1
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Di Gaetano L, Carugno G, Battiston F, Coghi F. Dynamical Fluctuations of Random Walks in Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 133:107401. [PMID: 39303236 DOI: 10.1103/physrevlett.133.107401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 06/04/2024] [Accepted: 07/26/2024] [Indexed: 09/22/2024]
Abstract
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation. Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks.
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Affiliation(s)
| | | | | | - Francesco Coghi
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SEa-106 91 Stockholm, Sweden
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2
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Mitchell EC, Story B, Boothe D, Franaszczuk PJ, Maroulas V. A topological deep learning framework for neural spike decoding. Biophys J 2024; 123:2781-2789. [PMID: 38402607 PMCID: PMC11393671 DOI: 10.1016/j.bpj.2024.01.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Revised: 01/10/2024] [Accepted: 01/23/2024] [Indexed: 02/27/2024] Open
Abstract
The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information are through head direction cells and grid cells. Brains use head direction cells to determine orientation, whereas grid cells consist of layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single head direction or grid. We want to capture this firing structure and use it to decode head direction and animal location from head direction and grid cell activity. Understanding, representing, and decoding these neural structures require models that encompass higher-order connectivity, more than the one-dimensional connectivity that traditional graph-based models provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network. Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the simplicial convolutional neural network is demonstrated on head direction and trajectory prediction via head direction and grid cell datasets.
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Affiliation(s)
- Edward C Mitchell
- University of Tennessee Knoxville, Knoxville, Tennessee; Joe Gibbs Human Performance Institute, Huntersville, North Carolina
| | - Brittany Story
- University of Tennessee Knoxville, Knoxville, Tennessee; Army Research Lab, Aberdeen, Maryland
| | | | - Piotr J Franaszczuk
- Army Research Lab, Aberdeen, Maryland; Johns Hopkins University, Baltimore, Maryland
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3
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Badalyan A, Ruggeri N, De Bacco C. Structure and inference in hypergraphs with node attributes. Nat Commun 2024; 15:7073. [PMID: 39152121 PMCID: PMC11329712 DOI: 10.1038/s41467-024-51388-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 08/06/2024] [Indexed: 08/19/2024] Open
Abstract
Many networked datasets with units interacting in groups of two or more, encoded with hypergraphs, are accompanied by extra information about nodes, such as the role of an individual in a workplace. Here we show how these node attributes can be used to improve our understanding of the structure resulting from higher-order interactions. We consider the problem of community detection in hypergraphs and develop a principled model that combines higher-order interactions and node attributes to better represent the observed interactions and to detect communities more accurately than using either of these types of information alone. The method learns automatically from the input data the extent to which structure and attributes contribute to explain the data, down weighing or discarding attributes if not informative. Our algorithmic implementation is efficient and scales to large hypergraphs and interactions of large numbers of units. We apply our method to a variety of systems, showing strong performance in hyperedge prediction tasks and in selecting community divisions that correlate with attributes when these are informative, but discarding them otherwise. Our approach illustrates the advantage of using informative node attributes when available with higher-order data.
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Affiliation(s)
- Anna Badalyan
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany
| | - Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany.
- Department of Computer Science, ETH, Zürich, Switzerland.
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, Tübingen, Germany.
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4
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Cheng A, Xu Y, Sun P, Tian Y. A simplex path integral and a simplex renormalization group for high-order interactions . REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:087601. [PMID: 39077989 DOI: 10.1088/1361-6633/ad5c99] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 06/27/2024] [Indexed: 07/31/2024]
Abstract
Modern theories of phase transitions and scale invariance are rooted in path integral formulation and renormalization groups (RGs). Despite the applicability of these approaches in simple systems with only pairwise interactions, they are less effective in complex systems with undecomposable high-order interactions (i.e. interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose a simplex path integral and a simplex RG (SRG) as the generalizations of classic approaches to arbitrary high-order and heterogeneous interactions. We first formalize the trajectories of units governed by high-order interactions to define path integrals on corresponding simplices based on a high-order propagator. Then, we develop a method to integrate out short-range high-order interactions in the momentum space, accompanied by a coarse graining procedure functioning on the simplex structure generated by high-order interactions. The proposed SRG, equipped with a divide-and-conquer framework, can deal with the absence of ergodicity arising from the sparse distribution of high-order interactions and can renormalize a system with intertwined high-order interactions at thep-order according to its properties at theq-order (p⩽q). The associated scaling relation and its corollaries provide support to differentiate among scale-invariant, weakly scale-invariant, and scale-dependent systems across different orders. We validate our theory in multi-order scale-invariance verification, topological invariance discovery, organizational structure identification, and information bottleneck analysis. These experiments demonstrate the capability of our theory to identify intrinsic statistical and topological properties of high-order interacting systems during system reduction.
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Affiliation(s)
- Aohua Cheng
- Department of Psychological and Cognitive Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- Infplane AI Technologies Ltd, Beijing 100080, People's Republic of China
- Tsien Excellence in Engineering Program, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yunhui Xu
- Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Pei Sun
- Laboratory of Computational Biology and Complex Systems, City University of Macau, Macau 999078, People's Republic of China
- Faculty of Health and Wellness, City University of Macau, Macau 999078, People's Republic of China
| | - Yang Tian
- Laboratory of Computational Biology and Complex Systems, City University of Macau, Macau 999078, People's Republic of China
- Faculty of Health and Wellness, City University of Macau, Macau 999078, People's Republic of China
- Infplane AI Technologies Ltd, Beijing 100080, People's Republic of China
- Faculty of Data Science, City University of Macau, Macau 999078, People's Republic of China
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5
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Nguyen N, Hou T, Amico E, Zheng J, Huang H, Kaplan AD, Petri G, Goñi J, Kaufmann R, Zhao Y, Duong-Tran D, Shen L. Volume-optimal persistence homological scaffolds of hemodynamic networks covary with MEG theta-alpha aperiodic dynamics. ARXIV 2024:arXiv:2407.05060v2. [PMID: 39108288 PMCID: PMC11302673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 08/23/2024]
Abstract
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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Affiliation(s)
- Nghi Nguyen
- Multidisciplinary Brain Research Center, Bar-Ilan University, Ramat Gan, Israel
| | - Tao Hou
- Department of Computer Science, University of Oregon, Eugene, Oregon, USA
| | - Enrico Amico
- Institute of Health and Neurodevelopment, College of Health and Life Sciences, Aston University, Birmingham, UK
| | - Jingyi Zheng
- Department of Mathematics and Statistics, Auburn University, Alabama, USA
| | - Huajun Huang
- Department of Mathematics and Statistics, Auburn University, Alabama, USA
| | - Alan D Kaplan
- Computational Engineering Division, Lawrence Livermore National Laboratory, Livermore, California, USA
| | - Giovanni Petri
- NPLab, Network Science Institute, Northeastern University London, London, UK
| | - Joaquín Goñi
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana, USA
- School of Biomedical Engineering, Purdue University, W. Lafayette, Indiana, USA
| | - Ralph Kaufmann
- Department of Mathematics, Purdue University, W. Lafayette, Indiana, USA
| | - Yize Zhao
- School of Public Health, Yale University, New Heaven, Connecticut, USA
| | - Duy Duong-Tran
- Department of Mathematics, U.S. Naval Academy, Annapolis, Maryland, USA
- Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA
| | - Li Shen
- Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA
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6
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Millán AP, Sun H, Torres JJ, Bianconi G. Triadic percolation induces dynamical topological patterns in higher-order networks. PNAS NEXUS 2024; 3:pgae270. [PMID: 39035037 PMCID: PMC11259606 DOI: 10.1093/pnasnexus/pgae270] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 06/27/2024] [Indexed: 07/23/2024]
Abstract
Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.
