36 research outputs found
Robust Detection of Dynamic Community Structure in Networks
We describe techniques for the robust detection of community structure in
some classes of time-dependent networks. Specifically, we consider the use of
statistical null models for facilitating the principled identification of
structural modules in semi-decomposable systems. Null models play an important
role both in the optimization of quality functions such as modularity and in
the subsequent assessment of the statistical validity of identified community
structure. We examine the sensitivity of such methods to model parameters and
show how comparisons to null models can help identify system scales. By
considering a large number of optimizations, we quantify the variance of
network diagnostics over optimizations (`optimization variance') and over
randomizations of network structure (`randomization variance'). Because the
modularity quality function typically has a large number of nearly-degenerate
local optima for networks constructed using real data, we develop a method to
construct representative partitions that uses a null model to correct for
statistical noise in sets of partitions. To illustrate our results, we employ
ensembles of time-dependent networks extracted from both nonlinear oscillators
and empirical neuroscience data.Comment: 18 pages, 11 figure
Cross-linked structure of network evolution
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice. Subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks
Dynamic Network Centrality Summarizes Learning in the Human Brain
We study functional activity in the human brain using functional Magnetic
Resonance Imaging and recently developed tools from network science. The data
arise from the performance of a simple behavioural motor learning task.
Unsupervised clustering of subjects with respect to similarity of network
activity measured over three days of practice produces significant evidence of
`learning', in the sense that subjects typically move between clusters (of
subjects whose dynamics are similar) as time progresses. However, the high
dimensionality and time-dependent nature of the data makes it difficult to
explain which brain regions are driving this distinction. Using network
centrality measures that respect the arrow of time, we express the data in an
extremely compact form that characterizes the aggregate activity of each brain
region in each experiment using a single coefficient, while reproducing
information about learning that was discovered using the full data set. This
compact summary allows key brain regions contributing to centrality to be
visualized and interpreted. We thereby provide a proof of principle for the use
of recently proposed dynamic centrality measures on temporal network data in
neuroscience
Transient disruption of M1 during response planning impairs subsequent offline consolidation
Transcranial magnetic stimulation (TMS) was used to probe the involvement of the left primary motor cortex (M1) in the consolidation of a sequencing skill. In particular we asked: (1) if M1 is involved in consolidation of planning processes prior to response execution (2) whether movement preparation and movement execution can undergo consolidation independently and (3) whether sequence consolidation can occur in a stimulus specific manner. TMS was applied to left M1 while subjects prepared left hand sequential finger responses for three different movement sequences, presented in an interleaved fashion. Subjects also trained on three control sequences, where no TMS was applied. Disruption of subsequent consolidation was observed, but only for sequences where subjects had been exposed to TMS during training. Further, reduced consolidation was only observed for movement preparation, not movement execution. We conclude that left M1 is causally involved in the consolidation of effective response planning for left hand movements prior to response execution, and mediates consolidation in a sequence specific manner. These results provide important new insights into the role of M1 in sequential memory consolidation and sequence response planning