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

NaDyNet: A toolbox for dynamic network analysis of naturalistic stimuli

Experiments with naturalistic stimuli (e.g., listening to stories or watching movies) are emerging paradigms in brain function research. The content of naturalistic stimuli is rich and continuous. The fMRI signals of naturalistic stimuli are complex and include different components. A major challenge is isolate the stimuli-induced signals while simultaneously tracking the brain's responses to these stimuli in real-time. To this end, we have developed a user-friendly graphical interface toolbox called NaDyNet (Naturalistic Dynamic Network Toolbox), which integrates existing dynamic brain network analysis methods and their improved versions. The main features of NaDyNet are: 1) extracting signals of interest from naturalistic fMRI signals; 2) incorporating six commonly used dynamic analysis methods and three static analysis methods; 3) improved versions of these dynamic methods by adopting inter-subject analysis to eliminate the effects of non-interest signals; 4) performing K-means clustering analysis to identify temporally reoccurring states along with their temporal and spatial attributes; 5) Visualization of spatiotemporal results. We then introduced the rationale for incorporating inter-subject analysis to improve existing dynamic brain network analysis methods and presented examples by analyzing naturalistic fMRI data. We hope that this toolbox will promote the development of naturalistic neuroscience. The toolbox is available at https://github.com/yuanbinke/Naturalistic-Dynamic-Network-Toolbox.

Comparative analysis of Ball Mapper and conventional Mapper in investigating air pollutants' behavior

This study investigates the effectiveness and efficiency of two topological data analysis (TDA) techniques, the conventional Mapper (CM) and its variant version, the Ball Mapper (BM), in analyzing the behavior of six major air pollutants (NO2, PM10, PM2.5, O3, CO, and SO2) across 60 air quality monitoring stations in Malaysia. Topological graphs produced by CM and BM reveal redundant monitoring stations and geographical relationships corresponding to air pollutant behavior, providing better visualization than traditional hierarchical clustering. Additionally, a comparative analysis of topological graph structures was conducted using node degree distribution, topological graph indices, and Dynamic Time Warping (DTW) to evaluate the sensitivity and performance of these TDA techniques. Both approaches yielded valuable insights in representing the air quality monitoring stations network; however, the complexity of CM, which requires multiple parameters, poses a challenge in graph construction. In contrast, the simplicity of BM, requiring only a single parameter, is preferable for representing air pollutant behavior. The findings suggest an alternative approach for assessing and identifying redundancies in air quality monitoring stations, which could contribute to improved air quality monitoring management and more effective regulatory policies.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from topological data analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of topological data analysis, Mapper results are highly impacted by parameter selection. Given that noninvasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding "true" state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper to any dataset.

The topology and geometry of neural representations

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here, we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis, an extension of representational similarity analysis that uses a family of geotopological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Psilocybin enhances insightfulness in meditation: a perspective on the global topology of brain imaging during meditation

In this study, for the first time, we explored a dataset of functional magnetic resonance images collected during focused attention and open monitoring meditation before and after a five-day psilocybin-assisted meditation retreat using a recently established approach, based on the Mapper algorithm from topological data analysis. After generating subject-specific maps for two groups (psilocybin vs. placebo, 18 subjects/group) of experienced meditators, organizational principles were uncovered using graph topological tools, including the optimal transport (OT) distance, a geometrically rich measure of similarity between brain activity patterns. This revealed characteristics of the topology (i.e. shape) in space (i.e. abstract space of voxels) and time dimension of whole-brain activity patterns during different styles of meditation and psilocybin-induced alterations. Most interestingly, we found that (psilocybin-induced) positive derealization, which fosters insightfulness specifically when accompanied by enhanced open-monitoring meditation, was linked to the OT distance between open-monitoring and resting state. Our findings suggest that enhanced meta-awareness through meditation practice in experienced meditators combined with potential psilocybin-induced positive alterations in perception mediate insightfulness. Together, these findings provide a novel perspective on meditation and psychedelics that may reveal potential novel brain markers for positive synergistic effects between mindfulness practices and psilocybin.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

