Evolution of network architecture in a granular material under compression

Statistics of a granular cluster ensemble at a liquid-solid-like phase transition

We report on the construction of a granular network of particles to study the formation, evolution, and statistical properties of clusters of particles developing at the vicinity of a liquid-solid-like phase transition within a vertically vibrated quasi-two-dimensional granular system. Using the data of particle positions and local order from Castillo et al. [G. Castillo, N. Mujica, and R. Soto, Phys. Rev. Lett. 109, 095701 (2012)0031-900710.1103/PhysRevLett.109.095701], we extract granular clusters taken as communities of the granular network via modularity optimization. Each one of these communities is a patch of particles with a very well defined local orientational order embedded within an array of other patches forming a complex cluster network. The distributions of cluster sizes and lifespans for the cluster network depend on the distance to the liquid-solid-like phase transition of the quasi-two-dimensional granular system. Specifically, the cluster size distribution displays a scale-invariant behavior for at least a decade in cluster sizes, while cluster lifespans grow monotonically with each cluster size. We believe this systematic community analysis for clustering in granular systems can help to study and understand the spatiotemporal evolution of mesoscale structures in systems displaying out-of-equilibrium phase transitions.

Forecasting landslides using community detection on geophysical satellite data

As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day, due to time lags between rainfall and pore-water pressure change at depth, or even after days to years of slow motion. While the prefailure deformation is sometimes apparent in retrospect, it remains challenging to predict the sudden transition from gradual deformation (creep) to runaway failure. We use a network science method-multilayer modularity optimization-to investigate the spatiotemporal patterns of deformation in a region near the 2017 Mud Creek, California landslide. We transform satellite radar data from the study site into a spatially embedded network in which the nodes are patches of ground and the edges connect the nearest neighbors, with a series of layers representing consecutive transits of the satellite. Each edge is weighted by the product of the local slope (susceptibility to failure) measured from a digital elevation model and ground surface deformation (current rheological state) from interferometric synthetic aperture radar (InSAR). We use multilayer modularity optimization to identify strongly connected clusters of nodes (communities) and are able to identify both the location of Mud Creek and nearby creeping landslides which have not yet failed. We develop a metric, i.e., community persistence, to quantify patterns of ground deformation leading up to failure, and find that this metric increased from a baseline value in the weeks leading up to Mud Creek's failure. These methods hold promise as a technique for highlighting regions at risk of catastrophic failure.

Multilayer brain network modeling and dynamic analysis of juvenile myoclonic epilepsy

Objective: It is indisputable that the functional connectivity of the brain network in juvenile myoclonic epilepsy (JME) patients is abnormal. As a mathematical extension of the traditional network model, the multilayer network can fully capture the fluctuations of brain imaging data with time, and capture subtle abnormal dynamic changes. This study assumed that the dynamic structure of JME patients is abnormal and used the multilayer network framework to analyze the change brain community structure in JME patients from the perspective of dynamic analysis.

Methods: First, functional magnetic resonance imaging (fMRI) data were obtained from 35 JME patients and 34 healthy control subjects. In addition, the communities of the two groups were explored with the help of a multilayer network model and a multilayer community detection algorithm. Finally, differences were described by metrics that are specific to the multilayer network.

Results: Compared with healthy controls, JME patients had a significantly lower modularity degree of the brain network. Furthermore, from the level of the functional network, the integration of the default mode network (DMN) and visual network (VN) in JME patients showed a significantly higher trend, and the flexibility of the attention network (AN) also increased significantly. At the node level, the integration of seven nodes of the DMN was significantly increased, the integration of five nodes of the VN was significantly increased, and the flexibility of three nodes of the AN was significantly increased. Moreover, through division of the core-peripheral system, we found that the left insula and left cuneus were core regions specific to the JME group, while most of the peripheral systems specific to the JME group were distributed in the prefrontal cortex and hippocampus. Finally, we found that the flexibility of the opercular part of the inferior frontal gyrus was significantly correlated with the severity of JME symptoms.

Conclusion: Our findings indicate that the dynamic community structure of JME patients is indeed abnormal. These results provide a new perspective for the study of dynamic changes in communities in JME patients.

