networks, 1,321 segments). In addition, hematocrit, flow rate, and pressure were derived for all segments from a mathematical simulation. All parameters obtained exhibit heterogeneous distributions with coefficients of variation ranging from 0.28 (capillary diameter) to > 1.5 (volume flow and pressure gradient). Several strong correlations exist between parameters, e.g., discharge hematocrit increases with vessel diameter, and shear rate increases with intravascular pressure. Because of such correlations, the extrapolation from average values for "typical vessels" to network properties can lead to substantial errors. For example, the mean network transit time estimated based on averaged quantities is 6.5 s, which is about 60% higher than the true value (4.08 s). Simplified models of the vascular bed may therefore be inadequate to describe functional properties of the microcirculation.

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Kasthurirathna, Dharshana, Mahendra Piraveenan, and Gnanakumar Thedchanamoorthy. "On the Influence of Topological Characteristics on Robustness of Complex Networks." Journal of Artificial Intelligence and Soft Computing Research 3, no. 2 (April 1, 2013): 89–100. http://dx.doi.org/10.2478/jaiscr-2014-0007.

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Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.

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Seibert, Tyler M., and James B. Brewer. "Default network correlations analyzed on native surfaces." Journal of Neuroscience Methods 198, no. 2 (June 2011): 301–11. http://dx.doi.org/10.1016/j.jneumeth.2011.04.010.

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Kim, Hyun-Joo, Youngki Lee, Byungnam Kahng, and In-mook Kim. "Weighted Scale-Free Network in Financial Correlations." Journal of the Physical Society of Japan 71, no. 9 (September 15, 2002): 2133–36. http://dx.doi.org/10.1143/jpsj.71.2133.

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Hawthorne, F. C. "Structural correlations in three-dimensional network solids." Acta Crystallographica Section A Foundations of Crystallography 43, a1 (August 12, 1987): C5. http://dx.doi.org/10.1107/s0108767387085386.

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Vuksanović, Vesna, Roger T. Staff, Trevor Ahearn, Alison D. Murray, and Claude M. Wischik. "Cortical Thickness and Surface Area Networks in Healthy Aging, Alzheimer’s Disease and Behavioral Variant Fronto-Temporal Dementia." International Journal of Neural Systems 29, no. 06 (July 29, 2019): 1850055. http://dx.doi.org/10.1142/s0129065718500557.

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Models of the human brain as a complex network of inter-connected sub-units are important in helping to understand the structural basis of the clinical features of neurodegenerative disorders. The aim of this study was to characterize in a systematic manner the differences in the structural correlation networks in cortical thickness (CT) and surface area (SA) in Alzheimer’s disease (AD) and behavioral variant Fronto-Temporal Dementia (bvFTD). We have used the baseline magnetic resonance imaging (MRI) data available from a large population of patients from three clinical trials in mild to moderate AD and mild bvFTD and compared this to a well-characterized healthy aging cohort. The study population comprised 202 healthy elderly subjects, 213 with bvFTD and 213 with AD. We report that both CT and SA network architecture can be described in terms of highly correlated networks whose positive and inverse links map onto the intrinsic modular organization of the four cortical lobes. The topology of the disturbance in structural network is different in the two disease conditions, and both are different from normal aging. The changes from normal are global in character and are not restricted to fronto-temporal and temporo-parietal lobes, respectively, in bvFTD and AD, and indicate an increase in both global correlational strength and in particular nonhomologous inter-lobar connectivity defined by inverse correlations. These inverse correlations appear to be adaptive in character, reflecting coordinated increases in CT and SA that may compensate for corresponding impairment in functionally linked nodes. The effects were more pronounced in the cortical thickness atrophy network in bvFTD and in the surface area network in AD. Although lobar modularity is preserved in the context of neurodegenerative disease, the hub-like organization of networks differs both from normal and between the two forms of dementia. This implies that hubs may be secondary features of the connectivity adaptation to neurodegeneration and may not be an intrinsic property of the brain. However, analysis of the topological differences in hub-like organization CT and SA networks, and their underlying positive and negative correlations, may provide a basis for assisting in the differential diagnosis of bvFTD and AD.