Capturing and tracking large-scale brain activity dynamics holds the potential to deepen our understanding of cognition. Previously, tools from Topological Data Analysis, especially Mapper, have been successfully used to mine brain activity dynamics at the highest spatiotemporal resolutions. Even though it is a relatively established tool within the field of Topological Data Analysis, Mapper results are highly impacted by parameter selection. Given that non-invasive human neuroimaging data (e.g., from fMRI) is typically fraught with artifacts and no gold standards exist regarding "true" state transitions, we argue for a thorough examination of Mapper parameter choices to better reveal their impact. Using synthetic data (with known transition structure) and real fMRI data, we explore a variety of parameter choices for each Mapper step, thereby providing guidance and heuristics for the field. We also release our parameter-exploration toolbox as a software package to make it easier for scientists to investigate and apply Mapper on any dataset.

Tree representations of brain structural connectivity via persistent homology

The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the structural connectome varies across individuals in relation to their traits, ranging from age and gender to neuropsychiatric outcomes. After applying tractography to dMRI to get white matter fiber bundles, a key question is how to represent the brain connectome to facilitate statistical analyses relating connectomes to traits. The current standard divides the brain into regions of interest (ROIs), and then relies on an adjacency matrix (AM) representation. Each cell in the AM is a measure of connectivity, e.g., number of fiber curves, between a pair of ROIs. Although the AM representation is intuitive, a disadvantage is the high-dimensionality due to the large number of cells in the matrix. This article proposes a simpler tree representation of the brain connectome, which is motivated by ideas in computational topology and takes topological and biological information on the cortical surface into consideration. We demonstrate that our tree representation preserves useful information and interpretability, while reducing dimensionality to improve statistical and computational efficiency. Applications to data from the Human Connectome Project (HCP) are considered and code is provided for reproducing our analyses.

Brain mitochondrial diversity and network organization predict anxiety-like behavior in male mice

The brain and behavior are under energetic constraints, limited by mitochondrial energy transformation capacity. However, the mitochondria-behavior relationship has not been systematically studied at a brain-wide scale. Here we examined the association between multiple features of mitochondrial respiratory chain capacity and stress-related behaviors in male mice with diverse behavioral phenotypes. Miniaturized assays of mitochondrial respiratory chain enzyme activities and mitochondrial DNA (mtDNA) content were deployed on 571 samples across 17 brain areas, defining specific patterns of mito-behavior associations. By applying multi-slice network analysis to our brain-wide mitochondrial dataset, we identified three large-scale networks of brain areas with shared mitochondrial signatures. A major network composed of cortico-striatal areas exhibited the strongest mitochondria-behavior correlations, accounting for up to 50% of animal-to-animal behavioral differences, suggesting that this mito-based network is functionally significant. The mito-based brain networks also overlapped with regional gene expression and structural connectivity, and exhibited distinct molecular mitochondrial phenotype signatures. This work provides convergent multimodal evidence anchored in enzyme activities, gene expression, and animal behavior that distinct, behaviorally-relevant mitochondrial phenotypes exist across the male mouse brain.

Low-frequency repetitive transcranial magnetic stimulation alters the individual functional dynamical landscape

Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive approach to modulate brain activity and behavior in humans. Still, how individual resting-state brain dynamics after rTMS evolves across different functional configurations is rarely studied. Here, using resting state fMRI data from healthy subjects, we aimed to examine the effects of rTMS to individual large-scale brain dynamics. Using Topological Data Analysis based Mapper approach, we construct the precise dynamic mapping (PDM) for each participant. To reveal the relationship between PDM and canonical functional representation of the resting brain, we annotated the graph using relative activation proportion of a set of large-scale resting-state networks (RSNs) and assigned the single brain volume to corresponding RSN-dominant or a hub state (not any RSN was dominant). Our results show that (i) low-frequency rTMS could induce changed temporal evolution of brain states; (ii) rTMS didn't alter the hub-periphery configurations underlined resting-state brain dynamics; and (iii) the rTMS effects on brain dynamics differ across the left frontal and occipital lobe. In conclusion, low-frequency rTMS significantly alters the individual temporo-spatial dynamics, and our finding further suggested a potential target-dependent alteration of brain dynamics. This work provides a new perspective to comprehend the heterogeneous effect of rTMS.