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Affiliation(s)
- Ana P Millán
- Electromagnetism and Matter Physics Department, Institute “Carlos I” for Theoretical and Computational Physics, University of Granada, Granada E-18071, Spain
| | - Hanlin Sun
- Nordita, KTH Royal Institute of Technology and Stockholm University, Stockholm SE-106 91, Sweden
| | - Joaquín J Torres
- Electromagnetism and Matter Physics Department, Institute “Carlos I” for Theoretical and Computational Physics, University of Granada, Granada E-18071, Spain
| | - Ginestra Bianconi
- Centre for Complex Systems, School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
- The Alan Turing Institute, London NW1 2DB, UK
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7
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Wang R, Muolo R, Carletti T, Bianconi G. Global topological synchronization of weighted simplicial complexes. Phys Rev E 2024; 110:014307. [PMID: 39160981 DOI: 10.1103/physreve.110.014307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2024] [Accepted: 06/17/2024] [Indexed: 08/21/2024]
Abstract
Higher-order networks are able to capture the many-body interactions present in complex systems and to unveil fundamental phenomena revealing the rich interplay between topology, geometry, and dynamics. Simplicial complexes are higher-order networks that encode higher-order topology and dynamics of complex systems. Specifically, simplicial complexes can sustain topological signals, i.e., dynamical variables not only defined on nodes of the network but also on their edges, triangles, and so on. Topological signals can undergo collective phenomena such as synchronization, however, only some higher-order network topologies can sustain global synchronization of topological signals. Here we consider global topological synchronization of topological signals on weighted simplicial complexes. We demonstrate that topological signals can globally synchronize on weighted simplicial complexes, even if they are odd-dimensional, e.g., edge signals, thus overcoming a limitation of the unweighted case. These results thus demonstrate that weighted simplicial complexes are more advantageous for observing these collective phenomena than their unweighted counterpart. In particular, we present two weighted simplicial complexes: the weighted triangulated torus and the weighted waffle. We completely characterize their higher-order spectral properties and demonstrate that, under suitable conditions on their weights, they can sustain global synchronization of edge signals. Our results are interpreted geometrically by showing, among the other results, that in some cases edge weights can be associated with the lengths of the sides of curved simplices.
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8
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Gallo L, Lacasa L, Latora V, Battiston F. Higher-order correlations reveal complex memory in temporal hypergraphs. Nat Commun 2024; 15:4754. [PMID: 38834592 DOI: 10.1038/s41467-024-48578-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2023] [Accepted: 05/02/2024] [Indexed: 06/06/2024] Open
Abstract
Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we use time-varying hypergraphs to describe such systems, and we introduce a framework based on higher-order correlations to characterize their temporal organization. The analysis of human interaction data reveals the existence of coherent and interdependent mesoscopic structures, thus capturing aggregation, fragmentation and nucleation processes in social systems. We introduce a model of temporal hypergraphs with non-Markovian group interactions, which reveals complex memory as a fundamental mechanism underlying the emerging pattern in the data.
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Affiliation(s)
- Luca Gallo
- Department of Network and Data Science, Central European University, Vienna, Austria.
| | - Lucas Lacasa
- Institute for Cross-Disciplinary Physics and Complex Systems (IFISC), CSIC-UIB, Palma de Mallorca, Spain
| | - Vito Latora
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
- Department of Physics and Astronomy, University of Catania, 95125, Catania, Italy
- INFN Sezione di Catania, Via S. Sofia, 64, 95125, Catania, Italy
- Complexity Science Hub Vienna, A-1080, Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, Vienna, Austria.
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9
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Zhang B, Lin H. Functional loops: Monitoring functional organization of deep neural networks using algebraic topology. Neural Netw 2024; 174:106239. [PMID: 38508049 DOI: 10.1016/j.neunet.2024.106239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Revised: 03/06/2024] [Accepted: 03/13/2024] [Indexed: 03/22/2024]
Abstract
Various topological methods have emerged in recent years to investigate the inner workings of deep neural networks (DNNs) based on the structural and weight information. However, their effectiveness is restricted due to the stratified structure and volatile weight information. In this study, we explore the relationship between functional organizations and network performance using algebraic topology. Our results indicate that functional loops reveal functional interaction patterns of multiple neurons in DNNs. We also propose functional persistence as a measure of functional complexity and develop an early stopping criterion that achieves competitive results without requiring a validation set.
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Affiliation(s)
- Ben Zhang
- School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058, Zhejiang Provence, China; State Key Lab. of CAD & CG, Zhejiang University, Hangzhou, 310058, Zhejiang Provence, China
| | - Hongwei Lin
- School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058, Zhejiang Provence, China; State Key Lab. of CAD & CG, Zhejiang University, Hangzhou, 310058, Zhejiang Provence, China.
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10
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Hoffmann C, Cho E, Zalesky A, Di Biase MA. From pixels to connections: exploring in vitro neuron reconstruction software for network graph generation. Commun Biol 2024; 7:571. [PMID: 38750282 PMCID: PMC11096190 DOI: 10.1038/s42003-024-06264-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Accepted: 04/29/2024] [Indexed: 05/18/2024] Open
Abstract
Digital reconstruction has been instrumental in deciphering how in vitro neuron architecture shapes information flow. Emerging approaches reconstruct neural systems as networks with the aim of understanding their organization through graph theory. Computational tools dedicated to this objective build models of nodes and edges based on key cellular features such as somata, axons, and dendrites. Fully automatic implementations of these tools are readily available, but they may also be purpose-built from specialized algorithms in the form of multi-step pipelines. Here we review software tools informing the construction of network models, spanning from noise reduction and segmentation to full network reconstruction. The scope and core specifications of each tool are explicitly defined to assist bench scientists in selecting the most suitable option for their microscopy dataset. Existing tools provide a foundation for complete network reconstruction, however more progress is needed in establishing morphological bases for directed/weighted connectivity and in software validation.
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Affiliation(s)
- Cassandra Hoffmann
- Systems Neuroscience Lab, Melbourne Neuropsychiatry Centre, Department of Psychiatry, The University of Melbourne, Parkville, Australia.
| | - Ellie Cho
- Biological Optical Microscopy Platform, University of Melbourne, Parkville, Australia
| | - Andrew Zalesky
- Systems Neuroscience Lab, Melbourne Neuropsychiatry Centre, Department of Psychiatry, The University of Melbourne, Parkville, Australia
- Department of Biomedical Engineering, The University of Melbourne, Parkville, Australia
| | - Maria A Di Biase
- Systems Neuroscience Lab, Melbourne Neuropsychiatry Centre, Department of Psychiatry, The University of Melbourne, Parkville, Australia
- Stem Cell Disease Modelling Lab, Department of Anatomy and Physiology, The University of Melbourne, Parkville, Australia
- Psychiatry Neuroimaging Laboratory, Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School, Boston, USA
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11
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Chung MK, Che JB, Nair VA, Ramos CG, Mathis JR, Prabhakaran V, Meyerand E, Hermann BP, Binder JR, Struck AF. Topological Embedding of Human Brain Networks with Applications to Dynamics of Temporal Lobe Epilepsy. ARXIV 2024:arXiv:2405.07835v1. [PMID: 38800648 PMCID: PMC11118617] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
We introduce a novel, data-driven topological data analysis (TDA) approach for embedding brain networks into a lower-dimensional space in quantifying the dynamics of temporal lobe epilepsy (TLE) obtained from resting-state functional magnetic resonance imaging (rs-fMRI). This embedding facilitates the orthogonal projection of 0D and 1D topological features, allowing for the visualization and modeling of the dynamics of functional human brain networks in a resting state. We then quantify the topological disparities between networks to determine the coordinates for embedding. This framework enables us to conduct a coherent statistical inference within the embedded space. Our results indicate that brain network topology in TLE patients exhibits increased rigidity in 0D topology but more rapid flections compared to that of normal controls in 1D topology.
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Affiliation(s)
- Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, WI, USA
| | | | - Veena A Nair
- Department of Radiology, University of Wisconsin-Madison, USA
| | | | | | | | - Elizabeth Meyerand
- Departments of Medical Physics & Biomedical Engineering, University of Wisconsin-Madison, USA
| | - Bruce P Hermann
- Department of Neurology, University of Wisconsin-Madison, USA
| | | | - Aaron F Struck
- Department of Neurology, University of Wisconsin-Madison, USA
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12
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Chung MK, Huang SG, Carroll IC, Calhoun VD, Goldsmith HH. Topological state-space estimation of functional human brain networks. PLoS Comput Biol 2024; 20:e1011869. [PMID: 38739671 PMCID: PMC11115255 DOI: 10.1371/journal.pcbi.1011869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2023] [Revised: 05/23/2024] [Accepted: 01/29/2024] [Indexed: 05/16/2024] Open
Abstract
We introduce an innovative, data-driven topological data analysis (TDA) technique for estimating the state spaces of dynamically changing functional human brain networks at rest. Our method utilizes the Wasserstein distance to measure topological differences, enabling the clustering of brain networks into distinct topological states. This technique outperforms the commonly used k-means clustering in identifying brain network state spaces by effectively incorporating the temporal dynamics of the data without the need for explicit model specification. We further investigate the genetic underpinnings of these topological features using a twin study design, examining the heritability of such state changes. Our findings suggest that the topology of brain networks, particularly in their dynamic state changes, may hold significant hidden genetic information.
