Assessing the consistency of community structure in complex networks

In recent years, community structure has emerged as a key component of complex network analysis. As more data has been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze changing communities, but most of these are limited to evolution of a single network over time. In addition, most of the existing methods are more concerned with change at the community level than at the level of the individual node. In this paper, we introduce scaled inclusivity, which is a method to quantify the change in community structure across networks. Scaled inclusivity evaluates the consistency of the classiffication of every node in a network independently. In addition, the method can be applied cross-sectionally as well as longitudinally. In this paper, we calculate the scaled inclusivity for a set of simulated networks of United States cities and a set of real networks consisting of teams that play in the top division of American college football. We found that scaled inclusivity yields reasonable results for the consistency of individual nodes in both sets of networks. We propose that scaled inclusivity may provide a useful way to quantify the change in a network's community structure

A peak-clustering method for MEG group analysis to minimise artefacts due to smoothness

Magnetoencephalography (MEG), a non-invasive technique for characterizing brain electrical activity, is gaining popularity as a tool for assessing group-level differences between experimental conditions. One method for assessing task-condition effects involves beamforming, where a weighted sum of field measurements is used to tune activity on a voxel-by-voxel basis. However, this method has been shown to produce inhomogeneous smoothness differences as a function of signal-to-noise across a volumetric image, which can then produce false positives at the group level. Here we describe a novel method for group-level analysis with MEG beamformer images that utilizes the peak locations within each participant's volumetric image to assess group-level effects. We compared our peak-clustering algorithm with SnPM using simulated data. We found that our method was immune to artefactual group effects that can arise as a result of inhomogeneous smoothness differences across a volumetric image. We also used our peak-clustering algorithm on experimental data and found that regions were identified that corresponded with task-related regions identified in the literature. These findings suggest that our technique is a robust method for group-level analysis with MEG beamformer images

More Specific Signal Detection in Functional Magnetic Resonance Imaging by False Discovery Rate Control for Hierarchically Structured Systems of Hypotheses

Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family at this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data

Universal fractal scaling of self-organized networks

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 46 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

Using Network Science to Evaluate Exercise-Associated Brain Changes in Older Adults

Literature has shown that exercise is beneficial for cognitive function in older adults and that aerobic fitness is associated with increased hippocampal tissue and blood volumes. The current study used novel network science methods to shed light on the neurophysiological implications of exercise-induced changes in the hippocampus of older adults. Participants represented a volunteer subgroup of older adults that were part of either the exercise training (ET) or healthy aging educational control (HAC) treatment arms from the Seniors Health and Activity Research Program Pilot (SHARP-P) trial. Following the 4-month interventions, MRI measures of resting brain blood flow and connectivity were performed. The ET group's hippocampal cerebral blood flow (CBF) exhibited statistically significant increases compared to the HAC group. Novel whole-brain network connectivity analyses showed greater connectivity in the hippocampi of the ET participants compared to HAC. Furthermore, the hippocampus was consistently shown to be within the same network neighborhood (module) as the anterior cingulate cortex only within the ET group. Thus, within the ET group, the hippocampus and anterior cingulate were highly interconnected and localized to the same network neighborhood. This project shows the power of network science to investigate potential mechanisms for exercise-induced benefits to the brain in older adults. We show a link between neurological network features and CBF, and it is possible that this alteration of functional brain networks may lead to the known improvement in cognitive function among older adults following exercise

A shadowing problem in the detection of overlapping communities: lifting the resolution limit through a cascading procedure

Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communities and unassigned links. We propose a generic cascading approach to community detection that circumvents the problem. Using real and artificial network datasets with three widely used community detection algorithms, we show how a simple cascading procedure allows for the detection of the missing communities. This work highlights a new detection limit of community structure, and we hope that our approach can inspire better community detection algorithms.Comment: 14 pages, 12 figures + supporting information (5 pages, 6 tables, 3 figures

The regulation of prostate cancer cell adhesion to human bone marrow endothelial cell monolayers by androgen dihydrotestosterone and cytokines

A previous study from our laboratory suggested that prostate cancer metastasis to bone may be mediated, in part, by preferential adhesion to human bone marrow endothelial (HBME) cells. Tumor cell adhesion to endothelial cells may be modulated by the effect of cytokines on cell adhesion molecules (CAMs). Tumor necrosis factor-alpha (TNF-α) regulates VCAM expression on the endothelium and this effect is enhanced by dihydrotestosterone (DHT). Transforming growth factor-beta (TGF-β) stimulates the expression of α 2 β 1 integrin on PC-3 cells. The current study investigated the effects of the above cytokines and DHT (singularly and in various combinations) upon HBME and prostate cancer cell expression of VCAM, α 2 integrin subunit, and β 1 integrin subunit by flow cytometry. We also monitored the effects of the above treatments on PC-3 cell adhesion to HBME monolayers. The data demonstrate that none of the treatments significantly altered the expression of selected CAMs on HBME cell and neoplastic prostate cell lines. The treatment of HBME monolayers with various combinations of cytokines and DHT prior to performing adhesion assays with PC-3 demonstrates that treatments containing TGF-β reduced PC-3 cell adhesion to HBME monolayers by 32% or greater ( P <0.05). The reduction in PC-3 cell adhesion to TGF-β-treated HBME monolayers was dose dependent. Interestingly, LNCaP cells but not PC-3 cells treated with TGF-β had a reduced ability to adhere to untreated HBME monolayers. These results suggest that TGF-β may reduce tumor cell adhesion to bone marrow microvascular endothelium, in vivo . The biological significance of this observation is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42583/1/10585_2004_Article_383338.pd