Abstract: 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.

Abstract: Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches.

Abstract: The modular organization of functional and structural brain connectivity networks has been investigated using graph theoretical approaches. Recently, it has been demonstrated that community detection methods based on the maximization of global fitness functions, suffer from a resolution limit, as they fail to detect modules that are smaller than an intrinsic scale. This resolution limit prevents detection of important details of the brain modular organization.Here, we show that Surprise, a recently proposed binary fitness function based on probability theory, behaves like a resolution-limit-free method. We propose an extension of Surprise to weighted networks, and heuristics for its optimization. We benchmark Surprise against widely applied algorithms, and quantitatively assess its performance in synthetic correlation networks with different levels of noise, and in human resting state functional connectivity data.In synthetic networks, Surprise shows better sensitivity and specificity in the detection of ground-truth structures, particularly in the presence of noise and variability such as those observed in experimental functional MRI data. Surprise optimization in human resting state networks reveals the presence of a rich structure of modules with heterogeneous size distribution undetectable by current methods. Our results indicate that the resolution limit may have substantially affected previous analyses of brain connectivity networks, and call for a revisitation of some of the current models of brain modular organization.

Abstract: We derive an equation of motion for the order parameter in the small world networks with temporal memory and long-range interaction and obtain a fractional differential equation for the order parameter as We analyze a spatial and temporal distribution of the order parameter in detail. Based on fMRI data, we construct brain functional networks and try to describe the dynamical properties of these networks using our result.

Abstract: In connectomics, the human brain is modelled as a complex network and the properties of this network are studied in order to understand the structure and function of the brain. However, defining the functional brain network is not straightforward. Particularly, there is no consensus on what the nodes of the network should depict. One typical approach for defining the nodes are Regions of Interest (ROIs) that are collections of fMRI measurement voxels, typically defined by anatomical landmarks.The ROI approach is based on the assumption that voxels in a ROI are functionally similar and have reasonably similar dynamics. However, we find that this assumption does not hold in general: ROIs are often functionally inhomogeneous. This is visible in the wide distribution of consistency of ROIs, defined as the mean Pearson correlation between the time series of voxels within a ROI. Further, the time series of low-consistency ROIs can at times be highly correlated. To our understanding, this indicates that the ROI approach affects the structure of resting-state functional brain networks by inducing spurious links.