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Affiliation(s)
- Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin, United States of America
| | | | - Ian C. Carroll
- Department of Child and Adolescent Psychiatry, New York University Grossman School of Medicine, New York, United States of America
| | - Vince D. Calhoun
- Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, Emory University, Atlanta, Georgia, United States of America
| | - H. Hill Goldsmith
- Department of Psychology & Waisman Center, University of Wisconsin, Madison, Wisconsin, United States of America
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13
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Guichet C, Banjac S, Achard S, Mermillod M, Baciu M. Modeling the neurocognitive dynamics of language across the lifespan. Hum Brain Mapp 2024; 45:e26650. [PMID: 38553863 PMCID: PMC10980845 DOI: 10.1002/hbm.26650] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2023] [Revised: 02/08/2024] [Accepted: 02/26/2024] [Indexed: 04/02/2024] Open
Abstract
Healthy aging is associated with a heterogeneous decline across cognitive functions, typically observed between language comprehension and language production (LP). Examining resting-state fMRI and neuropsychological data from 628 healthy adults (age 18-88) from the CamCAN cohort, we performed state-of-the-art graph theoretical analysis to uncover the neural mechanisms underlying this variability. At the cognitive level, our findings suggest that LP is not an isolated function but is modulated throughout the lifespan by the extent of inter-cognitive synergy between semantic and domain-general processes. At the cerebral level, we show that default mode network (DMN) suppression coupled with fronto-parietal network (FPN) integration is the way for the brain to compensate for the effects of dedifferentiation at a minimal cost, efficiently mitigating the age-related decline in LP. Relatedly, reduced DMN suppression in midlife could compromise the ability to manage the cost of FPN integration. This may prompt older adults to adopt a more cost-efficient compensatory strategy that maintains global homeostasis at the expense of LP performances. Taken together, we propose that midlife represents a critical neurocognitive juncture that signifies the onset of LP decline, as older adults gradually lose control over semantic representations. We summarize our findings in a novel synergistic, economical, nonlinear, emergent, cognitive aging model, integrating connectomic and cognitive dimensions within a complex system perspective.
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Affiliation(s)
| | - Sonja Banjac
- Université Grenoble Alpes, CNRS LPNC UMR 5105GrenobleFrance
| | - Sophie Achard
- LJK, UMR CNRS 5224, Université Grenoble AlpesGrenobleFrance
| | | | - Monica Baciu
- Université Grenoble Alpes, CNRS LPNC UMR 5105GrenobleFrance
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14
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Sarker A, Northrup N, Jadbabaie A. Higher-order homophily on simplicial complexes. Proc Natl Acad Sci U S A 2024; 121:e2315931121. [PMID: 38470928 PMCID: PMC10962986 DOI: 10.1073/pnas.2315931121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 02/12/2024] [Indexed: 03/14/2024] Open
Abstract
Higher-order network models are becoming increasingly relevant for their ability to explicitly capture interactions between three or more entities in a complex system at once. In this paper, we study homophily, the tendency for alike individuals to form connections, as it pertains to higher-order interactions. We find that straightforward extensions of classical homophily measures to interactions of size 3 and larger are often inflated by homophily present in pairwise interactions. This inflation can even hide the presence of anti-homophily in higher-order interactions. Hence, we develop a structural measure of homophily, simplicial homophily, which decouples homophily in pairwise interactions from that of higher-order interactions. The definition applies when the network can be modeled as a simplicial complex, a mathematical abstraction which makes a closure assumption that for any higher-order relationship in the network, all corresponding subsets of that relationship occur in the data. Whereas previous work has used this closure assumption to develop a rich theory in algebraic topology, here we use the assumption to make empirical comparisons between interactions of different sizes. The simplicial homophily measure is validated theoretically using an extension of a stochastic block model for simplicial complexes and empirically in large-scale experiments across 16 datasets. We further find that simplicial homophily can be used to identify when node features are valuable for higher-order link prediction. Ultimately, this highlights a subtlety in studying node features in higher-order networks, as measures defined on groups of size k can inherit features described by interactions of size [Formula: see text].
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Affiliation(s)
- Arnab Sarker
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Natalie Northrup
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Ali Jadbabaie
- Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA02139
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15
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Ruggeri N, Battiston F, De Bacco C. Framework to generate hypergraphs with community structure. Phys Rev E 2024; 109:034309. [PMID: 38632750 DOI: 10.1103/physreve.109.034309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 01/11/2024] [Indexed: 04/19/2024]
Abstract
In recent years hypergraphs have emerged as a powerful tool to study systems with multibody interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the standardized evaluation of algorithms and the statistical study of real-world networked data, these are scarcely available in the context of hypergraphs. Here we propose a flexible and efficient framework for the generation of hypergraphs with many nodes and large hyperedges, which allows specifying general community structures and tune different local statistics. We illustrate how to use our model to sample synthetic data with desired features (assortative or disassortative communities, mixed or hard community assignments, etc.), analyze community detection algorithms, and generate hypergraphs structurally similar to real-world data. Overcoming previous limitations on the generation of synthetic hypergraphs, our work constitutes a substantial advancement in the statistical modeling of higher-order systems.
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Affiliation(s)
- Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
- Department of Computer Science, ETH, 8004 Zürich, Switzerland
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
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16
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Kim JH, Goh KI. Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs. PHYSICAL REVIEW LETTERS 2024; 132:087401. [PMID: 38457718 DOI: 10.1103/physrevlett.132.087401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 11/13/2023] [Accepted: 01/25/2024] [Indexed: 03/10/2024]
Abstract
The presence of the giant component is a necessary condition for the emergence of collective behavior in complex networked systems. Unlike networks, hypergraphs have an important native feature that components of hypergraphs might be of higher order, which could be defined in terms of the number of common nodes shared between hyperedges. Although the extensive higher-order component (HOC) could be witnessed ubiquitously in real-world hypergraphs, the role of the giant HOC in collective behavior on hypergraphs has yet to be elucidated. In this Letter, we demonstrate that the presence of the giant HOC fundamentally alters the outbreak patterns of higher-order contagion dynamics on real-world hypergraphs. Most crucially, the giant HOC is required for the higher-order contagion to invade globally from a single seed. We confirm it by using synthetic random hypergraphs containing adjustable and analytically calculable giant HOC.
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Affiliation(s)
- Jung-Ho Kim
- Department of Physics, Korea University, Seoul 02841, Korea
| | - K-I Goh
- Department of Physics, Korea University, Seoul 02841, Korea
- Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095, USA
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17
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Muolo R, Njougouo T, Gambuzza LV, Carletti T, Frasca M. Phase chimera states on nonlocal hyperrings. Phys Rev E 2024; 109:L022201. [PMID: 38491593 DOI: 10.1103/physreve.109.l022201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 01/08/2024] [Indexed: 03/18/2024]
Abstract
Chimera states are dynamical states where regions of synchronous trajectories coexist with incoherent ones. A significant amount of research has been devoted to studying chimera states in systems of identical oscillators, nonlocally coupled through pairwise interactions. Nevertheless, there is increasing evidence, also supported by available data, that complex systems are composed of multiple units experiencing many-body interactions that can be modeled by using higher-order structures beyond the paradigm of classic pairwise networks. In this work we investigate whether phase chimera states appear in this framework, by focusing on a topology solely involving many-body, nonlocal, and nonregular interactions, hereby named nonlocal d-hyperring, (d+1) being the order of the interactions. We present the theory by using the paradigmatic Stuart-Landau oscillators as node dynamics, and we show that phase chimera states emerge in a variety of structures and with different coupling functions. For comparison, we show that, when higher-order interactions are "flattened" to pairwise ones, the chimera behavior is weaker and more elusive.
