A small world of neuronal synchrony

Abnormal suppression of thermal transport by long-range interactions in networks

Heat and electricity are two fundamental forms of energy widely utilized in our daily lives. Recently, in the study of complex networks, there is growing evidence that they behave significantly different at the micro-nanoscale. Here, we use a small-world network model to investigate the effects of reconnection probability p and decay exponent α on thermal and electrical transport within the network. Our results demonstrate that the electrical transport efficiency increases by nearly one order of magnitude, while the thermal transport efficiency falls off a cliff by three to four orders of magnitude, breaking the traditional rule that shortcuts enhance energy transport in small-world networks. Furthermore, we elucidate that phonon localization is a crucial factor in the weakening of thermal transport efficiency in small-world networks by characterizing the density of states, phonon participation ratio, and nearest-neighbor spacing distribution. These insights will pave new ways for designing thermoelectric materials with high electrical conductance and low thermal conductance.

Stimulus type shapes the topology of cellular functional networks in mouse visual cortex

On the timescale of sensory processing, neuronal networks have relatively fixed anatomical connectivity, while functional interactions between neurons can vary depending on the ongoing activity of the neurons within the network. We thus hypothesized that different types of stimuli could lead those networks to display stimulus-dependent functional connectivity patterns. To test this hypothesis, we analyzed single-cell resolution electrophysiological data from the Allen Institute, with simultaneous recordings of stimulus-evoked activity from neurons across 6 different regions of mouse visual cortex. Comparing the functional connectivity patterns during different stimulus types, we made several nontrivial observations: (1) while the frequencies of different functional motifs were preserved across stimuli, the identities of the neurons within those motifs changed; (2) the degree to which functional modules are contained within a single brain region increases with stimulus complexity. Altogether, our work reveals unexpected stimulus-dependence to the way groups of neurons interact to process incoming sensory information.

The quality and complexity of pairwise maximum entropy models for large cortical populations

We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.

Silences, spikes and bursts: Three-part knot of the neural code

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labelling action potentials emitted at a particularly high frequency with a metonym - bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial.

Graph analysis of cortical reorganization after virtual reality-based rehabilitation following stroke: a pilot randomized study

Introduction

Stroke is the leading cause of functional disability worldwide. With the increase of the global population, motor rehabilitation of stroke survivors is of ever-increasing importance. In the last decade, virtual reality (VR) technologies for rehabilitation have been extensively studied, to be used instead of or together with conventional treatments such as physiotherapy or occupational therapy. The aim of this work was to evaluate the GestureCollection VR-based rehabilitation tool in terms of the brain changes and clinical outcomes of the patients.

Methods

Two groups of chronic patients underwent a rehabilitation treatment with (experimental) or without (control) complementation with GestureCollection. Functional magnetic resonance imaging exams and clinical assessments were performed before and after the treatment. A functional connectivity graph-based analysis was used to assess differences between the connections and in the network parameters strength and clustering coefficient.

Results

Patients in both groups showed improvement in clinical scales, but there were more increases in functional connectivity in the experimental group than in the control group.

Discussion

The experimental group presented changes in the connections between the frontoparietal and the somatomotor networks, associative cerebellum and basal ganglia, which are regions associated with reward-based motor learning. On the other hand, the control group also had results in the somatomotor network, in its ipsilateral connections with the thalamus and with the motor cerebellum, which are regions more related to a purely mechanical activity. Thus, the use of the GestureCollection system was successfully shown to promote neuroplasticity in several motor-related areas.

Prominent in vivo influence of single interneurons in the developing barrel cortex

Spontaneous synchronous activity is a hallmark of developing brain circuits and promotes their formation. Ex vivo, synchronous activity was shown to be orchestrated by a sparse population of highly connected GABAergic 'hub' neurons. The recent development of all-optical methods to record and manipulate neuronal activity in vivo now offers the unprecedented opportunity to probe the existence and function of hub cells in vivo. Using calcium imaging, connectivity analysis and holographic optical stimulation, we show that single GABAergic, but not glutamatergic, neurons influence population dynamics in the barrel cortex of non-anaesthetized mouse pups. Single GABAergic cells mainly exert an inhibitory influence on both spontaneous and sensory-evoked population bursts. Their network influence scales with their functional connectivity, with highly connected hub neurons displaying the strongest impact. We propose that hub neurons function in tailoring intrinsic cortical dynamics to external sensory inputs.

Investigating structural and functional aspects of the brain's criticality in stroke

This paper addresses the question of the brain's critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for information transmission and responses to inputs. If structural damage could cause the critical point to disappear and thus make self-organized criticality unachievable, it would offer the theoretical explanation for the post-stroke impairment of brain function. In our contribution, however, we demonstrate using network models of the brain, that the dynamics remain critical even after a stroke. In cases where the average size of the second-largest cluster of active nodes, which is one of the commonly used indicators of criticality, shows an anomalous behavior, it results from the loss of integrity of the network, quantifiable within graph theory, and not from genuine non-critical dynamics. We propose a new simple model of an artificial stroke that explains this anomaly. The proposed interpretation of the results is confirmed by an analysis of real connectomes acquired from post-stroke patients and a control group. The results presented refer to neurobiological data; however, the conclusions reached apply to a broad class of complex systems that admit a critical state.

Mapping blood traits to structural organization of the brain in rhesus monkeys

Hematological and biochemical blood traits have been linked to brain structural characteristics in humans. However, the relationship between these two domains has not been systematically explored in nonhuman primates, which are crucial animal models for understanding the mechanisms of brain function and developing therapeutics for various disorders. Here we investigated the associations between hematological/biochemical parameters and the brain's gray matter volume and white matter integrity derived from T1-weighted and diffusion magnetic resonance imaging in 36 healthy macaques. We found that intersubject variations in basophil count and hemoglobin levels correlated with gray matter volumes in the anterior cingulum, prefrontal cortex, and putamen. Through interactions between these key elements, the blood parameters' covariation network was linked with that of the brain structures, forming overarching networks connecting blood traits with structural brain features. These networks exhibited hierarchical small-world architecture, indicating highly effective interactions between their constituent elements. In addition, different subnetworks of the brain areas or fiber tracts tended to correlate with unique groups of blood indices, revealing previously unknown brain structural organization. These results provide a quantitative characterization of the interactions between blood parameters and brain structures in macaques and may increase the understanding of the body-brain relationship and the pathogenesis of relevant disorders.