Structure and Dynamics of Force Clusters and Networks in Shear Thickening Suspensions

Dense suspensions can exhibit shear thickening in response to large deformation. A consensus has emerged over the past few years on the formation of force networks, that span the entire system size, that lead to increased resistance to motion. Nonetheless, the characteristics of these networks are to a large extent poorly understood. Here, force networks formed in continuous and discontinuous shear thickening dense suspensions (CST and DST, respectively) are studied. We first show the evolution of the network formation and its topological heterogeneities as the applied stress increases. Subsequently, we identify force communities and coarse grain the suspension into a cluster network, and show that cluster-level dynamics are responsible for stark differences between the CST and DST behavior. Our results suggest that the force clusters formed in the DST regime are considerably more constrained in their motion, while CST clusters are loosely connected to their surrounding clusters.

Experimental validation of a micromechanically based compaction law for mixtures of soft and hard grains

In this Letter, we report on an experimental study which analyzes the compressive behavior of two-dimensional bidisperse granular assemblies made of soft (hyperelastic) and hard grains in varying proportions (κ is the portion of soft grains). By means of a recently developed uniaxial compression setup [Vu and Barés, Phys. Rev. E 100, 042907 (2019)]2470-004510.1103/PhysRevE.100.042907 and using an advanced digital image correlation method, we follow, beyond the jamming point, the evolution of the main mechanical observables, from the global scale down to the strain field inside each deformable grain. First, we validate experimentally and extend to the uniaxial case a recently proposed micromechanical compaction model linking the evolution of the applied pressure P to the packing fraction ϕ [Cantor et al., Phys. Rev. Lett. 124, 208003 (2020)]0031-900710.1103/PhysRevLett.124.208003. Second, we reveal two different linear regimes depending on whether the system is above or below a crossover strain unraveling a transition from a discrete to a continuous-like system. Third, the evolution of these linear laws is found to vary linearly with κ. These results provide a comprehensive experimental and theoretical framework that can now be extended to a more general class of polydisperse soft granular systems.

Probabilistically Weighted Multilayer Networks disclose the link between default mode network instability and psychosis-like experiences in healthy adults

The brain is a complex system in which the functional interactions among its subunits vary over time. The trajectories of this dynamic variation contribute to inter-individual behavioral differences and psychopathologic phenotypes. Despite many methodological advancements, the study of dynamic brain networks still relies on biased assumptions in the temporal domain. The current paper has two goals. First, we present a novel method to study multilayer networks: by modelling intra-nodal connections in a probabilistic, biologically driven way, we introduce a temporal resolution of the multilayer network based on signal similarity across time series. This new method is tested on synthetic networks by varying the number of modules and the sources of noise in the simulation. Secondly, we implement these probabilistically weighted (PW) multilayer networks to study the association between network dynamics and subclinical, psychosis-relevant personality traits in healthy adults. We show that the PW method for multilayer networks outperforms the standard procedure in modular detection and is less affected by increasing noise levels. Additionally, the PW method highlighted associations between the temporal instability of default mode network connections and psychosis-like experiences in healthy adults. PW multilayer networks allow an unbiased study of dynamic brain functioning and its behavioral correlates.

A more unstable resting-state functional network in cognitively declining multiple sclerosis

Cognitive impairment is common in people with multiple sclerosis and strongly affects their daily functioning. Reports have linked disturbed cognitive functioning in multiple sclerosis to changes in the organization of the functional network. In a healthy brain, communication between brain regions and which network a region belongs to is continuously and dynamically adapted to enable adequate cognitive function. However, this dynamic network adaptation has not been investigated in multiple sclerosis, and longitudinal network data remain particularly rare. Therefore, the aim of this study was to longitudinally identify patterns of dynamic network reconfigurations that are related to the worsening of cognitive decline in multiple sclerosis. Resting-state functional MRI and cognitive scores (expanded Brief Repeatable Battery of Neuropsychological tests) were acquired in 230 patients with multiple sclerosis and 59 matched healthy controls, at baseline (mean disease duration: 15 years) and at 5-year follow-up. A sliding-window approach was used for functional MRI analyses, where brain regions were dynamically assigned to one of seven literature-based subnetworks. Dynamic reconfigurations of subnetworks were characterized using measures of promiscuity (number of subnetworks switched to), flexibility (number of switches), cohesion (mutual switches) and disjointedness (independent switches). Cross-sectional differences between cognitive groups and longitudinal changes were assessed, as well as relations with structural damage and performance on specific cognitive domains. At baseline, 23% of patients were cognitively impaired (≥2/7 domains Z < −2) and 18% were mildly impaired (≥2/7 domains Z < −1.5). Longitudinally, 28% of patients declined over time (0.25 yearly change on ≥2/7 domains based on reliable change index). Cognitively impaired patients displayed more dynamic network reconfigurations across the whole brain compared with cognitively preserved patients and controls, i.e. showing higher promiscuity (P = 0.047), flexibility (P = 0.008) and cohesion (P = 0.008). Over time, cognitively declining patients showed a further increase in cohesion (P = 0.004), which was not seen in stable patients (P = 0.544). More cohesion was related to more severe structural damage (average r = 0.166, P = 0.015) and worse verbal memory (r = −0.156, P = 0.022), information processing speed (r = −0.202, P = 0.003) and working memory (r = −0.163, P = 0.017). Cognitively impaired multiple sclerosis patients exhibited a more unstable network reconfiguration compared to preserved patients, i.e. brain regions switched between subnetworks more often, which was related to structural damage. This shift to more unstable network reconfigurations was also demonstrated longitudinally in patients that showed cognitive decline only. These results indicate the potential relevance of a progressive destabilization of network topology for understanding cognitive decline in multiple sclerosis.

