Network inference with confidence from multivariate time series

Intracranial EEG-Based Directed Functional Connectivity in Alpha to Gamma Frequency Range Reflects Local Circuits of the Human Mesiotemporal Network

To date, it is largely unknown how frequency range of neural oscillations measured with EEG is related to functional connectivity. To address this question, we investigated frequency-dependent directed functional connectivity among the structures of mesial and anterior temporal network including amygdala, hippocampus, temporal pole and parahippocampal gyrus in the living human brain. Intracranial EEG recording was obtained from 19 consecutive epilepsy patients with normal anterior mesial temporal MR imaging undergoing intracranial presurgical epilepsy diagnostics with multiple depth electrodes. We assessed intratemporal bidirectional functional connectivity using several causality measures such as Granger causality (GC), directed transfer function (DTF) and partial directed coherence (PDC) in a frequency-specific way. In order to verify the obtained results, we compared the spontaneous functional networks with intratemporal effective connectivity evaluated by means of SPES (single pulse electrical stimulation) method. The overlap with the evoked network was found for the functional connectivity assessed by the GC method, most prominent in the higher frequency bands (alpha, beta and low gamma), yet vanishing in the lower frequencies. Functional connectivity assessed by means of DTF and PCD obtained a similar directionality pattern with the exception of connectivity between hippocampus and parahippocampal gyrus which showed opposite directionality of predominant information flow. Whereas previous connectivity studies reported significant divergence between spontaneous and evoked networks, our data show the role of frequency bands for the consistency of functional and evoked intratemporal directed connectivity. This has implications for the suitability of functional connectivity methods in characterizing local brain circuits.

Duality between predictability and reconstructability in complex systems

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here, we find an intricate relationship between predictability and reconstructability using an information-theoretical point of view. We use the mutual information between a random graph and a stochastic process evolving on this random graph to quantify their codependence. Then, we show how the uncertainty coefficients, which are intimately related to that mutual information, quantify our ability to reconstruct a graph from an observed time series, and our ability to predict the evolution of a process from the structure of its interactions. We provide analytical calculations of the uncertainty coefficients for many different systems, including continuous deterministic systems, and describe a numerical procedure when exact calculations are intractable. Interestingly, we find that predictability and reconstructability, even though closely connected by the mutual information, can behave differently, even in a dual manner. We prove how such duality universally emerges when changing the number of steps in the process. Finally, we provide evidence that predictability-reconstruction dualities may exist in dynamical processes on real networks close to criticality.

The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives

Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.

Hypergraph reconstruction from uncertain pairwise observations

The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here, using Bayesian inference, we investigate the general problem of reconstructing a network in which higher-order interactions are also present. We study a minimal example of this problem, focusing on the case of hypergraphs with interactions between pairs and triplets of vertices, measured imperfectly and indirectly. We derive a Metropolis-Hastings-within-Gibbs algorithm for this model to highlight the unique challenges that come with estimating higher-order models. We show that this approach tends to reconstruct empirical and synthetic networks more accurately than an equivalent graph model without higher-order interactions.

Physiological and pathological neuronal connectivity in the living human brain based on intracranial EEG signals: the current state of research

Over the past decades, studies of human brain networks have received growing attention as the assessment and modelling of connectivity in the brain is a topic of high impact with potential application in the understanding of human brain organization under both physiological as well as various pathological conditions. Under specific diagnostic settings, human neuronal signal can be obtained from intracranial EEG (iEEG) recording in epilepsy patients that allows gaining insight into the functional organisation of living human brain. There are two approaches to assess brain connectivity in the iEEG-based signal: evaluation of spontaneous neuronal oscillations during ongoing physiological and pathological brain activity, and analysis of the electrophysiological cortico-cortical neuronal responses, evoked by single pulse electrical stimulation (SPES). Both methods have their own advantages and limitations. The paper outlines available methodological approaches and provides an overview of current findings in studies of physiological and pathological human brain networks, based on intracranial EEG recordings.

A perturbation-based approach to identifying potentially superfluous network constituents

Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.

Distinguishing between different percolation regimes in noisy dynamic networks with an application to epileptic seizures

In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks-in which edges indicate strong enough coupling between brain regions-are consistent with the notion of percolation, which is a phenomenon in complex networks corresponding to the sudden emergence of a giant connected component. Traditionally, work has concentrated on noise-free percolation with a monotonic process of network growth, but real-world networks are more complex. We develop a class of random graph hidden Markov models (RG-HMMs) for characterizing percolation regimes in noisy, dynamically evolving networks in the presence of edge birth and edge death. This class is used to understand the type of phase transitions undergone in a seizure, and in particular, distinguishing between different percolation regimes in epileptic seizures. We develop a hypothesis testing framework for inferring putative percolation mechanisms. As a necessary precursor, we present an EM algorithm for estimating parameters from a sequence of noisy networks only observed at a longitudinal subsampling of time points. Our results suggest that different types of percolation can occur in human seizures. The type inferred may suggest tailored treatment strategies and provide new insights into the fundamental science of epilepsy.

Multi-channel recordings reveal age-related differences in the sleep of juvenile and adult zebra finches

Despite their phylogenetic differences and distinct pallial structures, mammals and birds show similar electroencephalography (EEG) traces during sleep, consisting of distinct rapid eye movement (REM) sleep and slow wave sleep (SWS) stages. Studies in human and a limited number of other mammalian species show that this organization of sleep into interleaving stages undergoes radical changes during lifetime. Do these age-dependent variations in sleep patterns also occur in the avian brain? Does vocal learning have an effect on sleep patterns in birds? To answer these questions, we recorded multi-channel sleep EEG from juvenile and adult zebra finches for several nights. Whereas adults spent more time in SWS and REM sleep, juveniles spent more time in intermediate sleep (IS). The amount of IS was significantly larger in male juveniles engaged in vocal learning compared to female juveniles, which suggests that IS could be important for vocal learning. In addition, we observed that functional connectivity increased rapidly during maturation of young juveniles, and was stable or declined at older ages. Synchronous activity during sleep was larger for recording sites in the left hemisphere for both juveniles and adults, and generally intra-hemispheric synchrony was larger than inter-hemispheric synchrony during sleep. A graph theory analysis revealed that in adults, highly correlated EEG activity tended to be distributed across fewer networks that were spread across a wider area of the brain, whereas in juveniles, highly correlated EEG activity was distributed across more numerous, albeit smaller, networks in the brain. Overall, our results reveal that significant changes occur in the neural signatures of sleep during maturation in an avian brain.