Weakly Correlated Local Cortical State Switches under Anesthesia Lead to Strongly Correlated Global States

During recovery from anesthesia, brain activity switches abruptly between a small set of discrete states. Surprisingly, this switching also occurs under constant doses of anesthesia, even in the absence of stimuli. These metastable states and the transitions between them are thought to form a "scaffold" that ultimately guides the brain back to wakefulness. The processes that constrain cortical activity patterns to these states and govern how states are coordinated between different cortical regions are unknown. If state transitions were driven by subcortical modulation, different cortical sites should exhibit near-synchronous state transitions. Conversely, spatiotemporal heterogeneity would suggest that state transitions are coordinated through corticocortical interactions. To differentiate between these hypotheses, we quantified synchrony of brain states in male rats exposed to a fixed isoflurane concentration. States were defined from spectra of local field potentials recorded across layers of visual and motor cortices. A transition synchrony measure shows that most state transitions are highly localized. Furthermore, while most pairs of cortical sites exhibit statistically significant coupling of both states and state transition times, coupling strength is typically weak. States and state transitions in the thalamic input layer (L4) are particularly decoupled from those in supragranular and infragranular layers. This suggests that state transitions are not imposed on the cortex by broadly projecting modulatory systems. Although each pairwise interaction is typically weak, we show that the multitude of such weak interactions is sufficient to confine global activity to a small number of discrete states.SIGNIFICANCE STATEMENT The brain consistently recovers to wakefulness after anesthesia, but this process is poorly understood. Previous work revealed that, during recovery from anesthesia, corticothalamic activity falls into one of several discrete patterns. The neuronal mechanisms constraining the cortex to just a few discrete states remain unknown. Global states could be coordinated by fluctuations in subcortical nuclei that project broadly to the cortex. Alternatively, these states may emerge from interactions within the cortex itself. Here, we provide evidence for the latter possibility by demonstrating that most pairs of cortical sites exhibit weak coupling. We thereby lay groundwork for future investigations of the specific cellular and network mechanisms of corticocortical activity state coupling.

Therapeutic Neuromodulation toward a Critical State May Serve as a General Treatment Strategy

Brain disease has become one of this century’s biggest health challenges, urging the development of novel, more effective treatments. To this end, neuromodulation represents an excellent method to modulate the activity of distinct neuronal regions to alleviate disease. Recently, the medical indications for neuromodulation therapy have expanded through the adoption of the idea that neurological disorders emerge from deficits in systems-level structures, such as brain waves and neural topology. Connections between neuronal regions are thought to fluidly form and dissolve again based on the patterns by which neuronal populations synchronize. Akin to a fire that may spread or die out, the brain’s activity may similarly hyper-synchronize and ignite, such as seizures, or dwindle out and go stale, as in a state of coma. Remarkably, however, the healthy brain remains hedged in between these extremes in a critical state around which neuronal activity maneuvers local and global operational modes. While it has been suggested that perturbations of this criticality could underlie neuropathologies, such as vegetative states, epilepsy, and schizophrenia, a major translational impact is yet to be made. In this hypothesis article, we dissect recent computational findings demonstrating that a neural network’s short- and long-range connections have distinct and tractable roles in sustaining the critical regime. While short-range connections shape the dynamics of neuronal activity, long-range connections determine the scope of the neuronal processes. Thus, to facilitate translational progress, we introduce topological and dynamical system concepts within the framework of criticality and discuss the implications and possibilities for therapeutic neuromodulation guided by topological decompositions.

Learning populations with hubs govern the initiation and propagation of spontaneous bursts in neuronal networks after learning

Spontaneous bursts in neuronal networks with propagation involving a large number of synchronously firing neurons are considered to be a crucial feature of these networks both in vivo and in vitro. Recently, learning has been shown to improve the association and synchronization of spontaneous events in neuronal networks by promoting the firing of spontaneous bursts. However, little is known about the relationship between the learning phase and spontaneous bursts. By combining high-resolution measurement with a 4,096-channel complementary metal-oxide-semiconductor (CMOS) microelectrode array (MEA) and graph theory, we studied how the learning phase influenced the initiation of spontaneous bursts in cultured networks of rat cortical neurons in vitro. We found that a small number of selected populations carried most of the stimulus information and contributed to learning. Moreover, several new burst propagation patterns appeared in spontaneous firing after learning. Importantly, these "learning populations" had more hubs in the functional network that governed the initiation of spontaneous burst activity. These results suggest that changes in the functional structure of learning populations may be the key mechanism underlying increased bursts after learning. Our findings could increase understanding of the important role that synaptic plasticity plays in the regulation of spontaneous activity.

Dynamical Complexity Fingerprints of Occupation-Dependent Brain Functional Networks in Professional Seafarers

The complexity derived from resting-state functional magnetic resonance imaging (rs-fMRI) data has been applied for exploring cognitive states and occupational neuroplasticity. However, there is little information about the influence of occupational factors on dynamic complexity and topological properties of the connectivity networks. In this paper, we proposed a novel dynamical brain complexity analysis (DBCA) framework to explore the changes in dynamical complexity of brain activity at the voxel level and complexity topology for professional seafarers caused by long-term working experience. The proposed DBCA is made up of dynamical brain entropy mapping analysis and complex network analysis based on brain entropy sequences, which generate the dynamical complexity of local brain areas and the topological complexity across brain areas, respectively. First, the transient complexity of voxel-wise brain map was calculated; compared with non-seafarers, seafarers showed decreased dynamic entropy values in the cerebellum and increased values in the left fusiform gyrus (BA20). Further, the complex network analysis based on brain entropy sequences revealed small-worldness in terms of topological complexity in both seafarers and non-seafarers, indicating that it is an inherent attribute of human the brain. In addition, seafarers showed a higher average path length and lower average clustering coefficient than non-seafarers, suggesting that the information processing ability is reduced in seafarers. Moreover, the reduction in efficiency of seafarers suggests that they have a less efficient processing network. To sum up, the proposed DBCA is effective for exploring the dynamic complexity changes in voxel-wise activity and region-wise connectivity, showing that occupational experience can reshape seafarers’ dynamic brain complexity fingerprints.

