Scaleresolved analysis of brain functional connectivity networks with spectral entropy Abstract   Functional connectivity is derived from interregional correlations in spontaneous fluctuations of brain activity, and can be represented in terms of complete graphs with continuous (realvalued) edges. The structure of functional connectivity networks is strongly affected by signal processing procedures to remove the effects of motion, physiological noise and other sources of experimental error. However, in the absence of an established ground truth, it is difficult to determine the optimal procedure, and no consensus has been reached on the most effective approach to remove nuisance signals without unduly affecting the network intrinsic structural features. Here, we use a novel informationtheoretic approach, based on von Neumann entropy, which provides a measure of information encoded in the networks at different scales. We also define a measure of distance between networks, based on information divergence, and optimal null models appropriate for the description of functional connectivity networks, to test for the presence of nontrivial structural patterns that are not the result of simple local constraints. This formalism enables a scaleresolved analysis of the distance between a functional connectivity network and its maximally random counterpart, thus providing a means to assess the effects of noise and image processing on network structure. We apply this novel approach to address a few open questions in the analysis of brain functional connectivity networks. Specifically, we demonstrate a strongly beneficial effect of network sparsification by removal of the weakest links, and the existence of an optimal threshold that maximizes the ability to extract information on largescale network structures. Additionally, we investigate the effects of different degrees of motion at different scales, and compare the most popular processing pipelines designed to mitigate its deleterious effect on functional connectivity networks. We show that network sparsification, in combination with motion correction algorithms, dramatically improves detection of large scale network structure.

Spaceindependent community and hub structure of functional brain networks Abstract   Coordinated brain activity reflects underlying cognitive processes and can be modeled as a network of interregional functional connections. The most costly connections in the network are longdistance correlations that, in the absence of underlying structural connections, are maintained by sustained energetic inputs. Here, we present a spatial modeling approach that amplifies contributions made by longdistance functional connections to wholebrain network architecture, while simultaneously suppressing contributions made by shortrange connections. We use this method to characterize the longdistance architecture of functional networks and to identify aspects of community and hub structure that are driven by longdistance correlations and that, we argue, are of greater functional significance. We find that based only on patterns of longdistance connectivity, primary sensory cortices occupy increasingly central positions and appear more xe2x80x9chublikexe2x80x9d. Additionally, we show that the community structure of longdistance connections spans multiple topological levels and differs from the community structure detected in networks that include both shortrange and longdistance connections. In summary, these findings highlight the complex relationship between the brainxe2x80x99s physical layout and its functional architecture. The results presented here inform future analyses of community structure and network hubs in health, across development, and in the case of neuropsychiatric disorders.