A unified framework for simplicial Kuramoto models.

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: "simple" models, "Hodge-coupled" models, and "order-coupled" (Dirac) models. Our framework is based on topology and discrete differential geometry, as well as gradient systems and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.

Hyper-cores promote localization and efficient seeding in higher-order processes.

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.

Convolutional neural networks for vision neuroscience: significance, developments, and outstanding issues.

Convolutional Neural Networks (CNN) are a class of machine learning models predominately used in computer vision tasks and can achieve human-like performance through learning from experience. Their striking similarities to the structural and functional principles of the primate visual system allow for comparisons between these artificial networks and their biological counterparts, enabling exploration of how visual functions and neural representations may emerge in the real brain from a limited set of computational principles. After considering the basic features of CNNs, we discuss the opportunities and challenges of endorsing CNNs as in silico models of the primate visual system. Specifically, we highlight several emerging notions about the anatomical and physiological properties of the visual system that still need to be systematically integrated into current CNN models. These tenets include the implementation of parallel processing pathways from the early stages of retinal input and the reconsideration of several assumptions concerning the serial progression of information flow. We suggest design choices and architectural constraints that could facilitate a closer alignment with biology provide causal evidence of the predictive link between the artificial and biological visual systems. Adopting this principled perspective could potentially lead to new research questions and applications of CNNs beyond modeling object recognition.

Hi-Fi fMRI: High-resolution, fast-sampled and sub-second whole-brain functional MRI at 3T in humans.

Functional magnetic resonance imaging (fMRI) is a methodological cornerstone of neuroscience. Most studies measure blood-oxygen-level-dependent (BOLD) signal using echo-planar imaging (EPI), Cartesian sampling, and image reconstruction with a one-to-one correspondence between the number of acquired volumes and reconstructed images. However, EPI schemes are subject to trade-offs between spatial and temporal resolutions. We overcome these limitations by measuring BOLD with a gradient recalled echo (GRE) with 3D radial-spiral phyllotaxis trajectory at a high sampling rate (28.24ms) on standard 3T field-strength. The framework enables the reconstruction of 3D signal time courses with whole-brain coverage at simultaneously higher spatial (1mm 3 ) and temporal (up to 250ms) resolutions, as compared to optimized EPI schemes. Additionally, artifacts are corrected before image reconstruction; the desired temporal resolution is chosen after scanning and without assumptions on the shape of the hemodynamic response. By showing activation in the calcarine sulcus of 20 participants performing an ON-OFF visual paradigm, we demonstrate the reliability of our method for cognitive neuroscience research.

Social and asocial learning in zebrafish are encoded by a shared brain network that is differentially modulated by local activation.

Group living animals use social and asocial cues to predict the presence of reward or punishment in the environment through associative learning. The degree to which social and asocial learning share the same mechanisms is still a matter of debate. We have used a classical conditioning paradigm in zebrafish, in which a social (fish image) or an asocial (circle image) conditioned stimulus (CS) have been paired with an unconditioned stimulus (US=food), and we have used the expression of the immediate early gene c-fos to map the neural circuits associated with each learning type. Our results show that the learning performance is similar to social and asocial CSs. However, the brain regions activated in each learning type are distinct and a community analysis of brain network data reveals segregated functional submodules, which seem to be associated with different cognitive functions involved in the learning tasks. These results suggest that, despite localized differences in brain activity between social and asocial learning, they share a common learning module and social learning also recruits a specific social stimulus integration module. Therefore, our results support the occurrence of a common general-purpose learning module, that is differentially modulated by localized activation in social and asocial learning.

Multistability, intermittency, and hybrid transitions in social contagion models on hypergraphs.

Although ubiquitous, interactions in groups of individuals are not yet thoroughly studied. Frequently, single groups are modeled as critical-mass dynamics, which is a widespread concept used not only by academics but also by politicians and the media. However, less explored questions are how a collection of groups will behave and how their intersection might change the dynamics. Here, we formulate this process as binary-state dynamics on hypergraphs. We showed that our model has a rich behavior beyond discontinuous transitions. Notably, we have multistability and intermittency. We demonstrated that this phenomenology could be associated with community structures, where we might have multistability or intermittency by controlling the number or size of bridges between communities. Furthermore, we provided evidence that the observed transitions are hybrid. Our findings open new paths for research, ranging from physics, on the formal calculation of quantities of interest, to social sciences, where new experiments can be designed.

Evolutionarily conserved role of oxytocin in social fear contagion in zebrafish.