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Affiliation(s)
- Riccardo Muolo
- Department of Systems and Control Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Thierry Njougouo
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
- Faculty of Computer Science, University of Namur, B5000 Namur, Belgium
- Department of Electrical and Electronic Engineering, University of Buea, P.O. Box 63, Buea, Cameroon
| | - Lucia Valentina Gambuzza
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
| | - Timoteo Carletti
- Department of Mathematics, University of Namur, B5000 Namur, Belgium
- naXys, Namur Institute for Complex Systems, University of Namur, B5000 Namur, Belgium
| | - Mattia Frasca
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, 95125 Catania, Italy
- Istituto di Analisi dei Sistemi ed Informatica "A. Ruberti", IASI-CNR, 00185 Roma, Italy
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18
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Kar R, Yadav A, Chandrasekar VK, Senthilkumar DV. Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators. CHAOS (WOODBURY, N.Y.) 2024; 34:023110. [PMID: 38363957 DOI: 10.1063/5.0181279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 01/23/2024] [Indexed: 02/18/2024]
Abstract
We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams. The higher-order interaction facilitates the onset of the bifurcation transitions at a much lower disparity between the inter- and intra-population coupling strengths. Furthermore, the higher-order interaction facilitates the spread of breathing chimera in a large region of the parameter space while suppressing the spread of the stable chimera. A low degree of heterogeneity among the phase-lag parameters promotes the spread of both stable chimera and breathing chimera to a large region of the parameter space for a large fraction of the higher-order coupling. In contrast, a large degree of heterogeneity is found to decrease the spread of both chimera states for a large fraction of the higher-order coupling. A global synchronized state is observed above a critical value of heterogeneity among the phase-lag parameters. We have deduced the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen Ansatz. We have also deduced the analytical saddle-node and Hopf bifurcation curves from the evolution equations for the macroscopic order parameters and found them to match with the bifurcation curves obtained using the software XPPAUT and with the simulation results.
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Affiliation(s)
- Rumi Kar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
| | - Akash Yadav
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
| | - V K Chandrasekar
- Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, Tamil Nadu, India
| | - D V Senthilkumar
- School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, Kerala, India
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19
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Ruffini G, Lopez-Sola E, Vohryzek J, Sanchez-Todo R. Neural Geometrodynamics, Complexity, and Plasticity: A Psychedelics Perspective. ENTROPY (BASEL, SWITZERLAND) 2024; 26:90. [PMID: 38275498 PMCID: PMC11154528 DOI: 10.3390/e26010090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Revised: 01/14/2024] [Accepted: 01/17/2024] [Indexed: 01/27/2024]
Abstract
We explore the intersection of neural dynamics and the effects of psychedelics in light of distinct timescales in a framework integrating concepts from dynamics, complexity, and plasticity. We call this framework neural geometrodynamics for its parallels with general relativity's description of the interplay of spacetime and matter. The geometry of trajectories within the dynamical landscape of "fast time" dynamics are shaped by the structure of a differential equation and its connectivity parameters, which themselves evolve over "slow time" driven by state-dependent and state-independent plasticity mechanisms. Finally, the adjustment of plasticity processes (metaplasticity) takes place in an "ultraslow" time scale. Psychedelics flatten the neural landscape, leading to heightened entropy and complexity of neural dynamics, as observed in neuroimaging and modeling studies linking increases in complexity with a disruption of functional integration. We highlight the relationship between criticality, the complexity of fast neural dynamics, and synaptic plasticity. Pathological, rigid, or "canalized" neural dynamics result in an ultrastable confined repertoire, allowing slower plastic changes to consolidate them further. However, under the influence of psychedelics, the destabilizing emergence of complex dynamics leads to a more fluid and adaptable neural state in a process that is amplified by the plasticity-enhancing effects of psychedelics. This shift manifests as an acute systemic increase of disorder and a possibly longer-lasting increase in complexity affecting both short-term dynamics and long-term plastic processes. Our framework offers a holistic perspective on the acute effects of these substances and their potential long-term impacts on neural structure and function.
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Affiliation(s)
- Giulio Ruffini
- Brain Modeling Department, Neuroelectrics, 08035 Barcelona, Spain; (E.L.-S.); (R.S.-T.)
| | - Edmundo Lopez-Sola
- Brain Modeling Department, Neuroelectrics, 08035 Barcelona, Spain; (E.L.-S.); (R.S.-T.)
- Computational Neuroscience Group, Universitat Pompeu Fabra, 08018 Barcelona, Spain;
| | - Jakub Vohryzek
- Computational Neuroscience Group, Universitat Pompeu Fabra, 08018 Barcelona, Spain;
- Centre for Eudaimonia and Human Flourishing, Linacre College, University of Oxford, Oxford OX3 9BX, UK
| | - Roser Sanchez-Todo
- Brain Modeling Department, Neuroelectrics, 08035 Barcelona, Spain; (E.L.-S.); (R.S.-T.)
- Computational Neuroscience Group, Universitat Pompeu Fabra, 08018 Barcelona, Spain;
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20
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Di Gaetano L, Battiston F, Starnini M. Percolation and Topological Properties of Temporal Higher-Order Networks. PHYSICAL REVIEW LETTERS 2024; 132:037401. [PMID: 38307051 DOI: 10.1103/physrevlett.132.037401] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Revised: 10/23/2023] [Accepted: 12/11/2023] [Indexed: 02/04/2024]
Abstract
Many complex systems that exhibit temporal nonpairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variable formalism to analytically characterize a general class of higher-order network models. We apply our framework to a temporal higher-order activity-driven model, providing analytical expressions for the main topological properties of the time-integrated hypergraphs, depending on the integration time and the activity distributions characterizing the model. Furthermore, we provide analytical estimates for the percolation times of general classes of uncorrelated and correlated hypergraphs. Finally, we quantify the extent to which the percolation time of empirical social interactions is underestimated when their higher-order nature is neglected.
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Affiliation(s)
- Leonardo Di Gaetano
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Michele Starnini
- Departament de Fisica, Universitat Politecnica de Catalunya, Campus Nord, 08034 Barcelona, Spain
- CENTAI Institute, 10138 Turin, Italy
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21
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Anwar MS, Frolov N, Hramov AE, Ghosh D. Self-organized bistability on globally coupled higher-order networks. Phys Rev E 2024; 109:014225. [PMID: 38366474 DOI: 10.1103/physreve.109.014225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 01/04/2024] [Indexed: 02/18/2024]
Abstract
Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints. By applying Ott-Antonsen dimensionality reduction in the thermodynamic limit to the higher-order network, we derive SOB requirements under coupling limits that are in good agreement with numerical simulations on systems of finite size. We use continuous synchronization diagrams and statistical data from spontaneous synchronized events to demonstrate the crucial role SOB plays in initiating and terminating temporary synchronized events. We show that under weak-coupling consumption, these spontaneous occurrences closely resemble the statistical traits of the epileptic brain functioning.
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Affiliation(s)
- Md Sayeed Anwar
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Nikita Frolov
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, KU Leuven, Herestraat 49, 3000 Leuven, Belgium
| | - Alexander E Hramov
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo str., Kaliningrad 236016, Russia
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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22
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Duong-Tran D, Kaufmann R, Chen J, Wang X, Garai S, Xu F, Bao J, Amico E, Kaplan AD, Petri G, Goni J, Zhao Y, Shen L. Homological landscape of human brain functional sub-circuits. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.12.22.573062. [PMID: 38187668 PMCID: PMC10769445 DOI: 10.1101/2023.12.22.573062] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2024]
Abstract
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 H 1 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 H 0 , ii) Motor task H 1 , and iii) Working memory task H 2 . 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.
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Affiliation(s)
- Duy Duong-Tran
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
- Department of Mathematics, United States Naval Academy, Annapolis, MD, USA
| | - Ralph Kaufmann
- Department of Mathematics, Purdue University, West Lafayette, IN, USA
| | - Jiong Chen
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
- Department of Bioengineering, School of Engineering and Applied Science, University of Pennsylvania, PA, USA
| | - Xuan Wang
- Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA, USA
| | - Sumita Garai
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
| | - Frederick Xu
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
| | - Jingxuan Bao
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
| | - Enrico Amico
- Neuro-X Institute, EPFL, Geneva, Switzerland
- Department of Radiology and Medical Informatics, University of Geneva, Switzerland
| | - Alan David Kaplan
- Computational Engineering Division, Lawrence Livermore National Laboratory, Livermore, CA, USA
| | - Giovanni Petri
- CENTAI Institute, 10138 Torino, Italy
- NPLab, Network Science Institute, Northeastern University London, London, E1W 1LP, United Kingdom
- Networks Unit, IMT Lucca Institute, 55100 Lucca, Italy
| | - Joaquin Goni
- Purdue Institute for Integrative Neuroscience, Purdue University, West Lafayette, Indiana, USA
- School of Industrial Engineering, Purdue University, West Lafayette, Indiana, USA
- Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana, US
| | - Yize Zhao
- School of Public Health, Yale University, New Heaven, CT, USA
| | - Li Shen
- Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, PA, USA
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23
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Ohki T, Kunii N, Chao ZC. Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0. Rev Neurosci 2023; 34:839-868. [PMID: 36960579 DOI: 10.1515/revneuro-2022-0137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2022] [Accepted: 02/26/2023] [Indexed: 03/25/2023]
Abstract
There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.