Noise improves the association between effects of local stimulation and structural degree of brain networks

Stimulation to local areas remarkably affects brain activity patterns, which can be exploited to investigate neural bases of cognitive function and modify pathological brain statuses. There has been growing interest in exploring the fundamental action mechanisms of local stimulation. Nevertheless, how noise amplitude, an essential element in neural dynamics, influences stimulation-induced brain states remains unknown. Here, we systematically examine the effects of local stimulation by using a large-scale biophysical model under different combinations of noise amplitudes and stimulation sites. We demonstrate that noise amplitude nonlinearly and heterogeneously tunes the stimulation effects from both regional and network perspectives. Furthermore, by incorporating the role of the anatomical network, we show that the peak frequencies of unstimulated areas at different stimulation sites averaged across noise amplitudes are highly positively related to structural connectivity. Crucially, the association between the overall changes in functional connectivity as well as the alterations in the constraints imposed by structural connectivity with the structural degree of stimulation sites is nonmonotonically influenced by the noise amplitude, with the association increasing in specific noise amplitude ranges. Moreover, the impacts of local stimulation of cognitive systems depend on the complex interplay between the noise amplitude and average structural degree. Overall, this work provides theoretical insights into how noise amplitude and network structure jointly modulate brain dynamics during stimulation and introduces possibilities for better predicting and controlling stimulation outcomes.

Visibility graph for time series prediction and image classification: a review

The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

Critical dynamics in the spread of focal epileptic seizures: Network connectivity, neural excitability and phase transitions

Focal epileptic seizures can remain localized or, alternatively, spread across brain areas, often resulting in impairment of cognitive function and loss of consciousness. Understanding the factors that promote spread is important for developing better therapeutic approaches. Here, we show that: (1) seizure spread undergoes “critical” phase transitions in models (epileptor-networks) that capture the neural dynamics of spontaneous seizures while incorporating patient-specific brain network connectivity, axonal delays and identified epileptogenic zones (EZs). We define a collective variable for the spreading dynamics as the spread size, i.e. the number of areas or nodes in the network to which a seizure has spread. Global connectivity strength and excitability in the surrounding non-epileptic areas work as phase-transition control parameters for this collective variable. (2) Phase diagrams are predicted by stability analysis of the network dynamics. (3) In addition, the components of the Jacobian’s leading eigenvector, which tend to reflect the connectivity strength and path lengths from the EZ to surrounding areas, predict the temporal order of network-node recruitment into seizure. (4) However, stochastic fluctuations in spread size in a near-criticality region make predictability more challenging. Overall, our findings support the view that within-patient seizure-spread variability can be characterized by phase-transition dynamics under transient variations in network connectivity strength and excitability across brain areas. Furthermore, they point to the potential use and limitations of model-based prediction of seizure spread in closed-loop interventions for seizure control.

Evolution of Cortical Functional Networks in Healthy Infants

During normal childhood development, functional brain networks evolve over time in parallel with changes in neuronal oscillations. Previous studies have demonstrated differences in network topology with age, particularly in neonates and in cohorts spanning from birth to early adulthood. Here, we evaluate the developmental changes in EEG functional connectivity with a specific focus on the first 2 years of life. Functional connectivity networks (FCNs) were calculated from the EEGs of 240 healthy infants aged 0-2 years during wakefulness and sleep using a cross-correlation-based measure and the weighted phase lag index. Topological features were assessed via network strength, global clustering coefficient, characteristic path length, and small world measures. We found that cross-correlation FCNs maintained a consistent small-world structure, and the connection strengths increased after the first 3 months of infancy. The strongest connections in these networks were consistently located in the frontal and occipital regions across age groups. In the delta and theta bands, weighted phase lag index networks decreased in strength after the first 3 months in both wakefulness and sleep, and a similar result was found in the alpha and beta bands during wakefulness. However, in the alpha band during sleep, FCNs exhibited a significant increase in strength with age, particularly in the 21-24 months age group. During this period, a majority of the strongest connections in the networks were located in frontocentral regions, and a qualitatively similar distribution was seen in the beta band during sleep for subjects older than 3 months. Graph theory analysis suggested a small world structure for weighted phase lag index networks, but to a lesser degree than those calculated using cross-correlation. In general, graph theory metrics showed little change over time, with no significant differences between age groups for the clustering coefficient (wakefulness and sleep), characteristics path length (sleep), and small world measure (sleep). These results suggest that infant FCNs evolve during the first 2 years with more significant changes to network strength than features of the network structure. This study quantifies normal brain networks during infant development and can serve as a baseline for future investigations in health and neurological disease.

Network of autoscopic hallucinations elicited by intracerebral stimulations of periventricular nodular heterotopia: An SEEG study

Periventricular nodular heterotopias (PVNH) are areas of neurons abnormally located in the white matter that might be involved in physiological cortical functions. Autoscopic hallucinations are changes in self-consciousness determined by a mismatch in integration of multiple sensory inputs. Our goal is to highlight the brain network involved in generation of autoscopic hallucination elicited by electrical stimulation of a PVNH in a drug resistant epilepsy patient. Our patient was explored using stereo-electroencephalography with electrodes covering the right posterior temporal PVNH and the adjacent cortex. Direct electrical high frequency stimulation of the PVNH elicited autoscopic hallucinations mainly involving the face and upper trunk. We then used multiple modalities to determine brain connectivity: single pulse electrical stimulation of the PVNH and stimulation-evoked potentials were used to highlight resting state effective connectivity. High-frequency stimulation using alternating polarity pulses enabled us to identify the network involved, time-locked to the clinical effect and to map symptom-related effective connectivity. Functional connectivity using a non-linear regression method was used to determine dependencies between different cortical regions following the stimulation. Finally, structural connectivity was highlighted using deterministic fiber tracking. Multi-modal connectivity analysis identified a network involving the PVNH, occipital and temporal neocortex, fusiform gyrus and parietal cortex.