Emotional contagion is the most ancestral form of empathy. We tested to what extent the proximate mechanisms of emotional contagion are evolutionarily conserved by assessing the role of oxytocin, known to regulate empathic behaviors in mammals, in social fear contagion in zebrafish. Using oxytocin and oxytocin receptor mutants, we show that oxytocin is both necessary and sufficient for observer zebrafish to imitate the distressed behavior of conspecific demonstrators. The brain regions associated with emotional contagion in zebrafish are homologous to those involved in the same process in rodents (e.g., striatum, lateral septum), receiving direct projections from oxytocinergic neurons located in the pre-optic area. Together, our results support an evolutionary conserved role for oxytocin as a key regulator of basic empathic behaviors across vertebrates.

Homological landscape of human brain functional sub-circuits.

Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional sub-circuits have yet to be addressed. To that end, we proposed a homological formalism that enables the quantification of higher-order characteristics of human brain functional sub-circuits. Our results indicated that each homological order uniquely unravels diverse, complementary properties of human brain functional sub-circuits. Noticeably, the H1 homological distance between rest and motor task were observed at both whole-brain and sub-circuit consolidated level which suggested the self-similarity property of human brain functional connectivity unraveled by homological kernel. Furthermore, at the whole-brain level, the rest-task differentiation was found to be most prominent between rest and different tasks at different homological orders: i) Emotion task H0, ii) Motor task H1, and iii) Working memory task H2. At the functional sub-circuit level, the rest-task functional dichotomy of default mode network is found to be mostly prominent at the first and second homological scaffolds. Also at such scale, we found that the limbic network plays a significant role in homological reconfiguration across both task- and subject- domain which sheds light to subsequent Investigations on the complex neuro-physiological role of such network. From a wider perspective, our formalism can be applied, beyond brain connectomics, to study non-localized coordination patterns of localized structures stretching across complex network fibers.

Toward understanding the communication in sperm whales.

Machine learning has been advancing dramatically over the past decade. Most strides are human-based applications due to the availability of large-scale datasets; however, opportunities are ripe to apply this technology to more deeply understand non-human communication. We detail a scientific roadmap for advancing the understanding of communication of whales that can be built further upon as a template to decipher other forms of animal and non-human communication. Sperm whales, with their highly developed neuroanatomical features, cognitive abilities, social structures, and discrete click-based encoding make for an excellent model for advanced tools that can be applied to other animals in the future. We outline the key elements required for the collection and processing of massive datasets, detecting basic communication units and language-like higher-level structures, and validating models through interactive playback experiments. The technological capabilities developed by such an undertaking hold potential for cross-applications in broader communities investigating non-human communication and behavioral research.

Sex Differences in Aggression Are Paralleled by Differential Activation of the Brain Social Decision-Making Network in Zebrafish.

Although aggression is more prevalent in males, females also express aggressive behaviors and in specific ecological contexts females can be more aggressive than males. The aim of this work is to assess sex differences in aggression and to characterize the patterns of neuronal activation of the social-decision making network (SDMN) in response to intra-sexual aggression in both male and female zebrafish. Adult fish were exposed to social interaction with a same-sex opponent and all behavioral displays, latency, and time of resolution were quantified. After conflict resolution, brains were sampled and sex differences on functional connectivity throughout the SDMN were assessed by immunofluorescence of the neuronal activation marker pS6. Results suggest that both sexes share a similar level of motivation for aggression, but female encounters show shorter conflict resolution and a preferential use of antiparallel displays instead of overt aggression, showing a reduction of putative maladaptive effects. Although there are no sex differences in the neuronal activation in any individual brain area from the SDMN, agonistic interactions increased neuronal activity in most brain areas in both sexes. Functional connectivity was assessed using bootstrapped adjacency matrices that capture the co-activation of the SDMN nodes. Male winners increased the overall excitation and showed no changes in inhibition across the SDMN, whereas female winners and both male and female losers showed a decrease in both excitation and inhibition of the SDMN in comparison to non-interacting control fish. Moreover, network centrality analysis revealed both shared hubs, as well as sex-specific hubs, between the sexes for each social condition in the SDMN. In summary, a distinct neural activation pattern associated with social experience during fights was found for each sex, suggesting a sex-specific differential activation of the social brain as a consequence of social experience. Overall, our study adds insights into sex differences in agonistic behavior and on the neuronal architecture of intrasexual aggression in zebrafish.

Topological Features of Electroencephalography are Robust to Re-referencing and Preprocessing.

