Topological Neuroscience
We study when brain activity is better described by interactions among groups of regions than by pairs, and what those descriptions reveal. Using topology and information theory, we measure higher-order structure, test when it adds information beyond pairwise connectivity, and keep apart what describes the data, what captures statistical dependence, and what reflects interacting mechanisms. Recent work follows the dynamics of naturalistic emotion, the brain hierarchy that supports blindsight, signatures of anesthesia and hypnosis, and how cortex reorganizes after sensory loss.
Papers 29
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Zaffina, L., Diano, M., Petruso, F., Preti, M. G., Amico, E., Morgenroth, E., Petri, G., Van De Ville, D., Vuilleumier, P. O., Santoro, A.
Emotions are thought to emerge from co-activation among distributed brain systems, yet traditional fMRI analyses typically examine localized responses and pairwise connections, potentially overlooking interactions among groups of regions. Here, we use time-resolved higher-order topology to characterize these group interactions during naturalistic viewing of 14 films totaling over 2.5 h, continuously annotated across 50 affective features. The homological scaffold, representing evolving group-level topology, most closely tracks recurrent emotional states and best predicts fine-grained affective profiles. This sensitivity diminishes when emotion is compressed into dimensions of valence, arousal, and power, where pairwise connectivity captures the dominant arousal signal. Across three independent datasets, arousal predictions transfer most robustly through pairwise connectivity, while the relative geometry of broad affective states remains conserved across film narratives despite poor valence generalization. These findings reveal complementary neural representations of emotion: higher-order topology captures fine-grained affective structure, whereas pairwise connectivity provides a portable readout of broad arousal.
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Lorenz, G. M., Engel, N. M., Koçillari, L., Celotto, M., Orsenigo, D., Curreli, S., Blanco Malerba, S., Engel, A. K., Kayser, C., Fellin, T., Luppi, A. I., Panzeri, S.
Partial information decomposition (PID) has emerged as a principled way to decompose the information carried by neural activity into components identifying whether interactions among neurons or brain areas generate synergistic or redundant information. Here, we demonstrate that empirical measures of synergy and redundancy based on either Gaussian or discrete probability estimators suffer from a substantial limited-sampling estimation bias. This bias is much larger for synergy than for redundancy. The gap between them increases with the number of parameters specifying the probability distributions. We develop procedures that effectively correct for the bias and provide rules of thumb for the sample sizes required to obtain unbiased estimates. We show that, when used on empirical brain datasets, they successfully remove large synergy biases across species, recording modalities, and experimental designs. Our bias corrections extend the range of neuroscience questions and experimental designs addressable with PID and allow accurate comparisons between synergy and redundancy.
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Dohnány, S., Jerotic, K., Orsenigo, D., Serra, E., Ali, H., Buhler, J., Liu, Z.-Q., Muta, K., Hata, J., Okano, H., Deco, G., Kringelbach, M. L., Luppi, A. I.
How the activity and connectivity of the brain support consciousness remains a central question in neuroscience. Recent progress driven by the use of functional MRI has seen growing recognition that large-scale distributed functional organisation of the human and non-human primate brain are systematically and consistently reshaped by anaesthetic-induced unconsciousness, across anaesthetics and across human and macaque. Here, we generalise these results to a different primate species that is gaining traction as model organism in neuroscience, the marmoset ( Callithrix jacchus ). We also generalise results to an additional anaesthetic, isoflurane, which we compare with propofol and sevoflurane. We report that under anaesthesia with propofol, sevoflurane, or isoflurane, distributed brain activity from functional MRI is increasingly constrained by the underlying structural connectivity across scales. Anaesthesia also induces a collapse of the principal gradient and intrinsic functional geometry of the marmoset brain, coinciding with a breakdown of hierarchical integration. Altogether, the present results indicate generalisable signatures of anaesthesia in the large-scale organisation of the primate brain.
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Siu, C., Pirzada, S., Glick, C., Betzel, R. F., Petri, G., Manning, J. R., Williams, L. M., Saggar, M.
