Spatial Embedding and Wiring Cost Constrain the Functional Layout of the Cortical Network of Rodents and Primates

Brain dynamics supported by a hierarchy of complex correlation patterns defining a robust functional architecture

Functional magnetic resonance imaging (fMRI) provides insights into cognitive processes with significant clinical potential. However, delays in brain region communication and dynamic variations are often overlooked in functional network studies. We demonstrate that networks extracted from fMRI cross-correlation matrices, considering time lags between signals, show remarkable reliability when focusing on statistical distributions of network properties. This reveals a robust brain functional connectivity pattern, featuring a sparse backbone of strong 0-lag correlations and weaker links capturing coordination at various time delays. This dynamic yet stable network architecture is consistent across rats, marmosets, and humans, as well as in electroencephalogram (EEG) data, indicating potential universality in brain dynamics. Second-order properties of the dynamic functional network reveal a remarkably stable hierarchy of functional correlations in both group-level comparisons and test-retest analyses. Validation using alcohol use disorder fMRI data uncovers broader shifts in network properties than previously reported, demonstrating the potential of this method for identifying disease biomarkers.

Fluctuation in cortical excitation/inhibition modulates capability of attention across time scales ranging from hours to seconds

Sustained attention, as the basis of general cognitive ability, naturally varies across different time scales, spanning from hours, e.g. from wakefulness to drowsiness state, to seconds, e.g. trial-by-trail fluctuation in a task session. Whether there is a unified mechanism underneath such trans-scale variability remains unclear. Here we show that fluctuation of cortical excitation/inhibition (E/I) is a strong modulator to sustained attention in humans across time scales. First, we observed the ability to attend varied across different brain states (wakefulness, postprandial somnolence, sleep deprived), as well as within any single state with larger swings. Second, regardless of the time scale involved, we found highly attentive state was always linked to more balanced cortical E/I characterized by electroencephalography (EEG) features, while deviations from the balanced state led to temporal decline in attention, suggesting the fluctuation of cortical E/I as a common mechanism underneath trans-scale attentional variability. Furthermore, we found the variations of both sustained attention and cortical E/I indices exhibited fractal structure in the temporal domain, exhibiting features of self-similarity. Taken together, these results demonstrate that sustained attention naturally varies across different time scales in a more complex way than previously appreciated, with the cortical E/I as a shared neurophysiological modulator.

A strong direct link from the layer 3/4 border to layer 6 of cat primary visual cortex

The cat primary visual cortex (V1) is a cortical area for which we have one of the most detailed estimates of the connection 'weights' (expressed as number of synapses) between different neural populations in different layers (Binzegger et al in J Neurosci 24:8441-8453, 2004). Nevertheless, the majority of excitatory input sources to layer 6, the deepest layer in a local translaminar excitatory feedforward loop, was not accounted for by the known neuron types used to generate the quantitative Binzegger diagram. We aimed to fill this gap by using a retrograde tracer that would label neural cell bodies in and outside V1 that directly connect to layer 6 of V1. We found that more than 80% of labeled neurons projecting to layer 6 were within V1 itself. Our data indicate that a substantial fraction of the missing input is provided by a previously unidentified population of layer 3/4 border neurons, laterally distributed and connecting more strongly to layer 6 than the typical superficial layer pyramidal neurons considered by Binzegger et al. (Binzegger et al in J Neurosci 24:8441-8453, 2004). This layer 3/4 to layer 6 connection may be a parallel route to the layer 3 - layer 5 - layer 6 feedforward pathway, be associated with the fast-conducting, movement-related Y pathway and provide convergent input from distant (5-10 degrees) regions of the visual field.

Triadic percolation induces dynamical topological patterns in higher-order networks

Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.

The meso-connectomes of mouse, marmoset, and macaque: network organization and the emergence of higher cognition

The recent publications of the inter-areal connectomes for mouse, marmoset, and macaque cortex have allowed deeper comparisons across rodent vs. primate cortical organization. In general, these show that the mouse has very widespread, "all-to-all" inter-areal connectivity (i.e. a "highly dense" connectome in a graph theoretical framework), while primates have a more modular organization. In this review, we highlight the relevance of these differences to function, including the example of primary visual cortex (V1) which, in the mouse, is interconnected with all other areas, therefore including other primary sensory and frontal areas. We argue that this dense inter-areal connectivity benefits multimodal associations, at the cost of reduced functional segregation. Conversely, primates have expanded cortices with a modular connectivity structure, where V1 is almost exclusively interconnected with other visual cortices, themselves organized in relatively segregated streams, and hierarchically higher cortical areas such as prefrontal cortex provide top-down regulation for specifying precise information for working memory storage and manipulation. Increased complexity in cytoarchitecture, connectivity, dendritic spine density, and receptor expression additionally reveal a sharper hierarchical organization in primate cortex. Together, we argue that these primate specializations permit separable deconstruction and selective reconstruction of representations, which is essential to higher cognition.

Community detection in directed weighted networks using Voronoi partitioning

Community detection is a ubiquitous problem in applied network analysis, however efficient techniques do not yet exist for all types of network data. Directed and weighted networks are an example, where the different information encoded by link weights and the possibly high graph density can cause difficulties for some approaches. Here we present an algorithm based on Voronoi partitioning generalized to deal with directed weighted networks. As an added benefit, this method can directly employ edge weights that represent lengths, in contrast to algorithms that operate with connection strengths, requiring ad-hoc transformations of length data. We demonstrate the method on inter-areal brain connectivity, air transportation networks, and several social networks. We compare the performance with several other well-known algorithms, applying them on a set of randomly generated benchmark networks. The algorithm can handle dense graphs where weights are the main factor determining communities. The hierarchical structure of networks can also be detected, as shown for the brain. Its time efficiency is comparable or even outperforms some of the state-of-the-art algorithms, the part with the highest time-complexity being Dijkstra's shortest paths algorithm ( O ( | E | + | V | log | V | ) ).