Electroencephalography (EEG) is among the most widely diffused, inexpensive, and adopted neuroimaging techniques. Nonetheless, EEG requires measurements against a reference site(s), which is typically chosen by the experimenter, and specific pre-processing steps precede analyses. It is therefore valuable to obtain quantities that are minimally affected by reference and pre-processing choices. Here, we show that the topological structure of embedding spaces, constructed either from multi-channel EEG timeseries or from their temporal structure, are subject-specific and robust to re-referencing and pre-processing pipelines. By contrast, the shape of correlation spaces, that is, discrete spaces where each point represents an electrode and the distance between them that is in turn related to the correlation between the respective timeseries, was neither significantly subject-specific nor robust to changes of reference. Our results suggest that the shape of spaces describing the observed configurations of EEG signals holds information about the individual specificity of the underlying individual's brain dynamics, and that temporal correlations constrain to a large degree the set of possible dynamics. In turn, these encode the differences between subjects' space of resting state EEG signals. Finally, our results and proposed methodology provide tools to explore the individual topographical landscapes and how they are explored dynamically. We propose therefore to augment conventional topographic analyses with an additional-topological-level of analysis, and to consider them jointly. More generally, these results provide a roadmap for the incorporation of topological analyses within EEG pipelines.

Developmental Effects of Oxytocin Neurons on Social Affiliation and Processing of Social Information.

Hormones regulate behavior either through activational effects that facilitate the acute expression of specific behaviors or through organizational effects that shape the development of the nervous system thereby altering adult behavior. Much research has implicated the neuropeptide oxytocin (OXT) in acute modulation of various aspects of social behaviors across vertebrate species, and OXT signaling is associated with the developmental social deficits observed in autism spectrum disorders (ASDs); however, little is known about the role of OXT in the neurodevelopment of the social brain. We show that perturbation of OXT neurons during early zebrafish development led to a loss of dopaminergic neurons, associated with visual processing and reward, and blunted the neuronal response to social stimuli in the adult brain. Ultimately, adult fish whose OXT neurons were ablated in early life, displayed altered functional connectivity within social decision-making brain nuclei both in naive state and in response to social stimulus and became less social. We propose that OXT neurons have an organizational role, namely, to shape forebrain neuroarchitecture during development and to acquire an affiliative response toward conspecifics.SIGNIFICANCE STATEMENT Social behavior is developed over the lifetime of an organism and the neuropeptide oxytocin (OXT) modulates social behaviors across vertebrate species, and is associated with neuro-developmental social deficits such as autism. However, whether OXT plays a role in the developmental maturation of neural systems that are necessary for social behavior remains poorly explored. We show that proper behavioral and neural response to social stimuli depends on a developmental process orchestrated by OXT neurons. Animals whose OXT system is ablated in early life show blunted neuronal and behavioral responses to social stimuli as well as wide ranging disruptions in the functional connectivity of the social brain. We provide a window into the mechanisms underlying OXT-dependent developmental processes that implement adult sociality.

Simplicial and topological descriptions of human brain dynamics.

While brain imaging tools like functional magnetic resonance imaging (fMRI) afford measurements of whole-brain activity, it remains unclear how best to interpret patterns found amid the data's apparent self-organization. To clarify how patterns of brain activity support brain function, one might identify metric spaces that optimally distinguish brain states across experimentally defined conditions. Therefore, the present study considers the relative capacities of several metric spaces to disambiguate experimentally defined brain states. One fundamental metric space interprets fMRI data topographically, that is, as the vector of amplitudes of a multivariate signal, changing with time. Another perspective compares the brain's functional connectivity, that is, the similarity matrix computed between signals from different brain regions. More recently, metric spaces that consider the data's topology have become available. Such methods treat data as a sample drawn from an abstract geometric object. To recover the structure of that object, topological data analysis detects features that are invariant under continuous deformations (such as coordinate rotation and nodal misalignment). Moreover, the methods explicitly consider features that persist across multiple geometric scales. While, certainly, there are strengths and weaknesses of each brain dynamics metric space, wefind that those that track topological features optimally distinguish experimentally defined brain states.

Homological scaffold via minimal homology bases.

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.

Editorial: Topological Neuroscience.

Topology, in its many forms, describes relations. It has thus long been a central concept in neuroscience, capturing structural and functional aspects of the organization of the nervous system and their links to cognition. Recent advances in computational topology have extended the breadth and depth of topological descriptions. This Focus Feature offers a unified overview of the emerging field of topological neuroscience and of its applications across the many scales of the nervous system from macro-, over meso-, to microscales.