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Affiliation(s)
- Takefumi Ohki
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
| | - Naoto Kunii
- Department of Neurosurgery, The University of Tokyo, Tokyo 113-0033, Japan
| | - Zenas C Chao
- International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo 113-0033, Japan
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24
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Chung MK, Ramos CG, De Paiva FB, Mathis J, Prabhakaran V, Nair VA, Meyerand ME, Hermann BP, Binder JR, Struck AF. Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance. Neuroimage 2023; 284:120436. [PMID: 37931870 PMCID: PMC11074922 DOI: 10.1016/j.neuroimage.2023.120436] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 09/14/2023] [Accepted: 10/30/2023] [Indexed: 11/08/2023] Open
Abstract
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.
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Affiliation(s)
- Moo K Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, USA.
| | | | | | | | | | - Veena A Nair
- Department of Radiology, University of Wisconsin-Madison, USA.
| | - Mary E Meyerand
- Departments of Medical Physics & Biomedical Engineering, University of Wisconsin-Madison, USA.
| | - Bruce P Hermann
- Department of Neurology, University of Wisconsin-Madison, USA.
| | | | - Aaron F Struck
- Department of Neurology, University of Wisconsin-Madison, USA.
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25
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Bazinet V, Hansen JY, Misic B. Towards a biologically annotated brain connectome. Nat Rev Neurosci 2023; 24:747-760. [PMID: 37848663 DOI: 10.1038/s41583-023-00752-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/20/2023] [Indexed: 10/19/2023]
Abstract
The brain is a network of interleaved neural circuits. In modern connectomics, brain connectivity is typically encoded as a network of nodes and edges, abstracting away the rich biological detail of local neuronal populations. Yet biological annotations for network nodes - such as gene expression, cytoarchitecture, neurotransmitter receptors or intrinsic dynamics - can be readily measured and overlaid on network models. Here we review how connectomes can be represented and analysed as annotated networks. Annotated connectomes allow us to reconceptualize architectural features of networks and to relate the connection patterns of brain regions to their underlying biology. Emerging work demonstrates that annotated connectomes help to make more veridical models of brain network formation, neural dynamics and disease propagation. Finally, annotations can be used to infer entirely new inter-regional relationships and to construct new types of network that complement existing connectome representations. In summary, biologically annotated connectomes offer a compelling way to study neural wiring in concert with local biological features.
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Affiliation(s)
- Vincent Bazinet
- Montréal Neurological Institute, McGill University, Montréal, Quebec, Canada
| | - Justine Y Hansen
- Montréal Neurological Institute, McGill University, Montréal, Quebec, Canada
| | - Bratislav Misic
- Montréal Neurological Institute, McGill University, Montréal, Quebec, Canada.
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26
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Miranda M, Estrada-Rodriguez G, Estrada E. What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1599. [PMID: 38136479 PMCID: PMC10742477 DOI: 10.3390/e25121599] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Revised: 11/24/2023] [Accepted: 11/28/2023] [Indexed: 12/24/2023]
Abstract
Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque.
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Affiliation(s)
- Manuel Miranda
- Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), 07122 Palma de Mallorca, Spain;
| | | | - Ernesto Estrada
- Institute of Cross-Disciplinary Physics and Complex Systems, IFISC (UIB-CSIC), 07122 Palma de Mallorca, Spain;
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27
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Betzel RF, Faskowitz J, Sporns O. Living on the edge: network neuroscience beyond nodes. Trends Cogn Sci 2023; 27:1068-1084. [PMID: 37716895 PMCID: PMC10592364 DOI: 10.1016/j.tics.2023.08.009] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Revised: 07/14/2023] [Accepted: 08/10/2023] [Indexed: 09/18/2023]
Abstract
Network neuroscience has emphasized the connectional properties of neural elements - cells, populations, and regions. This has come at the expense of the anatomical and functional connections that link these elements to one another. A new perspective - namely one that emphasizes 'edges' - may prove fruitful in addressing outstanding questions in network neuroscience. We highlight one recently proposed 'edge-centric' method and review its current applications, merits, and limitations. We also seek to establish conceptual and mathematical links between this method and previously proposed approaches in the network science and neuroimaging literature. We conclude by presenting several avenues for future work to extend and refine existing edge-centric analysis.
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Affiliation(s)
- Richard F Betzel
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA; Cognitive Science Program, Indiana University, Bloomington, IN 47405, USA; Program in Neuroscience, Indiana University, Bloomington, IN 47405, USA; Network Science Institute, Indiana University, Bloomington, IN 47405, USA.
| | - Joshua Faskowitz
- Section on Functional Imaging Methods, National Institute of Mental Health, Bethesda, MD, USA
| | - Olaf Sporns
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA; Cognitive Science Program, Indiana University, Bloomington, IN 47405, USA; Program in Neuroscience, Indiana University, Bloomington, IN 47405, USA; Network Science Institute, Indiana University, Bloomington, IN 47405, USA
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28
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Moron-Fernández MJ, Amedeo LM, Monterroso Muñoz A, Molina-Abril H, Díaz-del-Río F, Bini F, Marinozzi F, Real P. Analysis of Connectome Graphs Based on Boundary Scale. SENSORS (BASEL, SWITZERLAND) 2023; 23:8607. [PMID: 37896699 PMCID: PMC10610691 DOI: 10.3390/s23208607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 10/10/2023] [Accepted: 10/11/2023] [Indexed: 10/29/2023]
Abstract
The purpose of this work is to advance in the computational study of connectome graphs from a topological point of view. Specifically, starting from a sequence of hypergraphs associated to a brain graph (obtained using the Boundary Scale model, BS2), we analyze the resulting scale-space representation using classical topological features, such as Betti numbers and average node and edge degrees. In this way, the topological information that can be extracted from the original graph is substantially enriched, thus providing an insightful description of the graph from a clinical perspective. To assess the qualitative and quantitative topological information gain of the BS2 model, we carried out an empirical analysis of neuroimaging data using a dataset that contains the connectomes of 96 healthy subjects, 52 women and 44 men, generated from MRI scans in the Human Connectome Project. The results obtained shed light on the differences between these two classes of subjects in terms of neural connectivity.
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Affiliation(s)
- María José Moron-Fernández
- Higher Technical School of Informatics Engineering, University of Seville, Avda. Reina Mercedes, s/n, 41012 Seville, Spain; (M.J.M.-F.); (A.M.M.); (H.M.-A.); (F.D.-d.-R.); (P.R.)
| | - Ludovica Maria Amedeo
- Department of Mechanical and Aerospace Engineering, “Sapienza” University of Rome, Via Eudossiana, 18, 00184 Rome, Italy; (F.B.); (F.M.)
| | - Alberto Monterroso Muñoz
- Higher Technical School of Informatics Engineering, University of Seville, Avda. Reina Mercedes, s/n, 41012 Seville, Spain; (M.J.M.-F.); (A.M.M.); (H.M.-A.); (F.D.-d.-R.); (P.R.)
| | - Helena Molina-Abril
- Higher Technical School of Informatics Engineering, University of Seville, Avda. Reina Mercedes, s/n, 41012 Seville, Spain; (M.J.M.-F.); (A.M.M.); (H.M.-A.); (F.D.-d.-R.); (P.R.)
| | - Fernando Díaz-del-Río
- Higher Technical School of Informatics Engineering, University of Seville, Avda. Reina Mercedes, s/n, 41012 Seville, Spain; (M.J.M.-F.); (A.M.M.); (H.M.-A.); (F.D.-d.-R.); (P.R.)
| | - Fabiano Bini
- Department of Mechanical and Aerospace Engineering, “Sapienza” University of Rome, Via Eudossiana, 18, 00184 Rome, Italy; (F.B.); (F.M.)
| | - Franco Marinozzi
- Department of Mechanical and Aerospace Engineering, “Sapienza” University of Rome, Via Eudossiana, 18, 00184 Rome, Italy; (F.B.); (F.M.)
| | - Pedro Real
- Higher Technical School of Informatics Engineering, University of Seville, Avda. Reina Mercedes, s/n, 41012 Seville, Spain; (M.J.M.-F.); (A.M.M.); (H.M.-A.); (F.D.-d.-R.); (P.R.)