PaIRKAT: A pathway integrated regression-based kernel association test with applications to metabolomics and COPD phenotypes

High-throughput data such as metabolomics, genomics, transcriptomics, and proteomics have become familiar data types within the "-omics" family. For this work, we focus on subsets that interact with one another and represent these "pathways" as graphs. Observed pathways often have disjoint components, i.e., nodes or sets of nodes (metabolites, etc.) not connected to any other within the pathway, which notably lessens testing power. In this paper we propose the Pathway Integrated Regression-based Kernel Association Test (PaIRKAT), a new kernel machine regression method for incorporating known pathway information into the semi-parametric kernel regression framework. This work extends previous kernel machine approaches. This paper also contributes an application of a graph kernel regularization method for overcoming disconnected pathways. By incorporating a regularized or "smoothed" graph into a score test, PaIRKAT can provide more powerful tests for associations between biological pathways and phenotypes of interest and will be helpful in identifying novel pathways for targeted clinical research. We evaluate this method through several simulation studies and an application to real metabolomics data from the COPDGene study. Our simulation studies illustrate the robustness of this method to incorrect and incomplete pathway knowledge, and the real data analysis shows meaningful improvements of testing power in pathways. PaIRKAT was developed for application to metabolomic pathway data, but the techniques are easily generalizable to other data sources with a graph-like structure.

Incorporation of causality structures to complex network analysis of time-varying behaviour of multivariate time series

This paper presents a new methodology for characterising the evolving behaviour of the time-varying causality between multivariate time series, from the perspective of change in the structure of the causality pattern. We propose that such evolutionary behaviour should be tracked by means of a complex network whose nodes are causality patterns and edges are transitions between those patterns of causality. In our new methodology each edge has a weight that includes the frequency of the given transition and two metrics relating to the gross and net structural change in causality pattern, which we call [Formula: see text] and [Formula: see text]. To characterise aspects of the behaviour within this network, five approaches are presented and motivated. To act as a demonstration of this methodology an application of sample data from the international oil market is presented. This example illustrates how our new methodology is able to extract information about evolving causality behaviour. For example, it reveals non-random time-varying behaviour that favours transitions resulting in predominantly similar causality patterns, and it discovers clustering of similar causality patterns and some transitional behaviour between these clusters. The example illustrates how our new methodology supports the inference that the evolution of causality in the system is related to the addition or removal of a few causality links, primarily keeping a similar causality pattern, and that the evolution is not related to some other measure such as the overall number of causality links.

Computational characteristics of interictal EEG as objective markers of epileptic spasms

OBJECTIVE

Favorable neurodevelopmental outcomes in epileptic spasms (ES) are tied to early diagnosis and prompt treatment, but uncertainty in the identification of the disease can delay this process. Therefore, we investigated five categories of computational electroencephalographic (EEG) measures as markers of ES.

METHODS

We measured 1) amplitude, 2) power spectra, 3) Shannon entropy and permutation entropy, 4) long-range temporal correlations, via detrended fluctuation analysis (DFA) and 5) functional connectivity using cross-correlation and phase lag index (PLI). EEG data were analyzed from ES patients (n = 40 patients) and healthy controls (n = 20 subjects), with multiple blinded measurements during wakefulness and sleep for each patient.

RESULTS

In ES patients, EEG amplitude was significantly higher in all electrodes when compared to controls. Shannon and permutation entropy were lower in ES patients than control subjects. The DFA intercept values in ES patients were significantly higher than control subjects, while DFA exponent values were not significantly different between the groups. EEG functional connectivity networks in ES patients were significantly stronger than controls when based on both cross-correlation and PLI. Significance for all statistical tests was p < 0.05, adjusted for multiple comparisons using the Benjamini-Hochberg procedure as appropriate. Finally, using logistic regression, a multi-attribute classifier was derived that accurately distinguished cases from controls (area under curve of 0.96).

CONCLUSIONS

Computational EEG features successfully distinguish ES patients from controls in a large, blinded study.

SIGNIFICANCE

These objective EEG markers, in combination with other clinical factors, may speed the diagnosis and treatment of the disease, thereby improving long-term outcomes.

Infant functional networks are modulated by state of consciousness and circadian rhythm

Functional connectivity networks are valuable tools for studying development, cognition, and disease in the infant brain. In adults, such networks are modulated by the state of consciousness and the circadian rhythm; however, it is unknown if infant brain networks exhibit similar variation, given the unique temporal properties of infant sleep and circadian patterning. To address this, we analyzed functional connectivity networks calculated from long-term EEG recordings (average duration 20.8 hr) from 19 healthy infants. Networks were subject specific, as intersubject correlations between weighted adjacency matrices were low. However, within individual subjects, both sleep and wake networks were stable over time, with stronger functional connectivity during sleep than wakefulness. Principal component analysis revealed the presence of two dominant networks; visual sleep scoring confirmed that these corresponded to sleep and wakefulness. Lastly, we found that network strength, degree, clustering coefficient, and path length significantly varied with time of day, when measured in either wakefulness or sleep at the group level. Together, these results suggest that modulation of healthy functional networks occurs over ∼24 hr and is robust and repeatable. Accounting for such temporal periodicities may improve the physiological interpretation and use of functional connectivity analysis to investigate brain function in health and disease.

Cingulate gyrus epilepsy: semiology, invasive EEG, and surgical approaches

OBJECTIVE

The semiology of cingulate gyrus epilepsy is varied and may involve the paracentral area, the adjacent limbic system, and/or the orbitofrontal gyrus. Invasive electroencephalography (iEEG) recording is usually required for patients with deeply located epileptogenic foci. This paper reports on the authors' experiences in the diagnosis and surgical treatment of patients with focal epilepsy originating in the cingulate gyrus.

METHODS

Eighteen patients (median age 24 years, range 5-53 years) with a mean seizure history of 23 years (range 2-32 years) were analyzed retrospectively. The results of presurgical evaluation, surgical strategy, and postoperative pathology are reported, as well as follow-up concerning functional morbidity and seizures (median follow-up 7 years, range 2-12 years).

RESULTS

Patients with cingulate gyrus epilepsy presented with a variety of semiologies and scalp EEG patterns. Prior to ictal onset, 11 (61%) of the patients presented with aura. Initial ictal symptoms included limb posturing in 12 (67%), vocalization in 5, and hypermotor movement in 4. In most patients (n = 16, 89%), ictal EEG presented as widespread patterns with bilateral hemispheric origin, as well as muscle artifacts obscuring the onset of EEG during the ictal period in 11 patients. Among the 18 patients who underwent resection, the pathology revealed mild malformation of cortical development in 2, focal cortical dysplasia (FCD) Ib in 4, FCD IIa in 4, FCD IIb in 4, astrocytoma in 1, ganglioglioma in 1, and gliosis in 2. The seizure outcome after surgery was satisfactory: Engel class IA in 12 patients, IIB in 3, IIIA in 1, IIIB in 1, and IVB in 1 at the 2-year follow-up.