Predictability of cortico-cortical connections in the mammalian brain

Despite a five order of magnitude range in size, the brains of mammals share many anatomical and functional characteristics that translate into cortical network commonalities. Here we develop a machine learning framework to quantify the degree of predictability of the weighted interareal cortical matrix. Partial network connectivity data were obtained with retrograde tract-tracing experiments generated with a consistent methodology, supplemented by projection length measurements in a nonhuman primate (macaque) and a rodent (mouse). We show that there is a significant level of predictability embedded in the interareal cortical networks of both species. At the binary level, links are predictable with an area under the ROC curve of at least 0.8 for the macaque. Weighted medium and strong links are predictable with an 85%-90% accuracy (mouse) and 70%-80% (macaque), whereas weak links are not predictable in either species. These observations reinforce earlier observations that the formation and evolution of the cortical network at the mesoscale is, to a large extent, rule based. Using the methodology presented here, we performed imputations on all area pairs, generating samples for the complete interareal network in both species. These are necessary for comparative studies of the connectome with minimal bias, both within and across species.

A generative model of the connectome with dynamic axon growth

Connectome generative models, otherwise known as generative network models, provide insight into the wiring principles underpinning brain network organization. While these models can approximate numerous statistical properties of empirical networks, they typically fail to explicitly characterize an important contributor to brain organization - axonal growth. Emulating the chemoaffinity guided axonal growth, we provide a novel generative model in which axons dynamically steer the direction of propagation based on distance-dependent chemoattractive forces acting on their growth cones. This simple dynamic growth mechanism, despite being solely geometry-dependent, is shown to generate axonal fiber bundles with brain-like geometry and features of complex network architecture consistent with the human brain, including lognormally distributed connectivity weights, scale-free nodal degrees, small-worldness, and modularity. We demonstrate that our model parameters can be fitted to individual connectomes, enabling connectome dimensionality reduction and comparison of parameters between groups. Our work offers an opportunity to bridge studies of axon guidance and connectome development, providing new avenues for understanding neural development from a computational perspective.

Relation of connectome topology to brain volume across 103 mammalian species

The brain connectome is an embedded network of anatomically interconnected brain regions, and the study of its topological organization in mammals has become of paramount importance due to its role in scaffolding brain function and behavior. Unlike many other observable networks, brain connections incur material and energetic cost, and their length and density are volumetrically constrained by the skull. Thus, an open question is how differences in brain volume impact connectome topology. We address this issue using the MaMI database, a diverse set of mammalian connectomes reconstructed from 201 animals, covering 103 species and 12 taxonomy orders, whose brain size varies over more than 4 orders of magnitude. Our analyses focus on relationships between volume and modular organization. After having identified modules through a multiresolution approach, we observed how connectivity features relate to the modular structure and how these relations vary across brain volume. We found that as the brain volume increases, modules become more spatially compact and dense, comprising more costly connections. Furthermore, we investigated how spatial embedding shapes network communication, finding that as brain volume increases, nodes' distance progressively impacts communication efficiency. We identified modes of variation in network communication policies, as smaller and bigger brains show higher efficiency in routing- and diffusion-based signaling, respectively. Finally, bridging network modularity and communication, we found that in larger brains, modular structure imposes stronger constraints on network signaling. Altogether, our results show that brain volume is systematically related to mammalian connectome topology and that spatial embedding imposes tighter restrictions on larger brains.

Towards a biologically annotated brain connectome

The brain is a network of interleaved neural circuits. In modern connectomics, brain connectivity is typically encoded as a network of nodes and edges, abstracting away the rich biological detail of local neuronal populations. Yet biological annotations for network nodes - such as gene expression, cytoarchitecture, neurotransmitter receptors or intrinsic dynamics - can be readily measured and overlaid on network models. Here we review how connectomes can be represented and analysed as annotated networks. Annotated connectomes allow us to reconceptualize architectural features of networks and to relate the connection patterns of brain regions to their underlying biology. Emerging work demonstrates that annotated connectomes help to make more veridical models of brain network formation, neural dynamics and disease propagation. Finally, annotations can be used to infer entirely new inter-regional relationships and to construct new types of network that complement existing connectome representations. In summary, biologically annotated connectomes offer a compelling way to study neural wiring in concert with local biological features.

The regional variation of laminar thickness in the human isocortex is related to cortical hierarchy and interregional connectivity

The human isocortex consists of tangentially organized layers with unique cytoarchitectural properties. These layers show spatial variations in thickness and cytoarchitecture across the neocortex, which is thought to support function through enabling targeted corticocortical connections. Here, leveraging maps of the 6 cortical layers based on 3D human brain histology, we aimed to quantitatively characterize the systematic covariation of laminar structure in the cortex and its functional consequences. After correcting for the effect of cortical curvature, we identified a spatial pattern of changes in laminar thickness covariance from lateral frontal to posterior occipital regions, which differentiated the dominance of infra- versus supragranular layer thickness. Corresponding to the laminar regularities of cortical connections along cortical hierarchy, the infragranular-dominant pattern of laminar thickness was associated with higher hierarchical positions of regions, mapped based on resting-state effective connectivity in humans and tract-tracing of structural connections in macaques. Moreover, we show that regions with similar laminar thickness patterns have a higher likelihood of structural connections and strength of functional connections. In sum, here we characterize the organization of laminar thickness in the human isocortex and its association with cortico-cortical connectivity, illustrating how laminar organization may provide a foundational principle of cortical function.

Spatially heterogeneous structure-function coupling in haemodynamic and electromagnetic brain networks

The relationship between structural and functional connectivity in the brain is a key question in connectomics. Here we quantify patterns of structure-function coupling across the neocortex, by comparing structural connectivity estimated using diffusion MRI with functional connectivity estimated using both neurophysiological (MEG-based) and haemodynamic (fMRI-based) recordings. We find that structure-function coupling is heterogeneous across brain regions and frequency bands. The link between structural and functional connectivity is generally stronger in multiple MEG frequency bands compared to resting state fMRI. Structure-function coupling is greater in slower and intermediate frequency bands compared to faster frequency bands. We also find that structure-function coupling systematically follows the archetypal sensorimotor-association hierarchy, as well as patterns of laminar differentiation, peaking in granular layer IV. Finally, structure-function coupling is better explained using structure-informed inter-regional communication metrics than using structural connectivity alone. Collectively, these results place neurophysiological and haemodynamic structure-function relationships in a common frame of reference and provide a starting point for a multi-modal understanding of structure-function coupling in the brain.

