scholarly journals Topological clustering of multilayer networks

2021 ◽  
Vol 118 (21) ◽  
pp. e2019994118
Author(s):  
Monisha Yuvaraj ◽  
Asim K. Dey ◽  
Vyacheslav Lyubchich ◽  
Yulia R. Gel ◽  
H. Vincent Poor
Keyword(s):  
Brain Regions ◽  
Higher Order ◽  
Topological Data Analysis ◽  
Critical Infrastructures ◽  
Network Clustering ◽  
Multilayer Networks ◽  
Network Layers ◽  
Brain Connectome ◽  
High Utility ◽  
Persistence Diagrams

Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.

scholarly journals Topological Segmentation of Time-Varying Functional Connectivity Highlights the Role of Preferred Cortical Circuits

2020 ◽  
Author(s):  
Jacob Billings ◽  
Manish Saggar ◽  
Shella Keilholz ◽  
Giovanni Petri
Keyword(s):  
Functional Connectivity ◽  
Brain Function ◽  
Persistent Homology ◽  
Brain Regions ◽  
Topological Data Analysis ◽  
Time Varying ◽  
Imaging Data ◽  
Experimental Conditions ◽  
Common Time ◽  
Brain Imaging Data

Functional connectivity (FC) and its time-varying analogue (TVFC) leverage brain imaging data to interpret brain function as patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s spontaneous self-organization. One tool from TDA, “persistent homology”, observes the occurrence and the persistence of n-dimensional holes presented in the metric space over a dataset. The occurrence of n-dimensional holes within the TVFC point cloud may denote conserved and preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional TVFC metrics at the task of segmenting brain states that differ across a common time-series of experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment volunteer performance during experimentally defined tasks, and generalize better across volunteers. Finally, we present empirical and theoretical observations that interpret brain function as a topological space defined by cyclic and interlinked motifs among distributed brain regions, especially, the attention networks.

scholarly journals Depth Penetration and Scope Extension of Failures in the Cascading of Multilayer Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wen-Jun Jiang ◽  
Run-Ran Liu ◽  
Chun-Xiao Jia
Keyword(s):  
Real World ◽  
Propagation Direction ◽  
Intervention Programs ◽  
Theoretical Studies ◽  
Percolation Transition ◽  
Multilayer Networks ◽  
Microscopic Mechanism ◽  
Network Layers ◽  
Avalanche Process ◽  
Random Failures

Real-world complex systems always interact with each other, which causes these systems to collapse in an avalanche or cascading manner in the case of random failures or malicious attacks. The robustness of multilayer networks has attracted great interest, where the modeling and theoretical studies of which always rely on the concept of multilayer networks and percolation methods. A straightforward and tacit assumption is that the interdependence across network layers is strong, which means that a node will fail entirely with the removal of all links if one of its interdependent nodes in other network layers fails. However, this oversimplification cannot describe the general form of interactions across the network layers in a real-world multilayer system. In this paper, we reveal the nature of the avalanche disintegration of general multilayer networks with arbitrary interdependency strength across network layers. Specifically, we identify that the avalanche process of the whole system can essentially be decomposed into two microscopic cascading dynamics in terms of the propagation direction of the failures: depth penetration and scope extension. In the process of depth penetration, the failures propagate from layer to layer, where the greater the number of failed nodes is, the greater is the destructive power that will emerge in an interdependency group. In the process of scope extension, failures propagate with the removal of connections in each network layer. Under the synergy of the two processes, we find that the percolation transition of the system can be discontinuous or continuous with changes in the interdependency strength across network layers, which means that a sudden system-wide collapse can be avoided by controlling the interdependency strength across network layers. Our work not only reveals the microscopic mechanism of global collapse in multilayer infrastructure systems but also provides stimulating ideas on intervention programs and approaches for cascade failures.

scholarly journals Estimation of gender-specific connectional brain templates using joint multi-view cortical morphological network integration

2020 ◽  
Author(s):  
Nada Chaari ◽  
Hatice Camgöz Akdağ ◽  
Islem Rekik
Keyword(s):  
Right Hemisphere ◽  
Occipital Cortex ◽  
Brain Regions ◽  
Middle Temporal Gyrus ◽  
Network Clustering ◽  
Male And Female ◽  
Clustering Model ◽  
Net Method ◽  
The Right ◽  
Gender Specific