CONCLUSIONS

In this study, the authors exploited the improved access to the cingulate epileptogenic network made possible by the use of 3D electrodes implanted using stereoelectroencephalography methodology. Under iEEG recording and intraoperative neuromonitoring, epilepsy surgery on lesions in the cingulate gyrus can result in good outcomes in terms of seizure recurrence and the incidence of postoperative permanent deficits.

The Human Organism as an Integrated Interaction Network: Recent Conceptual and Methodological Challenges

The field of Network Physiology aims to advance our understanding of how physiological systems and sub-systems interact to generate a variety of behaviors and distinct physiological states, to optimize the organism's functioning, and to maintain health. Within this framework, which considers the human organism as an integrated network, vertices are associated with organs while edges represent time-varying interactions between vertices. Likewise, vertices may represent networks on smaller spatial scales leading to a complex mixture of interacting homogeneous and inhomogeneous networks of networks. Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse physiological systems, current approaches focus on inferring properties of time-varying interactions-namely strength, direction, and functional form-from time-locked recordings of physiological observables. To this end, a variety of bivariate or, in general, multivariate time-series-analysis techniques, which are derived from diverse mathematical and physical concepts, are employed and the resulting time-dependent networks can then be further characterized with methods from network theory. Despite the many promising new developments, there are still problems that evade from a satisfactory solution. Here we address several important challenges that could aid in finding new perspectives and inspire the development of theoretic and analytical concepts to deal with these challenges and in studying the complex interactions between physiological systems.

Altered Coactive Micropattern Connectivity in the Default-Mode Network during the Sleep-Wake Cycle

The default-mode network (DMN) is believed to be associated with levels of consciousness, but how the functional connectivity (FC) of the DMN changes across different states of consciousness is still unclear. In the current work, we addressed this issue by exploring the coactive micropattern (CAMP) networks of the DMN according to the CAMPs of rat DMN activity during the sleep-wake cycle and tracking their topological alterations among different states of consciousness. Three CAMP networks were observed in DMN activity, and they displayed greater FC and higher efficiency than the original DMN structure in all states of consciousness, implying more efficient information processing in the CAMP networks. Furthermore, no significant differences in FC or network properties were found among the three CAMP networks in the waking state. However, the three networks were distinct in their characteristics in two sleep states, indicating that different CAMP networks played specific roles in distinct sleep states. In addition, we found that the changes in the FC and network properties of the CAMP networks were similar to those in the original DMN structure, suggesting intrinsic effects of various states of consciousness on DMN dynamics. Our findings revealed three underlying CAMP networks within the DMN dynamics and deepened the current knowledge concerning FC alterations in the DMN during conscious changes in the sleep-wake cycle.

Cingulate cortex function and multi-modal connectivity mapped using intracranial stimulation

The cingulate cortex is part of the limbic system. Its function and connectivity are organized in a rostro-caudal and ventral-dorsal manner which was addressed by various other studies using rather coarse cortical parcellations. In this study, we aim at describing its function and connectivity using invasive recordings from patients explored for focal drug-resistant epilepsy. We included patients that underwent stereo-electroencephalographic recordings using intracranial electrodes in the University Emergency Hospital Bucharest between 2012 and 2019. We reviewed all high frequency stimulations (50 ​Hz) performed for functional mapping of the cingulate cortex. We used two methods to characterize brain connectivity. Effective connectivity was inferred based on the analysis of cortico-cortical potentials (CCEPs) evoked by single pulse electrical stimulation (SPES) (15 ​s inter-pulse interval). Functional connectivity was estimated using the non-linear regression method applied to 60 ​s spontaneous electrical brain signal intervals. The effective (stimulation-evoked) and functional (non-evoked) connectivity analyses highlight brain networks in a different way. While non-evoked connectivity evidences areas having related activity, often in close proximity to each other, evoked connectivity highlights spatially extended networks. To highlight in a comprehensive way the cingulate cortex's network, we have performed a bi-modal connectivity analysis that combines the resting-state broadband h² non-linear correlation with cortico-cortical evoked potentials. We co-registered the patient's anatomy with the fsaverage FreeSurfer template to perform the automatic labeling based on HCP-MMP parcellation. At a group level, connectivity was estimated by averaging responses over stimulated/recorded or recorded sites in each pair of parcels. Finally, for multiple regions that evoked a clinical response during high frequency stimulation, we combined the connectivity of individual pairs using maximum intensity projection. Connectivity was assessed by applying SPES on 2094 contact pairs and recording CCEPs on 3580 contacts out of 8582 contacts of 660 electrodes implanted in 47 patients. Clinical responses elicited by high frequency stimulations in 107 sites (pairs of contacts) located in the cingulate cortex were divided in 10 groups: affective, motor behavior, motor elementary, versive, speech, vestibular, autonomic, somatosensory, visual and changes in body perception. Anterior cingulate cortex was shown to be connected to the mesial temporal, orbitofrontal and prefrontal cortex. In the middle cingulate cortex, we located affective, motor behavior in the anterior region, and elementary motor and somatosensory in the posterior part. This region is connected to the prefrontal, premotor and primary motor network. Finally, the posterior cingulate was shown to be connected with the visual areas, mesial and lateral parietal and temporal cortex.

Robust dynamic community detection with applications to human brain functional networks

While current technology permits inference of dynamic brain networks over long time periods at high temporal resolution, the detailed structure of dynamic network communities during human seizures remains poorly understood. We introduce a new methodology that addresses critical aspects unique to the analysis of dynamic functional networks inferred from noisy data. We propose a dynamic plex percolation method (DPPM) that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time. We show in simulation that DPPM outperforms existing methods in accurately capturing certain stereotypical dynamic community behaviors in noisy situations. We then illustrate the ability of this method to track dynamic community organization during human seizures, using invasive brain voltage recordings at seizure onset. We conjecture that application of this method will yield new targets for surgical treatment of epilepsy, and more generally could provide new insights in other network neuroscience applications.

Understanding how brain networks evolve in time remains a challenge, with the potential for significant impact to human health and disease. Here, the authors introduce a new methodology to track dynamic functional networks that is robust to edge noise, and yields well-defined spatiotemporal communities that span forward and backwards in time.

