174 research outputs found
Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks
Network theory provides various tools for investigating the structural or
functional topology of many complex systems found in nature, technology and
society. Nevertheless, it has recently been realised that a considerable number
of systems of interest should be treated, more appropriately, as interacting
networks or networks of networks. Here we introduce a novel graph-theoretical
framework for studying the interaction structure between subnetworks embedded
within a complex network of networks. This framework allows us to quantify the
structural role of single vertices or whole subnetworks with respect to the
interaction of a pair of subnetworks on local, mesoscopic and global
topological scales.
Climate networks have recently been shown to be a powerful tool for the
analysis of climatological data. Applying the general framework for studying
interacting networks, we introduce coupled climate subnetworks to represent and
investigate the topology of statistical relationships between the fields of
distinct climatological variables. Using coupled climate subnetworks to
investigate the terrestrial atmosphere's three-dimensional geopotential height
field uncovers known as well as interesting novel features of the atmosphere's
vertical stratification and general circulation. Specifically, the new measure
"cross-betweenness" identifies regions which are particularly important for
mediating vertical wind field interactions. The promising results obtained by
following the coupled climate subnetwork approach present a first step towards
an improved understanding of the Earth system and its complex interacting
components from a network perspective
Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
We introduce the \texttt{pyunicorn} (Pythonic unified complex network and
recurrence analysis toolbox) open source software package for applying and
combining modern methods of data analysis and modeling from complex network
theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully
object-oriented and easily parallelizable package written in the language
Python. It allows for the construction of functional networks such as climate
networks in climatology or functional brain networks in neuroscience
representing the structure of statistical interrelationships in large data sets
of time series and, subsequently, investigating this structure using advanced
methods of complex network theory such as measures and models for spatial
networks, networks of interacting networks, node-weighted statistics or network
surrogates. Additionally, \texttt{pyunicorn} provides insights into the
nonlinear dynamics of complex systems as recorded in uni- and multivariate time
series from a non-traditional perspective by means of recurrence quantification
analysis (RQA), recurrence networks, visibility graphs and construction of
surrogate time series. The range of possible applications of the library is
outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure
How complex climate networks complement eigen techniques for the statistical analysis of climatological data
Eigen techniques such as empirical orthogonal function (EOF) or coupled
pattern (CP) / maximum covariance analysis have been frequently used for
detecting patterns in multivariate climatological data sets. Recently,
statistical methods originating from the theory of complex networks have been
employed for the very same purpose of spatio-temporal analysis. This climate
network (CN) analysis is usually based on the same set of similarity matrices
as is used in classical EOF or CP analysis, e.g., the correlation matrix of a
single climatological field or the cross-correlation matrix between two
distinct climatological fields. In this study, formal relationships as well as
conceptual differences between both eigen and network approaches are derived
and illustrated using exemplary global precipitation, evaporation and surface
air temperature data sets. These results allow to pinpoint that CN analysis can
complement classical eigen techniques and provides additional information on
the higher-order structure of statistical interrelationships in climatological
data. Hence, CNs are a valuable supplement to the statistical toolbox of the
climatologist, particularly for making sense out of very large data sets such
as those generated by satellite observations and climate model intercomparison
exercises.Comment: 18 pages, 11 figure
Hierarchical structures in Northern Hemispheric extratropical winter ocean-atmosphere interactions
Acknowledgements MW and RVD have been supported by the German Federal Ministry for Education and Research via the BMBF Young Investigators Group CoSy-CC2 (grant no. 01LN1306A) and the Belmont Forum/JPI Climate project GOTHAM. JFD is grateful for financial support by the Stordalen Foundation (via the Planetary Boundary Research Network PB.net) and the Earth League's EarthDoc program. JK acknowledges the IRTG 1740 funded by Deutsche Forschungsgemeinschaft and FAPESP. Coupled climate network analysis has been performed using the Python package pyunicorn (Donges et al., 2015b) that is available at https://github.com/pik-copan/pyunicorn.Peer reviewedPostprin
A random interacting network model for complex networks
This paper was developed within the scope of the DAAD-DST PPP-Indien project 55516784 (INT/FRG/DAAD/P-215) which funded exchange visits between the two participating institutes. B.G. was supported by the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. J.K. acknowledges financial support from the Government of the Russian Federation (Agreement No. 14.Z50.31.0033). S.M.S. would like to thank University Grants Comission, New Delhi for the financial assistance as an SRF. B.G. and A.R. thank Niklas Boers for stimulating discussions and comments.Peer reviewedPublisher PD
Complex networks analysis in socioeconomic models
This chapter aims at reviewing complex networks models and methods that were
either developed for or applied to socioeconomic issues, and pertinent to the
theme of New Economic Geography. After an introduction to the foundations of
the field of complex networks, the present summary adds insights on the
statistical mechanical approach, and on the most relevant computational aspects
for the treatment of these systems. As the most frequently used model for
interacting agent-based systems, a brief description of the statistical
mechanics of the classical Ising model on regular lattices, together with
recent extensions of the same model on small-world Watts-Strogatz and
scale-free Albert-Barabasi complex networks is included. Other sections of the
chapter are devoted to applications of complex networks to economics, finance,
spreading of innovations, and regional trade and developments. The chapter also
reviews results involving applications of complex networks to other relevant
socioeconomic issues, including results for opinion and citation networks.
Finally, some avenues for future research are introduced before summarizing the
main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared
for Complexity and Geographical Economics - Topics and Tools, P.
Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published
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