Brain-wide visual habituation networks in wild type and fmr1 zebrafish

Habituation is a form of learning during which animals stop responding to repetitive stimuli, and deficits in habituation are characteristic of several psychiatric disorders. Due to technical challenges, the brain-wide networks mediating habituation are poorly understood. Here we report brain-wide calcium imaging during larval zebrafish habituation to repeated visual looming stimuli. We show that different functional categories of loom-sensitive neurons are located in characteristic locations throughout the brain, and that both the functional properties of their networks and the resulting behavior can be modulated by stimulus saliency and timing. Using graph theory, we identify a visual circuit that habituates minimally, a moderately habituating midbrain population proposed to mediate the sensorimotor transformation, and downstream circuit elements responsible for higher order representations and the delivery of behavior. Zebrafish larvae carrying a mutation in the fmr1 gene have a systematic shift toward sustained premotor activity in this network, and show slower behavioral habituation.

Network controllability mediates the relationship between rigid structure and flexible dynamics

Precisely how the anatomical structure of the brain supports a wide range of complex functions remains a question of marked importance in both basic and clinical neuroscience. Progress has been hampered by the lack of theoretical frameworks explaining how a structural network of relatively rigid interareal connections can produce a diverse repertoire of functional neural dynamics. Here, we address this gap by positing that the brain's structural network architecture determines the set of accessible functional connectivity patterns according to predictions of network control theory. In a large developmental cohort of 823 youths aged 8 to 23 years, we found that the flexibility of a brain region's functional connectivity was positively correlated with the proportion of its structural links extending to different cognitive systems. Notably, this relationship was mediated by nodes' boundary controllability, suggesting that a region's strategic location on the boundaries of modules may underpin the capacity to integrate information across different cognitive processes. Broadly, our study provides a mechanistic framework that illustrates how temporal flexibility observed in functional networks may be mediated by the controllability of the underlying structural connectivity.

Probing the association between resting-state brain network dynamics and psychological resilience

This study aimed at replicating a previously reported negative correlation between node flexibility and psychological resilience, that is, the ability to retain mental health in the face of stress and adversity. To this end, we used multiband resting-state BOLD fMRI (TR = .675 sec) from 52 participants who had filled out three psychological questionnaires assessing resilience. Time-resolved functional connectivity was calculated by performing a sliding window approach on averaged time series parcellated according to different established atlases. Multilayer modularity detection was performed to track network reconfigurations over time, and node flexibility was calculated as the number of times a node changes community assignment. In addition, node promiscuity (the fraction of communities a node participates in) and node degree (as proxy for time-varying connectivity) were calculated to extend previous work. We found no substantial correlations between resilience and node flexibility. We observed a small number of correlations between the two other brain measures and resilience scores that were, however, very inconsistently distributed across brain measures, differences in temporal sampling, and parcellation schemes. This heterogeneity calls into question the existence of previously postulated associations between resilience and brain network flexibility and highlights how results may be influenced by specific analysis choices.