Electrographic predictors of successful weaning from anaesthetics in refractory status epilepticus

Intravenous third-line anaesthetic agents are typically titrated in refractory status epilepticus to achieve either seizure suppression or burst suppression on continuous EEG. However, the optimum treatment paradigm is unknown and little data exist to guide the withdrawal of anaesthetics in refractory status epilepticus. Premature withdrawal of anaesthetics risks the recurrence of seizures, whereas the prolonged use of anaesthetics increases the risk of treatment-associated adverse effects. This study sought to measure the accuracy of features of EEG activity during anaesthetic weaning in refractory status epilepticus as predictors of successful weaning from intravenous anaesthetics. We prespecified a successful anaesthetic wean as the discontinuation of intravenous anaesthesia without developing recurrent status epilepticus, and a wean failure as either recurrent status epilepticus or the resumption of anaesthesia for the purpose of treating an EEG pattern concerning for incipient status epilepticus. We evaluated two types of features as predictors of successful weaning: spectral components of the EEG signal, and spatial-correlation-based measures of functional connectivity. The results of these analyses were used to train a classifier to predict wean outcome. Forty-seven consecutive anaesthetic weans (23 successes, 24 failures) were identified from a single-centre cohort of patients admitted with refractory status epilepticus from 2016 to 2019. Spectral components of the EEG revealed no significant differences between successful and unsuccessful weans. Analysis of functional connectivity measures revealed that successful anaesthetic weans were characterized by the emergence of larger, more densely connected, and more highly clustered spatial functional networks, yielding 75.5% (95% confidence interval: 73.1-77.8%) testing accuracy in a bootstrap analysis using a hold-out sample of 20% of data for testing and 74.6% (95% confidence interval 73.2-75.9%) testing accuracy in a secondary external validation cohort, with an area under the curve of 83.3%. Distinct signatures in the spatial networks of functional connectivity emerge during successful anaesthetic liberation in status epilepticus; these findings are absent in patients with anaesthetic wean failure. Identifying features that emerge during successful anaesthetic weaning may allow faster and more successful anaesthetic liberation after refractory status epilepticus.

Effect of interictal epileptiform discharges on EEG-based functional connectivity networks

OBJECTIVE

Functional connectivity networks (FCNs) based on interictal electroencephalography (EEG) can identify pathological brain networks associated with epilepsy. FCNs are altered by interictal epileptiform discharges (IEDs), but it is unknown whether this is due to the morphology of the IED or the underlying pathological activity. Therefore, we characterized the impact of IEDs on the FCN through simulations and EEG analysis.

METHODS

We introduced simulated IEDs to sleep EEG recordings of eight healthy controls and analyzed the effect of IED amplitude and rate on the FCN. We then generated FCNs based on epochs with and without IEDs and compared them to the analogous FCNs from eight subjects with infantile spasms (IS), based on 1340 visually marked IEDs. Differences in network structure and strength were assessed.

RESULTS

IEDs in IS subjects caused increased connectivity strength but no change in network structure. In controls, simulated IEDs with physiological amplitudes and rates did not alter network strength or structure.

CONCLUSIONS

Increases in connectivity strength in IS subjects are not artifacts caused by the interictal spike waveform and may be related to the underlying pathophysiology of IS.

SIGNIFICANCE

Dynamic changes in EEG-based FCNs during IEDs may be valuable for identification of pathological networks associated with epilepsy.

Small-worldness favours network inference in synthetic neural networks

A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC) or mutual information (MI), however, the main factors favouring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis elegans neural networks as well as in networks with similar randomness and small-worldness. We analyse the effectiveness and robustness of the inference process under different observations and collective dynamics, contrasting the results obtained from using membrane potentials and inter-spike interval time-series. We find that overall, small-worldness favours network inference and degree heterogeneity hinders it. In particular, success rates in C. elegans networks – that combine small-world properties with degree heterogeneity – are closer to success rates in Erdös-Rényi network models rather than those in Watts-Strogatz network models. These results are relevant to understand better the relationship between topological properties and function in different neural networks.

Emerging roles of network analysis for epilepsy

In recent years there has been increasing interest in applying network science tools to EEG data. At the 2018 American Epilepsy Society conference in New Orleans, LA, the yearly session of the Engineering and Neurostimulation Special Interest Group focused on emerging, translational technologies to analyze seizure networks. Each speaker demonstrated practical examples of how network tools can be utilized in clinical care and provide additional data to help care for patients with intractable epilepsy. The groups presented advances using tools from functional connectivity, control theory, and graph theory to analyze human EEG data. These tools have great potential to augment clinical interpretation of EEG signals.

Mapping epileptic directional brain networks using intracranial EEG data

The human brain is a directional network system, in which brain regions are network nodes and the influence exerted by one region on another is a network edge. We refer to this directional information flow from one region to another as directional connectivity. Seizures arise from an epileptic directional network; abnormal neuronal activities start from a seizure onset zone and propagate via a network to otherwise healthy brain regions. As such, effective epilepsy diagnosis and treatment require accurate identification of directional connections among regions, i.e., mapping of epileptic patients' brain networks. This article aims to understand the epileptic brain network using intracranial electroencephalographic data-recordings of epileptic patients' brain activities in many regions. The most popular models for directional connectivity use ordinary differential equations (ODE). However, ODE models are sensitive to data noise and computationally costly. To address these issues, we propose a high-dimensional state-space multivariate autoregression (SSMAR) model for the brain's directional connectivity. Different from standard multivariate autoregression and SSMAR models, the proposed SSMAR features a cluster structure, where the brain network consists of several clusters of densely connected brain regions. We develop an expectation-maximization algorithm to estimate the proposed model and use it to map the interregional networks of epileptic patients in different seizure stages. Our method reveals the evolution of brain networks during seizure development.

Ictal networks of temporal lobe epilepsy: views from high-frequency oscillations in stereoelectroencephalography

OBJECTIVE

In this study, the authors investigated high-frequency oscillation (HFO) networks during seizures in order to determine how HFOs spread from the focal cerebral cortex and become synchronized across various areas of the brain.

METHODS

All data were obtained from stereoelectroencephalography (SEEG) signals in patients with drug-resistant temporal lobe epilepsy (TLE). The authors calculated intercontact cross-coefficients between all pairs of contacts to construct HFO networks in 20 seizures that occurred in 5 patients. They then calculated HFO network topology metrics (i.e., network density and component size) after normalizing seizure duration data by dividing each seizure into 10 intervals of equal length (labeled I1-I10).

RESULTS

From the perspective of the dynamic topologies of cortical and subcortical HFO networks, the authors observed a significant increase in network density during intervals I5-I10. A significant increase was also observed in overall energy during intervals I3-I8. The results of subnetwork analysis revealed that the number of components continuously decreased following the onset of seizures, and those results were statistically significant during intervals I3-I10. Furthermore, the majority of nodes were connected to a single dominant component during the propagation of seizures, and the percentage of nodes within the largest component grew significantly until seizure termination.