High-order interactions explain the collective behavior of cortical populations in executive but not sensory areas

One influential view in neuroscience is that pairwise cell interactions explain the firing patterns of large populations. Despite its prevalence, this view originates from studies in the retina and visual cortex of anesthetized animals. Whether pairwise interactions predict the firing patterns of neurons across multiple brain areas in behaving animals remains unknown. Here, we performed multi-area electrical recordings to find that 2nd-order interactions explain a high fraction of entropy of the population response in macaque cortical areas V1 and V4. Surprisingly, despite the brain-state modulation of neuronal responses, the model based on pairwise interactions captured ∼90% of the spiking activity structure during wakefulness and sleep. However, regardless of brain state, pairwise interactions fail to explain experimentally observed entropy in neural populations from the prefrontal cortex. Thus, while simple pairwise interactions explain the collective behavior of visual cortical networks across brain states, explaining the population dynamics in downstream areas involves higher-order interactions.

Identification of Pattern Completion Neurons in Neuronal Ensembles Using Probabilistic Graphical Models

Neuronal ensembles are groups of neurons with coordinated activity that could represent sensory, motor, or cognitive states. The study of how neuronal ensembles are built, recalled, and involved in the guiding of complex behaviors has been limited by the lack of experimental and analytical tools to reliably identify and manipulate neurons that have the ability to activate entire ensembles. Such pattern completion neurons have also been proposed as key elements of artificial and biological neural networks. Indeed, the relevance of pattern completion neurons is highlighted by growing evidence that targeting them can activate neuronal ensembles and trigger behavior. As a method to reliably detect pattern completion neurons, we use conditional random fields (CRFs), a type of probabilistic graphical model. We apply CRFs to identify pattern completion neurons in ensembles in experiments using in vivo two-photon calcium imaging from primary visual cortex of male mice and confirm the CRFs predictions with two-photon optogenetics. To test the broader applicability of CRFs we also analyze publicly available calcium imaging data (Allen Institute Brain Observatory dataset) and demonstrate that CRFs can reliably identify neurons that predict specific features of visual stimuli. Finally, to explore the scalability of CRFs we apply them to in silico network simulations and show that CRFs-identified pattern completion neurons have increased functional connectivity. These results demonstrate the potential of CRFs to characterize and selectively manipulate neural circuits.SIGNIFICANCE STATEMENT We describe a graph theory method to identify and optically manipulate neurons with pattern completion capability in mouse cortical circuits. Using calcium imaging and two-photon optogenetics in vivo we confirm that key neurons identified by this method can recall entire neuronal ensembles. This method could be broadly applied to manipulate neuronal ensemble activity to trigger behavior or for therapeutic applications in brain prostheses.

Dopamine Transporter Is a Master Regulator of Dopaminergic Neural Network Connectivity

Dopaminergic neurons of the substantia nigra pars compacta (SNC) and ventral tegmental area (VTA) exhibit spontaneous firing activity. The dopaminergic neurons in these regions have been shown to exhibit differential sensitivity to neuronal loss and psychostimulants targeting dopamine transporter. However, it remains unclear whether these regional differences scale beyond individual neuronal activity to regional neuronal networks. Here, we used live-cell calcium imaging to show that network connectivity greatly differs between SNC and VTA regions with higher incidence of hub-like neurons in the VTA. Specifically, the frequency of hub-like neurons was significantly lower in SNC than in the adjacent VTA, consistent with the interpretation of a lower network resilience to SNC neuronal loss. We tested this hypothesis, in DAT-cre/loxP-GCaMP6f mice of either sex, when activity of an individual dopaminergic neuron is suppressed, through whole-cell patch clamp electrophysiology, in either SNC or VTA networks. Neuronal loss in the SNC increased network clustering, whereas the larger number of hub-neurons in the VTA overcompensated by decreasing network clustering in the VTA. We further show that network properties are regulatable via a dopamine transporter but not a D2 receptor dependent mechanism. Our results demonstrate novel regulatory mechanisms of functional network topology in dopaminergic brain regions.SIGNIFICANCE STATEMENT In this work, we begin to untangle the differences in complex network properties between the substantia nigra pars compacta (SNC) and VTA, that may underlie differential sensitivity between regions. The methods and analysis employed provide a springboard for investigations of network topology in multiple deep brain structures and disorders.

Improved inference in coupling, encoding, and decoding models and its consequence for neuroscientific interpretation

BACKGROUND

A central goal of systems neuroscience is to understand the relationships amongst constituent units in neural populations, and their modulation by external factors, using high-dimensional and stochastic neural recordings. Parametric statistical models (e.g., coupling, encoding, and decoding models), play an instrumental role in accomplishing this goal. However, extracting conclusions from a parametric model requires that it is fit using an inference algorithm capable of selecting the correct parameters and properly estimating their values. Traditional approaches to parameter inference have been shown to suffer from failures in both selection and estimation. The recent development of algorithms that ameliorate these deficiencies raises the question of whether past work relying on such inference procedures have produced inaccurate systems neuroscience models, thereby impairing their interpretation.

NEW METHOD

We used algorithms based on Union of Intersections, a statistical inference framework based on stability principles, capable of improved selection and estimation.