Early adversity changes the economic conditions of mouse structural brain network organization

Early adversity can change educational, cognitive, and mental health outcomes. However, the neural processes through which early adversity exerts these effects remain largely unknown. We used generative network modeling of the mouse connectome to test whether unpredictable postnatal stress shifts the constraints that govern the organization of the structural connectome. A model that trades off the wiring cost of long-distance connections with topological homophily (i.e., links between regions with shared neighbors) generated simulations that successfully replicate the rodent connectome. The imposition of early life adversity shifted the best-performing parameter combinations toward zero, heightening the stochastic nature of the generative process. Put simply, unpredictable postnatal stress changes the economic constraints that reproduce rodent connectome organization, introducing greater randomness into the development of the simulations. While this change may constrain the development of cognitive abilities, it could also reflect an adaptive mechanism that facilitates effective responses to future challenges.

The non-specific matrix thalamus facilitates the cortical information processing modes relevant for conscious awareness

The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of large-scale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

Neuroscience Needs Network Science

The brain is a complex system comprising a myriad of interacting neurons, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such interconnected systems, offering a framework for integrating multiscale data and complexity. To date, network methods have significantly advanced functional imaging studies of the human brain and have facilitated the development of control theory-based applications for directing brain activity. Here, we discuss emerging frontiers for network neuroscience in the brain atlas era, addressing the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease. We underscore the importance of fostering interdisciplinary opportunities through workshops, conferences, and funding initiatives, such as supporting students and postdoctoral fellows with interests in both disciplines. By bringing together the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way toward a deeper understanding of the brain and its functions, as well as offering new challenges for network science.

Functional geometry of auditory cortical resting state networks derived from intracranial electrophysiology

Understanding central auditory processing critically depends on defining underlying auditory cortical networks and their relationship to the rest of the brain. We addressed these questions using resting state functional connectivity derived from human intracranial electroencephalography. Mapping recording sites into a low-dimensional space where proximity represents functional similarity revealed a hierarchical organization. At a fine scale, a group of auditory cortical regions excluded several higher-order auditory areas and segregated maximally from the prefrontal cortex. On mesoscale, the proximity of limbic structures to the auditory cortex suggested a limbic stream that parallels the classically described ventral and dorsal auditory processing streams. Identities of global hubs in anterior temporal and cingulate cortex depended on frequency band, consistent with diverse roles in semantic and cognitive processing. On a macroscale, observed hemispheric asymmetries were not specific for speech and language networks. This approach can be applied to multivariate brain data with respect to development, behavior, and disorders.

Species-specific wiring of cortical circuits for small-world networks in the primary visual cortex

Long-range horizontal connections (LRCs) are conspicuous anatomical structures in the primary visual cortex (V1) of mammals, yet their detailed functions in relation to visual processing are not fully understood. Here, we show that LRCs are key components to organize a "small-world network" optimized for each size of the visual cortex, enabling the cost-efficient integration of visual information. Using computational simulations of a biologically inspired model neural network, we found that sparse LRCs added to networks, combined with dense local connections, compose a small-world network and significantly enhance image classification performance. We confirmed that the performance of the network appeared to be strongly correlated with the small-world coefficient of the model network under various conditions. Our theoretical model demonstrates that the amount of LRCs to build a small-world network depends on each size of cortex and that LRCs are beneficial only when the size of the network exceeds a certain threshold. Our model simulation of various sizes of cortices validates this prediction and provides an explanation of the species-specific existence of LRCs in animal data. Our results provide insight into a biological strategy of the brain to balance functional performance and resource cost.

Critical scaling of whole-brain resting-state dynamics

Scale invariance is a characteristic of neural activity. How this property emerges from neural interactions remains a fundamental question. Here, we studied the relation between scale-invariant brain dynamics and structural connectivity by analyzing human resting-state (rs-) fMRI signals, together with diffusion MRI (dMRI) connectivity and its approximation as an exponentially decaying function of the distance between brain regions. We analyzed the rs-fMRI dynamics using functional connectivity and a recently proposed phenomenological renormalization group (PRG) method that tracks the change of collective activity after successive coarse-graining at different scales. We found that brain dynamics display power-law correlations and power-law scaling as a function of PRG coarse-graining based on functional or structural connectivity. Moreover, we modeled the brain activity using a network of spins interacting through large-scale connectivity and presenting a phase transition between ordered and disordered phases. Within this simple model, we found that the observed scaling features were likely to emerge from critical dynamics and connections exponentially decaying with distance. In conclusion, our study tests the PRG method using large-scale brain activity and theoretical models and suggests that scaling of rs-fMRI activity relates to criticality.

Assortative mixing in micro-architecturally annotated brain connectomes

The wiring of the brain connects micro-architecturally diverse neuronal populations, but the conventional graph model, which encodes macroscale brain connectivity as a network of nodes and edges, abstracts away the rich biological detail of each regional node. Here, we annotate connectomes with multiple biological attributes and formally study assortative mixing in annotated connectomes. Namely, we quantify the tendency for regions to be connected based on the similarity of their micro-architectural attributes. We perform all experiments using four cortico-cortical connectome datasets from three different species, and consider a range of molecular, cellular, and laminar annotations. We show that mixing between micro-architecturally diverse neuronal populations is supported by long-distance connections and find that the arrangement of connections with respect to biological annotations is associated to patterns of regional functional specialization. By bridging scales of cortical organization, from microscale attributes to macroscale connectivity, this work lays the foundation for next-generation annotated connectomics.