Functional connectivity in network neuroscience is traditionally characterized using time-averaged correlations between brain regions. While these summaries capture stable large-scale organization, they do not fully reflect the temporal structure of moment-to-moment interactions. Here, we investigate how the order of interaction used to represent brain dynamics shapes the organization recovered from neural data. We compare three interaction representations of fMRI dynamics: regional activation (node time series), pairwise co-fluctuations (edge time series), and higher-order triplet interactions (triangle time series); within a common topological framework using Mapper from topological data analysis (TDA). Across task and resting-state data, Mapper representations derived from pairwise co-fluctuations more distinctly segregate task conditions than activation-based or higher-order representations. This organization reflects structured coordination patterns beyond activation polarity and is driven by high-amplitude interaction events. Beyond task states, modularity quality computed across all Mapper representations is highest for edge time series and selectively associated with stable individual differences: higher modularity relates to higher conscientiousness and lower internalizing and externalizing symptom dimensions. Together, these findings suggest that behaviorally relevant information is reflected in the topology of moment-to-moment brain interactions. Topological analysis of interaction-level dynamics therefore provides a complementary and interpretable framework for linking large-scale neural coordination to cognition, personality, and mental health.
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Orsenigo, D., Luppi, A. I., Diano, M., Ciorli, T., Borriero, A., Willis, H. E., Petri, G., Bridge, H., Tamietto, M.
Damage to the primary visual cortex causes loss of conscious vision, yet some patients retain the ability to respond to stimuli despite reporting no visual experience. Why similar lesions produce such different behavioral phenotypes remains unclear. While research to date has focused primarily on spared pathways that bypass V1, here we asked whether these divergent outcomes are also linked to the brain's intrinsic functional architecture. In the largest resting-state fMRI cohort of patients with unilateral V1 damage reported to date, we quantified information sharing between regions across cortical and subcortical parcels in blindsight-positive and blindsight-negative patients, as well as in age-matched healthy controls. Despite comparable lesions, the two patient groups displayed distinct hierarchical patterns on the cortex: B+ patients preserved a sensory-to-association organization as in healthy controls, whereas B- patients exhibited a marked flattening of this hierarchy. The effect was driven by abnormally low shared-information coupling within unimodal cortices and scaled continuously with single-subject behavioral blind-field detection performance. A thalamic region consistent with the pulvinar, linking the contralesional visual cortex and the frontal eye field, discriminated B+ from B- patients. These findings highlight the system-level consequences of V1 damage supporting blindsight, suggesting that the unimodal-transmodal axis might track not only global states of consciousness, but also whether sensory information can guide behavior without awareness.
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Nurisso, M., Leroy, P., Petri, G., Vaccarino, F.
Understanding the properties of the parameter space in feed-forward ReLU networks is critical for effectively analyzing and guiding training dynamics. After initialization, training under gradient flow decisively restricts the parameter space to an algebraic variety that emerges from the homogeneous nature of the ReLU activation function. In this study, we examine two key challenges associated with feed-forward ReLU networks built on general directed acyclic graph (DAG) architectures: the (dis)connectedness of the parameter space and the existence of singularities within it. We extend previous results by providing a thorough characterization of connectedness, highlighting the roles of bottleneck nodes and balance conditions associated with specific subsets of the network. Our findings clearly demonstrate that singularities are intricately connected to the topology of the underlying DAG and its induced sub-networks. We discuss the reachability of these singularities and establish a principled connection with differentiable pruning. We validate our theory with simple numerical experiments.
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Santoro, A., Neri, M., Poetto, S., Orsenigo, D., Diano, M., Gatica, M., Petri, G.
We present the first large-scale comparison of higher-order interaction (HOI) metrics — spanning information theory and topology — applied to resting-state and task fMRI data from 100 Human Connectome Project subjects. We identify three distinct classes of HOI metrics: redundant, synergistic, and topological, with the latter bridging the two. Despite their differences, all metrics align with the brain's unimodal-to-transmodal hierarchy and, in some cases, with receptor architecture. HOI metrics outperform classical functional connectivity in fingerprinting and are more predictive of behavior, positioning them as key tools for linking brain architecture and cognition.
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Lucas, M., Aime, N., Callara, A., Fontanelli, L., Sebastiani, L., Santarcangelo, E. L., Petri, G.
