Decoupling of brain function from structure reveals regional behavioral specialization in humans

The brain is an assembly of neuronal populations interconnected by structural pathways. Brain activity is expressed on and constrained by this substrate. Therefore, statistical dependencies between functional signals in directly connected areas can be expected higher. However, the degree to which brain function is bound by the underlying wiring diagram remains a complex question that has been only partially answered. Here, we introduce the structural-decoupling index to quantify the coupling strength between structure and function, and we reveal a macroscale gradient from brain regions more strongly coupled, to regions more strongly decoupled, than expected by realistic surrogate data. This gradient spans behavioral domains from lower-level sensory function to high-level cognitive ones and shows for the first time that the strength of structure-function coupling is spatially varying in line with evidence derived from other modalities, such as functional connectivity, gene expression, microstructural properties and temporal hierarchy

Augmented Slepians: Bandlimited Functions that Counterbalance Energy in Selected Intervals

Slepian functions provide a solution to the optimization problem of joint time-frequency localization. Here, this concept is extended by using a generalized optimization criterion that favors energy concentration in one interval while penalizing energy in another interval, leading to the "augmented" Slepian functions. Mathematical foundations together with examples are presented in order to illustrate the most interesting properties that these generalized Slepian functions show. Also the relevance of this novel energy-concentration criterion is discussed along with some of its applications

Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.Comment: 43 pages, 7 figures, submitted to Network Neuroscienc

An impossibility result for Markov Chain Monte Carlo sampling from micro-canonical bipartite graph ensembles

Markov Chain Monte Carlo (MCMC) algorithms are commonly used to sample from graph ensembles. Two graphs are neighbors in the state space if one can be obtained from the other with only a few modifications, e.g., edge rewirings. For many common ensembles, e.g., those preserving the degree sequences of bipartite graphs, rewiring operations involving two edges are sufficient to create a fully-connected state space, and they can be performed efficiently. We show that, for ensembles of bipartite graphs with fixed degree sequences and number of butterflies (k2,2 bi-cliques), there is no universal constant c such that a rewiring of at most c edges at every step is sufficient for any such ensemble to be fully connected. Our proof relies on an explicit construction of a family of pairs of graphs with the same degree sequences and number of butterflies, with each pair indexed by a natural c, and such that any sequence of rewiring operations transforming one graph into the other must include at least one rewiring operation involving at least c edges. Whether rewiring these many edges is sufficient to guarantee the full connectivity of the state space of any such ensemble remains an open question. Our result implies the impossibility of developing efficient, graph-agnostic, MCMC algorithms for these ensembles, as the necessity to rewire an impractically large number of edges may hinder taking a step on the state space

Mining Dense Subgraphs with Similar Edges

When searching for interesting structures in graphs, it is often important to take into account not only the graph connectivity, but also the metadata available, such as node and edge labels, or temporal information. In this paper we are interested in settings where such metadata is used to define a similarity between edges. We consider the problem of finding subgraphs that are dense and whose edges are similar to each other with respect to a given similarity function. Depending on the application, this function can be, for example, the Jaccard similarity between the edge label sets, or the temporal correlation of the edge occurrences in a temporal graph. We formulate a Lagrangian relaxation-based optimization problem to search for dense subgraphs with high pairwise edge similarity. We design a novel algorithm to solve the problem through parametric MinCut, and provide an efficient search scheme to iterate through the values of the Lagrangian multipliers. Our study is complemented by an evaluation on real-world datasets, which demonstrates the usefulness and efficiency of the proposed approach

Discovering Dense Correlated Subgraphs in Dynamic Networks

Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal subgraphs that satisfy specific density and similarity thresholds. To measure the similarity of the temporal behavior, we use the correlation between the binary time series that represent the activity of the edges. For the density, we study two variants based on the average degree. For these problem variants we enumerate the maximal subgraphs and compute a compact subset of subgraphs that have limited overlap. We propose an approximate algorithm that scales well with the size of the network, while achieving a high accuracy. We evaluate our framework on both real and synthetic datasets. The results of the synthetic data demonstrate the high accuracy of the approximation and show the scalability of the framework.Comment: Full version of the paper included in the proceedings of the PAKDD 2021 conferenc

Dynamics of functional connectivity at high spatial resolution reveal long-range interactions and fine-scale organization

Dynamic functional connectivity (dFC) derived from resting-state functional magnetic resonance imaging sheds light onto moment-to-moment reconfigurations of large-scale functional brain networks. Due to computational limits, connectivity is typically computed using pre-defined atlases, a non-trivial choice that might influence results. Here, we leverage new computational methods to retrieve dFC at the voxel level in terms of dominant patterns of fluctuations, and demonstrate that this new representation is informative to derive meaningful brain parcellations, capturing both long-range interactions and fine-scale local organization. Specifically, voxelwise dFC dominant patterns were captured through eigenvector centrality followed by clustering across time/subjects to yield most representative dominant patterns (RDPs). Voxel-wise labeling according to positive/negative contributions to RDPs, led to 37 unique labels identifying strikingly symmetric dFC long-range patterns. These included 449 contiguous regions, defining a fine-scale parcellation consistent with known cortical/subcortical subdivisions. Our contribution provides an alternative to obtain a whole-brain parcellation that is for the first time driven by voxel-level dFC and bridges the gap between voxel-based approaches and graph theoretical analysis

Eigenmaps Of Dynamic Functional Connectivity: Voxel-Level Dominant Patterns Through Eigenvector Centrality

Dynamic functional connectivity (dFC) based on resting-state functional magnetic resonance imaging (fMRI) explores the ongoing temporal configuration of brain networks. To reduce the large dimensionality of the data, conventional dFC analysis usually foresees an atlasing step, in which the brain is parcellated into specific regions of interest, and voxels' time-courses are spatially averaged within these regions before assessing connectivity. In this study, we addressed for the first time the exploration of dFC at the voxel level; i.e., without the use of any brain parcellation prior to the connectivity analysis. We used a sliding-window approach and extracted window-specific dominant patterns. To overcome the limitations due to the huge size of voxelwise connectivity matrices, we adopted the fast eigenvector centrality method with some adaptations to make it suitable for the dFC framework. After concatenation of the dominant patterns of all subjects, principal component analysis (PCA) was used to extract the eigenmaps; i.e., the most recurring voxelwise brain patterns characterizing resting-state. The obtained eigenmaps appeared consistent with previously observed resting-state eigenconnectivities, but with the substantial advantage of characterizing brain networks at the voxel level without the need of an atlas. The effect of the connection-wise temporal demeaning, usually performed in dFC analysis to remove the influence of static connectivity, was explored and does not seem to have an influence when voxelwise brain patterns are targeted