12,828 research outputs found
Graph analysis of functional brain networks: practical issues in translational neuroscience
The brain can be regarded as a network: a connected system where nodes, or
units, represent different specialized regions and links, or connections,
represent communication pathways. From a functional perspective communication
is coded by temporal dependence between the activities of different brain
areas. In the last decade, the abstract representation of the brain as a graph
has allowed to visualize functional brain networks and describe their
non-trivial topological properties in a compact and objective way. Nowadays,
the use of graph analysis in translational neuroscience has become essential to
quantify brain dysfunctions in terms of aberrant reconfiguration of functional
brain networks. Despite its evident impact, graph analysis of functional brain
networks is not a simple toolbox that can be blindly applied to brain signals.
On the one hand, it requires a know-how of all the methodological steps of the
processing pipeline that manipulates the input brain signals and extract the
functional network properties. On the other hand, a knowledge of the neural
phenomenon under study is required to perform physiological-relevant analysis.
The aim of this review is to provide practical indications to make sense of
brain network analysis and contrast counterproductive attitudes
Characterization of complex networks: A survey of measurements
Each complex network (or class of networks) presents specific topological
features which characterize its connectivity and highly influence the dynamics
of processes executed on the network. The analysis, discrimination, and
synthesis of complex networks therefore rely on the use of measurements capable
of expressing the most relevant topological features. This article presents a
survey of such measurements. It includes general considerations about complex
network characterization, a brief review of the principal models, and the
presentation of the main existing measurements. Important related issues
covered in this work comprise the representation of the evolution of complex
networks in terms of trajectories in several measurement spaces, the analysis
of the correlations between some of the most traditional measurements,
perturbation analysis, as well as the use of multivariate statistics for
feature selection and network classification. Depending on the network and the
analysis task one has in mind, a specific set of features may be chosen. It is
hoped that the present survey will help the proper application and
interpretation of measurements.Comment: A working manuscript with 78 pages, 32 figures. Suggestions of
measurements for inclusion are welcomed by the author
Model-free reconstruction of neuronal network connectivity from calcium imaging signals
A systematic assessment of global neural network connectivity through direct
electrophysiological assays has remained technically unfeasible even in
dissociated neuronal cultures. We introduce an improved algorithmic approach
based on Transfer Entropy to reconstruct approximations to network structural
connectivities from network activity monitored through calcium fluorescence
imaging. Based on information theory, our method requires no prior assumptions
on the statistics of neuronal firing and neuronal connections. The performance
of our algorithm is benchmarked on surrogate time-series of calcium
fluorescence generated by the simulated dynamics of a network with known
ground-truth topology. We find that the effective network topology revealed by
Transfer Entropy depends qualitatively on the time-dependent dynamic state of
the network (e.g., bursting or non-bursting). We thus demonstrate how
conditioning with respect to the global mean activity improves the performance
of our method. [...] Compared to other reconstruction strategies such as
cross-correlation or Granger Causality methods, our method based on improved
Transfer Entropy is remarkably more accurate. In particular, it provides a good
reconstruction of the network clustering coefficient, allowing to discriminate
between weakly or strongly clustered topologies, whereas on the other hand an
approach based on cross-correlations would invariantly detect artificially high
levels of clustering. Finally, we present the applicability of our method to
real recordings of in vitro cortical cultures. We demonstrate that these
networks are characterized by an elevated level of clustering compared to a
random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted
for publicatio
Statistical Network Analysis for Functional MRI: Summary Networks and Group Comparisons
Comparing weighted networks in neuroscience is hard, because the topological
properties of a given network are necessarily dependent on the number of edges
of that network. This problem arises in the analysis of both weighted and
unweighted networks. The term density is often used in this context, in order
to refer to the mean edge weight of a weighted network, or to the number of
edges in an unweighted one. Comparing families of networks is therefore
statistically difficult because differences in topology are necessarily
associated with differences in density. In this review paper, we consider this
problem from two different perspectives, which include (i) the construction of
summary networks, such as how to compute and visualize the mean network from a
sample of network-valued data points; and (ii) how to test for topological
differences, when two families of networks also exhibit significant differences
in density. In the first instance, we show that the issue of summarizing a
family of networks can be conducted by adopting a mass-univariate approach,
which produces a statistical parametric network (SPN). In the second part of
this review, we then highlight the inherent problems associated with the
comparison of topological functions of families of networks that differ in
density. In particular, we show that a wide range of topological summaries,
such as global efficiency and network modularity are highly sensitive to
differences in density. Moreover, these problems are not restricted to
unweighted metrics, as we demonstrate that the same issues remain present when
considering the weighted versions of these metrics. We conclude by encouraging
caution, when reporting such statistical comparisons, and by emphasizing the
importance of constructing summary networks.Comment: 16 pages, 5 figure
Beyond Node Degree: Evaluating AS Topology Models
This is the accepted version of 'Beyond Node Degree: Evaluating AS Topology Models', archived originally at arXiv:0807.2023v1 [cs.NI] 13 July 2008.Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies. In contrast to most previous works, we avoid making assumptions about which topological properties are important to characterize the AS topology. Our analysis shows that, although matching degree-based properties, the existing AS topology generation models fail to capture the complexity of the local interconnection structure between ASs. Furthermore, we use BGP data from multiple vantage points to show that additional measurement locations significantly affect local structure properties, such as clustering and node centrality. Degree-based properties, however, are not notably affected by additional measurements locations. These observations are particularly valid in the core. The shortcomings of AS topology generation models stems from an underestimation of the complexity of the connectivity in the core caused by inappropriate use of BGP data
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