CONCLUSIONS

The consistent topological changes that the authors observed suggest that TLE is affected by common epileptogenic patterns. Indeed, the findings help to elucidate the epileptogenic network that characterizes TLE, which may be of interest to researchers and physicians working to improve treatment modalities for epilepsy, including resection, cortical stimulation, and neuromodulation treatments that are responsive to network topologies.

Network Reconstruction and Community Detection from Dynamics

We present a scalable nonparametric Bayesian method to perform network reconstruction from observed functional behavior that at the same time infers the communities present in the network. We show that the joint reconstruction with community detection has a synergistic effect, where the edge correlations used to inform the existence of communities are also inherently used to improve the accuracy of the reconstruction which, in turn, can better inform the uncovering of communities. We illustrate the use of our method with observations arising from epidemic models and the Ising model, both on synthetic and empirical networks, as well as on data containing only functional information.

Solitonic State in Microscopic Dynamic Failures

Onset of permanent deformation in crystalline materials under a sharp indenter tip is accompanied by nucleation and propagation of defects. By measuring the spatio-temporal strain field near the indenter tip during indentation tests, we demonstrate that the dynamic strain history at the moment of a displacement burst carries characteristics of the formation and interaction of local excitations, or solitons. We show that dynamic propagation of multiple solitons is followed by a short time interval where the propagating fronts can accelerate suddenly. As a result of such abrupt local accelerations, duration of the fast-slip phase of a failure event is shortened. Our results show that formation and annihilation of solitons mediate the microscopic fast weakening phase, during which extreme acceleration and collision of solitons lead to non-Newtonian behavior and Lorentz contraction, i.e., shortening of solitons’ characteristic length. The results open new horizons for understanding dynamic material response during failure and, more generally, complexity of earthquake sources.

A Comparison of Evoked and Non-evoked Functional Networks

The growing interest in brain networks to study the brain's function in cognition and diseases has produced an increase in methods to extract these networks. Typically, each method yields a different network. Therefore, one may ask what the resulting networks represent. To address this issue we consider electrocorticography (ECoG) data where we compare three methods. We derive networks from on-going ECoG data using two traditional methods: cross-correlation (CC) and Granger causality (GC). Next, connectivity is probed actively using single pulse electrical stimulation (SPES). We compare the overlap in connectivity between these three methods as well as their ability to reveal well-known anatomical connections in the language circuit. We find that strong connections in the CC network form more or less a subset of the SPES network. GC and SPES are related more weakly, although GC connections coincide more frequently with SPES connections compared to non-existing SPES connections. Connectivity between the two major hubs in the language circuit, Broca's and Wernicke's area, is only found in SPES networks. Our results are of interest for the use of patient-specific networks obtained from ECoG. In epilepsy research, such networks form the basis for methods that predict the effect of epilepsy surgery. For this application SPES networks are interesting as they disclose more physiological connections compared to CC and GC networks.

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.

Data-driven brain network models differentiate variability across language tasks

The relationship between brain structure and function has been probed using a variety of approaches, but how the underlying structural connectivity of the human brain drives behavior is far from understood. To investigate the effect of anatomical brain organization on human task performance, we use a data-driven computational modeling approach and explore the functional effects of naturally occurring structural differences in brain networks. We construct personalized brain network models by combining anatomical connectivity estimated from diffusion spectrum imaging of individual subjects with a nonlinear model of brain dynamics. By performing computational experiments in which we measure the excitability of the global brain network and spread of synchronization following a targeted computational stimulation, we quantify how individual variation in the underlying connectivity impacts both local and global brain dynamics. We further relate the computational results to individual variability in the subjects' performance of three language-demanding tasks both before and after transcranial magnetic stimulation to the left-inferior frontal gyrus. Our results show that task performance correlates with either local or global measures of functional activity, depending on the complexity of the task. By emphasizing differences in the underlying structural connectivity, our model serves as a powerful tool to assess individual differences in task performances, to dissociate the effect of targeted stimulation in tasks that differ in cognitive demand, and to pave the way for the development of personalized therapeutics.

Strength and stability of EEG functional connectivity predict treatment response in infants with epileptic spasms

OBJECTIVE

Epileptic spasms (ES) are associated with pathological neuronal networks, which may underlie characteristic EEG patterns such as hypsarrhythmia. Here we evaluate EEG functional connectivity as a quantitative marker of treatment response, in comparison to classic visual EEG features.

METHODS

We retrospectively identified 21 ES patients and 21 healthy controls. EEG data recorded before treatment and after ≥10 days of treatment underwent blinded visual assessment, and functional connectivity was measured using cross-correlation techniques. Short-term treatment response and long-term outcome data were collected.

RESULTS

Subjects with ES had stronger, more stable functional networks than controls. After treatment initiation, all responders (defined by cessation of spasms) exhibited decreases in functional connectivity strength, while an increase in connectivity strength occurred only in non-responders. There were six subjects with unusually strong pre-treatment functional connectivity, and all were responders. Visually assessed EEG features were not predictive of treatment response.

CONCLUSIONS

Changes in network connectivity and stability correlate to treatment response for ES, and high pre-treatment connectivity may predict favorable short-term treatment response. Quantitative measures outperform visual analysis of the EEG.

SIGNIFICANCE

Functional networks may have value as objective markers of treatment response in ES, with potential to facilitate rapid identification of personalized, effective treatments.

Topology of brain functional connectivity networks in posttraumatic stress disorder

Here we present functional neuroimaging-based network data (focused on the default mode network) collected from a cohort of US Veterans with history of combat exposure, combined with clinical assessments for PTSD and other psychiatric comorbidities. The data has been processed and analyzed using several network construction methods (signed, thresholded, normalized to phase-randomized and rewired surrogates, functional and multimodal parcellation). An interpretation and discussion of the data can be found in the main NeuroImage article by Akiki et al. [51].