Crystalline shielding mitigates structural rearrangement and localizes memory in jammed systems under oscillatory shear

The nature of yield in amorphous materials under stress has yet to be fully elucidated. In particular, understanding how microscopic rearrangement gives rise to macroscopic structural and rheological signatures in disordered systems is vital for the prediction and characterization of yield and the study of how memory is stored in disordered materials. Here, we investigate the evolution of local structural homogeneity on an individual particle level in amorphous jammed two-dimensional (athermal) systems under oscillatory shear and relate this evolution to rearrangement, memory, and macroscale rheological measurements. We define the structural metric crystalline shielding, and show that it is predictive of rearrangement propensity and structural volatility of individual particles under shear. We use this metric to identify localized regions of the system in which the material's memory of its preparation is preserved. Our results contribute to a growing understanding of how local structure relates to dynamic response and memory in disordered systems.

Longitudinal functional brain network reconfiguration in healthy aging

Healthy aging is associated with changes in cognitive performance and functional brain organization. In fact, cross-sectional studies imply lower modularity and significant heterogeneity in modular architecture across older subjects. Here, we used a longitudinal dataset consisting of four occasions of resting-state-fMRI and cognitive testing (spanning 4 years) in 150 healthy older adults. We applied a graph-theoretic analysis to investigate the time-evolving modular structure of the whole-brain network, by maximizing the multilayer modularity across four time points. Global flexibility, which reflects the tendency of brain nodes to switch between modules across time, was significantly higher in healthy elderly than in a temporal null model. Further, global flexibility, as well as network-specific flexibility of the default mode, frontoparietal control, and somatomotor networks, were significantly associated with age at baseline. These results indicate that older age is related to higher variability in modular organization. The temporal metrics were not associated with simultaneous changes in processing speed or learning performance in the context of memory encoding. Finally, this approach provides global indices for longitudinal change across a given time span and it may contribute to uncovering patterns of modular variability in healthy and clinical aging populations.

Connecting particle clustering and rheology in attractive particle networks

The structural properties of suspensions and other multiphase systems are vital to overall processability, functionality and acceptance among consumers. Therefore, it is crucial to understand the intrinsic connection between the microstructure of a material and the resulting rheological properties. Here, we demonstrate how the transitions in the microstructural conformations can be quantified and correlated to rheological measurements. We find semi-local parameters from graph theory, the mathematical study of networks, to be useful in linking structure and rheology. Our results, using capillary suspensions as a model system, show that the use of the clustering coefficient, in combination with the coordination number, is able to capture not only the agglomeration of particles, but also measures the formation of groups. These phenomena are tightly connected to the rheological properties. The present sparse networks cannot be described by established techniques such as betweenness centrality.

Understanding diaschisis models of attention dysfunction with rTMS

Visual attentive tracking requires a balance of excitation and inhibition across large-scale frontoparietal cortical networks. Using methods borrowed from network science, we characterize the induced changes in network dynamics following low frequency (1 Hz) repetitive transcranial magnetic stimulation (rTMS) as an inhibitory noninvasive brain stimulation protocol delivered over the intraparietal sulcus. When participants engaged in visual tracking, we observed a highly stable network configuration of six distinct communities, each with characteristic properties in node dynamics. Stimulation to parietal cortex had no significant impact on the dynamics of the parietal community, which already exhibited increased flexibility and promiscuity relative to the other communities. The impact of rTMS, however, was apparent distal from the stimulation site in lateral prefrontal cortex. rTMS temporarily induced stronger allegiance within and between nodal motifs (increased recruitment and integration) in dorsolateral and ventrolateral prefrontal cortex, which returned to baseline levels within 15 min. These findings illustrate the distributed nature by which inhibitory rTMS perturbs network communities and is preliminary evidence for downstream cortical interactions when using noninvasive brain stimulation for behavioral augmentations.