Neuroscience needs Network Science

The brain is a complex system comprising a myriad of interacting elements, posing significant challenges in understanding its structure, function, and dynamics. Network science has emerged as a powerful tool for studying such intricate systems, offering a framework for integrating multiscale data and complexity. Here, we discuss the application of network science in the study of the brain, addressing topics such as network models and metrics, the connectome, and the role of dynamics in neural networks. We explore the challenges and opportunities in integrating multiple data streams for understanding the neural transitions from development to healthy function to disease, and discuss the potential for collaboration between network science and neuroscience communities. We underscore the importance of fostering interdisciplinary opportunities through funding initiatives, workshops, and conferences, as well as supporting students and postdoctoral fellows with interests in both disciplines. By uniting the network science and neuroscience communities, we can develop novel network-based methods tailored to neural circuits, paving the way towards a deeper understanding of the brain and its functions.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

A deep generative adversarial network capturing complex spiral waves in disinhibited circuits of the cerebral cortex

BACKGROUND

In the cerebral cortex, disinhibited activity is characterized by propagating waves that spread across neural tissue. In this pathological state, a widely reported form of activity are spiral waves that travel in a circular pattern around a fixed spatial locus termed the center of mass. Spiral waves exhibit stereotypical activity and involve broad patterns of co-fluctuations, suggesting that they may be of lower complexity than healthy activity.

RESULTS

To evaluate this hypothesis, we performed dense multi-electrode recordings of cortical networks where disinhibition was induced by perfusing a pro-epileptiform solution containing 4-Aminopyridine as well as increased potassium and decreased magnesium. Spiral waves were identified based on a spatially delimited center of mass and a broad distribution of instantaneous phases across electrodes. Individual waves were decomposed into "snapshots" that captured instantaneous neural activation across the entire network. The complexity of these snapshots was examined using a measure termed the participation ratio. Contrary to our expectations, an eigenspectrum analysis of these snapshots revealed a broad distribution of eigenvalues and an increase in complexity compared to baseline networks. A deep generative adversarial network was trained to generate novel exemplars of snapshots that closely captured cortical spiral waves. These synthetic waves replicated key features of experimental data including a tight center of mass, a broad eigenvalue distribution, spatially-dependent correlations, and a high complexity. By adjusting the input to the model, new samples were generated that deviated in systematic ways from the experimental data, thus allowing the exploration of a broad range of states from healthy to pathologically disinhibited neural networks.

CONCLUSIONS

Together, results show that the complexity of population activity serves as a marker along a continuum from healthy to disinhibited brain states. The proposed generative adversarial network opens avenues for replicating the dynamics of cortical seizures and accelerating the design of optimal neurostimulation aimed at suppressing pathological brain activity.

Toward Best Practices for Imaging Transcriptomics of the Human Brain

Modern brainwide transcriptional atlases provide unprecedented opportunities for investigating the molecular correlates of brain organization, as quantified using noninvasive neuroimaging. However, integrating neuroimaging data with transcriptomic measures is not straightforward, and careful consideration is required to make valid inferences. In this article, we review recent work exploring how various methodological choices affect 3 main phases of imaging transcriptomic analyses, including 1) processing of transcriptional atlas data; 2) relating transcriptional measures to independently derived neuroimaging phenotypes; and 3) evaluating the functional implications of identified associations through gene enrichment analyses. Our aim is to facilitate the development of standardized and reproducible approaches for this rapidly growing field. We identify sources of methodological variability, key choices that can affect findings, and considerations for mitigating false positive and/or spurious results. Finally, we provide an overview of freely available open-source toolboxes implementing current best-practice procedures across all 3 analysis phases.

Putative cause of seizure-induced cognitive alterations: The oscillatory reconfiguration of seizure network

Introduction

The dynamic reconfiguration of network oscillations is connected with cognitive processes. Changes in how neural networks and signaling pathways work are crucial to how epilepsy and related conditions develop. Specifically, there is evidence that prolonged or recurrent seizures may induce or exacerbate cognitive impairment. However, it still needs to be determined how the seizure brain configures its functional structure to shape the battle of strong local oscillations vs. slow global oscillations in the network to impair cognitive function.

Methods

In this paper, we aim to deduce the network mechanisms underlying seizure-induced cognitive impairment by comparing the evolution of strong local oscillations with slow global oscillations and their link to the resting state of healthy controls. Here, we construct a dynamically efficient network of pathological seizures by calculating the synchrony and directionality of information flow between nine patients' SEEG signals. Then, using a pattern-based method, we found hierarchical modules in the brain's functional network and measured the functional balance between the network's local strong and slow global oscillations.

Results and discussion

According to the findings, a tremendous rise in strong local oscillations during seizures and an increase in slow global oscillations after seizures corresponded to the initiation and recovery of cognitive impairment. Specifically, during the interictal period, local strong and slow global oscillations are in metastable balance, which is the same as a normal cognitive process and can be switched easily. During the pre-ictal period, the two show a bimodal pattern of separate peaks that cannot be easily switched, and some flexibility is lost. During the seizure period, a single-peak pattern with negative peaks is showcased, and the network eventually transitions to a very intense strong local oscillation state. These results shed light on the mechanism behind network oscillations in epilepsy-induced cognitive impairment. On the other hand, the differential (similarity) of oscillatory reorganization between the local (non) epileptogenic network and the global network may be an emergency protective mechanism of the brain, preventing the spread of pathological information flow to more healthy brain regions.

Connectome topology of mammalian brains and its relationship to taxonomy and phylogeny

Network models of anatomical connections allow for the extraction of quantitative features describing brain organization, and their comparison across brains from different species. Such comparisons can inform our understanding of between-species differences in brain architecture and can be compared to existing taxonomies and phylogenies. Here we performed a quantitative comparative analysis using the MaMI database (Tel Aviv University), a collection of brain networks reconstructed from ex vivo diffusion MRI spanning 125 species and 12 taxonomic orders or superorders. We used a broad range of metrics to measure between-mammal distances and compare these estimates to the separation of species as derived from taxonomy and phylogeny. We found that within-taxonomy order network distances are significantly closer than between-taxonomy network distances, and this relation holds for several measures of network distance. Furthermore, to estimate the evolutionary divergence between species, we obtained phylogenetic distances across 10,000 plausible phylogenetic trees. The anatomical network distances were rank-correlated with phylogenetic distances 10,000 times, creating a distribution of coefficients that demonstrate significantly positive correlations between network and phylogenetic distances. Collectively, these analyses demonstrate species-level organization across scales and informational sources: we relate brain networks distances, derived from MRI, with evolutionary distances, derived from genotyping data.