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29
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Jiang C, He Y, Betzel RF, Wang YS, Xing XX, Zuo XN. Optimizing network neuroscience computation of individual differences in human spontaneous brain activity for test-retest reliability. Netw Neurosci 2023; 7:1080-1108. [PMID: 37781147 PMCID: PMC10473278 DOI: 10.1162/netn_a_00315] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2022] [Accepted: 03/22/2023] [Indexed: 10/03/2023] Open
Abstract
A rapidly emerging application of network neuroscience in neuroimaging studies has provided useful tools to understand individual differences in intrinsic brain function by mapping spontaneous brain activity, namely intrinsic functional network neuroscience (ifNN). However, the variability of methodologies applied across the ifNN studies-with respect to node definition, edge construction, and graph measurements-makes it difficult to directly compare findings and also challenging for end users to select the optimal strategies for mapping individual differences in brain networks. Here, we aim to provide a benchmark for best ifNN practices by systematically comparing the measurement reliability of individual differences under different ifNN analytical strategies using the test-retest design of the Human Connectome Project. The results uncovered four essential principles to guide ifNN studies: (1) use a whole brain parcellation to define network nodes, including subcortical and cerebellar regions; (2) construct functional networks using spontaneous brain activity in multiple slow bands; and (3) optimize topological economy of networks at individual level; and (4) characterize information flow with specific metrics of integration and segregation. We built an interactive online resource of reliability assessments for future ifNN (https://ibraindata.com/research/ifNN).
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Affiliation(s)
- Chao Jiang
- School of Psychology, Capital Normal University, Beijing, China
| | - Ye He
- School of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing, China
| | - Richard F. Betzel
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana, USA
| | - Yin-Shan Wang
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
- Developmental Population Neuroscience Research Center, International Data Group/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
| | - Xiu-Xia Xing
- Department of Applied Mathematics, College of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, China
| | - Xi-Nian Zuo
- State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China
- Developmental Population Neuroscience Research Center, International Data Group/McGovern Institute for Brain Research, Beijing Normal University, Beijing, China
- National Basic Science Data Center, Beijing, China
- Institute of Psychology, Chinese Academy of Sciences, Beijing, China
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30
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Pisarchik AN, Andreev AV, Kurkin SA, Stoyanov D, Badarin AA, Paunova R, Hramov AE. Topology switching during window thresholding fMRI-based functional networks of patients with major depressive disorder: Consensus network approach. CHAOS (WOODBURY, N.Y.) 2023; 33:093122. [PMID: 37712918 DOI: 10.1063/5.0166148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 08/29/2023] [Indexed: 09/16/2023]
Abstract
We present a novel method for analyzing brain functional networks using functional magnetic resonance imaging data, which involves utilizing consensus networks. In this study, we compare our approach to a standard group-based method for patients diagnosed with major depressive disorder (MDD) and a healthy control group, taking into account different levels of connectivity. Our findings demonstrate that the consensus network approach uncovers distinct characteristics in network measures and degree distributions when considering connection strengths. In the healthy control group, as connection strengths increase, we observe a transition in the network topology from a combination of scale-free and random topologies to a small-world topology. Conversely, the MDD group exhibits uncertainty in weak connections, while strong connections display small-world properties. In contrast, the group-based approach does not exhibit significant differences in behavior between the two groups. However, it does indicate a transition in topology from a scale-free-like structure to a combination of small-world and scale-free topologies. The use of the consensus network approach also holds immense potential for the classification of MDD patients, as it unveils substantial distinctions between the two groups.
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Affiliation(s)
- Alexander N Pisarchik
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo Str., Kaliningrad 236016, Russia
- Center for Biomedical Technology, Universidad Politécnica de Madrid, Campus Montegancedo, Pozuelo de Alarcón 28223, Spain
| | - Andrey V Andreev
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo Str., Kaliningrad 236016, Russia
| | - Semen A Kurkin
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo Str., Kaliningrad 236016, Russia
| | - Drozdstoy Stoyanov
- Department of Psychiatry and Medical Psychology, Research Institute, Medical University Plovdiv, 15A Vassil Aprilov Blvd., Plovdiv 4002, Bulgaria
| | - Artem A Badarin
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo Str., Kaliningrad 236016, Russia
| | - Rossitsa Paunova
- Department of Psychiatry and Medical Psychology, Research Institute, Medical University Plovdiv, 15A Vassil Aprilov Blvd., Plovdiv 4002, Bulgaria
| | - Alexander E Hramov
- Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 14, A. Nevskogo Str., Kaliningrad 236016, Russia
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31
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Dutta S, Mondal A, Kundu P, Khanra P, Pal P, Hens C. Impact of phase lag on synchronization in frustrated Kuramoto model with higher-order interactions. Phys Rev E 2023; 108:034208. [PMID: 37849147 DOI: 10.1103/physreve.108.034208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 08/25/2023] [Indexed: 10/19/2023]
Abstract
The study of first order transition (explosive synchronization) in an ensemble (network) of coupled oscillators has been the topic of paramount interest among the researchers for more than one decade. Several frameworks have been proposed to induce explosive synchronization in a network and it has been reported that phase frustration in a network usually suppresses first order transition in the presence of pairwise interactions among the oscillators. However, on the contrary, by considering networks of phase frustrated coupled oscillators in the presence of higher-order interactions (up to 2-simplexes) we show here, under certain conditions, phase frustration can promote explosive synchronization in a network. A low-dimensional model of the network in the thermodynamic limit is derived using the Ott-Antonsen ansatz to explain this surprising result. Analytical treatment of the low-dimensional model, including bifurcation analysis, explains the apparent counter intuitive result quite clearly.
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Affiliation(s)
- Sangita Dutta
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Abhijit Mondal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo 14260, USA
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Chittaranjan Hens
- Center for Computational Natural Science and Bioinformatics, International Institute of Informational Technology, Gachibowli, Hyderabad 500032, India
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32
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Dutta S, Kundu P, Khanra P, Hens C, Pal P. Perfect synchronization in complex networks with higher-order interactions. Phys Rev E 2023; 108:024304. [PMID: 37723785 DOI: 10.1103/physreve.108.024304] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 07/11/2023] [Indexed: 09/20/2023]
Abstract
Achieving perfect synchronization in a complex network, specially in the presence of higher-order interactions (HOIs) at a targeted point in the parameter space, is an interesting, yet challenging task. Here we present a theoretical framework to achieve the same under the paradigm of the Sakaguchi-Kuramoto (SK) model. We analytically derive a frequency set to achieve perfect synchrony at some desired point in a complex network of SK oscillators with higher-order interactions. Considering the SK model with HOIs on top of the scale-free, random, and small world networks, we perform extensive numerical simulations to verify the proposed theory. Numerical simulations show that the analytically derived frequency set not only provides stable perfect synchronization in the network at a desired point but also proves to be very effective in achieving a high level of synchronization around it compared to the other choices of frequency sets. The stability and the robustness of the perfect synchronization state of the system are determined using the low-dimensional reduction of the network and by introducing a Gaussian noise around the derived frequency set, respectively.
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Affiliation(s)
- Sangita Dutta
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Pitambar Khanra
- Department of Mathematics, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Chittaranjan Hens
- Center for Computational Natural Science and Bioinformatics, International Institute of Informational Technology, Gachibowli, Hyderabad 500032, India
| | - Pinaki Pal
- Department of Mathematics, National Institute of Technology, Durgapur 713209, India
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33
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Ruggeri N, Contisciani M, Battiston F, De Bacco C. Community detection in large hypergraphs. SCIENCE ADVANCES 2023; 9:eadg9159. [PMID: 37436987 PMCID: PMC10337898 DOI: 10.1126/sciadv.adg9159] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 06/12/2023] [Indexed: 07/14/2023]
Abstract
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. Here, we propose a principled framework to model the organization of higher-order data. Our approach recovers community structure with accuracy exceeding that of currently available state-of-the-art algorithms, as tested in synthetic benchmarks with both hard and overlapping ground-truth partitions. Our model is flexible and allows capturing both assortative and disassortative community structures. Moreover, our method scales orders of magnitude faster than competing algorithms, making it suitable for the analysis of very large hypergraphs, containing millions of nodes and interactions among thousands of nodes. Our work constitutes a practical and general tool for hypergraph analysis, broadening our understanding of the organization of real-world higher-order systems.