Resting state fMRI based multilayer network configuration in patients with schizophrenia

Novel methods for measuring large-scale dynamic brain organisation are needed to provide new biomarkers of schizophrenia. Using a method for modelling dynamic modular organisation (Mucha et al., 2010), evidence suggests higher 'flexibility' (switching between multilayer network communities) to be a feature of schizophrenia (Braun et al., 2016). The current study compared flexibility between 55 patients with schizophrenia and 72 controls (the COBRE Dataset). In addition, novel methods of 'between resting state network synchronisation' (BRSNS) and the probability of transition from one community to another were used to further describe group differences in dynamic community structure. There was significantly higher schizophrenia group flexibility scores in cerebellar (F (1124) = 9.33, p (FDR) = 0.017), subcortical (F (1124) = 13.14, p (FDR) = 0.005), and fronto-parietal task control (F (1124) = 7.19, p (FDR) = 0.033) resting state networks (RSNs), as well as in the left thalamus (MNI XYZ: -2, -13, 12; F(1, 124) = 17.1, p (FDR) < 0.001) and the right crus I (MNI XYZ: 35, -67, -34; F (1, 124) = 19.65, p (FDR) < 0.001). Flexibility in the left thalamus reflected transitions between communities covering default mode and sensory-somatomotor RSNs. BRSNS scores suggested altered dynamic inter-RSN modular configuration in schizophrenia. This study suggests less stable community structure in a schizophrenia group at an RSN and node level and provides novel methods of exploring dynamic community structure. Mediation of group differences by mean time window correlation did however suggest flexibility to be no better as a schizophrenia biomarker than simpler measures and a range of methodological choices affected results.

Characterization of fracture in topology-optimized bioinspired networks

Designing strong and robust bioinspired structures requires an understanding of how function arises from the architecture and geometry of materials found in nature. We draw from trabecular bone, a lightweight bone tissue that exhibits a complex, anisotropic microarchitecture, to generate networked structures using multiobjective topology optimization. Starting from an identical volume, we generate multiple different models by varying the objective weights for compliance, surface area, and stability. We examine the relative effects of these objectives on how resultant models respond to simulated mechanical loading and element failure. We adapt a network-based method developed initially in the context of modeling trabecular bone to describe the topology-optimized structures with a graph-theoretical framework, and we use community detection to characterize locations of fracture. This complementary combination of computational methods can provide valuable insights into the strength of bioinspired structures and mechanisms of fracture.

Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity

We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size L of (i) statistics of individual relaxation events in terms of stress relaxation S, and individual event mean-squared displacement M, and the subsequent load increments Δγ, required to initiate the next event; (ii) static properties of the system encoded by x=σ_{y}-σ, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M. We find a strong correlation between S and M for any particular event, with S∼M^{q} with q≈0.65. The exponent q completely determines the scaling exponents for P(M) given those for P(S). For the distribution of local thresholds, we find P(x) is analytic at x=0, and has a value P(x)|_{x=0}=p_{0} which scales with lateral system length as p_{0}∝L^{-0.6}. The size dependence of the average load increment 〈Δγ〉 appears to be asymptotically controlled by the plateau behavior of P(x) rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing P(x) and those governing P(S). Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by 〈Δγ〉 and the scaling properties of P(M) (in particular from 〈M〉) rather than directly from P(S) as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.

Disrupted dynamic network reconfiguration of the language system in temporal lobe epilepsy

Temporal lobe epilepsy tends to reshape the language system causing maladaptive reorganization that can be characterized by task-based functional MRI, and eventually can contribute to surgical decision making processes. However, the dynamic interacting nature of the brain as a complex system is often neglected, with many studies treating the language system as a static monolithic structure. Here, we demonstrate that as a specialized and integrated system, the language network is inherently dynamic, characterized by rich patterns of regional interactions, whose transient dynamics are disrupted in patients with temporal lobe epilepsy. Specifically, we applied tools from dynamic network neuroscience to functional MRI data collected from 50 temporal lobe epilepsy patients and 30 matched healthy controls during performance of a verbal fluency task, as well as during rest. By assigning 16 language-related regions into four subsystems (i.e. bilateral frontal and temporal), we observed regional specialization in both the probability of transient interactions and the frequency of such changes, in both healthy controls and patients during task performance but not rest. Furthermore, we found that both left and right temporal lobe epilepsy patients displayed reduced interactions within the left frontal 'core' subsystem compared to the healthy controls, while left temporal lobe epilepsy patients were unique in showing enhanced interactions between the left frontal 'core' and the right temporal subsystems. Also, both patient groups displayed reduced flexibility in the transient interactions of the left temporal and right frontal subsystems, which formed the 'periphery' of the language network. Importantly, such group differences were again evident only during task condition. Lastly, through random forest regression, we showed that dynamic reconfiguration of the language system tracks individual differences in verbal fluency with superior prediction accuracy compared to traditional activation-based static measures. Our results suggest dynamic network measures may be an effective biomarker for detecting the language dysfunction associated with neurological diseases such as temporal lobe epilepsy, specifying both the type of neuronal communications that are missing in these patients and those that are potentially added but maladaptive. Further advancements along these lines, transforming how we characterize and map language networks in the brain, have a high probability of altering clinical decision making in neurosurgical centres.10.1093/brain/awy042_video1awy042media15754656112001.