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Hertz, John. "Cross-Correlations in High-Conductance States of a Model Cortical Network." Neural Computation 22, no. 2 (February 2010): 427–47. http://dx.doi.org/10.1162/neco.2009.06-08-806.

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Neuronal firing correlations are studied using simulations of a simple network model for a cortical column in a high-conductance state with dynamically balanced excitation and inhibition. Although correlations between individual pairs of neurons exhibit considerable heterogeneity, population averages show systematic behavior. When the network is in a stationary state, the average correlations are generically small: correlation coefficients are of order 1/N, where N is the number of neurons in the network. However, when the input to the network varies strongly in time, much larger values are found. In this situation, the network is out of balance, and the synaptic conductance is low, at times when the strongest firing occurs. However, examination of the correlation functions of synaptic currents reveals that after these bursts, balance is restored within a few milliseconds by a rapid increase in inhibitory synaptic conductance. These findings suggest an extension of the notion of the balanced state to include balanced fluctuations of synaptic currents, with a characteristic timescale of a few milliseconds.

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Kriener, Birgit, Tom Tetzlaff, Ad Aertsen, Markus Diesmann, and Stefan Rotter. "Correlations and Population Dynamics in Cortical Networks." Neural Computation 20, no. 9 (September 2008): 2185–226. http://dx.doi.org/10.1162/neco.2008.02-07-474.

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The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

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Lee, Renee, and Anne S. Kiremidjian. "Uncertainty and Correlation for Loss Assessment of Spatially Distributed Systems." Earthquake Spectra 23, no. 4 (November 2007): 753–70. http://dx.doi.org/10.1193/1.2791001.

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Seismic risk assessment for a spatially distributed system, such as a lifeline network, involves characterization of ground shaking and structural damage for multiple structures in a region. The expected value of monetary loss, a common measure of the risk, has been previously formulated but with little attention to the uncertainty around this monetary loss. Furthermore, prior research on risk assessment for lifeline systems, in particular transportation networks, assumes no spatial ground motion correlation and no structure-to-structure damage correlation between sites in the network. In this paper, a framework for treating these correlations in the network risk analysis is presented. A demonstration of this methodology is carried out for two transportation networks located in the San Francisco Bay region. Coefficients of variation for network physical loss using a non–distance dependent ground motion correlation model in the framework range between 0.6 and 1.5 for the sample networks presented here. Coefficients of variation for network physical loss using a distance-dependent ground motion correlation model in the framework range between 1.0 and 1.4 for the same networks. It is demonstrated through these applications that assuming no correlation in ground motion and in damage may potentially underestimate uncertainty in the overall loss estimation.

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Ueda, Issei, Kazuhiro Takemoto, Keita Watanabe, Koichiro Sugimoto, Atsuko Ikenouchi, Shingo Kakeda, Asuka Katsuki, Reiji Yoshimura, and Yukunori Korogi. "The brain-derived neurotrophic factor Val66Met polymorphism increases segregation of structural correlation networks in healthy adult brains." PeerJ 8 (August 5, 2020): e9632. http://dx.doi.org/10.7717/peerj.9632.

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Background Although structural correlation network (SCN) analysis is an approach to evaluate brain networks, the neurobiological interpretation of SCNs is still problematic. Brain-derived neurotrophic factor (BDNF) is well-established as a representative protein related to neuronal differentiation, maturation, and survival. Since a valine-to-methionine substitution at codon 66 of the BDNF gene (BDNF Val66Met single nucleotide polymorphism (SNP)) is well-known to have effects on brain structure and function, we hypothesized that SCNs are affected by the BDNF Val66Met SNP. To gain insight into SCN analysis, we investigated potential differences between BDNF valine (Val) homozygotes and methionine (Met) carriers in the organization of their SCNs derived from inter-regional cortical thickness correlations. Methods Forty-nine healthy adult subjects (mean age = 41.1 years old) were divided into two groups according to their genotype (n: Val homozygotes = 16, Met carriers = 33). We obtained regional cortical thickness from their brain T1 weighted images. Based on the inter-regional cortical thickness correlations, we generated SCNs and used graph theoretical measures to assess differences between the two groups in terms of network integration, segregation, and modularity. Results The average local efficiency, a measure of network segregation, of BDNF Met carriers’ network was significantly higher than that of the Val homozygotes’ (permutation p-value = 0.002). Average shortest path lengths (a measure of integration), average local clustering coefficient (another measure of network segregation), small-worldness (a balance between integration and segregation), and modularity (a representative measure for modular architecture) were not significantly different between group (permutation p-values ≧ 0.01). Discussion and Conclusion Our results suggest that the BDNF Val66Met polymorphism may potentially influence the pattern of brain regional morphometric (cortical thickness) correlations. Comparing networks derived from inter-regional cortical thickness correlations, Met carrier SCNs have denser connections with neighbors and are more distant from random networks than Val homozygote networks. Thus, it may be necessary to consider potential effects of BDNF gene mutations in SCN analyses. This is the first study to demonstrate a difference between Val homozygotes and Met carriers in brain SCNs.