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Affiliation(s)
- Nicolò Ruggeri
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
- Department of Computer Science, ETH, 8004 Zürich, Switzerland
| | - Martina Contisciani
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
| | - Federico Battiston
- Department of Network and Data Science, Central European University, 1100 Vienna, Austria
| | - Caterina De Bacco
- Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
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34
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Rouse TC, Ni AM, Huang C, Cohen MR. Topological insights into the neural basis of flexible behavior. Proc Natl Acad Sci U S A 2023; 120:e2219557120. [PMID: 37279273 PMCID: PMC10268229 DOI: 10.1073/pnas.2219557120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/28/2023] [Indexed: 06/08/2023] Open
Abstract
It is widely accepted that there is an inextricable link between neural computations, biological mechanisms, and behavior, but it is challenging to simultaneously relate all three. Here, we show that topological data analysis (TDA) provides an important bridge between these approaches to studying how brains mediate behavior. We demonstrate that cognitive processes change the topological description of the shared activity of populations of visual neurons. These topological changes constrain and distinguish between competing mechanistic models, are connected to subjects' performance on a visual change detection task, and, via a link with network control theory, reveal a tradeoff between improving sensitivity to subtle visual stimulus changes and increasing the chance that the subject will stray off task. These connections provide a blueprint for using TDA to uncover the biological and computational mechanisms by which cognition affects behavior in health and disease.
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Affiliation(s)
- Tevin C. Rouse
- Division of Biological Sciences, Department of Neurobiology, University of Chicago, Chicago, IL60637
| | - Amy M. Ni
- Dietrich School of Arts and Sciences, Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA15260
| | - Chengcheng Huang
- Dietrich School of Arts and Sciences, Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA15260
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA15260
| | - Marlene R. Cohen
- Division of Biological Sciences, Department of Neurobiology, University of Chicago, Chicago, IL60637
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35
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Carletti T, Giambagli L, Bianconi G. Global Topological Synchronization on Simplicial and Cell Complexes. PHYSICAL REVIEW LETTERS 2023; 130:187401. [PMID: 37204901 DOI: 10.1103/physrevlett.130.187401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Revised: 02/17/2023] [Accepted: 04/11/2023] [Indexed: 05/21/2023]
Abstract
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However, the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures signals of any dimension can achieve global synchronization.
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Affiliation(s)
- Timoteo Carletti
- Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
| | - Lorenzo Giambagli
- Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
- Department of Physics and Astronomy, University of Florence, INFN and CSDC, 50019 Sesto Fiorentino, Italy
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom
- The Alan Turing Institute, 96 Euston Road, London, NW1 2DB, United Kingdom
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36
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Anand DV, Chung MK. Hodge Laplacian of Brain Networks. IEEE TRANSACTIONS ON MEDICAL IMAGING 2023; 42:1563-1573. [PMID: 37018280 PMCID: PMC10909176 DOI: 10.1109/tmi.2022.3233876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
The closed loops or cycles in a brain network embeds higher order signal transmission paths, which provide fundamental insights into the functioning of the brain. In this work, we propose an efficient algorithm for systematic identification and modeling of cycles using persistent homology and the Hodge Laplacian. Various statistical inference procedures on cycles are developed. We validate the our methods on simulations and apply to brain networks obtained through the resting state functional magnetic resonance imaging. The computer codes for the Hodge Laplacian are given in https://github.com/laplcebeltrami/hodge.
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37
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Zhang Y, Lucas M, Battiston F. Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes. Nat Commun 2023; 14:1605. [PMID: 36959174 PMCID: PMC10036330 DOI: 10.1038/s41467-023-37190-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 03/03/2023] [Indexed: 03/25/2023] Open
Abstract
Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations such as simplicial complexes and hypergraphs. So far, the choice between simplicial complexes and hypergraphs has often been motivated by technical convenience. Here, using synchronization as an example, we demonstrate that the effects of higher-order interactions are highly representation-dependent. In particular, higher-order interactions typically enhance synchronization in hypergraphs but have the opposite effect in simplicial complexes. We provide theoretical insight by linking the synchronizability of different hypergraph structures to (generalized) degree heterogeneity and cross-order degree correlation, which in turn influence a wide range of dynamical processes from contagion to diffusion. Our findings reveal the hidden impact of higher-order representations on collective dynamics, highlighting the importance of choosing appropriate representations when studying systems with nonpairwise interactions.
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Affiliation(s)
| | - Maxime Lucas
- ISI Foundation, Torino, Italy.
- CENTAI Institute, Torino, Italy.
| | - Federico Battiston
- Department of Network and Data Science, Central European University, Vienna, Austria.
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38
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Das S, Anand DV, Chung MK. Topological data analysis of human brain networks through order statistics. PLoS One 2023; 18:e0276419. [PMID: 36913351 PMCID: PMC10010566 DOI: 10.1371/journal.pone.0276419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 09/21/2022] [Indexed: 03/14/2023] Open
Abstract
Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.
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Affiliation(s)
- Soumya Das
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
| | - D. Vijay Anand
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
| | - Moo K. Chung
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, United States of America
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39
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Sun H, Radicchi F, Kurths J, Bianconi G. The dynamic nature of percolation on networks with triadic interactions. Nat Commun 2023; 14:1308. [PMID: 36894591 PMCID: PMC9998640 DOI: 10.1038/s41467-023-37019-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 02/24/2023] [Indexed: 03/11/2023] Open
Abstract
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.
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Affiliation(s)
- Hanlin Sun
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
| | - Filippo Radicchi
- Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, 47408, USA
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
- Department of Physics, Humboldt University of Berlin, Berlin, Germany
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK.
- The Alan Turing Institute, The British Library, London, NW1 2DB, UK.
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40
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George VK, Gupta A, Silva GA. Identifying Steady State in the Network Dynamics of Spiking Neural Networks. Heliyon 2023; 9:e13913. [PMID: 36967881 PMCID: PMC10036509 DOI: 10.1016/j.heliyon.2023.e13913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2022] [Revised: 12/15/2022] [Accepted: 02/15/2023] [Indexed: 03/04/2023] Open
Abstract
Analysis of the dynamics of complex networks can provide valuable information. For example, the dynamics can be used to characterize and differentiate between different network inputs and configurations. However, without quantitatively delineating the network's dynamic regimes, analysis of the network's dynamics is based on heuristics and qualitative signatures of transient or steady-state regimes. This is not ideal because interesting phenomena can occur during the transient regime, steady-state regime, or at the transition between the two dynamic regimes. Moreover, for simulated and observed systems, precise knowledge of the network's dynamical regime is imperative when considering metrics on minimal mathematical descriptions of the dynamics, otherwise either too much or too little data is analyzed. Here, we develop quantitative methods to ascertain the starting point and period of steady-state network activity. Using the precise knowledge of the network's dynamic regimes, we build minimal representations of the network dynamics that form the basis for future work. We show applications of our techniques on idealized signals and on the dynamics of a biologically inspired spiking neural network.
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41
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Calmon L, Krishnagopal S, Bianconi G. Local Dirac Synchronization on networks. CHAOS (WOODBURY, N.Y.) 2023; 33:033117. [PMID: 37003807 DOI: 10.1063/5.0132468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 02/13/2023] [Indexed: 06/19/2023]
Abstract
We propose Local Dirac Synchronization that uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely while the other modes are interacting non-linearly, leading to a collectively synchronized state when the coupling constant of the model is increased. Local Dirac Synchronization is characterized by discontinuous transitions and the emergence of a rhythmic coherent phase. In this rhythmic phase, one of the two complex order parameters oscillates in the complex plane at a slow frequency (called emergent frequency) in the frame in which the intrinsic frequencies have zero average. Our theoretical results obtained within the annealed approximation are validated by extensive numerical results on fully connected networks and sparse Poisson and scale-free networks. Local Dirac Synchronization on both random and real networks, such as the connectome of Caenorhabditis Elegans, reveals the interplay between topology (Betti numbers and harmonic modes) and non-linear dynamics. This unveils how topology might play a role in the onset of brain rhythms.
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Affiliation(s)
- Lucille Calmon
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Sanjukta Krishnagopal
- Department of Electrical Engineering and Computer Science, University of California Berkeley, California 94720, USA
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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42
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Adhikari S, Restrepo JG, Skardal PS. Synchronization of phase oscillators on complex hypergraphs. CHAOS (WOODBURY, N.Y.) 2023; 33:033116. [PMID: 37003819 DOI: 10.1063/5.0116747] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 02/17/2023] [Indexed: 06/19/2023]
Abstract
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for the system's order parameters. We illustrate our framework with the example of a hypergraph with hyperedges of sizes 2 (links) and 3 (triangles). For this case, we obtain a set of two coupled nonlinear algebraic equations for the order parameters. For strong values of coupling via triangles, the system exhibits bistability and explosive synchronization transitions. We find conditions that lead to bistability in terms of hypergraph properties and validate our predictions with numerical simulations. Our results provide a general framework to study the synchronization of phase oscillators in hypergraphs, and they can be extended to hypergraphs with hyperedges of arbitrary sizes, dynamic-structural correlations, and other features.