Abstract The estimation of a connectional brain template (CBT) integrating a population of brain networks while capturing shared and differential connectional patterns across individuals remains unexplored in gender fingerprinting. This paper presents the first study to estimate gender-specific CBTs using multi-view cortical morphological networks (CMNs) estimated from conventional T1-weighted magnetic resonance imaging (MRI). Specifically, each CMN view is derived from a specific cortical attribute (e.g. thickness), encoded in a network quantifying the dissimilarity in morphology between pairs of cortical brain regions. To this aim, we propose Multi-View Clustering and Fusion Network (MVCF-Net), a novel multi-view network fusion method, which can jointly identify consistent and differential clusters of multi-view datasets in order to capture simultaneously similar and distinct connectional traits of samples. Our MVCF-Net method estimates a representative and well-centered CBTs for male and female populations, independently, to eventually identify their fingerprinting regions of interest (ROIs) in four main steps. First, we perform multi-view network clustering model based on manifold optimization which groups CMNs into shared and differential clusters while preserving their alignment across views. Second, for each view, we linearly fuse CMNs belonging to each cluster, producing local CBTs. Third, for each cluster, we non-linearly integrate the local CBTs across views, producing a cluster-specific CBT. Finally, by linearly fusing the cluster-specific centers we estimate a final CBT of the input population. MVCF-Net produced the most centered and representative CBTs for male and female populations and identified the most discriminative ROIs marking gender differences. The most two gender-discriminative ROIs involved the lateral occipital cortex and pars opercularis in the left hemisphere and the middle temporal gyrus and lingual gyrus in the right hemisphere.

scholarly journals Frequency-based brain networks: From a multiplex framework to a full multilayer description

2018 ◽  
Vol 2 (4) ◽  
pp. 418-441 ◽  
Author(s):  
Javier M. Buldú ◽  
Mason A. Porter
Keyword(s):  
Brain Networks ◽  
Network Models ◽  
Real Data ◽  
Laplacian Matrix ◽  
Brain Regions ◽  
Brain Diseases ◽  
Multilayer Networks ◽  
Frequency Bands ◽  
Multiplex Network ◽  
The Brain

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.

scholarly journals GENERALIZED NETWORK CLUSTERING AND ITS DYNAMICAL IMPLICATIONS

2010 ◽  
Vol 13 (03) ◽  
pp. 281-291 ◽  
Author(s):  
THOMAS HOUSE
Keyword(s):  
Contact Process ◽  
Higher Order ◽  
Order Structure ◽  
Network Clustering ◽  
Clustered Networks

A parametrization of generalised network clustering, in the form of four-motif prevalences, is presented. This involves three real parameters that are conditional on one-, two- and three-motif prevalences. Interpretations of these real parameters are presented that motivate a set of rewiring schemes to create appropriately clustered networks. Finally, the dynamical implications of higher order structure, as parameterised, for a contact process are considered.

scholarly journals Topological Analysis of Differential Effects of Ketamine and Propofol Anesthesia on Brain Dynamics

2020 ◽  
Author(s):  
Thomas F. Varley ◽  
Vanessa Denny ◽  
Olaf Sporns ◽  
Alice Patania
Keyword(s):  
State Transition ◽  
Conscious Experience ◽  
Topological Analysis ◽  
Higher Order ◽  
Topological Data Analysis ◽  
Brain Dynamics ◽  
Dimensional Manifold ◽  
Discrete State ◽  
Almost All ◽  
Awake Condition

AbstractResearch into the neural correlates of consciousness has found that the vividness and complexity of conscious experience is related to the structure of brain dynamics, and that alterations to consciousness track changes in temporal evolution of brain states. Despite inducing externally similar states, propofol and ketamine produce different subjective states of consciousness: here we explore the different effects of these two anaesthetics on the structure of dynamical attractors reconstructed from electrophysiological activity recorded from cerebral cortex of two non-human primates. We used two different methods of attractor reconstruction: the first embeds the recordings in a continuous high-dimensional manifold on which we use topological data analysis to infer the presence (or absence) of higher-order dynamics. The second reconstruction, an ordinal partition network embedding, allows us to create a discrete state-transition network approximation of a continuous attractor, which is amenable to information-theoretic analysis and contains rich information about state-transition dynamics. We find that the awake condition generally had the “richest” structure, with the widest repertoire of available states, the presence of pronounced higher-order structures, and the least deterministic dynamics. In contrast, the propofol condition had the most dissimilar dynamics to normal consciousness, transitioning to a more impoverished, constrained, low-structure regime. The ketamine condition, interestingly, seemed to combine aspects of both: while it was generally less complex than the awake condition, it remained well above propofol in almost all measures. These results may provides insights into how consciousness can persist under the influence of ketamine and the battery of measures used provides deeper and more comprehensive insights than what is typically gained by using point-measures of complexity.