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Minces, Victor, Lucas Pinto, Yang Dan, and Andrea A. Chiba. "Cholinergic shaping of neural correlations." Proceedings of the National Academy of Sciences 114, no. 22 (May 15, 2017): 5725–30. http://dx.doi.org/10.1073/pnas.1621493114.

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A primary function of the brain is to form representations of the sensory world. Its capacity to do so depends on the relationship between signal correlations, associated with neuronal receptive fields, and noise correlations, associated with neuronal response variability. It was recently shown that the behavioral relevance of sensory stimuli can modify the relationship between signal and noise correlations, presumably increasing the encoding capacity of the brain. In this work, we use data from the visual cortex of the awake mouse watching naturalistic stimuli and show that a similar modification is observed under heightened cholinergic modulation. Increasing cholinergic levels in the cortex through optogenetic stimulation of basal forebrain cholinergic neurons decreases the dependency that is commonly observed between signal and noise correlations. Simulations of correlated neural networks with realistic firing statistics indicate that this change in the correlation structure increases the encoding capacity of the network.

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Kabo, Felichism. "The architecture of network collective intelligence : correlations between social network structure, spatial layout and prestige outcomes in an office." Philosophical Transactions of the Royal Society B: Biological Sciences 373, no. 1753 (July 2, 2018): 20170238. http://dx.doi.org/10.1098/rstb.2017.0238.

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A social network represents interactions and knowledge that transcend the intelligence of any of its individual members. In this study, I examine the correlations between this network collective intelligence , spatial layout, and prestige or status outcomes at the individual and team levels in an organization. I propose that spatially influenced social cognition shapes which individuals become members of prestigious teams in organizations, and the prestige perception of teams by others in the organization. Prestige is a pathway to social rank, influence and upward mobility for individuals in organizations. For groups, perceived prestige of work teams is related to how team members identify with the group and with their collaborative behaviours. Prestige enhances a team's survivability and its access to resources. At the individual level, I ran two-stage Heckman sample selection models to examine the correlation between social network position and the number of prestigious projects a person is a member of, contingent on the association between physical space and social ties and networks. At the team level, I used linear regressions to examine the relationship among network structure, spatial proximity and the perceived prestige or innovativeness of a project team. In line with my hypotheses, for individuals there is a significant correlation between physical space and social networks, and contingent on that, between social network positions and the number of prestigious projects that a person is a member of. Also in accordance with my hypotheses, for teams there is a significant correlation between network structure and spatial proximity, and perceived prestige. While cross-sectional, the study findings illustrate the importance of considering the spatial domain in examinations of how network collective intelligence is related to organizational outcomes at the individual and team levels. This article is part of the theme issue ‘Interdisciplinary approaches for uncovering the impacts of architecture on collective behaviour’.

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Boothe, David L., Avis H. Cohen, and Todd W. Troyer. "Temporal Correlations in Stochastic Models of Double Bursting During Simulated Locomotion." Journal of Neurophysiology 95, no. 3 (March 2006): 1556–70. http://dx.doi.org/10.1152/jn.01157.2005.