Topological data analysis for revealing dynamic brain reconfiguration in MEG data

In recent years, the focus of the functional connectivity community has shifted from stationary approaches to the ones that include temporal dynamics. Especially, non-invasive electrophysiological data (magnetoencephalography/electroencephalography (MEG/EEG)) with high temporal resolution and good spatial coverage have made it possible to measure the fast alterations in the neural activity in the brain during ongoing cognition. In this article, we analyze dynamic brain reconfiguration using MEG images collected from subjects during the rest and the cognitive tasks. Our proposed topological data analysis method, called Mapper, produces biomarkers that differentiate cognitive tasks without prior spatial and temporal collapse of the data. The suggested method provides an interactive visualization of the rapid fluctuations in electrophysiological data during motor and cognitive tasks; hence, it has the potential to extract clinically relevant information at an individual level without temporal and spatial collapse.

Temporal Mapper: Transition networks in simulated and real neural dynamics

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.

Neural resources shift under Methylphenidate: A computational approach to examine anxiety-cognition interplay

The reciprocal interplay between anxiety and cognition is well documented. Anxiety negatively impacts cognition, while cognitive engagement can down-regulate anxiety. The brain mechanisms and dynamics underlying such interplay are not fully understood. To study this question, we experimentally and orthogonally manipulated anxiety (using a threat of shock paradigm) and cognition (using methylphenidate; MPH). The effects of these manipulations on the brain and behavior were evaluated in 50 healthy participants (25 MPH, 25 placebo), using an n-back working memory fMRI task (with low and high load conditions). Behaviorally, improved response accuracy was observed as a main effect of the drug across all conditions. We employed two approaches to understand the neural mechanisms underlying MPH-based cognitive enhancement in safe and threat conditions. First, we performed a hypothesis-driven computational analysis using a mathematical framework to examine how MPH putatively affects cognitive enhancement in the face of induced anxiety across two levels of cognitive load. Second, we performed an exploratory data analysis using Topological Data Analysis (TDA)-based Mapper to examine changes in spatiotemporal brain activity across the entire cortex. Both approaches provided converging evidence that MPH facilitated greater differential engagement of neural resources (brain activity) across low and high working memory load conditions. Furthermore, load-based differential management of neural resources reflects enhanced efficiency that is most powerful during higher load and induced anxiety conditions. Overall, our results provide novel insights regarding brain mechanisms that facilitate cognitive enhancement under MPH and, in future research, may be used to help mitigate anxiety-related cognitive underperformance.

From calcium imaging to graph topology

Systems neuroscience is facing an ever-growing mountain of data. Recent advances in protein engineering and microscopy have together led to a paradigm shift in neuroscience; using fluorescence, we can now image the activity of every neuron through the whole brain of behaving animals. Even in larger organisms, the number of neurons that we can record simultaneously is increasing exponentially with time. This increase in the dimensionality of the data is being met with an explosion of computational and mathematical methods, each using disparate terminology, distinct approaches, and diverse mathematical concepts. Here we collect, organize, and explain multiple data analysis techniques that have been, or could be, applied to whole-brain imaging, using larval zebrafish as an example model. We begin with methods such as linear regression that are designed to detect relations between two variables. Next, we progress through network science and applied topological methods, which focus on the patterns of relations among many variables. Finally, we highlight the potential of generative models that could provide testable hypotheses on wiring rules and network progression through time, or disease progression. While we use examples of imaging from larval zebrafish, these approaches are suitable for any population-scale neural network modeling, and indeed, to applications beyond systems neuroscience. Computational approaches from network science and applied topology are not limited to larval zebrafish, or even to systems neuroscience, and we therefore conclude with a discussion of how such methods can be applied to diverse problems across the biological sciences.