Chaotic dynamics in spatially distributed neuronal networks generate population-wide shared variability

Neural activity in the cortex is highly variable in response to repeated stimuli. Population recordings across the cortex demonstrate that the variability of neuronal responses is shared among large groups of neurons and concentrates in a low dimensional space. However, the source of the population-wide shared variability is unknown. In this work, we analyzed the dynamical regimes of spatially distributed networks of excitatory and inhibitory neurons. We found chaotic spatiotemporal dynamics in networks with similar excitatory and inhibitory projection widths, an anatomical feature of the cortex. The chaotic solutions contain broadband frequency power in rate variability and have distance-dependent and low-dimensional correlations, in agreement with experimental findings. In addition, rate chaos can be induced by globally correlated noisy inputs. These results suggest that spatiotemporal chaos in cortical networks can explain the shared variability observed in neuronal population responses.

Power spectrum and critical exponents in the 2D stochastic Wilson-Cowan model

The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, [Formula: see text], with an exponent [Formula: see text] close to 1 (pink noise). This exponent is predicted to be connected with the exponent [Formula: see text] related to the scaling of the average size with the duration of avalanches of activity. "Mean field" models of neural dynamics predict exponents [Formula: see text] and [Formula: see text] equal or near 2 at criticality (brown noise), including the simple branching model and the fully-connected stochastic Wilson-Cowan model. We here show that a 2D version of the stochastic Wilson-Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents [Formula: see text] and [Formula: see text] markedly different from those of mean field, respectively around 1 and 1.3. The exponents [Formula: see text] and [Formula: see text] of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to [Formula: see text] and [Formula: see text]. This seems to suggest the possibility of a different universality class for the model in finite dimension.

An integrated resource for functional and structural connectivity of the marmoset brain

Comprehensive integration of structural and functional connectivity data is required to model brain functions accurately. While resources for studying the structural connectivity of non-human primate brains already exist, their integration with functional connectivity data has remained unavailable. Here we present a comprehensive resource that integrates the most extensive awake marmoset resting-state fMRI data available to date (39 marmoset monkeys, 710 runs, 12117 mins) with previously published cellular-level neuronal tracing data (52 marmoset monkeys, 143 injections) and multi-resolution diffusion MRI datasets. The combination of these data allowed us to (1) map the fine-detailed functional brain networks and cortical parcellations, (2) develop a deep-learning-based parcellation generator that preserves the topographical organization of functional connectivity and reflects individual variabilities, and (3) investigate the structural basis underlying functional connectivity by computational modeling. This resource will enable modeling structure-function relationships and facilitate future comparative and translational studies of primate brains.

Benchmarking functional connectivity by the structure and geometry of the human brain

The brain's structural connectivity supports the propagation of electrical impulses, manifesting as patterns of coactivation, termed functional connectivity. Functional connectivity emerges from the underlying sparse structural connections, particularly through polysynaptic communication. As a result, functional connections between brain regions without direct structural links are numerous, but their organization is not completely understood. Here we investigate the organization of functional connections without direct structural links. We develop a simple, data-driven method to benchmark functional connections with respect to their underlying structural and geometric embedding. We then use this method to reweigh and reexpress functional connectivity. We find evidence of unexpectedly strong functional connectivity among distal brain regions and within the default mode network. We also find unexpectedly strong functional connectivity at the apex of the unimodal-transmodal hierarchy. Our results suggest that both phenomena-functional modules and functional hierarchies-emerge from functional interactions that transcend the underlying structure and geometry. These findings also potentially explain recent reports that structural and functional connectivity gradually diverge in transmodal cortex. Collectively, we show how structural connectivity and geometry can be used as a natural frame of reference with which to study functional connectivity patterns in the brain.

Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits

A range of perceptual and cognitive processes have been characterized from the perspective of probabilistic representations and inference. To understand the neural circuit mechanism underlying these probabilistic computations, we develop a theory based on complex spatiotemporal dynamics of neural population activity. We first implement and explore this theory in a biophysically realistic, spiking neural circuit. Population activity patterns emerging from the circuit capture realistic variability or fluctuations of neural dynamics both in time and in space. These activity patterns implement a type of probabilistic computations that we name fractional neural sampling (FNS). We further develop a mathematical model to reveal the algorithmic nature of FNS and its computational advantages for representing multimodal distributions, a major challenge faced by existing theories. We demonstrate that FNS provides a unified account of a diversity of experimental observations of neural spatiotemporal dynamics and perceptual processes such as visual perception inference, and that FNS makes experimentally testable predictions.

Dynamics of neural circuits mapping brain functions such as sensory processing and decision making, can be characterized by probabilistic representations and inference. The authors elaborate the role of spatiotemporal neural dynamics for more efficient performance of probabilistic computations.

Theory of the Multiregional Neocortex: Large-Scale Neural Dynamics and Distributed Cognition

The neocortex is a complex neurobiological system with many interacting regions. How these regions work together to subserve flexible behavior and cognition has become increasingly amenable to rigorous research. Here, I review recent experimental and theoretical work on the modus operandi of a multiregional cortex. These studies revealed several general principles for the neocortical interareal connectivity, low-dimensional macroscopic gradients of biological properties across cortical areas, and a hierarchy of timescales for information processing. Theoretical work suggests testable predictions regarding differential excitation and inhibition along feedforward and feedback pathways in the cortical hierarchy. Furthermore, modeling of distributed working memory and simple decision-making has given rise to a novel mathematical concept, dubbed bifurcation in space, that potentially explains how different cortical areas, with a canonical circuit organization but gradients of biological heterogeneities, are able to subserve their respective (e.g., sensory coding versus executive control) functions in a modularly organized brain.