COMPARISON

We fit functional coupling, encoding, and decoding models across a battery of neural datasets using both UoI and baseline inference procedures (e.g., ℓ₁-penalized GLMs), and compared the structure of their fitted parameters.

RESULTS

Across recording modality, brain region, and task, we found that UoI inferred models with increased sparsity, improved stability, and qualitatively different parameter distributions, while maintaining predictive performance. We obtained highly sparse functional coupling networks with substantially different community structure, more parsimonious encoding models, and decoding models that relied on fewer single-units.

CONCLUSIONS

Together, these results demonstrate that improved parameter inference, achieved via UoI, reshapes interpretation in diverse neuroscience contexts.

Fast, cell-resolution, contiguous-wide two-photon imaging to reveal functional network architectures across multi-modal cortical areas

Fast and wide field-of-view imaging with single-cell resolution, high signal-to-noise ratio, and no optical aberrations have the potential to inspire new avenues of investigations in biology. However, such imaging is challenging because of the inevitable tradeoffs among these parameters. Here, we overcome these tradeoffs by combining a resonant scanning system, a large objective with low magnification and high numerical aperture, and highly sensitive large-aperture photodetectors. The result is a practically aberration-free, fast-scanning high optical invariant two-photon microscopy (FASHIO-2PM) that enables calcium imaging from a large network composed of ∼16,000 neurons at 7.5 Hz from a 9 mm² contiguous image plane, including more than 10 sensory-motor and higher-order areas of the cerebral cortex in awake mice. Network analysis based on single-cell activities revealed that the brain exhibits small-world rather than scale-free behavior. The FASHIO-2PM is expected to enable studies on biological dynamics by simultaneously monitoring macroscopic activities and their compositional elements.

Inhibitory neurons exhibit high controlling ability in the cortical microconnectome

The brain is a network system in which excitatory and inhibitory neurons keep activity balanced in the highly non-random connectivity pattern of the microconnectome. It is well known that the relative percentage of inhibitory neurons is much smaller than excitatory neurons in the cortex. So, in general, how inhibitory neurons can keep the balance with the surrounding excitatory neurons is an important question. There is much accumulated knowledge about this fundamental question. This study quantitatively evaluated the relatively higher functional contribution of inhibitory neurons in terms of not only properties of individual neurons, such as firing rate, but also in terms of topological mechanisms and controlling ability on other excitatory neurons. We combined simultaneous electrical recording (~2.5 hours) of ~1000 neurons in vitro, and quantitative evaluation of neuronal interactions including excitatory-inhibitory categorization. This study accurately defined recording brain anatomical targets, such as brain regions and cortical layers, by inter-referring MRI and immunostaining recordings. The interaction networks enabled us to quantify topological influence of individual neurons, in terms of controlling ability to other neurons. Especially, the result indicated that highly influential inhibitory neurons show higher controlling ability of other neurons than excitatory neurons, and are relatively often distributed in deeper layers of the cortex. Furthermore, the neurons having high controlling ability are more effectively limited in number than central nodes of k-cores, and these neurons also participate in more clustered motifs. In summary, this study suggested that the high controlling ability of inhibitory neurons is a key mechanism to keep balance with a large number of other excitatory neurons beyond simple higher firing rate. Application of the selection method of limited important neurons would be also applicable for the ability to effectively and selectively stimulate E/I imbalanced disease states.

How small numbers of inhibitory neurons functionally keep balance with large numbers of excitatory neurons in the brain by controlling each other is a fundamental question. Especially, this study quantitatively evaluated a topological mechanism of interaction networks in terms of controlling abilities of individual cortical neurons to other neurons. Combination of simultaneous electrical recording of ~1000 neurons and a quantitative evaluation method of neuronal interactions including excitatory-inhibitory categories, enabled us to evaluate the influence of individual neurons not only about firing rate but also about their relative positions in the networks and controllable ability of other neurons. Especially, the result showed that inhibitory neurons have more controlling ability than excitatory neurons, and such neurons were more often observed in deep layers. Because the limited number of neurons in terms controlling ability were much smaller than neurons based on centrality measure and, of course, more directly selected neurons based on their ability to control other neurons, the selection method of important neurons will help not only to produce realistic computational models but also will help to stimulate brain to effectively treat imbalanced disease states.

A model integrating multiple processes of synchronization and coherence for information instantiation within a cortical area

What is the form of dynamic, e.g., sensory, information in the mammalian cortex? Information in the cortex is modeled as a coherence map of a mixed chimera state of synchronous, phasic, and disordered minicolumns. The theoretical model is built on neurophysiological evidence. Complex spatiotemporal information is instantiated through a system of interacting biological processes that generate a synchronized cortical area, a coherent aperture. Minicolumn elements are grouped in macrocolumns in an array analogous to a phased-array radar, modeled as an aperture, a "hole through which radiant energy flows." Coherence maps in a cortical area transform inputs from multiple sources into outputs to multiple targets, while reducing complexity and entropy. Coherent apertures can assume extremely large numbers of different information states as coherence maps, which can be communicated among apertures with corresponding very large bandwidths. The coherent aperture model incorporates considerable reported research, integrating five conceptually and mathematically independent processes: 1) a damped Kuramoto network model, 2) a pumped area field potential, 3) the gating of nearly coincident spikes, 4) the coherence of activity across cortical lamina, and 5) complex information formed through functions in macrocolumns. Biological processes and their interactions are described in equations and a functional circuit such that the mathematical pieces can be assembled the same way the neurophysiological ones are. The model can be conceptually convolved over the specifics of local cortical areas within and across species. A coherent aperture becomes a node in a graph of cortical areas with a corresponding distribution of information.

EEG, MEG and neuromodulatory approaches to explore cognition: Current status and future directions

Neural oscillations and their association with brain states and cognitive functions have been object of extensive investigation over the last decades. Several electroencephalography (EEG) and magnetoencephalography (MEG) analysis approaches have been explored and oscillatory properties have been identified, in parallel with the technical and computational advancement. This review provides an up-to-date account of how EEG/MEG oscillations have contributed to the understanding of cognition. Methodological challenges, recent developments and translational potential, along with future research avenues, are discussed.