Rosas F, A. M. Mediano P, Diez I, P. Swinnen S, Orio P, Cofré R, M. Cortes J. High-order functional redundancy in ageing explained via alterations in the connectome in a whole-brain model

The human brain generates a rich repertoire of spatio-temporal activity patterns, which support a wide variety of motor and cognitive functions. These patterns of activity change with age in a multi-factorial manner. One of these factors is the variations in the brain's connectomics that occurs along the lifespan. However, the precise relationship between high-order functional interactions and connnectomics, as well as their variations with age are largely unknown, in part due to the absence of mechanistic models that can efficiently map brain connnectomics to functional connectivity in aging. To investigate this issue, we have built a neurobiologically-realistic whole-brain computational model using both anatomical and functional MRI data from 161 participants ranging from 10 to 80 years old. We show that the differences in high-order functional interactions between age groups can be largely explained by variations in the connectome. Based on this finding, we propose a simple neurodegeneration model that is representative of normal physiological aging. As such, when applied to connectomes of young participant it reproduces the age-variations that occur in the high-order structure of the functional data. Overall, these results begin to disentangle the mechanisms by which structural changes in the connectome lead to functional differences in the ageing brain. Our model can also serve as a starting point for modeling more complex forms of pathological ageing or cognitive deficits.

Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest

In the absence of external stimuli, neural activity continuously evolves from one configuration to another. Whether these transitions or explorations follow some underlying arrangement or lack a predictable ordered plan remains to be determined. Here, using fMRI data from highly sampled individuals (~5 hours of resting-state data per individual), we aimed to reveal the rules that govern transitions in brain activity at rest. Our Topological Data Analysis based Mapper approach characterized a highly visited transition state of the brain that acts as a switch between different neural configurations to organize the spontaneous brain activity. Further, while the transition state was characterized by a uniform representation of canonical resting-state networks (RSNs), the periphery of the landscape was dominated by a subject-specific combination of RSNs. Altogether, we revealed rules or principles that organize spontaneous brain activity using a precision dynamics approach.

NeuMapper: A scalable computational framework for multiscale exploration of the brain's dynamical organization

For better translational outcomes, researchers and clinicians alike demand novel tools to distill complex neuroimaging data into simple yet behaviorally relevant representations at the single-participant level. Recently, the Mapper approach from topological data analysis (TDA) has been successfully applied on noninvasive human neuroimaging data to characterize the entire dynamical landscape of whole-brain configurations at the individual level without requiring any spatiotemporal averaging at the outset. Despite promising results, initial applications of Mapper to neuroimaging data were constrained by (1) the need for dimensionality reduction and (2) lack of a biologically grounded heuristic for efficiently exploring the vast parameter space. Here, we present a novel computational framework for Mapper-designed specifically for neuroimaging data-that removes limitations and reduces computational costs associated with dimensionality reduction and parameter exploration. We also introduce new meta-analytic approaches to better anchor Mapper-generated representations to neuroanatomy and behavior. Our new NeuMapper framework was developed and validated using multiple fMRI datasets where participants engaged in continuous multitask experiments that mimic "ongoing" cognition. Looking forward, we hope our framework will help researchers push the boundaries of psychiatric neuroimaging toward generating insights at the single-participant level across consortium-size datasets.

Embedding Functional Brain Networks in Low Dimensional Spaces Using Manifold Learning Techniques

Background: fMRI data is inherently high-dimensional and difficult to visualize. A recent trend has been to find spaces of lower dimensionality where functional brain networks can be projected onto manifolds as individual data points, leading to new ways to analyze and interpret the data. Here, we investigate the potential of two powerful non-linear manifold learning techniques for functional brain networks representation: (1) T-stochastic neighbor embedding (t-SNE) and (2) Uniform Manifold Approximation Projection (UMAP) a recent breakthrough in manifold learning. Methods: fMRI data from the Human Connectome Project (HCP) and an independent study of aging were used to generate functional brain networks. We used fMRI data collected during resting state data and during a working memory task. The relative performance of t-SNE and UMAP were investigated by projecting the networks from each study onto 2D manifolds. The levels of discrimination between different tasks and the preservation of the topology were evaluated using different metrics. Results: Both methods effectively discriminated the resting state from the memory task in the embedding space. UMAP discriminated with a higher classification accuracy. However, t-SNE appeared to better preserve the topology of the high-dimensional space. When networks from the HCP and aging studies were combined, the resting state and memory networks in general aligned correctly. Discussion: Our results suggest that UMAP, a more recent development in manifold learning, is an excellent tool to visualize functional brain networks. Despite dramatic differences in data collection and protocols, networks from different studies aligned correctly in the embedding space.