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The output of the spinal central pattern generator for locomotion falls into two broad categories: alternation between antagonistic muscles and double bursting within muscles acting on multiple joints. We first model an alternating half-center and then present two different models of double bursting. The first double-bursting model consists of a central clock with an explicit one-to-one mapping between interneuron activity and model output. The second double-bursting model consists of a half-center with an added feedback neuron. Models are built using rate-coded leaky integrator neurons with slow self-inhibition. Structure-function relationships are explored by the addition of noise. The interaction of noise with the dynamics of each network creates a unique pattern of correlation between phases of the simulated cycle. The effects of noise can be explained by perturbation of deterministic versions of the networks. Three basic results were obtained: slow self-inhibitory currents lead to correlations between parts of the step cycle that are separated in time and network relative; model outputs are most sensitive to perturbations presented just before competitive switches in network activity, and clock-like models possess substantial symmetries within the correlation structure of burst durations, whereas the correlation structure of feedback models are asymmetric. Our models suggest that variability in burst length durations can be analyzed to make inferences about the structure of the spinal networks for locomotion. In particular, correlation patterns within double-bursting outputs may yield important clues regarding the interaction between more central, clock-like networks and feedback from more peripheral interneurons.

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de Brito, J. B., C. I. N. Sampaio Filho, A. A. Moreira, and J. S. Andrade. "Characterizing the intrinsic correlations of scale-free networks." International Journal of Modern Physics C 27, no. 03 (February 23, 2016): 1650024. http://dx.doi.org/10.1142/s0129183116500248.

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When studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree–degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square root of the network size. In this situation, these correlations can significantly affect the dependence of the average degree of the nearest neighbors of a given vertex on this vertices degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scale-free network models are not self-averaging, that is, the second moment of their degree distribution may vary orders of magnitude among different realizations. Finally, we argue that the intrinsic correlations investigated here may have profound impact on the critical properties of random scale-free networks.

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Silva, Anderson Rodrigo da, Elizanilda Ramalho do Rêgo, Angela Maria dos Santos Pessoa, and Maílson Monteiro do Rêgo. "Correlation network analysis between phenotypic and genotypic traits of chili pepper." Pesquisa Agropecuária Brasileira 51, no. 4 (April 2016): 372–77. http://dx.doi.org/10.1590/s0100-204x2016000400010.

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Abstract: The objective of this work was to build weighted correlation networks, in order to discover correlation structures and link patterns among 28 morphoagronomic traits of chili pepper related to seedling, plant, inflorescence, and fruit. Phenotypic and genotypic information of 16 Capsicum genotypes were analyzed. Correlation structures and link patterns can be easily identified in the matrices using the Fruchterman-Reingold algorithm with correlation network information. Both types of correlations showed the same general link pattern among fruit traits, with high broad-sense heritability values and high aptitude of the genotypes for agronomic and ornamental breeding. Leaf dimensions are correlated with a cluster of fruit traits. Correlation networks of chili pepper traits may increase the effectiveness of genotype selection, since both correlated traits and groups can be identified.

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Meghanathan, Natarajan. "Correlations between Centrality Measures for Mobile Ad hoc Networks." International Journal of Wireless Networks and Broadband Technologies 4, no. 2 (April 2015): 15–27. http://dx.doi.org/10.4018/ijwnbt.2015040102.

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The author conducts an extensive correlation coefficient analysis of four prominent centrality measures for mobile ad hoc networks. The centrality measures considered are the degree-based degree centrality and eigenvector centrality, and the shortest path-based betweenness centrality and closeness centrality. The author evaluates the correlation coefficient between any two of the above four centrality measures as a function of network connectivity and node mobility. He observes a consistent ranking (with respect to the correlation coefficients) among the pairs of centrality measures for all levels of network connectivity, node mobility and across the duration of the simulation session. The shortest path-based closeness centrality measure exhibits high correlation with the degree-based centrality measures, whereas the betweenness centrality exhibits relatively weak correlation with the degree-based centrality measures. For a given level of node mobility and network connectivity, the author does not observe the correlation coefficient values between any two centrality measures to significantly change with time.

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Buice, Michael A., Jack D. Cowan, and Carson C. Chow. "Systematic Fluctuation Expansion for Neural Network Activity Equations." Neural Computation 22, no. 2 (February 2010): 377–426. http://dx.doi.org/10.1162/neco.2009.02-09-960.