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Affiliation(s)
- Sabina Adhikari
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309, USA
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Skardal PS, Adhikari S, Restrepo JG. Multistability in coupled oscillator systems with higher-order interactions and community structure. CHAOS (WOODBURY, N.Y.) 2023; 33:023140. [PMID: 36859233 DOI: 10.1063/5.0106906] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by either higher-order interactions or community structure alone, including synchronized states with communities organized into clusters in-phase, anti-phase, and a novel skew-phase, as well as an incoherent-synchronized state. Moreover, the system displays strong multistability with many of these states stable at the same time. We demonstrate our findings by deriving the low dimensional dynamics of the system and examining the system's bifurcations using stability analysis and perturbation theory.
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Affiliation(s)
| | - Sabina Adhikari
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA
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Pitsik EN, Maximenko VA, Kurkin SA, Sergeev AP, Stoyanov D, Paunova R, Kandilarova S, Simeonova D, Hramov AE. The topology of fMRI-based networks defines the performance of a graph neural network for the classification of patients with major depressive disorder. CHAOS, SOLITONS & FRACTALS 2023; 167:113041. [DOI: 10.1016/j.chaos.2022.113041] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/01/2024]
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45
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Vezzani A, Muñoz MA, Burioni R. Anomalous finite-size scaling in higher-order processes with absorbing states. Phys Rev E 2023; 107:014105. [PMID: 36797930 DOI: 10.1103/physreve.107.014105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Accepted: 12/21/2022] [Indexed: 01/09/2023]
Abstract
Here we study standard and higher-order birth-death processes on fully connected networks, within the perspective of large-deviation theory [also referred to as the Wentzel-Kramers-Brillouin (WKB) method in some contexts]. We obtain a general expression for the leading and next-to-leading terms of the stationary probability distribution of the fraction of "active" sites as a function of parameters and network size N. We reproduce several results from the literature and, in particular, we derive all the moments of the stationary distribution for the q-susceptible-infected-susceptible (q-SIS) model, i.e., a high-order epidemic model requiring q active ("infected") sites to activate an additional one. We uncover a very rich scenario for the fluctuations of the fraction of active sites, with nontrivial finite-size-scaling properties. In particular, we show that the variance-to-mean ratio diverges at criticality for [1≤q≤3], with a maximal variability at q=2, confirming that complex-contagion processes can exhibit peculiar scaling features including wild variability. Moreover, the leading order in a large-deviation approach does not suffice to describe them: next-to-leading terms are essential to capture the intrinsic singularity at the origin of systems with absorbing states. Some possible extensions of this work are also discussed.
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Affiliation(s)
- Alessandro Vezzani
- Istituto dei Materiali per l'Elettronica ed il Magnetismo (IMEM-CNR), Parco Area delle Scienze, 37/A-43124 Parma, Italy; Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy; and INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada. E-18071 Granada, Spain
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università degli Studi di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy and INFN, Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43124 Parma, Italy
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46
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Giambagli L, Calmon L, Muolo R, Carletti T, Bianconi G. Diffusion-driven instability of topological signals coupled by the Dirac operator. Phys Rev E 2022; 106:064314. [PMID: 36671168 DOI: 10.1103/physreve.106.064314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2022] [Accepted: 11/30/2022] [Indexed: 12/24/2022]
Abstract
The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now, reaction-diffusion systems have been studied only when species are defined on the nodes of a network. However, in a number of real systems including, e.g., the brain and the climate, dynamical variables are not only defined on nodes but also on links, faces, and higher-dimensional cells of simplicial or cell complexes, leading to topological signals. In this work, we study reaction-diffusion processes of topological signals coupled through the Dirac operator. The Dirac operator allows topological signals of different dimension to interact or cross-diffuse as it projects the topological signals defined on simplices or cells of a given dimension to simplices or cells of one dimension up or one dimension down. By focusing on the framework involving nodes and links, we establish the conditions for the emergence of Turing patterns and we show that the latter are never localized only on nodes or only on links of the network. Moreover, when the topological signals display a Turing pattern their projection does as well. We validate the theory hereby developed on a benchmark network model and on square lattices with periodic boundary conditions.
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Affiliation(s)
- Lorenzo Giambagli
- Department of Physics and Astronomy, University of Florence, INFN & CSDC, Sesto Fiorentino, Italy.,Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
| | - Lucille Calmon
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Riccardo Muolo
- Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium.,Department of Applied Mathematics, Mathematical Institute Federal University of Rio de Janeiro, Avenida Athos da Silveira Ramos, 149, Rio de Janeiro 21941-909, Brazil
| | - Timoteo Carletti
- Department of Mathematics & naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium
| | - Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.,The Alan Turing Institute, 96 Euston Road, London NW1 2DB, United Kingdom
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Barthelemy M. Class of models for random hypergraphs. Phys Rev E 2022; 106:064310. [PMID: 36671196 DOI: 10.1103/physreve.106.064310] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2022] [Accepted: 12/01/2022] [Indexed: 12/23/2022]
Abstract
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as 1/sqrt[EN] where N is the number of nodes and E the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as r_{c}^{*}∼1/sqrt[E]. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.
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Affiliation(s)
- Marc Barthelemy
- Université Paris-Saclay, CEA, CNRS, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France and Centre d'Analyse et de Mathématique Sociales (CNRS/EHESS) 54 Avenue de Raspail, 75006 Paris, France
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Inference of hyperedges and overlapping communities in hypergraphs. Nat Commun 2022; 13:7229. [PMID: 36433942 PMCID: PMC9700742 DOI: 10.1038/s41467-022-34714-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 11/02/2022] [Indexed: 11/27/2022] Open
Abstract
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to characterize the structural organization of hypergraphs. The method allows to infer missing hyperedges of any size in a principled way, and to jointly detect overlapping communities in presence of higher-order interactions. Furthermore, our model has an efficient numerical implementation, and it runs faster than dyadic algorithms on pairwise records projected from higher-order data. We apply our method to a variety of real-world systems, showing strong performance in hyperedge prediction tasks, detecting communities well aligned with the information carried by interactions, and robustness against addition of noisy hyperedges. Our approach illustrates the fundamental advantages of a hypergraph probabilistic model when modeling relational systems with higher-order interactions.
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Unraveling the functional attributes of the language connectome: crucial subnetworks, flexibility and variability. Neuroimage 2022; 263:119672. [PMID: 36209795 DOI: 10.1016/j.neuroimage.2022.119672] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 10/04/2022] [Accepted: 10/05/2022] [Indexed: 11/23/2022] Open
Abstract
Language processing is a highly integrative function, intertwining linguistic operations (processing the language code intentionally used for communication) and extra-linguistic processes (e.g., attention monitoring, predictive inference, long-term memory). This synergetic cognitive architecture requires a distributed and specialized neural substrate. Brain systems have mainly been examined at rest. However, task-related functional connectivity provides additional and valuable information about how information is processed when various cognitive states are involved. We gathered thirteen language fMRI tasks in a unique database of one hundred and fifty neurotypical adults (InLang [Interactive networks of Language] database), providing the opportunity to assess language features across a wide range of linguistic processes. Using this database, we applied network theory as a computational tool to model the task-related functional connectome of language (LANG atlas). The organization of this data-driven neurocognitive atlas of language was examined at multiple levels, uncovering its major components (or crucial subnetworks), and its anatomical and functional correlates. In addition, we estimated its reconfiguration as a function of linguistic demand (flexibility) or several factors such as age or gender (variability). We observed that several discrete networks could be specifically shaped to promote key functional features of language: coding-decoding (Net1), control-executive (Net2), abstract-knowledge (Net3), and sensorimotor (Net4) functions. The architecture of these systems and the functional connectivity of the pivotal brain regions varied according to the nature of the linguistic process, gender, or age. By accounting for the multifaceted nature of language and modulating factors, this study can contribute to enriching and refining existing neurocognitive models of language. The LANG atlas can also be considered a reference for comparative or clinical studies involving various patients and conditions.
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Tozzi A, Mariniello L. Unusual Mathematical Approaches Untangle Nervous Dynamics. Biomedicines 2022; 10:biomedicines10102581. [PMID: 36289843 PMCID: PMC9599563 DOI: 10.3390/biomedicines10102581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2022] [Revised: 10/10/2022] [Accepted: 10/10/2022] [Indexed: 11/16/2022] Open
Abstract
The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.
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Affiliation(s)
- Arturo Tozzi
- Center for Nonlinear Science, University of North Texas, Denton, TX 76203-5017, USA
- Correspondence:
| | - Lucio Mariniello
- Department of Pediatrics, University Federico II, 80131 Naples, Italy
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