Spontaneous and deliberate modes of creativity: Multitask eigen-connectivity analysis captures latent cognitive modes during creative thinking

Despite substantial progress in the quest of demystifying the brain basis of creativity, several questions remain open. One such issue concerns the relationship between two latent cognitive modes during creative thinking, i.e., deliberate goal-directed cognition and spontaneous thought generation. Although an interplay between deliberate and spontaneous thinking is often implicated in the creativity literature (e.g., dual-process models), a bottom-up data-driven validation of the cognitive processes associated with creative thinking is still lacking. Here, we attempted to capture the latent modes of creative thinking by utilizing a data-driven approach on a novel continuous multitask paradigm (CMP) that widely sampled a hypothetical two-dimensional cognitive plane of deliberate and spontaneous thinking in a single fMRI session. The CMP consisted of eight task blocks ranging from undirected mind wandering to goal-directed working memory task, while also included two widely-used creativity tasks, i.e., alternate uses task (AUT) and remote association task (RAT). Using eigen-connectivity (EC) analysis on the multitask whole-brain functional connectivity (FC) patterns, we embedded the multitask FCs into a low-dimensional latent space. The first two latent components, as revealed by the EC analysis, broadly mapped onto the two cognitive modes of deliberate and spontaneous thinking, respectively. Further, in this low-dimensional space, both creativity tasks were located in the upper right corner of high deliberate and spontaneous thinking (creative cognitive space). Neuroanatomically, the creative cognitive space was represented by not only increased intra-network connectivity within executive control and default mode network, but also by higher coupling between the two canonical brain networks. Further, individual differences reflected in the low-dimensional connectivity embeddings were related to differences in deliberate and spontaneous thinking abilities. Altogether, using a continuous multitask paradigm and a data-driven approach, we provide initial empirical evidence for the contribution of both deliberate and spontaneous modes of cognition during creative thinking.

Cholinergic neuromodulation of inhibitory interneurons facilitates functional integration in whole-brain models

Segregation and integration are two fundamental principles of brain structural and functional organization. Neuroimaging studies have shown that the brain transits between different functionally segregated and integrated states, and neuromodulatory systems have been proposed as key to facilitate these transitions. Although whole-brain computational models have reproduced this neuromodulatory effect, the role of local inhibitory circuits and their cholinergic modulation has not been studied. In this article, we consider a Jansen & Rit whole-brain model in a network interconnected using a human connectome, and study the influence of the cholinergic and noradrenergic neuromodulatory systems on the segregation/integration balance. In our model, we introduce a local inhibitory feedback as a plausible biophysical mechanism that enables the integration of whole-brain activity, and that interacts with the other neuromodulatory influences to facilitate the transition between different functional segregation/integration regimes in the brain.

Interpreting Deep Learning Features for Myoelectric Control: A Comparison With Handcrafted Features

Existing research on myoelectric control systems primarily focuses on extracting discriminative characteristics of the electromyographic (EMG) signal by designing handcrafted features. Recently, however, deep learning techniques have been applied to the challenging task of EMG-based gesture recognition. The adoption of these techniques slowly shifts the focus from feature engineering to feature learning. Nevertheless, the black-box nature of deep learning makes it hard to understand the type of information learned by the network and how it relates to handcrafted features. Additionally, due to the high variability in EMG recordings between participants, deep features tend to generalize poorly across subjects using standard training methods. Consequently, this work introduces a new multi-domain learning algorithm, named ADANN (Adaptive Domain Adversarial Neural Network), which significantly enhances (p = 0.00004) inter-subject classification accuracy by an average of 19.40% compared to standard training. Using ADANN-generated features, this work provides the first topological data analysis of EMG-based gesture recognition for the characterization of the information encoded within a deep network, using handcrafted features as landmarks. This analysis reveals that handcrafted features and the learned features (in the earlier layers) both try to discriminate between all gestures, but do not encode the same information to do so. In the later layers, the learned features are inclined to instead adopt a one-vs.-all strategy for a given class. Furthermore, by using convolutional network visualization techniques, it is revealed that learned features actually tend to ignore the most activated channel during contraction, which is in stark contrast with the prevalence of handcrafted features designed to capture amplitude information. Overall, this work paves the way for hybrid feature sets by providing a clear guideline of complementary information encoded within learned and handcrafted features.

Metrics for graph comparison: A practitioner's guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.

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.