Diffusion MRI tractography filtering techniques change the topology of structural connectomes

OBJECTIVE

The use of non-invasive techniques for the estimation of structural brain networks (i.e. connectomes) opened the door to large-scale investigations on the functioning and the architecture of the brain, unveiling the link between neurological disorders and topological changes of the brain network. This study aims at assessing if and how the topology of structural connectomes estimated non-invasively with diffusion MRI is affected by the employment of tractography filtering techniques in structural connectomic pipelines. Additionally, this work investigates the robustness of topological descriptors of filtered connectomes to the common practice of density-based thresholding.

APPROACH

We investigate the changes in global efficiency, characteristic path length, modularity and clustering coefficient on filtered connectomes obtained with the spherical deconvolution informed filtering of tractograms and using the convex optimization modelling for microstructure informed tractography. The analysis is performed on both healthy subjects and patients affected by traumatic brain injury and with an assessment of the robustness of the computed graph-theoretical measures with respect to density-based thresholding of the connectome.

MAIN RESULT

Our results demonstrate that tractography filtering techniques change the topology of brain networks, and thus alter network metrics both in the pathological and the healthy cases. Moreover, the measures are shown to be robust to density-based thresholding.

SIGNIFICANCE

The present work highlights how the inclusion of tractography filtering techniques in connectomic pipelines requires extra caution as they systematically change the network topology both in healthy subjects and patients affected by traumatic brain injury. Finally, the practice of low-to-moderate density-based thresholding of the connectomes is confirmed to have negligible effects on the topological analysis.

A pruning feedforward small-world neural network based on Katz centrality for nonlinear system modeling

Approaching to the biological neural network, small-world neural networks have been demonstrated to improve the generalization performance of artificial neural networks. However, the architecture of small-world neural networks is typically large and predefined. This may cause the problems of overfitting and time consuming, and cannot obtain an optimal network structure automatically for a given problem. To solve the above problems, this paper proposes a pruning feedforward small-world neural network (PFSWNN), and applies it to nonlinear system modeling. Firstly, a feedforward small-world neural network (FSWNN) is constructed according to the rewiring rule of Watts-Strogatz. Secondly, the importance of each hidden neuron is evaluated based on its Katz centrality. If the Katz centrality of a hidden neuron is below the predefined threshold, this neuron is considered to be an unimportant node and then merged with its most correlated neuron in the same hidden layer. The connection weights are trained using the gradient-based algorithm, and the convergence of the proposed PFSWNN is theoretically analyzed in this paper. Finally, the PFSWNN model is tested on some problems for nonlinear system modeling, including the approximation for a rapidly changing function, CATS missing time-series prediction, four benchmark problems of UCI public datasets and a practical problem for wastewater treatment process. Experimental results demonstrate that PFSWNN exhibits superior generalization performance by small-world property as well as the pruning algorithm, and the training time of PFSWNN is shortened owning to a compact structure.

Correlated activity favors synergistic processing in local cortical networks in vitro at synaptically relevant timescales

Neural information processing is widely understood to depend on correlations in neuronal activity. However, whether correlation is favorable or not is contentious. Here, we sought to determine how correlated activity and information processing are related in cortical circuits. Using recordings of hundreds of spiking neurons in organotypic cultures of mouse neocortex, we asked whether mutual information between neurons that feed into a common third neuron increased synergistic information processing by the receiving neuron. We found that mutual information and synergistic processing were positively related at synaptic timescales (0.05-14 ms), where mutual information values were low. This effect was mediated by the increase in information transmission-of which synergistic processing is a component-that resulted as mutual information grew. However, at extrasynaptic windows (up to 3,000 ms), where mutual information values were high, the relationship between mutual information and synergistic processing became negative. In this regime, greater mutual information resulted in a disproportionate increase in redundancy relative to information transmission. These results indicate that the emergence of synergistic processing from correlated activity differs according to timescale and correlation regime. In a low-correlation regime, synergistic processing increases with greater correlation, and in a high-correlation regime, synergistic processing decreases with greater correlation.

Modeling the effects of sinusoidal stimulation and synaptic plasticity on linked neural oscillators

The brain exhibits intrinsic oscillatory behavior, which plays a vital role in communication and information processing. Abnormalities in brain rhythms have been linked to numerous disorders, including depression and schizophrenia. Rhythmic electrical stimulation (e.g., transcranial magnetic stimulation and transcranial alternating current stimulation) has been used to modulate these oscillations and produce lasting changes in neural activity. In this computational study, we investigate the combined effects of sinusoidal stimulation and synaptic plasticity on model networks comprised of simple, tunable four-neuron oscillators. While not intended to model a specific brain circuit, this idealization was created to provide some intuition on how electrical modulation can induce plastic changes in the oscillatory state. Linked pairs of oscillators were stimulated with sinusoidal current, and their behavior was measured as a function of their intrinsic frequencies, inter-oscillator synaptic strengths, and stimulus strength and frequency. Under certain stimulus conditions, sinusoidal current can disrupt the network's natural firing patterns. Synaptic plasticity can induce weight imbalances that permanently change the characteristic firing behavior of the network. Grids of 100 oscillators with random frequencies were also subjected to a wide array of stimulus conditions. The characteristics of the post-stimulus network activity depend heavily on the stimulus frequency and amplitude as well as the initial strength of inter-oscillator connections. Synchronization arises at the network level from complex patterns of activity propagation, which are enhanced or disrupted by different stimuli. The findings may prove important to the design of novel neuromodulation treatments and techniques seeking to affect oscillatory activity in the brain.

Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs

The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying universal model. Here, we determined the synchronization behavior of this model by solving it numerically on a large, weighted human connectome network, containing 836733 nodes, in an assumed homeostatic state. Since this graph has a topological dimension d < 4, a real synchronization phase transition is not possible in the thermodynamic limit, still we could locate a transition between partially synchronized and desynchronized states. At this crossover point we observe power-law–tailed synchronization durations, with τ_t ≃ 1.2(1), away from experimental values for the brain. For comparison, on a large two-dimensional lattice, having additional random, long-range links, we obtain a mean-field value: τ_t ≃ 1.6(1). However, below the transition of the connectome we found global coupling control-parameter dependent exponents 1 < τ_t ≤ 2, overlapping with the range of human brain experiments. We also studied the effects of random flipping of a small portion of link weights, mimicking a network with inhibitory interactions, and found similar results. The control-parameter dependent exponent suggests extended dynamical criticality below the transition point.

From Synaptic Interactions to Collective Dynamics in Random Neuronal Networks Models: Critical Role of Eigenvectors and Transient Behavior

The study of neuronal interactions is at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, and the Brainome) that attempt to obtain a detailed map of the entire brain. Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix. This work explores the application of free random variables to the study of large synaptic interaction matrices. Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott (2006), we extend them to heavy-tailed distributions of interactions. More important, we analytically derive the behavior of eigenvector overlaps, which determine the stability of the spectra. We observe that on imposing the neuronal excitation/inhibition balance, despite the eigenvalues remaining unchanged, their stability dramatically decreases due to the strong nonorthogonality of associated eigenvectors. This leads us to the conclusion that understanding the temporal evolution of asymmetric neural networks requires considering the entangled dynamics of both eigenvectors and eigenvalues, which might bear consequences for learning and memory processes in these models. Considering the success of free random variables theory in a wide variety of disciplines, we hope that the results presented here foster the additional application of these ideas in the area of brain sciences.

Synaptic Scaling Improves the Stability of Neural Mass Models Capable of Simulating Brain Plasticity

Neural mass models offer a way of studying the development and behavior of large-scale brain networks through computer simulations. Such simulations are currently mainly research tools, but as they improve, they could soon play a role in understanding, predicting, and optimizing patient treatments, particularly in relation to effects and outcomes of brain injury. To bring us closer to this goal, we took an existing state-of-the-art neural mass model capable of simulating connection growth through simulated plasticity processes. We identified and addressed some of the model's limitations by implementing biologically plausible mechanisms. The main limitation of the original model was its instability, which we addressed by incorporating a representation of the mechanism of synaptic scaling and examining the effects of optimizing parameters in the model. We show that the updated model retains all the merits of the original model, while being more stable and capable of generating networks that are in several aspects similar to those found in real brains.

A Comparison of the Maximum Entropy Principle Across Biological Spatial Scales

Despite their differences, biological systems at different spatial scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are often hard to grasp due to the highly specialized nature of modern science and the parcelled terminology employed by various scientific sub-disciplines. To explore these common organizational features, this paper provides a comparative study of diverse applications of the maximum entropy principle, which has found many uses at different biological spatial scales ranging from amino acids up to societies. By presenting these studies under a common approach and language, this paper aims to establish a unified view over these seemingly highly heterogeneous scenarios.

Pairwise Interactions among Brain Regions Organize Large-Scale Functional Connectivity during Execution of Various Tasks

Spatially separated brain areas interact with each other to form networks with coordinated activities, supporting various brain functions. Interaction structures among brain areas have been widely investigated through pairwise measures. However, interactions among multiple (e.g., triple and quadruple) areas cannot be reduced to pairwise interactions. Such higher order interactions (HOIs), e.g., exclusive-or (XOR) operation, are widely implemented in computation systems and are crucial for effective information processing. However, it is currently unclear whether any HOIs are present in large-scale brain functional networks when subjects are executing specific tasks. Here we analyzed functional magnetic resonance imaging (fMRI) data collected from human subjects executing various perceptual, motor, and cognitive tasks. We found that HOI strength in the macroscopic functional networks was very weak for all tasks, suggesting that major brain activities do not rely on HOIs on the macroscopic level at the timescale of hundreds of milliseconds. These weak HOIs during tasks were further investigated with a neural network model activated by external inputs, which suggested that weak pairwise interactions among brain areas organized the system without involving HOIs. Taken together, these results demonstrated the dominance of pairwise interactions in organizing coordinated activities among different brain areas to support various brain functions.

Ensemble inhibition and excitation in the human cortex: An Ising-model analysis with uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov-chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I neurons dramatically overestimates synchrony among E neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.

Maximum entropy principle analysis in network systems with short-time recordings

In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in general is often required, e.g., hours of spiking recordings of neurons in neuronal networks. The issue of whether the MEP analysis can be successfully applied to network systems with data from short-time recordings has yet to be fully addressed. In this work, we investigate relationships underlying the probability distributions, moments, and effective interactions in the MEP analysis and then show that, with short-time recordings of network dynamics, the MEP analysis can be applied to reconstructing probability distributions of network states that is much more accurate than the one directly measured from the short-time recording. Using spike trains obtained from both Hodgkin-Huxley neuronal networks and electrophysiological experiments, we verify our results and demonstrate that MEP analysis provides a tool to investigate the neuronal population coding properties for short-time recordings.

Neuronal networks underlying the conjoint modulation of response selection by subliminal and consciously induced cognitive conflicts

Goal-directed behavior has been shown to be affected by consciously and subliminally induced conflicts. Both types of conflict conjointly modulate behavioral performance, but the underlying neuronal mechanisms have remained unclear. While cognitive control is linked to oscillations in the theta frequency band, there are several mechanisms via which theta oscillations may enable cognitive control: via the coordination and synchronization of a large and complex neuronal network and/or via local processes within the medial frontal cortex. We, therefore, investigated this issue with a focus on theta oscillations and the underlying neuronal networks. For this purpose, n = 40 healthy young participants performed a conflict paradigm that combines conscious and subliminal distractors while an EEG was recorded. The data show that separate processes modulate the theta-based activation and organization of cognitive control networks: EEG beamforming analyses showed that variations in theta band power generated in the supplementary motor area reflected the need for control and task-relevant goal shielding, as both conflicts as well as their conjoint effect on behavior increased theta power. Yet, large networks were not modulated by this and graph theoretical analyses of the efficiency (i.e. small worldness) of theta-driven networks did not reflect the need for control. Instead, theta network efficiency was decreased by subliminal conflicts only. This dissociation suggests that while both kinds of conflict require control and goal shielding, which are induced by an increase in theta band power and modulate processes in the medial frontal cortex, only non-conscious conflicts diminish the efficiency of theta-driven large-scale networks.