Sparsification of long range force networks for molecular dynamics simulations

Atomic interactions in solid materials are described using network theory. The tools of network theory focus on understanding the properties of a system based upon the underlying interactions which govern their dynamics. While the full atomistic network is dense, we apply a spectral sparsification technique to construct a sparse interaction network model that reduces the computational complexity while preserving macroscopic conservation properties. This sparse network is compared to a reduced network created using a cut-off radius (threshold method) that is commonly used to speed-up computations while approximating interatomic forces. The approximations used to estimate the total forces on each atom are quantified to assess how local interatomic force errors propagate errors at the global or continuum scale by comparing spectral sparsification to thresholding. In particular, we quantify the performance of the spectral sparsification algorithm for the short-range Lennard-Jones potential and the long-range Coulomb potential. Spectral sparsification of the Lennard–Jones potential yields comparable results to thresholding while spectral sparsification yields improvements when considering a long-range Coulomb potential. The present network-theoretic formulation is implemented on two sample problems: relaxation of atoms near a surface and a tensile test of a solid with a circular hole.

A nature inspired modularity function for unsupervised learning involving spatially embedded networks

The quality of network clustering is often measured in terms of a commonly used metric known as "modularity". Modularity compares the clusters found in a network to those present in a random graph (a "null model"). Unfortunately, modularity is somewhat ill suited for studying spatially embedded networks, since a random graph contains no basic geometrical notions. Regardless of their distance, the null model assigns a nonzero probability for an edge to appear between any pair of nodes. Here, we propose a variant of modularity that does not rely on the use of a null model. To demonstrate the essentials of our method, we analyze networks generated from granular ensemble. We show that our method performs better than the most commonly used Newman-Girvan (NG) modularity in detecting the best (physically transparent) partitions in those systems. Our measure further properly detects hierarchical structures, whenever these are present.

Betweenness centrality as predictor for forces in granular packings

A load applied to a jammed frictional granular system will be localized into a network of force chains making inter-particle connections throughout the system. Because such systems are typically under-constrained, the observed force network is not unique to a given particle configuration, but instead varies upon repeated formation. In this paper, we examine the ensemble of force chain configurations created under repeated assembly in order to develop tools to statistically forecast the observed force network. In experiments on a gently suspended 2D layer of photoelastic particles, we subject the assembly to hundreds of repeated cyclic compressions. As expected, we observe the non-unique nature of the force network, which differs for each compression cycle, by measuring all vector inter-particle contact forces using our open source PeGS software. We find that total pressure on each particle in the system correlates to its betweenness centrality value extracted from the geometric contact network. Thus, the mesoscale network structure is a key control on individual particle pressures.

Evaluation of confound regression strategies for the mitigation of micromovement artifact in studies of dynamic resting-state functional connectivity and multilayer network modularity

Dynamic functional connectivity reflects the spatiotemporal organization of spontaneous brain activity in health and disease. Dynamic functional connectivity may be susceptible to artifacts induced by participant motion. This report provides a systematic evaluation of 12 commonly used participant-level confound regression strategies designed to mitigate the effects of micromovements in a sample of 393 youths (ages 8-22 years). Each strategy was evaluated according to a number of benchmarks, including (a) the residual association between participant motion and edge dispersion, (b) distance-dependent effects of motion on edge dispersion, (c) the degree to which functional subnetworks could be identified by multilayer modularity maximization, and (d) measures of module reconfiguration, including node flexibility and node promiscuity. Results indicate variability in the effectiveness of the evaluated pipelines across benchmarks. Methods that included global signal regression were the most consistently effective de-noising strategies.