This study investigates the neural correlates of hypnosis using network and topological analysis of EEG data, providing evidence relevant to the state-nonstate debate in hypnosis research.
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Lanciano, T., Petri, G., Gili, T., Bonchi, F.
We apply contrast subgraph mining to functional brain connectivity networks, identifying specific patterns of altered connectivity in autism spectrum disorder that distinguish ASD subjects from neurotypical controls.
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Santoro, A., Nurisso, M., Petri, G.
We propose edge-based Laplacian operators for processing brain signals, moving beyond traditional node-centric approaches to capture higher-order topological features of brain functional data.
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Wardynski, M., Iacopini, I., Petri, G., Latora, V., Crimi, A.
We model the spread of misfolded proteins in Alzheimer's disease using simplicial contagion on brain networks, showing that higher-order interactions improve the modeling of protein propagation patterns compared to pairwise models.
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Orsenigo, D., Setti, F., Pagani, M., Petri, G., Luppi, A., Tamietto, M., Ricciardi, E.
We show that while the brain's large-scale functional architecture is shaped by innate hierarchical gradients, sensory deprivation induces targeted, experience-driven reorganization that flexibly reconfigures cortical connectivity without disrupting the brain's core scaffold. This work demonstrates how congenital sensory deprivation leads to specific adaptations in brain networks while preserving fundamental organizational principles.
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Poetto, S., Merritt, H., Santoro, A., Rabuffo, G., Battaglia, D., Vaccarino, F., Saggar, M., Brovelli, A., Petri, G.
We show that topological fingerprinting, based on homological scaffolds, significantly outperforms FC-based one. We also show that these scaffolds are distributed across functional subnetworks and we link the structure of topological cycles to information synergy.
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Gatica, M., Atkinson-Clement, C., Coronel-Oliveros, C., Alkhawashki, M., Mediano, P.A.M. , Tagliazucchi, E., Rosas, F.E., Kaiser, M., Petri, G.
Transcranial ultrasound stimulation (TUS) is an emerging non-invasive neuromodulation technique, offering a potential alternative to pharmacological treatments for psychiatric and neurological disorders. While functional analysis has been instrumental in characterizing TUS effects, understanding the underlying mechanisms remains a challenge. Here, we developed a whole-brain model to represent functional changes as measured by fMRI, enabling us to investigate how TUS-induced effects propagate throughout the brain with increasing stimulus intensity. We implemented two mechanisms: one based on anatomical distance and another on broadcasting dynamics, to explore plasticity-driven changes in specific brain regions. Finally, we highlighted the role of higher-order functional interactions in localizing spatial effects of off-line TUS at two target areas—the right thalamus and inferior frontal cortex—revealing distinct patterns of functional reorganization. This work lays the foundation for mechanistic insights and predictive models of TUS, advancing its potential clinical applications.
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Neri, M., Brovelli, A., Castro, S., Fraisopi, F., Gatica, M., Herzog, R., Mindlin, I., Mediano, P., Petri, G., Bor, D., Rosas, F., Tramacere, A., Estarellas, M.
In recent decades, neuroscience has advanced with increasingly sophisticated strategies for recording and analyzing brain activity, enabling detailed investigations into the roles of functional units, such as individual neurons, brain regions, and their interactions. Recently, new strategies for the investigation of cognitive functions regard the study of higher-order interactions---that is, the interactions involving more than two brain regions or neurons. While methods focusing on individual units and their interactions at various levels offer valuable and often complementary insights, each approach comes with its own set of limitations. In this context, a conceptual map to categorize and locate diverse strategies could be crucial to orient researchers and guide future research directions. To this end, we define the spectrum of orders of interaction, namely a framework that categorizes the interactions among neurons or brain regions based on the number of elements involved in these interactions. We use a simulation of a toy model and a few case studies to demonstrate the utility and the challenges of the exploration of the spectrum. We conclude by proposing future research directions aimed at enhancing our understanding of brain function and cognition through a more nuanced methodological framework.
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Combrisson, E., Basanisi, R., Neri, M., Auzias, G., Petri, G., Marinazzo, D., Panzeri, S., Brovelli, A.