scholarly journals Reactivation of hedonic but not sensory representations in human emotional learning

2021 ◽  
Author(s):  
Mana R Ehlers ◽  
James H Kryklywy ◽  
Andre O Beukers ◽  
Sarah R Moore ◽  
Forys J Brandon ◽  
...  
Keyword(s):  
Conditioned Stimulus ◽  
Unconditioned Stimulus ◽  
Brain Regions ◽  
Higher Order ◽  
Fmri Data ◽  
Similarity Analysis ◽  
Appetitive Conditioning ◽  
Activation Patterns ◽  
The Us ◽  
Novel Variation

Learning which stimuli in our environment co-occur with painful or pleasurable events is critical for survival. Previous research has established the basic neural and behavioural mechanisms of aversive and appetitive conditioning; however, it is unclear what precisely is learned. Here we examined what aspects of the unconditioned stimulus (US), sensory and hedonic, are transferred to the conditioned stimulus (CS). To decode the content of brain activation patterns elicited during appetitive (soft touch) and aversive (painful touch) conditioning of faces, a novel variation of representational similarity analysis (RSA) based on theoretically driven representational patterns of interest (POIs) was applied to fMRI data. Once face associations were learned through conditioning, globally the CS reactivated US representational patterns showing conditioning dependent reactivation. More specifically, in higher order brain regions, the CS only reactivated hedonic but not sensory aspects of the US, suggesting that affective conditioning primarily carries forward the valence of the experience rather than its sensory origins.

scholarly journals Heterogeneity of EEG resting-state brain networks in absolute pitch

2020 ◽  
Author(s):  
Marielle Greber ◽  
Carina Klein ◽  
Simon Leipold ◽  
Silvano Sele ◽  
Lutz Jäncke
Keyword(s):  
Functional Connectivity ◽  
Auditory Cortex ◽  
Resting State ◽  
Large Scale ◽  
Absolute Pitch ◽  
Brain Regions ◽  
Brain Network ◽  
Higher Order ◽  
Neural Basis ◽  
Whole Brain

AbstractThe neural basis of absolute pitch (AP), the ability to effortlessly identify a musical tone without an external reference, is poorly understood. One of the key questions is whether perceptual or cognitive processes underlie the phenomenon as both sensory and higher-order brain regions have been associated with AP. One approach to elucidate the neural underpinnings of a specific expertise is the examination of resting-state networks.Thus, in this paper, we report a comprehensive functional network analysis of intracranial resting-state EEG data in a large sample of AP musicians (n = 54) and non-AP musicians (n = 51). We adopted two analysis approaches: First, we applied an ROI-based analysis to examine the connectivity between the auditory cortex and the dorsolateral prefrontal cortex (DLPFC) using several established functional connectivity measures. This analysis is a replication of a previous study which reported increased connectivity between these two regions in AP musicians. Second, we performed a whole-brain network-based analysis on the same functional connectivity measures to gain a more complete picture of the brain regions involved in a possibly large-scale network supporting AP ability.In our sample, the ROI-based analysis did not provide evidence for an AP-specific connectivity increase between the auditory cortex and the DLPFC. In contrast, the whole-brain analysis revealed three networks with increased connectivity in AP musicians comprising nodes in frontal, temporal, subcortical, and occipital areas. Commonalities of the networks were found in both sensory and higher-order brain regions of the perisylvian area. Further research will be needed to confirm these exploratory results.

scholarly journals Higher-Order Networks

2021 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Complex Systems ◽  
Network Topology ◽  
Simplicial Complexes ◽  
Higher Order ◽  
Topological Data Analysis ◽  
Mathematical Framework ◽  
Wide Range ◽  
Underlying Network ◽  
Many Body Interactions ◽  
Higher Order Networks

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

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