δ-MAPS: from spatio-temporal data to a weighted and lagged network between functional domains

In real physical systems the underlying spatial components might not have crisp boundaries and their interactions might not be instantaneous. To this end, we propose δ-MAPS; a method that identifies spatially contiguous and possibly overlapping components referred to as domains, and identifies the lagged functional relationships between them. Informally, a domain is a spatially contiguous region that somehow participates in the same dynamic effect or function. The latter will result in highly correlated temporal activity between grid cells of the same domain. δ-MAPS first identifies the epicenters of activity of a domain. Next, it identifies a domain as the maximum possible set of spatially contiguous grid cells that include the detected epicenters and satisfy a homogeneity constraint. After identifying the domains, δ-MAPS infers a functional network between them. The proposed network inference method examines the statistical significance of each lagged correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge reflecting the magnitude of interaction between two domains. δ-MAPS is related to clustering, multivariate statistical techniques and network community detection. However, as we discuss and also show with synthetic data, it is also significantly different, avoiding many of the known limitations of these methods. We illustrate the application of δ-MAPS on data from two domains: climate science and neuroscience. First, the sea-surface temperature climate network identifies some well-known teleconnections (such as the lagged connection between the El Nin õ Southern Oscillation and the Indian Ocean). Second, the analysis of resting state fMRI cortical data confirms the presence of known functional resting state networks (default mode, occipital, motor/somatosensory and auditory), and shows that the cortical network includes a backbone of relatively few regions that are densely interconnected.

Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions among coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

Default mode network abnormalities in posttraumatic stress disorder: A novel network-restricted topology approach

Disruption in the default mode network (DMN) has been implicated in numerous neuropsychiatric disorders, including posttraumatic stress disorder (PTSD). However, studies have largely been limited to seed-based methods and involved inconsistent definitions of the DMN. Recent advances in neuroimaging and graph theory now permit the systematic exploration of intrinsic brain networks. In this study, we used resting-state functional magnetic resonance imaging (fMRI), diffusion MRI, and graph theoretical analyses to systematically examine the DMN connectivity and its relationship with PTSD symptom severity in a cohort of 65 combat-exposed US Veterans. We employed metrics that index overall connectivity strength, network integration (global efficiency), and network segregation (clustering coefficient). Then, we conducted a modularity and network-based statistical analysis to identify DMN regions of particular importance in PTSD. Finally, structural connectivity analyses were used to probe whether white matter abnormalities are associated with the identified functional DMN changes. We found decreased DMN functional connectivity strength to be associated with increased PTSD symptom severity. Further topological characterization suggests decreased functional integration and increased segregation in subjects with severe PTSD. Modularity analyses suggest a spared connectivity in the posterior DMN community (posterior cingulate, precuneus, angular gyrus) despite overall DMN weakened connections with increasing PTSD severity. Edge-wise network-based statistical analyses revealed a prefrontal dysconnectivity. Analysis of the diffusion networks revealed no alterations in overall strength or prefrontal structural connectivity. DMN abnormalities in patients with severe PTSD symptoms are characterized by decreased overall interconnections. On a finer scale, we found a pattern of prefrontal dysconnectivity, but increased cohesiveness in the posterior DMN community and relative sparing of connectivity in this region. The DMN measures established in this study may serve as a biomarker of disease severity and could have potential utility in developing circuit-based therapeutics.

PageRank versatility analysis of multilayer modality-based network for exploring the evolution of oil-water slug flow

Numerous irregular flow structures exist in the complicated multiphase flow and result in lots of disparate spatial dynamical flow behaviors. The vertical oil-water slug flow continually attracts plenty of research interests on account of its significant importance. Based on the spatial transient flow information acquired through our designed double-layer distributed-sector conductance sensor, we construct multilayer modality-based network to encode the intricate spatial flow behavior. Particularly, we calculate the PageRank versatility and multilayer weighted clustering coefficient to quantitatively explore the inferred multilayer modality-based networks. Our analysis allows characterizing the complicated evolution of oil-water slug flow, from the opening formation of oil slugs, to the succedent inter-collision and coalescence among oil slugs, and then to the dispersed oil bubbles. These properties render our developed method particularly powerful for mining the essential flow features from the multilayer sensor measurements.

Directed weighted network structure analysis of complex impedance measurements for characterizing oil-in-water bubbly flow

Characterizing the flow structure underlying the evolution of oil-in-water bubbly flow remains a contemporary challenge of great interests and complexity. In particular, the oil droplets dispersing in a water continuum with diverse size make the study of oil-in-water bubbly flow really difficult. To study this issue, we first design a novel complex impedance sensor and systematically conduct vertical oil-water flow experiments. Based on the multivariate complex impedance measurements, we define modalities associated with the spatial transient flow structures and construct modality transition-based network for each flow condition to study the evolution of flow structures. In order to reveal the unique flow structures underlying the oil-in-water bubbly flow, we filter the inferred modality transition-based network by removing the edges with small weight and resulting isolated nodes. Then, the weighted clustering coefficient entropy and weighted average path length are employed for quantitatively assessing the original network and filtered network. The differences in network measures enable to efficiently characterize the evolution of the oil-in-water bubbly flow structures.

Microscopic Evolution of Laboratory Volcanic Hybrid Earthquakes

Characterizing the interaction between fluids and microscopic defects is one of the long-standing challenges in understanding a broad range of cracking processes, in part because they are so difficult to study experimentally. We address this issue by reexamining records of emitted acoustic phonon events during rock mechanics experiments under wet and dry conditions. The frequency spectrum of these events provides direct information regarding the state of the system. Such events are typically subdivided into high frequency (HF) and low frequency (LF) events, whereas intermediate "Hybrid" events, have HF onsets followed by LF ringing. At a larger scale in volcanic terranes, hybrid events are used empirically to predict eruptions, but their ambiguous physical origin limits their diagnostic use. By studying acoustic phonon emissions from individual microcracking events we show that the onset of a secondary instability-related to the transition from HF to LF-occurs during the fast equilibration phase of the system, leading to sudden increase of fluid pressure in the process zone. As a result of this squeezing process, a secondary instability akin to the LF event occurs. This mechanism is consistent with observations of hybrid earthquakes.

Stimulation-Based Control of Dynamic Brain Networks

The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain stimulation as a form of neuromodulation, much remains unknown about the network-level impact of these focal perturbations. To study the system wide impact of regional stimulation, we employ a data-driven computational model of nonlinear brain dynamics to systematically explore the effects of targeted stimulation. Validating predictions from network control theory, we uncover the relationship between regional controllability and the focal versus global impact of stimulation, and we relate these findings to differences in the underlying network architecture. Finally, by mapping brain regions to cognitive systems, we observe that the default mode system imparts large global change despite being highly constrained by structural connectivity. This work forms an important step towards the development of personalized stimulation protocols for medical treatment or performance enhancement.