Modeling spatial, developmental, physiological, and topological constraints on human brain connectivity

The complex connectivity of nervous systems is thought to have been shaped by competitive selection pressures to minimize wiring costs and support adaptive function. Accordingly, recent modeling work indicates that stochastic processes, shaped by putative trade-offs between the cost and value of each connection, can successfully reproduce many topological properties of macroscale human connectomes measured with diffusion magnetic resonance imaging. Here, we derive a new formalism that more accurately captures the competing pressures of wiring cost minimization and topological complexity. We further show that model performance can be improved by accounting for developmental changes in brain geometry and associated wiring costs, and by using interregional transcriptional or microstructural similarity rather than topological wiring rules. However, all models struggled to capture topographical (i.e., spatial) network properties. Our findings highlight an important role for genetics in shaping macroscale brain connectivity and indicate that stochastic models offer an incomplete account of connectome organization.

Early brain activity: Translations between bedside and laboratory

Neural activity is both a driver of brain development and a readout of developmental processes. Changes in neuronal activity are therefore both the cause and consequence of neurodevelopmental compromises. Here, we review the assessment of neuronal activities in both preclinical models and clinical situations. We focus on issues that require urgent translational research, the challenges and bottlenecks preventing translation of biomedical research into new clinical diagnostics or treatments, and possibilities to overcome these barriers. The key questions are (i) what can be measured in clinical settings versus animal experiments, (ii) how do measurements relate to particular stages of development, and (iii) how can we balance practical and ethical realities with methodological compromises in measurements and treatments.

Longitudinal Changes in Structural Connectivity in Young People at High Genetic Risk for Bipolar Disorder

OBJECTIVE

Recent studies of patients with bipolar disorder or at high genetic risk reveal structural dysconnections among key brain networks supporting cognitive and affective processes. Understanding the longitudinal trajectories of these networks across the peak age range of bipolar disorder onset could inform mechanisms of illness onset or resilience.

METHODS

Longitudinal diffusion-weighted MRI and phenotypic data were acquired at baseline and after 2 years in 183 individuals ages 12-30 years in two cohorts: 97 unaffected individuals with a first-degree relative with bipolar disorder (the high-risk group) and 86 individuals with no family history of mental illness (the control group). Whole-brain structural networks were derived using tractography, and longitudinal changes in these networks were studied using network-based statistics and mixed linear models.

RESULTS

Both groups showed widespread longitudinal changes, comprising both increases and decreases in structural connectivity, consistent with a shared neurodevelopmental process. On top of these shared changes, high-risk participants showed weakening of connectivity in a network encompassing the left inferior and middle frontal areas, left striatal and thalamic structures, the left fusiform, and right parietal and occipital regions. Connections among these regions strengthened in the control group, whereas they weakened in the high-risk group, shifting toward a cohort with established bipolar disorder. There was marginal evidence for even greater network weakening in those who had their first manic or hypomanic episode before follow-up.

CONCLUSIONS

Neurodevelopment from adolescence into early adulthood is associated with a substantial reorganization of structural brain networks. Differences in these maturational processes occur in a multisystem network in individuals at high genetic risk of bipolar disorder. This may represent a novel candidate to understand resilience and predict conversion to bipolar disorder.

Edges in brain networks: Contributions to models of structure and function

Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relationships, including connectivity and similarity among nodes. Adopting a specific definition of edges can fundamentally alter how we analyze and interpret a brain network. Furthermore, edges can associate into collectives and higher order arrangements, describe time series, and form edge communities that provide insights into brain network topology complementary to the traditional node-centric perspective. Focusing on the edges, and the higher order or dynamic information they can provide, discloses previously underappreciated aspects of structural and functional network organization.

Modularity maximization as a flexible and generic framework for brain network exploratory analysis

The modular structure of brain networks supports specialized information processing, complex dynamics, and cost-efficient spatial embedding. Inter-individual variation in modular structure has been linked to differences in performance, disease, and development. There exist many data-driven methods for detecting and comparing modular structure, the most popular of which is modularity maximization. Although modularity maximization is a general framework that can be modified and reparamaterized to address domain-specific research questions, its application to neuroscientific datasets has, thus far, been narrow. Here, we highlight several strategies in which the "out-of-the-box" version of modularity maximization can be extended to address questions specific to neuroscience. First, we present approaches for detecting "space-independent" modules and for applying modularity maximization to signed matrices. Next, we show that the modularity maximization frame is well-suited for detecting task- and condition-specific modules. Finally, we highlight the role of multi-layer models in detecting and tracking modules across time, tasks, subjects, and modalities. In summary, modularity maximization is a flexible and general framework that can be adapted to detect modular structure resulting from a wide range of hypotheses. This article highlights multiple frontiers for future research and applications.

The role of spatial embedding in mouse brain networks constructed from diffusion tractography and tracer injections

Diffusion MRI tractography is the only noninvasive method to measure the structural connectome in humans. However, recent validation studies have revealed limitations of modern tractography approaches, which lead to significant mistracking caused in part by local uncertainties in fiber orientations that accumulate to produce larger errors for longer streamlines. Characterizing the role of this length bias in tractography is complicated by the true underlying contribution of spatial embedding to brain topology. In this work, we compare graphs constructed with ex vivo tractography data in mice and neural tracer data from the Allen Mouse Brain Connectivity Atlas to random geometric surrogate graphs which preserve the low-order distance effects from each modality in order to quantify the role of geometry in various network properties. We find that geometry plays a substantially larger role in determining the topology of graphs produced by tractography than graphs produced by tracers. Tractography underestimates weights at long distances compared to neural tracers, which leads tractography to place network hubs close to the geometric center of the brain, as do corresponding tractography-derived random geometric surrogates, while tracer graphs place hubs further into peripheral areas of the cortex. We also explore the role of spatial embedding in modular structure, network efficiency and other topological measures in both modalities. Throughout, we compare the use of two different tractography streamline node assignment strategies and find that the overall differences between tractography approaches are small relative to the differences between tractography- and tracer-derived graphs. These analyses help quantify geometric biases inherent to tractography and promote the use of geometric benchmarking in future tractography validation efforts.