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Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity. The shortcoming of these equations is that they take into account only the average firing rate, while leaving out higher-order statistics like correlations between firing. A stochastic theory of neural networks that includes statistics at all orders was recently formulated. We describe how this theory yields a systematic extension to population rate equations by introducing equations for correlations and appropriate coupling terms. Each level of the approximation yields closed equations; they depend only on the mean and specific correlations of interest, without an ad hoc criterion for doing so. We show in an example of an all-to-all connected network how our system of generalized activity equations captures phenomena missed by the mean field rate equations alone.

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Rocca, Maria A., Paola Valsasina, Victoria M. Leavitt, Mariaemma Rodegher, Marta Radaelli, Gianna C. Riccitelli, Vittorio Martinelli, et al. "Functional network connectivity abnormalities in multiple sclerosis: Correlations with disability and cognitive impairment." Multiple Sclerosis Journal 24, no. 4 (March 15, 2017): 459–71. http://dx.doi.org/10.1177/1352458517699875.

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Objective: To investigate resting state (RS) functional connectivity (FC) abnormalities within the principal brain networks in a large cohort of multiple sclerosis (MS) patients, to define the trajectory of FC changes over disease stages and their relation with clinical and structural magnetic resonance imaging (MRI) measures. Methods: RS functional magnetic resonance imaging (fMRI), clinical, and neuropsychological evaluation were obtained from 215 MS patients and 98 healthy controls. Connectivity abnormalities and correlations with clinical/neuropsychological/imaging measures were evaluated. We analyzed seed-voxel FC with seven major hubs, producing one visual/sensory, one motor, two cognitive, one cerebellar, and two subcortical networks. Results: MS patients showed reduced network average RS FC versus controls in the default-mode network. At regional level, a complex pattern of decreased and increased RS FC was found. Reduced RS FC mainly involved sensorimotor, cognitive, thalamic, and cerebellar networks, whereas increased RS FC involved visual/sensory and subcortical networks. Reduced RS FC correlated with T2 lesions. Reduced thalamic RS FC correlated with better neuropsychological performance, whereas for all remaining networks reduced FC correlated with more severe clinical/cognitive impairment. Conclusion: Increased and decreased RS FC occurs in MS and contributes to a wide spectrum of clinical manifestations. RS FC reduction is related to T2 lesions. Such a paradigm is inverted for the thalamic network.

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MASUCCI, A. P., and G. J. RODGERS. "DIFFERENCES BETWEEN NORMAL AND SHUFFLED TEXTS: STRUCTURAL PROPERTIES OF WEIGHTED NETWORKS." Advances in Complex Systems 12, no. 01 (February 2009): 113–29. http://dx.doi.org/10.1142/s0219525909002039.

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In this paper we deal with the structural properties of weighted networks. Starting from an empirical analysis of a linguistic network, we analyze the differences between the statistical properties of a real and a shuffled network. We show that the scale-free degree distribution and the scale-free weight distribution are induced by the scale-free strength distribution, that is Zipf's law. We test the result on a scientific collaboration network, that is a social network, and we define a measure – the vertex selectivity – that can distinguish a real network from a shuffled network. We prove, via an ad hoc stochastic growing network with second order correlations, that this measure can effectively capture the correlations within the topology of the network.

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Gharbi, Ridha B. C., and Adel M. Elsharkawy. "Neural Network Model for Estimating the PVT Properties of Middle East Crude Oils." SPE Reservoir Evaluation & Engineering 2, no. 03 (June 1, 1999): 255–65. http://dx.doi.org/10.2118/56850-pa.

