104,459 research outputs found
Hierarchical modularity in human brain functional networks
The idea that complex systems have a hierarchical modular organization
originates in the early 1960s and has recently attracted fresh support from
quantitative studies of large scale, real-life networks. Here we investigate
the hierarchical modular (or "modules-within-modules") decomposition of human
brain functional networks, measured using functional magnetic resonance imaging
(fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a
customized template to extract networks with more than 1800 regional nodes, and
we applied a fast algorithm to identify nested modular structure at several
hierarchical levels. We used mutual information, 0 < I < 1, to estimate the
similarity of community structure of networks in different subjects, and to
identify the individual network that is most representative of the group.
Results show that human brain functional networks have a hierarchical modular
organization with a fair degree of similarity between subjects, I=0.63. The
largest 5 modules at the highest level of the hierarchy were medial occipital,
lateral occipital, central, parieto-frontal and fronto-temporal systems;
occipital modules demonstrated less sub-modular organization than modules
comprising regions of multimodal association cortex. Connector nodes and hubs,
with a key role in inter-modular connectivity, were also concentrated in
association cortical areas. We conclude that methods are available for
hierarchical modular decomposition of large numbers of high resolution brain
functional networks using computationally expedient algorithms. This could
enable future investigations of Simon's original hypothesis that hierarchy or
near-decomposability of physical symbol systems is a critical design feature
for their fast adaptivity to changing environmental conditions
Multiple dynamical time-scales in networks with hierarchically nested modular organization
Many natural and engineered complex networks have intricate mesoscopic
organization, e.g., the clustering of the constituent nodes into several
communities or modules. Often, such modularity is manifested at several
different hierarchical levels, where the clusters defined at one level appear
as elementary entities at the next higher level. Using a simple model of a
hierarchical modular network, we show that such a topological structure gives
rise to characteristic time-scale separation between dynamics occurring at
different levels of the hierarchy. This generalizes our earlier result for
simple modular networks, where fast intra-modular and slow inter-modular
processes were clearly distinguished. Investigating the process of
synchronization of oscillators in a hierarchical modular network, we show the
existence of as many distinct time-scales as there are hierarchical levels in
the system. This suggests a possible functional role of such mesoscopic
organization principle in natural systems, viz., in the dynamical separation of
events occurring at different spatial scales.Comment: 10 pages, 4 figure
Organization of modular networks
We examine the global organization of heterogeneous equilibrium networks
consisting of a number of well distinguished interconnected
parts--``communities'' or modules. We develop an analytical approach allowing
us to obtain the statistics of connected components and an intervertex distance
distribution in these modular networks, and to describe their global
organization and structure. In particular, we study the evolution of the
intervertex distance distribution with an increasing number of interlinks
connecting two infinitely large uncorrelated networks. We demonstrate that even
a relatively small number of shortcuts unite the networks into one. In more
precise terms, if the number of the interlinks is any finite fraction of the
total number of connections, then the intervertex distance distribution
approaches a delta-function peaked form, and so the network is united.Comment: 9 pages, 3 figure
Modularity and the spread of perturbations in complex dynamical systems
We propose a method to decompose dynamical systems based on the idea that
modules constrain the spread of perturbations. We find partitions of system
variables that maximize 'perturbation modularity', defined as the
autocovariance of coarse-grained perturbed trajectories. The measure
effectively separates the fast intramodular from the slow intermodular dynamics
of perturbation spreading (in this respect, it is a generalization of the
'Markov stability' method of network community detection). Our approach
captures variation of modular organization across different system states, time
scales, and in response to different kinds of perturbations: aspects of
modularity which are all relevant to real-world dynamical systems. It offers a
principled alternative to detecting communities in networks of statistical
dependencies between system variables (e.g., 'relevance networks' or
'functional networks'). Using coupled logistic maps, we demonstrate that the
method uncovers hierarchical modular organization planted in a system's
coupling matrix. Additionally, in homogeneously-coupled map lattices, it
identifies the presence of self-organized modularity that depends on the
initial state, dynamical parameters, and type of perturbations. Our approach
offers a powerful tool for exploring the modular organization of complex
dynamical systems
The envirome and the connectome: exploring the structural noise in the human brain associated with socioeconomic deprivation
Complex cognitive functions are widely recognized to be the result of a number of brain regions working together as large-scale networks. Recently, complex network analysis has been used to characterize various structural properties of the large scale network organization of the brain. For example, the human brain has been found to have a modular architecture i.e. regions within the network form communities (modules) with more connections between regions within the community compared to regions outside it. The aim of this study was to examine the modular and overlapping modular architecture of the brain networks using complex network analysis. We also examined the association between neighborhood level deprivation and brain network structure – modularity and grey nodes. We compared network structure derived from anatomical MRI scans of 42 middle-aged neurologically healthy men from the least (LD) and the most deprived (MD) neighborhoods of Glasgow with their corresponding random networks. Cortical morphological covariance networks were constructed from the cortical thickness derived from the MRI scans of the brain. For a given modularity threshold, networks derived from the MD group showed similar number of modules compared to their corresponding random networks, while networks derived from the LD group had more modules compared to their corresponding random networks. The MD group also had fewer grey nodes – a measure of overlapping modular structure. These results suggest that apparent structural difference in brain networks may be driven by differences in cortical thicknesses between groups. This demonstrates a structural organization that is consistent with a system that is less robust and less efficient in information processing. These findings provide some evidence of the relationship between socioeconomic deprivation and brain network topology
Optimal modularity and memory capacity of neural reservoirs
The neural network is a powerful computing framework that has been exploited
by biological evolution and by humans for solving diverse problems. Although
the computational capabilities of neural networks are determined by their
structure, the current understanding of the relationships between a neural
network's architecture and function is still primitive. Here we reveal that
neural network's modular architecture plays a vital role in determining the
neural dynamics and memory performance of the network of threshold neurons. In
particular, we demonstrate that there exists an optimal modularity for memory
performance, where a balance between local cohesion and global connectivity is
established, allowing optimally modular networks to remember longer. Our
results suggest that insights from dynamical analysis of neural networks and
information spreading processes can be leveraged to better design neural
networks and may shed light on the brain's modular organization
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks,
have recently been suggested to provide a mechanism, rid of fine parameter
tuning, to explain the critical behavior of complex systems. One conjectured
requirement for systems with modular structures was that the network of modules
must be hierarchically organized and possess finite dimension. We investigate
the dynamical behavior of an activity spreading model, evolving on
heterogeneous random networks with highly modular structure and organized
non-hierarchically. We observe that loosely coupled modules act as effective
rare-regions, slowing down the extinction of activation. As a consequence, we
find extended control parameter regions with continuously changing dynamical
exponents for single network realizations, preserved after finite size
analyses, as in a real GP. The avalanche size distributions of spreading events
exhibit robust power-law tails. Our findings relax the requirement of
hierarchical organization of the modular structure, which can help to
rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure
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