43,204 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
Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
Complex network theory provides a powerful framework to statistically
investigate the topology of local and non-local statistical interrelationships,
i.e. teleconnections, in the climate system. Climate networks constructed from
the same global climatological data set using the linear Pearson correlation
coefficient or the nonlinear mutual information as a measure of dynamical
similarity between regions, are compared systematically on local, mesoscopic
and global topological scales. A high degree of similarity is observed on the
local and mesoscopic topological scales for surface air temperature fields
taken from AOGCM and reanalysis data sets. We find larger differences on the
global scale, particularly in the betweenness centrality field. The global
scale view on climate networks obtained using mutual information offers
promising new perspectives for detecting network structures based on nonlinear
physical processes in the climate system.Comment: 24 pages, 10 figure
Topological Schemas of Memory Spaces
Hippocampal cognitive map---a neuronal representation of the spatial
environment---is broadly discussed in the computational neuroscience literature
for decades. More recent studies point out that hippocampus plays a major role
in producing yet another cognitive framework that incorporates not only
spatial, but also nonspatial memories---the memory space. However, unlike
cognitive maps, memory spaces have been barely studied from a theoretical
perspective. Here we propose an approach for modeling hippocampal memory spaces
as an epiphenomenon of neuronal spiking activity. First, we suggest that the
memory space may be viewed as a finite topological space---a hypothesis that
allows treating both spatial and nonspatial aspects of hippocampal function on
equal footing. We then model the topological properties of the memory space to
demonstrate that this concept naturally incorporates the notion of a cognitive
map. Lastly, we suggest a formal description of the memory consolidation
process and point out a connection between the proposed model of the memory
spaces to the so-called Morris' schemas, which emerge as the most compact
representation of the memory structure.Comment: 24 pages, 8 Figures, 1 Suppl. Figur
Modeling commuting systems through a complex network analysis: a study of the Italian islands of Sardinia and Sicily
This study analyzes the inter-municipal commuting systems of the Italian islands of Sardinia and Sicily, employing weighted network analysis technique. Based on the results obtained for the Sardinian commuting network, the network analysis is used to identify similarities and dissimilarities between the two systems
Recurrence networks - A novel paradigm for nonlinear time series analysis
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis
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