2,648 research outputs found
Temporal Networks
A great variety of systems in nature, society and technology -- from the web
of sexual contacts to the Internet, from the nervous system to power grids --
can be modeled as graphs of vertices coupled by edges. The network structure,
describing how the graph is wired, helps us understand, predict and optimize
the behavior of dynamical systems. In many cases, however, the edges are not
continuously active. As an example, in networks of communication via email,
text messages, or phone calls, edges represent sequences of instantaneous or
practically instantaneous contacts. In some cases, edges are active for
non-negligible periods of time: e.g., the proximity patterns of inpatients at
hospitals can be represented by a graph where an edge between two individuals
is on throughout the time they are at the same ward. Like network topology, the
temporal structure of edge activations can affect dynamics of systems
interacting through the network, from disease contagion on the network of
patients to information diffusion over an e-mail network. In this review, we
present the emergent field of temporal networks, and discuss methods for
analyzing topological and temporal structure and models for elucidating their
relation to the behavior of dynamical systems. In the light of traditional
network theory, one can see this framework as moving the information of when
things happen from the dynamical system on the network, to the network itself.
Since fundamental properties, such as the transitivity of edges, do not
necessarily hold in temporal networks, many of these methods need to be quite
different from those for static networks
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
Navigation of brain networks
Understanding the mechanisms of neural communication in large-scale brain
networks remains a major goal in neuroscience. We investigated whether
navigation is a parsimonious routing model for connectomics. Navigating a
network involves progressing to the next node that is closest in distance to a
desired destination. We developed a measure to quantify navigation efficiency
and found that connectomes in a range of mammalian species (human, mouse and
macaque) can be successfully navigated with near-optimal efficiency (>80% of
optimal efficiency for typical connection densities). Rewiring network topology
or repositioning network nodes resulted in 45%-60% reductions in navigation
performance. Specifically, we found that brain networks cannot be progressively
rewired (randomized or clusterized) to result in topologies with significantly
improved navigation performance. Navigation was also found to: i) promote a
resource-efficient distribution of the information traffic load, potentially
relieving communication bottlenecks; and, ii) explain significant variation in
functional connectivity. Unlike prevalently studied communication strategies in
connectomics, navigation does not mandate biologically unrealistic assumptions
about global knowledge of network topology. We conclude that the wiring and
spatial embedding of brain networks is conducive to effective decentralized
communication. Graph-theoretic studies of the connectome should consider
measures of network efficiency and centrality that are consistent with
decentralized models of neural communication
Transport on complex networks: Flow, jamming and optimization
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics
Resting-State Functional Connectivity in Late-Life Depression: Higher Global Connectivity and More Long Distance Connections
Functional magnetic resonance imaging recordings in the resting-state (RS)
from the human brain are characterized by spontaneous low-frequency
fluctuations in the blood oxygenation level dependent signal that reveal
functional connectivity (FC) via their spatial synchronicity. This RS study
applied network analysis to compare FC between late-life depression (LLD)
patients and control subjects. Raw cross-correlation matrices (CM) for LLD were
characterized by higher FC. We analyzed the small-world (SW) and modular
organization of these networks consisting of 110 nodes each as well as the
connectivity patterns of individual nodes of the basal ganglia. Topological
network measures showed no significant differences between groups. The
composition of top hubs was similar between LLD and control subjects, however
in the LLD group posterior medial-parietal regions were more highly connected
compared to controls. In LLD, a number of brain regions showed connections with
more distant neighbors leading to an increase of the average Euclidean distance
between connected regions compared to controls. In addition, right caudate
nucleus connectivity was more diffuse in LLD. In summary, LLD was associated
with overall increased FC strength and changes in the average distance between
connected nodes, but did not lead to global changes in SW or modular
organization
Recurrence-based time series analysis by means of complex network methods
Complex networks are an important paradigm of modern complex systems sciences
which allows quantitatively assessing the structural properties of systems
composed of different interacting entities. During the last years, intensive
efforts have been spent on applying network-based concepts also for the
analysis of dynamically relevant higher-order statistical properties of time
series. Notably, many corresponding approaches are closely related with the
concept of recurrence in phase space. In this paper, we review recent
methodological advances in time series analysis based on complex networks, with
a special emphasis on methods founded on recurrence plots. The potentials and
limitations of the individual methods are discussed and illustrated for
paradigmatic examples of dynamical systems as well as for real-world time
series. Complex network measures are shown to provide information about
structural features of dynamical systems that are complementary to those
characterized by other methods of time series analysis and, hence,
substantially enrich the knowledge gathered from other existing (linear as well
as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos
(2011
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