130 research outputs found
Hierarchical organization of functional connectivity in the mouse brain: a complex network approach
This paper represents a contribution to the study of the brain functional
connectivity from the perspective of complex networks theory. More
specifically, we apply graph theoretical analyses to provide evidence of the
modular structure of the mouse brain and to shed light on its hierarchical
organization. We propose a novel percolation analysis and we apply our approach
to the analysis of a resting-state functional MRI data set from 41 mice. This
approach reveals a robust hierarchical structure of modules persistent across
different subjects. Importantly, we test this approach against a statistical
benchmark (or null model) which constrains only the distributions of empirical
correlations. Our results unambiguously show that the hierarchical character of
the mouse brain modular structure is not trivially encoded into this
lower-order constraint. Finally, we investigate the modular structure of the
mouse brain by computing the Minimal Spanning Forest, a technique that
identifies subnetworks characterized by the strongest internal correlations.
This approach represents a faster alternative to other community detection
methods and provides a means to rank modules on the basis of the strength of
their internal edges.Comment: 11 pages, 9 figure
Thermodynamics of network model fitting with spectral entropies
An information theoretic approach inspired by quantum statistical mechanics
was recently proposed as a means to optimize network models and to assess their
likelihood against synthetic and real-world networks. Importantly, this method
does not rely on specific topological features or network descriptors, but
leverages entropy-based measures of network distance. Entertaining the analogy
with thermodynamics, we provide a physical interpretation of model
hyperparameters and propose analytical procedures for their estimate. These
results enable the practical application of this novel and powerful framework
to network model inference. We demonstrate this method in synthetic networks
endowed with a modular structure, and in real-world brain connectivity
networks.Comment: 11 pages, 3 figure
Thermodynamics of network model fitting with spectral entropies
An information theoretic approach inspired by quantum statistical mechanics
was recently proposed as a means to optimize network models and to assess their
likelihood against synthetic and real-world networks. Importantly, this method
does not rely on specific topological features or network descriptors, but
leverages entropy-based measures of network distance. Entertaining the analogy
with thermodynamics, we provide a physical interpretation of model
hyperparameters and propose analytical procedures for their estimate. These
results enable the practical application of this novel and powerful framework
to network model inference. We demonstrate this method in synthetic networks
endowed with a modular structure, and in real-world brain connectivity
networks.Comment: 11 pages, 3 figure
Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold
Neuroimaging data can be represented as networks of nodes and edges that
capture the topological organization of the brain connectivity. Graph theory
provides a general and powerful framework to study these networks and their
structure at various scales. By way of example, community detection methods
have been widely applied to investigate the modular structure of many natural
networks, including brain functional connectivity networks. Sparsification
procedures are often applied to remove the weakest edges, which are the most
affected by experimental noise, and to reduce the density of the graph, thus
making it theoretically and computationally more tractable. However, weak links
may also contain significant structural information, and procedures to identify
the optimal tradeoff are the subject of active research. Here, we explore the
use of percolation analysis, a method grounded in statistical physics, to
identify the optimal sparsification threshold for community detection in brain
connectivity networks. By using synthetic networks endowed with a ground-truth
modular structure and realistic topological features typical of human brain
functional connectivity networks, we show that percolation analysis can be
applied to identify the optimal sparsification threshold that maximizes
information on the networks' community structure. We validate this approach
using three different community detection methods widely applied to the
analysis of brain connectivity networks: Newman's modularity, InfoMap and
Asymptotical Surprise. Importantly, we test the effects of noise and data
variability, which are critical factors to determine the optimal threshold.
This data-driven method should prove particularly useful in the analysis of the
community structure of brain networks in populations characterized by different
connectivity strengths, such as patients and controls.Comment: 15 pages, 7 figure
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