Brain rhythms define distinct interaction networks with differential dependence on anatomy

Cognitive functions are subserved by rhythmic neuronal synchronization across widely distributed brain areas. In 105 area pairs, we investigated functional connectivity (FC) through coherence, power correlation, and Granger causality (GC) in the theta, beta, high-beta, and gamma rhythms. Between rhythms, spatial FC patterns were largely independent. Thus, the rhythms defined distinct interaction networks. Importantly, networks of coherence and GC were not explained by the spatial distributions of the strengths of the rhythms. Those networks, particularly the GC networks, contained clear modules, with typically one dominant rhythm per module. To understand how this distinctiveness and modularity arises on a common anatomical backbone, we correlated, across 91 area pairs, the metrics of functional interaction with those of anatomical projection strength. Anatomy was primarily related to coherence and GC, with the largest effect sizes for GC. The correlation differed markedly between rhythms, being less pronounced for the beta and strongest for the gamma rhythm.

Dynamic reconfiguration of macaque brain networks during natural vision

Natural vision engages a wide range of higher-level regions that integrate visual information over the large-scale brain network. How interareal connectivity reconfigures during the processing of ongoing natural visual scenes and how these dynamic functional changes relate to the underlaying anatomical links between regions is not well understood. Here, we hypothesized that macaque visual brain regions are poly-functional sharing the capacity to change their configuration state depending on the nature of visual input. To address this hypothesis, we reconstructed networks from in-vivo diffusion-weighted imaging (DWI) and functional magnetic resonance imaging (fMRI) data obtained in four alert macaque monkeys viewing naturalistic movie scenes. At first, we characterized network properties and found greater interhemispheric density and greater inter-subject variability in free-viewing networks as compared to structural networks. From the structural connectivity, we then captured modules on which we identified hubs during free-viewing that formed a widespread visuo-saccadic network across frontal (FEF, 46v), parietal (LIP, Tpt), and occipitotemporal modules (MT, V4, TEm), and that excluded primary visual cortex. Inter-subject variability of well-connected hubs reflected subject-specific configurations that largely recruited occipito-parietal and frontal modules. Across the cerebral hemispheres, free-viewing networks showed higher correlations among long-distance brain regions as compared to structural networks. From these findings, we hypothesized that long-distance interareal connectivity could reconfigure depending on the ongoing changes in visual scenes. Testing this hypothesis by applying temporally resolved functional connectivity we observed that many structurally defined areas (such as areas V4, MT/MST and LIP) were poly-functional as they were recruited as hub members of multiple network states that changed during the presentation of scenes containing objects, motion, faces, and actions. We suggest that functional flexibility in macaque macroscale brain networks is required for the efficient interareal communication during active natural vision. To further promote the use of naturalistic free-viewing paradigms and increase the development of macaque neuroimaging resources, we share our datasets in the PRIME-DE consortium.

Where the genome meets the connectome: Understanding how genes shape human brain connectivity

The integration of modern neuroimaging methods with genetically informative designs and data can shed light on the molecular mechanisms underlying the structural and functional organization of the human connectome. Here, we review studies that have investigated the genetic basis of human brain network structure and function through three complementary frameworks: (1) the quantification of phenotypic heritability through classical twin designs; (2) the identification of specific DNA variants linked to phenotypic variation through association and related studies; and (3) the analysis of correlations between spatial variations in imaging phenotypes and gene expression profiles through the integration of neuroimaging and transcriptional atlas data. We consider the basic foundations, strengths, limitations, and discoveries associated with each approach. We present converging evidence to indicate that anatomical connectivity is under stronger genetic influence than functional connectivity and that genetic influences are not uniformly distributed throughout the brain, with phenotypic variation in certain regions and connections being under stronger genetic control than others. We also consider how the combination of imaging and genetics can be used to understand the ways in which genes may drive brain dysfunction in different clinical disorders.

Anatomical and functional connectomes underlying hierarchical visual processing in mouse visual system

Over the last 10 years, there has been a surge in interest in the rodent visual system resulting from the discovery of visual processing functions shared with primates V1, and of a complex anatomical structure in the extrastriate visual cortex. This surprisingly intricate visual system was elucidated by recent investigations using rapidly growing genetic tools primarily available in the mouse. Here, we examine the structural and functional connections of visual areas that have been identified in mice mostly during the past decade, and the impact of these findings on our understanding of brain functions associated with vision. Special attention is paid to structure-function relationships arising from the hierarchical organization, which is a prominent feature of the primate visual system. Recent evidence supports the existence of a hierarchical organization in rodents that contains levels that are poorly resolved relative to those observed in primates. This shallowness of the hierarchy indicates that the mouse visual system incorporates abundant non-hierarchical processing. Thus, the mouse visual system provides a unique opportunity to study non-hierarchical processing and its relation to hierarchical processing.

Standardizing workflows in imaging transcriptomics with the abagen toolbox

Gene expression fundamentally shapes the structural and functional architecture of the human brain. Open-access transcriptomic datasets like the Allen Human Brain Atlas provide an unprecedented ability to examine these mechanisms in vivo; however, a lack of standardization across research groups has given rise to myriad processing pipelines for using these data. Here, we develop the abagen toolbox, an open-access software package for working with transcriptomic data, and use it to examine how methodological variability influences the outcomes of research using the Allen Human Brain Atlas. Applying three prototypical analyses to the outputs of 750,000 unique processing pipelines, we find that choice of pipeline has a large impact on research findings, with parameters commonly varied in the literature influencing correlations between derived gene expression and other imaging phenotypes by as much as ρ ≥ 1.0. Our results further reveal an ordering of parameter importance, with processing steps that influence gene normalization yielding the greatest impact on downstream statistical inferences and conclusions. The presented work and the development of the abagen toolbox lay the foundation for more standardized and systematic research in imaging transcriptomics, and will help to advance future understanding of the influence of gene expression in the human brain.