Modeling and interpreting mesoscale network dynamics

Recent advances in brain imaging techniques, measurement approaches, and storage capacities have provided an unprecedented supply of high temporal resolution neural data. These data present a remarkable opportunity to gain a mechanistic understanding not just of circuit structure, but also of circuit dynamics, and its role in cognition and disease. Such understanding necessitates a description of the raw observations, and a delineation of computational models and mathematical theories that accurately capture fundamental principles behind the observations. Here we review recent advances in a range of modeling approaches that embrace the temporally-evolving interconnected structure of the brain and summarize that structure in a dynamic graph. We describe recent efforts to model dynamic patterns of connectivity, dynamic patterns of activity, and patterns of activity atop connectivity. In the context of these models, we review important considerations in statistical testing, including parametric and non-parametric approaches. Finally, we offer thoughts on careful and accurate interpretation of dynamic graph architecture, and outline important future directions for method development.

Dynamic graph metrics: Tutorial, toolbox, and tale

The central nervous system is composed of many individual units - from cells to areas - that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and parsimonious representation of such a system is a graph in which nodes (units) are connected by edges (interactions). While applicable across spatiotemporal scales, species, and cohorts, the traditional graph approach is unable to address the complexity of time-varying connectivity patterns that may be critically important for an understanding of emotional and cognitive state, task-switching, adaptation and development, or aging and disease progression. Here we survey a set of tools from applied mathematics that offer measures to characterize dynamic graphs. Along with this survey, we offer suggestions for visualization and a publicly-available MATLAB toolbox to facilitate the application of these metrics to existing or yet-to-be acquired neuroimaging data. We illustrate the toolbox by applying it to a previously published data set of time-varying functional graphs, but note that the tools can also be applied to time-varying structural graphs or to other sorts of relational data entirely. Our aim is to provide the neuroimaging community with a useful set of tools, and an intuition regarding how to use them, for addressing emerging questions that hinge on accurate and creative analyses of dynamic graphs.

Dynamic graph metrics: Tutorial, toolbox, and tale

The central nervous system is composed of many individual units - from cells to areas - that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and parsimonious representation of such a system is a graph in which nodes (units) are connected by edges (interactions). While applicable across spatiotemporal scales, species, and cohorts, the traditional graph approach is unable to address the complexity of time-varying connectivity patterns that may be critically important for an understanding of emotional and cognitive state, task-switching, adaptation and development, or aging and disease progression. Here we survey a set of tools from applied mathematics that offer measures to characterize dynamic graphs. Along with this survey, we offer suggestions for visualization and a publicly-available MATLAB toolbox to facilitate the application of these metrics to existing or yet-to-be acquired neuroimaging data. We illustrate the toolbox by applying it to a previously published data set of time-varying functional graphs, but note that the tools can also be applied to time-varying structural graphs or to other sorts of relational data entirely. Our aim is to provide the neuroimaging community with a useful set of tools, and an intuition regarding how to use them, for addressing emerging questions that hinge on accurate and creative analyses of dynamic graphs.

Applications of community detection techniques to brain graphs: Algorithmic considerations and implications for neural function

The human brain can be represented as a graph in which neural units such as cells or small volumes of tissue are heterogeneously connected to one another through structural or functional links. Brain graphs are parsimonious representations of neural systems that have begun to offer fundamental insights into healthy human cognition, as well as its alteration in disease. A critical open question in network neuroscience lies in how neural units cluster into densely interconnected groups that can provide the coordinated activity that is characteristic of perception, action, and adaptive behaviors. Tools that have proven particularly useful for addressing this question are community detection approaches, which can identify communities or modules: groups of neural units that are densely interconnected with other units in their own group but sparsely interconnected with units in other groups. In this paper, we describe a common community detection algorithm known as modularity maximization, and we detail its applications to brain graphs constructed from neuroimaging data. We pay particular attention to important algorithmic considerations, especially in recent extensions of these techniques to graphs that evolve in time. After recounting a few fundamental insights that these techniques have provided into brain function, we highlight potential avenues of methodological advancements for future studies seeking to better characterize the patterns of coordinated activity in the brain that accompany human behavior. This tutorial provides a naive reader with an introduction to theoretical considerations pertinent to the generation of brain graphs, an understanding of modularity maximization for community detection, a resource of statistical measures that can be used to characterize community structure, and an appreciation of the usefulness of these approaches in uncovering behaviorally-relevant network dynamics in neuroimaging data.