Mitochondria are a substrate of cellular memory

Cellular memory underlies cellular identity, and thus constitutes a unifying mechanism of genetic disposition, environmental influences, and cellular adaptation. Here, we demonstrate that enduring physicochemical changes of mitochondrial networks invoked by transient stress, a phenomenon we term 'mitoengrams', underlie the transgenerational persistence of epigenetically scripted cellular behavior. Using C2C12 myogenic stem-like cells, we show that stress memory elicited by transient, low-level arsenite exposure is stored within a self-renewing subpopulation of progeny cells in a mitochondrial-dependent fashion. Importantly, we demonstrate that erasure of mitoengrams by administration of mitochondria-targeted electron scavenger was sufficient to reset key epigenetic marks of cellular memory and redirect the identity of the mitoengram-harboring progeny cells to a non-stress-like state. Together, our findings indicate that mnemonic information emanating from mitochondria support the balance between the persistence and transience of cellular memory.

Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network

We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [long-term potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Modelling Peri-Perceptual Brain Processes in a Deep Learning Spiking Neural Network Architecture

Familiarity of marketing stimuli may affect consumer behaviour at a peri-perceptual processing level. The current study introduces a method for deep learning of electroencephalogram (EEG) data using a spiking neural network (SNN) approach that reveals the complexity of peri-perceptual processes of familiarity. The method is applied to data from 20 participants viewing familiar and unfamiliar logos. The results support the potential of SNN models as novel tools in the exploration of peri-perceptual mechanisms that respond differentially to familiar and unfamiliar stimuli. Specifically, the activation pattern of the time-locked response identified by the proposed SNN model at approximately 200 milliseconds post-stimulus suggests greater connectivity and more widespread dynamic spatio-temporal patterns for familiar than unfamiliar logos. The proposed SNN approach can be applied to study other peri-perceptual or perceptual brain processes in cognitive and computational neuroscience.

Numerical optimization of coordinated reset stimulation for desynchronizing neuronal network dynamics

Excessive synchronization in neural activity is a hallmark of Parkinson's disease (PD). A promising technique for treating PD is coordinated reset (CR) neuromodulation in which a neural population is desynchronized by the delivery of spatially-distributed current stimuli using multiple electrodes. In this study, we perform numerical optimization to find the energy-optimal current waveform for desynchronizing neuronal network with CR stimulation, by proposing and applying a new optimization method based on the direct search algorithm. In the proposed optimization method, the stimulating current is described as a Fourier series, and each Fourier coefficient as well as the stimulation period are directly optimized by evaluating the order parameter, which quantifies the synchrony level, from network simulation. This direct optimization scheme has an advantage that arbitrary changes in the dynamical properties of the network can be taken into account in the search process. By harnessing this advantage, we demonstrate the significant influence of externally applied oscillatory inputs and non-random network topology on the efficacy of CR modulation. Our results suggest that the effectiveness of brain stimulation for desynchronization may depend on various factors modulating the dynamics of the target network. We also discuss the possible relevance of the results to the efficacy of the stimulation in PD treatment.

Active learning of cortical connectivity from two-photon imaging data

Understanding how groups of neurons interact within a network is a fundamental question in system neuroscience. Instead of passively observing the ongoing activity of a network, we can typically perturb its activity, either by external sensory stimulation or directly via techniques such as two-photon optogenetics. A natural question is how to use such perturbations to identify the connectivity of the network efficiently. Here we introduce a method to infer sparse connectivity graphs from in-vivo, two-photon imaging of population activity in response to external stimuli. A novel aspect of the work is the introduction of a recommended distribution, incrementally learned from the data, to optimally refine the inferred network. Unlike existing system identification techniques, this “active learning” method automatically focuses its attention on key undiscovered areas of the network, instead of targeting global uncertainty indicators like parameter variance. We show how active learning leads to faster inference while, at the same time, provides confidence intervals for the network parameters. We present simulations on artificial small-world networks to validate the methods and apply the method to real data. Analysis of frequency of motifs recovered show that cortical networks are consistent with a small-world topology model.

State-dependent representation of stimulus-evoked activity in high-density recordings of neural cultures

Neuronal responses to external stimuli vary from trial to trial partly because they depend on continuous spontaneous variations of the state of neural circuits, reflected in variations of ongoing activity prior to stimulus presentation. Understanding how post-stimulus responses relate to the pre-stimulus spontaneous activity is thus important to understand how state dependence affects information processing and neural coding, and how state variations can be discounted to better decode single-trial neural responses. Here we exploited high-resolution CMOS electrode arrays to record simultaneously from thousands of electrodes in in-vitro cultures stimulated at specific sites. We used information-theoretic analyses to study how ongoing activity affects the information that neuronal responses carry about the location of the stimuli. We found that responses exhibited state dependence on the time between the last spontaneous burst and the stimulus presentation and that the dependence could be described with a linear model. Importantly, we found that a small number of selected neurons carry most of the stimulus information and contribute to the state-dependent information gain. This suggests that a major value of large-scale recording is that it individuates the small subset of neurons that carry most information and that benefit the most from knowledge of its state dependence.

Blindfold learning of an accurate neural metric

The brain has no direct access to physical stimuli but only to the spiking activity evoked in sensory organs. It is unclear how the brain can learn representations of the stimuli based on those noisy, correlated responses alone. Here we show how to build an accurate distance map of responses solely from the structure of the population activity of retinal ganglion cells. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions.

