Task-Related modulations of BOLD low-frequency fluctuations within the default mode Network

Spontaneous low-frequency Blood-Oxygenation Level-Dependent (BOLD) signals acquired during resting state are characterized by spatial patterns of synchronous fluctuations, ultimately leading to the identification of robust brain networks. The resting-state brain networks, including the Default Mode Network (DMN), are demonstrated to persist during sustained task execution, but the exact features of task-related changes of network properties are still not well characterized. In this work we sought to examine in a group of 20 healthy volunteers (age 33 ± 6 years, 8 F/12 M) the relationship between changes of spectral and spatiotemporal features of one prominent resting-state network, namely the DMN, during the continuous execution of a working memory n-back task. We found that task execution impacted on both functional connectivity and amplitude of BOLD fluctuations within large parts of the DMN, but these changes correlated between each other only in a small area of the posterior cingulate. We conclude that combined analysis of multiple parameters related to connectivity, and their changes during the transition from resting state to continuous task execution, can contribute to a better understanding of how brain networks rearrange themselves in response to a task

Multi-scale Laplacian community detection in heterogeneous networks

Heterogeneous and complex networks represent the intertwined interactions between real-world elements or agents. A fundamental problem of complex network theory involves finding inherent partitions, clusters, or communities. By taking advantage of the recent Laplacian Renormalization Group approach, we scrutinize information diffusion pathways throughout networks to shed further light on this issue. Based on inter-node communicability, our definition provides a unifying framework for multiple partitioning measures: multi-scale Laplacian (MSL) community detection algorithm. This new framework permits to introduce a scale-dependent optimal partition in communities and to determine the existence of a particular class of nodes, called metastable nodes, that switching community at different scales are expected to play a central role in the communication between different communities and, therefore in the control of the whole network.Comment: 14 pages, 12 figure

Characterizing spatial point processes by percolation transitions

A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical ecology to analyze, e.g., the spatial percolation of a tree species in a tropical forest or a savanna. Here, we revisit the problem of aggregating random points in continuum systems (from $2$ to $6-$dimensional Euclidean spaces) to analyze the nature of the corresponding percolation transition in spatial point processes. This problem finds a natural description in terms of the canonical ensemble but not in the usual grand-canonical one, customarily employed to describe percolation transitions. This leads us to analyze the question of ensemble equivalence and study whether the resulting canonical continuum percolation transition shares its universal properties with standard percolation transitions, analyzing diverse homogeneous and heterogeneous spatial point processes. We, therefore, provide a powerful tool to characterize and classify a vast class of natural point patterns, revealing their fundamental properties based on percolation phase transitions.Comment: 22 pages, 13 figure

Laplacian renormalization group for heterogeneous networks

The renormalization group is the cornerstone of the modern theory of universality and phase transitions and it is a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its application to complex networks has proven particularly challenging, owing to correlations between intertwined scales. To date, existing approaches have been based on hidden geometries hypotheses, which rely on the embedding of complex networks into underlying hidden metric spaces. Here we propose a Laplacian renormalization group diffusion-based picture for complex networks, which is able to identify proper spatiotemporal scales in heterogeneous networks. In analogy with real-space renormalization group procedures, we first introduce the concept of Kadanoff supernodes as block nodes across multiple scales, which helps to overcome detrimental small-world effects that are responsible for cross-scale correlations. We then rigorously define the momentum space procedure to progressively integrate out fast diffusion modes and generate coarse-grained graphs. We validate the method through application to several real-world networks, demonstrating its ability to perform network reduction keeping crucial properties of the systems intact

Metastable States of Multiscale Brain Networks Are Keys to Crack the Timing Problem

The dynamics of the environment where we live in and the interaction with it, predicting events, provided strong evolutionary pressures for the brain functioning to process temporal information and generate timed responses. As a result, the human brain is able to process temporal information and generate temporal patterns. Despite the clear importance of temporal processing to cognition, learning, communication and sensory, motor and emotional processing, the basal mechanisms of how animals differentiate simple intervals or provide timed responses are still under debate. The lesson we learned from the last decade of research in neuroscience is that functional and structural brain connectivity matter. Specifically, it has been accepted that the organization of the brain in interacting segregated networks enables its function. In this paper we delineate the route to a promising approach for investigating timing mechanisms. We illustrate how novel insight into timing mechanisms can come by investigating brain functioning as a multi-layer dynamical network whose clustered dynamics is bound to report the presence of metastable states. We anticipate that metastable dynamics underlie the real-time coordination necessary for the brain's dynamic functioning associated to time perception. This new point of view will help further clarifying mechanisms of neuropsychiatric disorders

Laplacian paths in complex networks: Information core emerges from entropic transitions

Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network topology. Moreover, small-world effects correlate with the different network hierarchies complicating the identification of coexisting mesoscopic structures and functional cores.We present a communicability analysis of effective information pathways throughout complex networks based on information diffusion to shed further light on these issues. We employ a variety of brand-new theoretical techniques allowing for: (i) bring the theoretical framework to quantify the probability of information diffusion among nodes, (ii) identify critical scales and structures of complex networks regardless of their intrinsic properties, and (iii) demonstrate their dynamical relevance in synchronization phenomena. By combining these ideas, we evidence how the information flow on complex networks unravels different resolution scales. Using computational techniques, we focus on entropic transitions, uncovering a generic mesoscale object, the information core, and controlling information processing in complex networks. Altogether, this study sheds much light on allowing new theoretical techniques paving the way to introduce future renormalization group approaches based on diffusion distances

Organization and hierarchy of the human functional brain network lead to a chain-like core

The brain is a paradigmatic example of a complex system: its functionality emerges as a global property of local mesoscopic and microscopic interactions. Complex network theory allows to elicit the functional architecture of the brain in terms of links (correlations) between nodes (grey matter regions) and to extract information out of the noise. Here we present the analysis of functional magnetic resonance imaging data from forty healthy humans at rest for the investigation of the basal scaffold of the functional brain network organization. We show how brain regions tend to coordinate by forming ahighly hierarchical chain-like structure of homogeneously clustered anatomical areas. A maximum spanning tree approach revealed the centrality of the occipital cortex and the peculiar aggregation of cerebellar regions to form a closed core. We also report the hierarchy of network segregation and the level of clusters integration as a function of the connectivity strength between brain regions

Complexity in Neural and Financial Systems: From Time-Series to Networks (editorial)

When can a system be unambiguously defined as “complex”? Although many real-world systems are believed to bear the signature of complexity, the question above remains unanswered. Our special issue aims at contributing to this ongoing discussion by collecting a number of studies tackling two aspects of complexity that have recently gained increasing attention: the temporal one and the structural one