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Summary The importance of pressure/volume/temperature (PVT) properties, such as the bubblepoint pressure, solution gas-oil ratio, and oil formation volume factor, makes their accurate determination necessary for reservoir performance calculations. An enormous amount of PVT data has been collected and correlated over many years for different types of hydrocarbon systems. Almost all of these correlations were developed with linear or nonlinear multiple regression or graphical techniques. Artificial neural networks, once successfully trained, offer an alternative way to obtain reliable results for the determination of crude oil PVT properties. In this study, we present neural-network-based models for the prediction of PVT properties of crude oils from the Middle East. The data on which the network was trained represent the largest data set ever collected to be used in developing PVT models for Middle East crude oils. The neural-network model is able to predict the bubblepoint pressure and the oil formation volume factor as a function of the solution gas-oil ratio, the gas specific gravity, the oil specific gravity, and the temperature. A detailed comparison between the results predicted by the neural-network models and those predicted by other correlations are presented for these Middle East crude-oil samples. Introduction In absence of experimentally measured pressure/volume/temperature (PVT) properties, two methods are widely used. These methods are equation of state (EOS) and PVT correlations. The equation of state is based on knowing the detailed compositions of the reservoir fluids. The determination of such quantities is expensive and time consuming. The equation of state involves numerous numerical computations. On the other hand, PVT correlations are based on easily measured field data: reservoir pressure, reservoir temperature, oil, and gas specific gravity. In the petroleum process industries, reliable experimental data are always to be preferred over data obtained from correlations. However, very often reliable experimental data are not available, and the advantage of a correlation is that it may be used to predict properties for which very little experimental information is available. The importance of accurate PVT data for material-balance calculations is well understood. It is crucial that all calculations in reservoir performance, in production operations and design, and in formation evaluation be as good as the PVT properties used in these calculations. The economics of the process also depends on the accuracy of such properties. The development of correlations for PVT calculations has been the subject of extensive research, resulting in a large volume of publications.1–10 Several graphical and mathematical correlations for determining the bubblepoint pressure (Pb) and the oil formation volume factor (Bob) have been proposed during the last five decades. These correlations are essentially based on the assumption that P b and Bob are strong functions of the solution gas-oil ratio (Rs) the reservoir temperature (T), the gas specific gravity (?g) and the oil specific gravity (?o) or P b = f 1 ( R s , T , Î³ g , Î³ o ) , ( 1 ) B o b = f 2 ( R s , T , Î³ g , Î³ o ) . ( 2 ) In 1947, Standing1 presented graphical correlations for the determination of bubblepoint pressure (Pb) and the oil formation volume factor (Bob) In developing these correlations, Standing used 105 experimentally measured data points from 22 different crude-oil and gas mixtures from California oil fields. Average relative errors of 4.8% and of 1.17% were reported for Pb and Bob respectively. Later, in 1958, Lasater9 developed an empirical equation based on Henry's law for estimating the bubblepoint pressure. He correlated the mole fraction of gas in solution to a bubblepoint pressure factor. A total of 137 crude-oil and gas mixtures from North and South America was used for developing this correlation. An average error of 3.8% was reported. Lasater did not present a correlation for Bob In 1980, two sets of correlations were reported, one by Vasquez and Beggs10 and the other by Glasø.7 Vasquez and Beggs used 600 data points from various locations all over the world to develop correlations for Pb and Bob. Two different types of correlations were presented, one for crudes with °API>30 and the other for crudes with °API 30. An average error of 4.7% was reported for their correlation of Bob Glasø used a total of 45 oil samples from the North Sea to develop his correlations for calculating Pb and Bob. He reported an average error of 1.28% for the bubblepoint pressure and ?0.43% for the formation volume factor. Recently, Al-Marhoun4 used 160 experimentally determined data points from the PVT analysis of 69 Middle Eastern hydrocarbon mixtures to develop his correlations. Average errors of 0.03% and ?0.01% were reported for Pb and Bob respectively. Dokla and Osman6 used a total of 50 data points from reservoirs in the United Arab Emirates to develop correlations for Pb and Bob. They reported an average error of 0.45% for the bubblepoint pressure and 0.023% for the formation volume factor. The conventional approach to develop PVT correlations is based on multiple-regression techniques. An alternative approach will be to use an artificial neural network (ANN). PVT models based on a successfully trained ANN can be excellent, reliable tools for the prediction of crude-oil PVT properties. The massive interconnections in the ANN produces a large number of degrees of freedom, or fitting parameters, and thus may allow it to capture the system's nonlinearity better than conventional regression techniques. Recently, artificial neural networks have found use in a number of areas in petroleum engineering.11–20 The objective of this study is to use ANNs to develop accurate PVT correlations for Middle East crude oil to estimate Pb and Bob as functions of Rs, T, ?g, ?o. With additional experimental data, the neural-network model can be further refined to incorporate these new data. In addition, in this article we evaluate the accuracy of the ANN models developed in this study compared to other PVT correlations.