Brain stimulation is increasingly used in clinical settings to treat neurological disorders, but much remains unknown about how stimulation to a single brain region impacts large-scale, brain network activity. Using structural neuroimaging scans, we create computational models of brain dynamics for eight participants to explore how structure-function relationships constrain the effect of stimulation to a single region on the brain as a whole. Our results show that network control theory can be used to predict if the effects of stimulation remain focal or spread globally, and structural connectivity differentially constrains the effects of regional stimulation. Additionally, we study how stimulation of different cognitive systems spreads throughout the brain and find that stimulation of regions within the default mode network provide a mechanism to impart large change in overall brain dynamics through a densely connected structural network. By revealing how the stimulation of different brain regions and cognitive systems spreads differently through the brain, we provide a modeling framework to develop stimulation protocols to personalize medical treatments, enable performance enhancements, and facilitate cortical plasticity.

THE GRAPHICAL STRUCTURE OF RESPONDENT-DRIVEN SAMPLING

Respondent-driven sampling (RDS) is a chain-referral method for sampling members of hidden or hard-to-reach populations, such as sex workers, homeless people, or drug users, via their social networks. Most methodological work on RDS has focused on inference of population means under the assumption that subjects' network degree determines their probability of being sampled. Criticism of existing estimators is usually focused on missing data: the underlying network is only partially observed, so it is difficult to determine correct sampling probabilities. In this article, the author shows that data collected in ordinary RDS studies contain information about the structure of the respondents' social network. The author constructs a continuous-time model of RDS recruitment that incorporates the time series of recruitment events, the pattern of coupon use, and the network degrees of sampled subjects. Together, the observed data and the recruitment model place a well-defined probability distribution on the recruitment-induced subgraph of respondents. The author shows that this distribution can be interpreted as an exponential random graph model and develops a computationally efficient method for estimating the hidden graph. The author validates the method using simulated data and applies the technique to an RDS study of injection drug users in St. Petersburg, Russia.

Understanding Policy Diffusion in the U.S.: An Information-Theoretical Approach to Unveil Connectivity Structures in Slowly Evolving Complex Systems

Detecting and explaining the relationships among interacting components has long been a focal point of dynamical systems research. In this paper, we extend these types of data-driven analyses to the realm of public policy, whereby individual legislative entities interact to produce changes in their legal and political environments. We focus on the U.S. public health policy landscape, whose complexity determines our capacity as a society to effectively tackle pressing health issues. It has long been thought that some U.S. states innovate and enact new policies, while others mimic successful or competing states. However, the extent to which states learn from others, and the state characteristics that lead two states to influence one another, are not fully understood. Here, we propose a model-free, information-theoretical method to measure the existence and direction of influence of one state's policy or legal activity on others. Specifically, we tailor a popular notion of causality to handle the slow time-scale of policy adoption dynamics and unravel relationships among states from their recent law enactment histories. The method is validated using surrogate data generated from a new stochastic model of policy activity. Through the analysis of real data in alcohol, driving safety, and impaired driving policy, we provide evidence for the role of geography, political ideology, risk factors, and demographic and economic indicators on a state's tendency to learn from others when shaping its approach to public health regulation. Our method offers a new model-free approach to uncover interactions and establish cause-and-effect in slowly-evolving complex dynamical systems.

Percolation under noise: Detecting explosive percolation using the second-largest component

We consider the problem of distinguishing between different rates of percolation under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed nonstationary process, where the observed graph process is corrupted by type-I and type-II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (Erdős-Rényi) percolation is visually indistinguishable from a more rapid form of percolation. In this setting, we compare two different criteria for discriminating between these two percolation models, based on the interquartile range (IQR) of the first component's size, and on the maximal size of the second-largest component. We show through data simulations that this second criterion outperforms the IQR of the first component's size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between different rates of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for the detection of clinically relevant percolation in the context of applied neuroscience is also discussed.

Disrupted Ipsilateral Network Connectivity in Temporal Lobe Epilepsy

OBJECTIVE

The current practice under which patients with refractory epilepsy are surgically treated is based mainly on the identification of specific cortical areas, mainly the epileptogenic zone, which is believed to be responsible for generation of seizures. A better understanding of the whole epileptic network and its components and properties is required before more effective and less invasive therapies can be developed. The aim of the present study was to partially characterize the evolution of the functional network during the preictal-ictal transition in partial seizures in patients with temporal lobe epilepsy (TLE).

METHODS

Scalp and foramen ovale (FOE) recordings from twenty-two TLE patients were analyzed under the complex network perspective. The density of links, average path length, average clustering coefficient, and modularity were calculated during the preictal and the ictal stages. Both linear-Pearson correlation-and non-linear-phase synchronization-measures were used as proxies of functional connectivity between the electrode locations areas. The transition from one stage to the other was evaluated in the whole network and in the mesial sub-networks. The results were compared with a voltage-dependent measure, namely, the spectral entropy.

RESULTS

Changes in the global functional network during the transition from the preictal to the ictal stage show, in the linear case, that in sixteen cases (72.7%) the density of the links increased during the seizure, with a decrease in the average path length in fifteen cases (68.1%). There was also a preictal and ictal imbalance in functional connectivity during both stages (77.2% to 86.3%). The SE dropped during the seizure in 95.4% of the cases, but did not show any tendency towards lateralization. When using the nonlinear measure of functional connectivity, the phase synchronization, similar results were obtained.

CONCLUSIONS

In TLE patients, the transition to the ictal stage is accompanied by increasing global synchronization and a more ordered spectral content of the signals, indicated by lower spectral entropy. The interictal connectivity imbalance (lower ipsilateral connectivity) is sustained during the seizure, irrespective of any appreciable imbalance in the spectral entropy of the mesial recordings.

Data-driven prediction and prevention of extreme events in a spatially extended excitable system

Extreme events occur in many spatially extended dynamical systems, often devastatingly affecting human life, which makes their reliable prediction and efficient prevention highly desirable. We study the prediction and prevention of extreme events in a spatially extended system, a system of coupled FitzHugh-Nagumo units, in which extreme events occur in a spatially and temporally irregular way. Mimicking typical constraints faced in field studies, we assume not to know the governing equations of motion and to be able to observe only a subset of all phase-space variables for a limited period of time. Based on reconstructing the local dynamics from data and despite being challenged by the rareness of events, we are able to predict extreme events remarkably well. With small, rare, and spatiotemporally localized perturbations which are guided by our predictions, we are able to completely suppress extreme events in this system.