This study combines information decomposition theory with MEG to explore cortico-cortical functional interactions in goal-directed learning. Results show that 'information gain' is encoded through synergistic and higher-order interactions in cortical circuits, particularly involving prefrontal regions, suggesting a distributed neural mechanism for rational decision-making.
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Nguyen, N., Hou, T., Amico, E., Zheng, J., Huang, H., Kaplan, A.D., Petri, G., Goñi, J., Kaufmann, R., Zhao, Y., Duong-Tran, D., Shen, L.
Higher-order properties of functional magnetic resonance imaging (fMRI) induced connectivity have been shown to unravel many exclusive topological and dynamical insights beyond pairwise interactions. Nonetheless, whether these fMRI-induced higher-order properties play a role in disentangling other neuroimaging modalities’ insights remains largely unexplored and poorly understood. In this work, by analyzing fMRI data from the Human Connectome Project Young Adult dataset using persistent homology, we discovered that the volume-optimal persistence homological scaffolds of fMRI-based functional connectomes exhibited conservative topological reconfigurations from the resting state to attentional task-positive state. Specifically, while reflecting the extent to which each cortical region contributed to functional cycles following different cognitive demands, these reconfigurations were constrained such that the spatial distribution of cavities in the connectome is relatively conserved. Most importantly, such level of contributions covaried with powers of aperiodic activities mostly within the theta-alpha (4-12 Hz) band measured by magnetoencephalography (MEG). This comprehensive result suggests that fMRI-induced hemodynamics and MEG theta-alpha aperiodic activities are governed by the same functional constraints specific to each cortical morpho-structure. Methodologically, our work paves the way toward an innovative computing paradigm in multimodal neuroimaging topological learning. The code for our analyses is provided in https://github.com/ngcaonghi/scaffold_noise.
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Santoro, A., Battiston, F., Lucas, M., Petri, G., Amico, E.
Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. To address this question, we conducted a comprehensive analysis using fMRI time series of 100 unrelated subjects from the Human Connectome Project. We show that higher-order approaches greatly enhance our ability to decode dynamically between various tasks, to improve the individual identification of unimodal and transmodal functional subsystems, and to strengthen significantly the associations between brain activity and behavior. Overall, our approach sheds new light on the higher-order organization of fMRI time series, improving the characterization of dynamic group dependencies in rest and tasks, and revealing a vast space of unexplored structures within human functional brain data, which may remain hidden when using traditional pairwise approaches.
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D'acunto, G., Bonchi, F., De Francisci Morales, G., Petri, G.
The bulk of the research effort on brain connectivity revolves around statistical associations among brain regions, which do not directly relate to the causal mechanisms governing brain dynamics. Here we propose the multiscale causal backbone (MCB) of brain dynamics shared by a set of individuals across multiple temporal scales, and devise a principled methodology to extract it. Our approach leverages recent advances in multiscale causal structure learning and optimizes the trade-off between the model fitting and its complexity. Empirical assessment on synthetic data shows the superiority of our methodology over a baseline based on canonical functional connectivity networks. When applied to resting-state fMRI data, we find sparse MCBs for both the left and right brain hemispheres. Thanks to its multiscale nature, our approach shows that at low-frequency bands, causal dynamics are driven by brain regions associated with high-level cognitive functions; at higher frequencies instead, nodes related to sensory processing play a crucial role. Finally, our analysis of individuals’ multiscale causal structures confirms the existence of a causal fingerprint of brain connectivity, thus supporting from a causal perspective the existing extensive research in brain connectivity fingerprinting.
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Duong-Tran, D., Kaufmann, R., Chen, J., Wang, X., Garai, S., Xu, F. H., Bao, J., Amico, E., Kaplan, A. D., Petri, G., Goni, J., Zhao, Y., Shen, L.
This study proposes a homological formalism to quantify higher-order characteristics in human brain functional sub-circuits, revealing complementary properties and self-similarity across homological orders in brain connectivity during rest and tasks.
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Lucas, M., Morris, A., Townsend-Teague, A., Tichit, L., Habermann, B., Barrat, A.