Multi-scale brain networks

The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its alteration in disease or injury. Traditional tools and approaches to study this architecture have largely focused on single scales-of topology, time, and space. Expanding beyond this narrow view, we focus this review on pertinent questions and novel methodological advances for the multi-scale brain. We separate our exposition into content related to multi-scale topological structure, multi-scale temporal structure, and multi-scale spatial structure. In each case, we recount empirical evidence for such structures, survey network-based methodological approaches to reveal these structures, and outline current frontiers and open questions. Although predominantly peppered with examples from human neuroimaging, we hope that this account will offer an accessible guide to any neuroscientist aiming to measure, characterize, and understand the full richness of the brain's multiscale network structure-irrespective of species, imaging modality, or spatial resolution.

Versatility of nodal affiliation to communities

Graph theoretical analysis of the community structure of networks attempts to identify the communities (or modules) to which each node affiliates. However, this is in most cases an ill-posed problem, as the affiliation of a node to a single community is often ambiguous. Previous solutions have attempted to identify all of the communities to which each node affiliates. Instead of taking this approach, we introduce versatility, V, as a novel metric of nodal affiliation: V ≈ 0 means that a node is consistently assigned to a specific community; V >> 0 means it is inconsistently assigned to different communities. Versatility works in conjunction with existing community detection algorithms, and it satisfies many theoretically desirable properties in idealised networks designed to maximise ambiguity of modular decomposition. The local minima of global mean versatility identified the resolution parameters of a hierarchical community detection algorithm that least ambiguously decomposed the community structure of a social (karate club) network and the mouse brain connectome. Our results suggest that nodal versatility is useful in quantifying the inherent ambiguity of modular decomposition.

Emerging Frontiers of Neuroengineering: A Network Science of Brain Connectivity

Neuroengineering is faced with unique challenges in repairing or replacing complex neural systems that are composed of many interacting parts. These interactions form intricate patterns over large spatiotemporal scales and produce emergent behaviors that are difficult to predict from individual elements. Network science provides a particularly appropriate framework in which to study and intervene in such systems by treating neural elements (cells, volumes) as nodes in a graph and neural interactions (synapses, white matter tracts) as edges in that graph. Here, we review the emerging discipline of network neuroscience, which uses and develops tools from graph theory to better understand and manipulate neural systems from micro- to macroscales. We present examples of how human brain imaging data are being modeled with network analysis and underscore potential pitfalls. We then highlight current computational and theoretical frontiers and emphasize their utility in informing diagnosis and monitoring, brain-machine interfaces, and brain stimulation. A flexible and rapidly evolving enterprise, network neuroscience provides a set of powerful approaches and fundamental insights that are critical for the neuroengineer's tool kit.

Positive affect, surprise, and fatigue are correlates of network flexibility

Advances in neuroimaging have made it possible to reconstruct functional networks from the activity patterns of brain regions distributed across the cerebral cortex. Recent work has shown that flexible reconfiguration of human brain networks over short timescales supports cognitive flexibility and learning. However, modulating network flexibility to enhance learning requires an understanding of an as-yet unknown relationship between flexibility and brain state. Here, we investigate the relationship between network flexibility and affect, leveraging an unprecedented longitudinal data set. We demonstrate that indices associated with positive mood and surprise are both associated with network flexibility - positive mood portends a more flexible brain while increased levels of surprise portend a less flexible brain. In both cases, these relationships are driven predominantly by a subset of brain regions comprising the somatomotor system. Our results simultaneously suggest a network-level mechanism underlying learning deficits in mood disorders as well as a potential target - altering an individual's mood or task novelty - to improve learning.

The modular organization of human anatomical brain networks: Accounting for the cost of wiring

Brain networks are expected to be modular. However, existing techniques for estimating a network's modules make it difficult to assess the influence of organizational principles such as wiring cost reduction on the detected modules. Here we present a modification of an existing module detection algorithm that allowed us to focus on connections that are unexpected under a cost-reduction wiring rule and to identify modules from among these connections. We applied this technique to anatomical brain networks and showed that the modules we detected differ from those detected using the standard technique. We demonstrated that these novel modules are spatially distributed, exhibit unique functional fingerprints, and overlap considerably with rich clubs, giving rise to an alternative and complementary interpretation of the functional roles of specific brain regions. Finally, we demonstrated that, using the modified module detection approach, we can detect modules in a developmental dataset that track normative patterns of maturation. Collectively, these findings support the hypothesis that brain networks are composed of modules and provide additional insight into the function of those modules.

Small-World Brain Networks Revisited

It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.