Rare long-range cortical connections enhance human information processing

What are the key topological features of connectivity critically relevant for generating the dynamics underlying efficient cortical function? A candidate feature that has recently emerged is that the connectivity of the mammalian cortex follows an exponential distance rule, which includes a small proportion of long-range high-weight anatomical exceptions to this rule. Whole-brain modeling of large-scale human neuroimaging data in 1,003 participants offers the unique opportunity to create two models, with and without long-range exceptions, and explicitly study their functional consequences. We found that rare long-range exceptions are crucial for significantly improving information processing. Furthermore, modeling in a simplified ring architecture shows that this improvement is greatly enhanced by the turbulent regime found in empirical neuroimaging data. Overall, the results provide strong empirical evidence for the immense functional benefits of long-range exceptions combined with turbulence for information processing.

Profiling Transcription Initiation in Peripheral Leukocytes Reveals Severity-Associated Cis-Regulatory Elements in Critical COVID-19

The contribution of transcription factors (TFs) and gene regulatory programs in the immune response to COVID-19 and their relationship to disease outcome is not fully understood. Analysis of genome-wide changes in transcription at both promoter-proximal and distal cis-regulatory DNA elements, collectively termed the 'active cistrome,' offers an unbiased assessment of TF activity identifying key pathways regulated in homeostasis or disease. Here, we profiled the active cistrome from peripheral leukocytes of critically ill COVID-19 patients to identify major regulatory programs and their dynamics during SARS-CoV-2 associated acute respiratory distress syndrome (ARDS). We identified TF motifs that track the severity of COVID- 19 lung injury, disease resolution, and outcome. We used unbiased clustering to reveal distinct cistrome subsets delineating the regulation of pathways, cell types, and the combinatorial activity of TFs. We found critical roles for regulatory networks driven by stimulus and lineage determining TFs, showing that STAT and E2F/MYB regulatory programs targeting myeloid cells are activated in patients with poor disease outcomes and associated with single nucleotide genetic variants implicated in COVID-19 susceptibility. Integration with single-cell RNA-seq found that STAT and E2F/MYB activation converged in specific neutrophils subset found in patients with severe disease. Collectively we demonstrate that cistrome analysis facilitates insight into disease mechanisms and provides an unbiased approach to evaluate global changes in transcription factor activity and stratify patient disease severity.

Structural Attributes and Principles of the Neocortical Connectome in the Marmoset Monkey

The marmoset monkey has become an important primate model in Neuroscience. Here, we characterize salient statistical properties of interareal connections of the marmoset cerebral cortex, using data from retrograde tracer injections. We found that the connectivity weights are highly heterogeneous, spanning 5 orders of magnitude, and are log-normally distributed. The cortico-cortical network is dense, heterogeneous and has high specificity. The reciprocal connections are the most prominent and the probability of connection between 2 areas decays with their functional dissimilarity. The laminar dependence of connections defines a hierarchical network correlated with microstructural properties of each area. The marmoset connectome reveals parallel streams associated with different sensory systems. Finally, the connectome is spatially embedded with a characteristic length that obeys a power law as a function of brain volume across rodent and primate species. These findings provide a connectomic basis for investigations of multiple interacting areas in a complex large-scale cortical system underlying cognitive processes.

Genetic influences on hub connectivity of the human connectome

Brain network hubs are both highly connected and highly inter-connected, forming a critical communication backbone for coherent neural dynamics. The mechanisms driving this organization are poorly understood. Using diffusion-weighted magnetic resonance imaging in twins, we identify a major role for genes, showing that they preferentially influence connectivity strength between network hubs of the human connectome. Using transcriptomic atlas data, we show that connected hubs demonstrate tight coupling of transcriptional activity related to metabolic and cytoarchitectonic similarity. Finally, comparing over thirteen generative models of network growth, we show that purely stochastic processes cannot explain the precise wiring patterns of hubs, and that model performance can be improved by incorporating genetic constraints. Our findings indicate that genes play a strong and preferential role in shaping the functionally valuable, metabolically costly connections between connectome hubs.

Constructing graphs from genetic encodings

Our understanding of real-world connected systems has benefited from studying their evolution, from random wirings and rewirings to growth-dependent topologies. Long overlooked in this search has been the role of the innate: networks that connect based on identity-dependent compatibility rules. Inspired by the genetic principles that guide brain connectivity, we derive a network encoding process that can utilize wiring rules to reproducibly generate specific topologies. To illustrate the representational power of this approach, we propose stochastic and deterministic processes for generating a wide range of network topologies. Specifically, we detail network heuristics that generate structured graphs, such as feed-forward and hierarchical networks. In addition, we characterize a Random Genetic (RG) family of networks, which, like Erdős-Rényi graphs, display critical phase transitions, however their modular underpinnings lead to markedly different behaviors under targeted attacks. The proposed framework provides a relevant null-model for social and biological systems, where diverse metrics of identity underpin a node's preferred connectivity.

Ring vaccination strategy in networks: A mixed percolation approach

Ring vaccination is a mitigation strategy that consists in seeking and vaccinating the contacts of a sick patient, in order to provide immunization and halt the spread of disease. We study an extension of the susceptible-infected-recovered (SIR) epidemic model with ring vaccination in complex and spatial networks. Previously, a correspondence between this model and a link percolation process has been established, however, this is only valid in complex networks. Here, we propose that the SIR model with ring vaccination is equivalent to a mixed percolation process of links and nodes, which offers a more complete description of the process. We verify that this approach is valid in both complex and spatial networks, the latter being built according to the Waxman model. This model establishes a distance-dependent cost of connection between individuals arranged in a square lattice. We determine the epidemic-free regions in a phase diagram based on the wiring cost and the parameters of the epidemic model (vaccination and infection probabilities and recovery time). In addition, we find that for long recovery times this model maps into a pure node percolation process, in contrast to the SIR model without ring vaccination, which maps into link percolation.