The temporal organization of biological systems is key for understanding them, but current methods for identifying this organization are often ad hoc and require prior knowledge. We present Phasik, a method that automatically identifies this multiscale organization by combining time series data (protein or gene expression) and interaction data (protein-protein interaction network). Phasik builds a (partially) temporal network and uses clustering to infer temporal phases. We demonstrate the method’s effectiveness by recovering well-known phases and sub-phases of the cell cycle of budding yeast and phase arrests of mutants. We also show its general applicability using temporal gene expression data from circadian rhythms in wild-type and mutant mouse models. We systematically test Phasik’s robustness and investigate the effect of having only partial temporal information. As time-resolved, multiomics datasets become more common, this method will allow the study of temporal regulation in lesser-known biological contexts, such as development, metabolism, and disease.
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Celeghin, A., Borriero, A., Orsenigo, D., Diano, M., Méndez Guerrero, C. A., Perotti, A., Petri, G., Tamietto, M.
This paper examines Convolutional Neural Networks (CNNs) as in silico models of the primate visual system, highlighting structural and functional parallels. It discusses challenges in modeling visual processing pathways and proposes architectural constraints to align CNNs more closely with biological vision, extending their applicability beyond object recognition.
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Akinrinade, I., Kareklas, K., Teles, M. C., Reis, T. K., Gliksberg, M., Petri, G., Levkowitz, G., Oliveira, R. F.
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.
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Scaia, M. F., Akinrinade, I., Petri, G., Oliveira, R. F.
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.
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Billings, J., Tivadar, R., Murray, M. M., Franceschiello, B., Petri, G.
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.
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Petri, G., Musslick, S., Dey, B., Ozcimder, K., Turner, D., Ahmed, N.K., Willke, T.L., Cohen, J.D.
The ability to learn new tasks and generalize to others is a remarkable characteristic of both human brains and recent artificial intelligence systems. The ability to perform multiple tasks simultaneously is also a key characteristic of parallel architectures, as is evident in the human brain and exploited in traditional parallel architectures. Here we show that these two characteristics reflect a fundamental tradeoff between interactive parallelism, which supports learning and generalization, and independent parallelism, which supports processing efficiency through concurrent multitasking. Although the maximum number of possible parallel tasks grows linearly with network size, under realistic scenarios their expected number grows sublinearly. Hence, even modest reliance on shared representations, which support learning and generalization, constrains the number of parallel tasks. This has profound consequences for understanding the human brain’s mix of sequential and parallel capabilities, as well as for the development of artificial intelligence systems that can optimally manage the tradeoff between learning and processing efficiency.
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Nunes, A. R., Gliksberg, M., Varela, S. A. M., Teles, M., Wircer, E., Blechman, J., Petri, G., Levkowitz, G., Oliveira, R. F.
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.
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Petri, G., Leitao, A.
We propose a topological description of neural network expressive power. We adopt the topology of the space of decision boundaries realized by a neural architecture as a measure of its intrinsic expressive power. By sampling a large number of neural architectures with different sizes and design, we show how such measure of expressive power depends on the properties of the architectures, like depth, width and other related quantities.
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Petri, G., Expert, P., Turkheimer, F., Carhart-Harris, R., Nutt, D., Hellyer, P.J., Vaccarino, F.
Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10, 186–198. (doi:10.1038/nrn2618)). Traditionally, the structure of complex networks has been studied through their statistical properties and metrics concerned with node and link properties, e.g. degree-distribution, node centrality and modularity. Here, we study the characteristics of functional brain networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects—homological cycles—associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds, a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. As a proof of principle, we apply these tools to compare resting-state functional brain activity in 15 healthy volunteers after intravenous infusion of placebo and psilocybin—the main psychoactive component of magic mushrooms. The results show that the homological structure of the brain's functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.
Tools & data
Modelling TUS
GitHub ↗Python code to reproduce the computational model of transcranial ultrasound stimulation (TUS) at different stimulation intensities.
Holes
GitHub ↗A Python module for detecting, analysing and visualising persistent homological features of complex networks.
Brain HORS
GitHub ↗Code for replicating analyses of Nature Communications paper on higher-order connectomics of human brain function.