Topological gene expression networks recapitulate brain anatomy and function.

Understanding how gene expression translates to and affects human behavior is one of the ultimate goals of neuroscience. In this paper, we present a pipeline based on Mapper, a topological simplification tool, to analyze gene co-expression data. We first validate the method by reproducing key results from the literature on the Allen Human Brain Atlas and the correlations between resting-state fMRI and gene co-expression maps. We then analyze a dopamine-related gene set and find that co-expression networks produced by Mapper return a structure that matches the well-known anatomy of the dopaminergic pathway. Our results suggest that network based descriptions can be a powerful tool to explore the relationships between genetic pathways and their association with brain function and its perturbation due to illness and/or pharmacological challenges.

Generating dynamical neuroimaging spatiotemporal representations (DyNeuSR) using topological data analysis.

In this article, we present an open source neuroinformatics platform for exploring, analyzing, and validating distilled graphical representations of high-dimensional neuroimaging data extracted using topological data analysis (TDA). TDA techniques like Mapper have been recently applied to examine the brain's dynamical organization during ongoing cognition without averaging data in space, in time, or across participants at the outset. Such TDA-based approaches mark an important deviation from standard neuroimaging analyses by distilling complex high-dimensional neuroimaging data into simple-yet neurophysiologically valid and behaviorally relevant-representations that can be interactively explored at the single-participant level. To facilitate wider use of such techniques within neuroimaging and general neuroscience communities, our work provides several tools for visualizing, interacting with, and grounding TDA-generated graphical representations in neurophysiology. Through Python-based Jupyter notebooks and open datasets, we provide a platform to assess and visualize different intermittent stages of Mapper and examine the influence of Mapper parameters on the generated representations. We hope this platform could enable researchers and clinicians alike to explore topological representations of neuroimaging data and generate biological insights underlying complex mental disorders.

Topology highlights mesoscopic functional equivalence between imagery and perception: The case of hypnotizability.

The functional equivalence (FE) between imagery and perception or motion has been proposed on the basis of neuroimaging evidence of large spatially overlapping activations between real and imagined sensori-motor conditions. However, similar local activation patterns do not imply the same mesoscopic integration of brain regions, which can be described by tools from Topological Data Analysis (TDA). On the basis of behavioral findings, stronger FE has been hypothesized in the individuals with high scores of hypnotizability scores (highs) with respect to low hypnotizable participants (lows) who differ between each other in the proneness to modify memory, perception and behavior according to specific imaginative suggestions. Here we present the first EEG evidence of stronger FE in highs. In fact, persistent homology shows that the highs EEG topological asset during real and imagined sensory conditions is significantly more similar than the lows. As a corollary finding, persistent homology shows lower restructuring of the EEG asset in highs than in lows during both sensory and imagery tasks with respect to basal conditions. Present findings support the view that greater embodiment of mental images may be responsible for the highs greater proneness to respond to sensori-motor suggestions and to report involuntariness in action. In addition, findings indicate hypnotizability-related sensory and cognitive information processing and suggest that the psycho-physiological trait of hypnotizability may modulate more than one aspect of the everyday life.

Simplicial models of social contagion.

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.

Spectral and topological analyses of the cortical representation of the head position: Does hypnotizability matter?

INTRODUCTION: The aim of this exploratory study was to assess the EEG correlates of head positions (which have never been studied in humans) in participants with different psychophysiological characteristics, as encoded by their hypnotizability scores. This choice is motivated by earlier studies suggesting different processing of vestibular/neck proprioceptive information in subjects with high (highs) and low (lows) hypnotizability scores maintaining their head rotated toward one side (RH). METHODS: We analyzed EEG signals recorded in 20 highs and 19 lows in basal conditions (head forward) and during RH using spectral analysis, which captures changes localized to specific recording sites, and topological data analysis (TDA), which instead describes large-scale differences in processing and representing sensorimotor information. RESULTS: Spectral analysis revealed significant differences related to head position for alpha 1, beta 2, beta 3, and gamma bands, but not to hypnotizability. TDA instead revealed global hypnotizability-related differences in the strengths of the correlations among recording sites during RH. Significant changes were observed in lows on the left parieto-occipital side and in highs in right frontoparietal region. Significant differences between the two groups were found in the occipital region, where changes were larger in lows than in highs. CONCLUSIONS: This study reports finding of the EEG correlates of changes in the head posture for the first time, indicating that hypnotizability is related to the head posture representation/processing on large-scale networks and that spectral and topological data analyses provide complementary results.