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Savoldi, Filippo, Maria A. Rocca, Paola Valsasina, Gianna C. Riccitelli, Sarlota Mesaros, Jelena Drulovic, Marta Radaelli, and Massimo Filippi. "Functional brain connectivity abnormalities and cognitive deficits in neuromyelitis optica spectrum disorder." Multiple Sclerosis Journal 26, no. 7 (May 13, 2019): 795–805. http://dx.doi.org/10.1177/1352458519845109.

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Background: Functional magnetic resonance imaging (fMRI) correlates of cognitive deficits have not been thoroughly studied in patients with neuromyelitis optica spectrum disorders (NMOSDs). Objective: To investigate resting state (RS) functional connectivity (FC) abnormalities within the main cognitive networks in NMOSD patients and their correlation with cognitive performance. Methods: We acquired RS fMRI from 25 NMOSD patients and 30 healthy controls (HC). Patients underwent an extensive neuropsychological evaluation. Between-group RS FC comparisons and correlations with cognitive performance were assessed on the main cognitive RS networks identified by independent component analysis. Results: NMOSD patients showed higher RS FC versus HC in the precuneus of the default mode network (DMN) and right working memory network (WMN), as well as in several frontoparietal regions of the salience network (SN) and bilateral WMNs. Reduced frontal RS FC in NMOSD versus HC was detected in the left WMN. Increased RS FC in the DMN and right WMN was correlated with better cognitive performance, while decreased RS FC in the left WMN was associated with worse cognitive performance. Conclusion: Cognitive-network reorganization occurs in NMOSD. Clinico-imaging correlations suggest an adaptive role of increased RS FC. Conversely, reduced RS FC seems to be a maladaptive mechanism associated with a worse cognitive performance.

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Arias-Castro, Ery, Gábor Lugosi, and Nicolas Verzelen. "Detecting a Path of Correlations in a Network." Latin American Journal of Probability and Mathematical Statistics 14, no. 1 (2017): 33. http://dx.doi.org/10.30757/alea.v14-03.

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Talman, William. "Central Autonomic Network: Functional Organization and Clinical Correlations." Mayo Clinic Proceedings 73, no. 7 (July 1998): 710. http://dx.doi.org/10.1016/s0025-6196(11)64909-4.

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Santos, Gustavo S., Elakkat G. Dharmaraj, Dietmar Plenz, and Hiroyuki Nakahara. "Modeling instantaneous network correlations over multiple spatial scales." Neuroscience Research 65 (January 2009): S133. http://dx.doi.org/10.1016/j.neures.2009.09.648.

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Jellinger, K. A. "Central autonomic network: functional organization and clinical correlations." European Journal of Neurology 5, no. 2 (March 1998): 216. http://dx.doi.org/10.1046/j.1468-1331.1998.520216.x.

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Benocci, Roberto, H. Eduardo Roman, Chiara Confalonieri, and Giovanni Zambon. "Temporal correlations in an urban noise monitoring network." Journal of Physics: Conference Series 1603 (September 2020): 012028. http://dx.doi.org/10.1088/1742-6596/1603/1/012028.

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Obermayer, Benedikt, and Erel Levine. "Exploring the miRNA Regulatory Network Using Evolutionary Correlations." PLoS Computational Biology 10, no. 10 (October 9, 2014): e1003860. http://dx.doi.org/10.1371/journal.pcbi.1003860.

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Bogner, R. E., and B. R. Davis. "Correlations of wave variables in a passive network." IEE Proceedings G (Electronic Circuits and Systems) 133, no. 4 (1986): 165. http://dx.doi.org/10.1049/ip-g-1.1986.0027.

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Vanni, Fabio, and Paolo Barucca. "Degree-correlations in a bursting dynamic network model." Journal of Economic Interaction and Coordination 14, no. 3 (September 27, 2018): 663–95. http://dx.doi.org/10.1007/s11403-018-0232-9.

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Journal articles on the topic 'Network Correlations'

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