From Structure to Activity: Using Centrality Measures to Predict Neuronal Activity

It is clear that the topological structure of a neural network somehow determines the activity of the neurons within it. In the present work, we ask to what extent it is possible to examine the structural features of a network and learn something about its activity? Specifically, we consider how the centrality (the importance of a node in a network) of a neuron correlates with its firing rate. To investigate, we apply an array of centrality measures, including In-Degree, Closeness, Betweenness, Eigenvector, Katz, PageRank, Hyperlink-Induced Topic Search (HITS) and NeuronRank to Leaky-Integrate and Fire neural networks with different connectivity schemes. We find that Katz centrality is the best predictor of firing rate given the network structure, with almost perfect correlation in all cases studied, which include purely excitatory and excitatory–inhibitory networks, with either homogeneous connections or a small-world structure. We identify the properties of a network which will cause this correlation to hold. We argue that the reason Katz centrality correlates so highly with neuronal activity compared to other centrality measures is because it nicely captures disinhibition in neural networks. In addition, we argue that these theoretical findings are applicable to neuroscientists who apply centrality measures to functional brain networks, as well as offer a neurophysiological justification to high level cognitive models which use certain centrality measures.

Dynamical networks: Finding, measuring, and tracking neural population activity using network science

Systems neuroscience is in a headlong rush to record from as many neurons at the same time as possible. As the brain computes and codes using neuron populations, it is hoped these data will uncover the fundamentals of neural computation. But with hundreds, thousands, or more simultaneously recorded neurons come the inescapable problems of visualizing, describing, and quantifying their interactions. Here I argue that network science provides a set of scalable, analytical tools that already solve these problems. By treating neurons as nodes and their interactions as links, a single network can visualize and describe an arbitrarily large recording. I show that with this description we can quantify the effects of manipulating a neural circuit, track changes in population dynamics over time, and quantitatively define theoretical concepts of neural populations such as cell assemblies. Using network science as a core part of analyzing population recordings will thus provide both qualitative and quantitative advances to our understanding of neural computation.

Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity

We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre- and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre- and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.

Weak Higher-Order Interactions in Macroscopic Functional Networks of the Resting Brain

Interactions among different brain regions are usually examined through functional connectivity (FC) analysis, which is exclusively based on measuring pairwise correlations in activities. However, interactions beyond the pairwise level, that is, higher-order interactions (HOIs), are vital in understanding the behavior of many complex systems. So far, whether HOIs exist among brain regions and how they can affect the brain's activities remains largely elusive. To address these issues, here, we analyzed blood oxygenation level-dependent (BOLD) signals recorded from six typical macroscopic functional networks of the brain in 100 human subjects (46 males and 54 females) during the resting state. Through examining the binarized BOLD signals, we found that HOIs within and across individual networks were both very weak regardless of the network size, topology, degree of spatial proximity, spatial scales, and whether the global signal was regressed. To investigate the potential mechanisms underlying the weak HOIs, we analyzed the dynamics of a network model and also found that HOIs were generally weak within a wide range of key parameters provided that the overall dynamic feature of the model was similar to the empirical data and it was operating close to a linear fluctuation regime. Our results suggest that weak HOI may be a general property of brain's macroscopic functional networks, which implies the dominance of pairwise interactions in shaping brain activities at such a scale and warrants the validity of widely used pairwise-based FC approaches.SIGNIFICANCE STATEMENT To explain how activities of different brain areas are coordinated through interactions is essential to revealing the mechanisms underlying various brain functions. Traditionally, such an interaction structure is commonly studied using pairwise-based functional network analyses. It is unclear whether the interactions beyond the pairwise level (higher-order interactions or HOIs) play any role in this process. Here, we show that HOIs are generally weak in macroscopic brain networks. We also suggest a possible dynamical mechanism that may underlie this phenomenon. These results provide plausible explanation for the effectiveness of widely used pairwise-based approaches in analyzing brain networks. More importantly, it reveals a previously unknown, simple organization of the brain's macroscopic functional systems.

Inferring structural connectivity using Ising couplings in models of neuronal networks

Functional connectivity metrics have been widely used to infer the underlying structural connectivity in neuronal networks. Maximum entropy based Ising models have been suggested to discount the effect of indirect interactions and give good results in inferring the true anatomical connections. However, no benchmarking is currently available to assess the performance of Ising couplings against other functional connectivity metrics in the microscopic scale of neuronal networks through a wide set of network conditions and network structures. In this paper, we study the performance of the Ising model couplings to infer the synaptic connectivity in in silico networks of neurons and compare its performance against partial and cross-correlations for different correlation levels, firing rates, network sizes, network densities, and topologies. Our results show that the relative performance amongst the three functional connectivity metrics depends primarily on the network correlation levels. Ising couplings detected the most structural links at very weak network correlation levels, and partial correlations outperformed Ising couplings and cross-correlations at strong correlation levels. The result was consistent across varying firing rates, network sizes, and topologies. The findings of this paper serve as a guide in choosing the right functional connectivity tool to reconstruct the structural connectivity.

Collective behavior of large-scale neural networks with GPU acceleration

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.

Energy landscape analysis of neuroimaging data

Computational neuroscience models have been used for understanding neural dynamics in the brain and how they may be altered when physiological or other conditions change. We review and develop a data-driven approach to neuroimaging data called the energy landscape analysis. The methods are rooted in statistical physics theory, in particular the Ising model, also known as the (pairwise) maximum entropy model and Boltzmann machine. The methods have been applied to fitting electrophysiological data in neuroscience for a decade, but their use in neuroimaging data is still in its infancy. We first review the methods and discuss some algorithms and technical aspects. Then, we apply the methods to functional magnetic resonance imaging data recorded from healthy individuals to inspect the relationship between the accuracy of fitting, the size of the brain system to be analysed and the data length.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.