Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

Nature Communications, Год журнала: 2023, Номер 14(1)

Опубликована: Март 23, 2023

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 simplicial complexes hypergraphs. So far, the choice between hypergraphs has often been motivated by technical convenience. Here, using synchronization an example, we demonstrate that effects higher-order interactions are highly representation-dependent. In particular, typically enhance in but opposite effect complexes. We provide theoretical insight linking synchronizability different hypergraph structures (generalized) degree heterogeneity cross-order correlation, which turn influence wide range dynamical processes from contagion diffusion. Our findings reveal hidden impact on dynamics, highlighting importance choosing appropriate when studying with nonpairwise interactions.

Язык: Английский

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Dirac signal processing of higher-order topological signals

New Journal of Physics, Год журнала: 2023, Номер 25(9), С. 093013 - 093013

Опубликована: Авг. 23, 2023

Abstract Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also links, triangles and in general higher dimensional simplices of simplicial complexes. These describe a large variety real systems including currents ocean, synaptic between neurons biological transportation networks. In scenarios signal data might be noisy an important task is process these by improving their noise ratio. So far typically processed independently each other. For instance, node link signals, algorithms that enforce consistent processing across different dimensions largely lacking. Here we propose Dirac processing, adaptive, unsupervised algorithm learns jointly filter supported on links complexes way. The proposed formulated terms discrete operator interpreted as ‘square root’ higher-order Hodge Laplacian. We discuss detail properties its spectrum chirality eigenvectors adopt this formulate defined test our synthetic drifters ocean find learn efficiently reconstruct true outperforming based exclusively

Язык: Английский

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Complex quantum networks: a topical review

Journal of Physics A Mathematical and Theoretical, Год журнала: 2024, Номер 57(23), С. 233001 - 233001

Опубликована: Апрель 22, 2024

Abstract These are exciting times for quantum physics as new technologies expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving ideal mathematical and computational framework capture the complexity of large interacting systems. Here we provide a comprehensive timely review rising field complex networks. On one side, this subject key harness potential networks in order design principles boost enhance algorithms technologies. other side can generation infer significant properties. The features fundamental research questions diverse designing shape Hamiltonians their corresponding phase diagram, taming many-body systems with theory, revealing how predict novel properties transitions, studying interplay between architecture, topology performance communication Our covers all these multifaceted aspects self-contained presentation aimed both network-curious physicists quantum-curious theorists. We that unifies along four main lines: network-generalized, quantum-applied, quantum-generalized quantum-enhanced. Finally draw attention connections lines, which lead opportunities discoveries interface science.

Язык: Английский

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A unified framework for simplicial Kuramoto models

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2024, Номер 34(5)

Опубликована: Май 1, 2024

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

Язык: Английский

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Topology shapes dynamics of higher-order networks

Nature Physics, Год журнала: 2025, Номер unknown

Опубликована: Фев. 19, 2025

Язык: Английский

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Local Dirac Synchronization on networks

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2023, Номер 33(3)

Опубликована: Март 1, 2023

We propose Local Dirac Synchronization that uses the operator to capture dynamics of coupled nodes and link signals on an arbitrary network. In Synchronization, harmonic modes oscillate freely while other are interacting non-linearly, leading a collectively synchronized state when coupling constant model is increased. characterized by discontinuous transitions emergence rhythmic coherent phase. this phase, one two complex order parameters oscillates in plane at slow frequency (called emergent frequency) frame which intrinsic frequencies have zero average. Our theoretical results obtained within annealed approximation validated extensive numerical fully connected networks sparse Poisson scale-free networks. both random real networks, such as connectome Caenorhabditis Elegans, reveals interplay between topology (Betti numbers modes) non-linear dynamics. This unveils how might play role onset brain rhythms.

Язык: Английский

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Persistent Dirac for molecular representation

Scientific Reports, Год журнала: 2023, Номер 13(1)

Опубликована: Июль 11, 2023

Molecular representations are of fundamental importance for the modeling and analysing molecular systems. The successes in drug design materials discovery have been greatly contributed by representation models. In this paper, we present a computational framework that is mathematically rigorous based on persistent Dirac operator. properties discrete weighted unweighted matrix systematically discussed, biological meanings both homological non-homological eigenvectors studied. We also evaluate impact various weighting schemes matrix. Additionally, set physical attributes characterize persistence variation spectrum matrices during filtration process proposed to be fingerprints. Our used classify configurations nine different types organic-inorganic halide perovskites. combination with gradient boosting tree model has achieved great success solvation free energy prediction. results show our effective characterizing structures, demonstrating power featurization approach.

Язык: Английский

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The simpliciality of higher-order networks

EPJ Data Science, Год журнала: 2024, Номер 13(1)

Опубликована: Март 7, 2024

Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring situations where specific participate an interaction, and subsets of those also interact with each other. Traditional modeling approaches tend either not consider all (e.g., hypergraph models) or explicitly assume perfect complete simplicial models). To allow for a nuanced assessment introduce the concept "simpliciality" several corresponding measures. Contrary current practice, show that empirically observed rarely lie end simpliciality spectrum. addition, generative models fitted these datasets struggle capture their structure. These findings suggest new directions field network science.

Язык: Английский

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Robustness of interdependent hypergraphs: A bipartite network framework

Physical Review Research, Год журнала: 2024, Номер 6(1)

Опубликована: Янв. 12, 2024

In this paper, we develop a bipartite network framework to study the robustness of interdependent hypergraphs. From such perspective, nodes and hyperedges hypergraph are equivalent each other, property that largely simplifies their mathematical treatment. We general percolation theory based on representation apply it hypergraphs against random damage, which verify with numerical simulations. analyze variety interacting patterns, from heterogeneous correlated hyperstructures, full- partial-dependency couplings between an arbitrary number hypergraphs, characterize structural stability via phase diagrams. Given its generality, expect our will provide useful insights for development more realistic venues cascading failures in higher-order systems. Published by American Physical Society 2024

Язык: Английский

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Framework to generate hypergraphs with community structure

Physical review. E, Год журнала: 2024, Номер 109(3)

Опубликована: Март 19, 2024

In recent years hypergraphs have emerged as a powerful tool to study systems with multibody interactions which cannot be trivially reduced pairs. While highly structured methods generate synthetic data proved fundamental for the standardized evaluation of algorithms and statistical real-world networked data, these are scarcely available in context hypergraphs. Here we propose flexible efficient framework generation many nodes large hyperedges, allows specifying general community structures tune different local statistics. We illustrate how use our model sample desired features (assortative or disassortative communities, mixed hard assignments, etc.), analyze detection algorithms, structurally similar data. Overcoming previous limitations on hypergraphs, work constitutes substantial advancement modeling higher-order systems.

Язык: Английский

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