Complex Quantum Networks: a Topical Review DOI Creative Commons
Johannes Nokkala, Jyrki Piilo, Ginestra Bianconi

и другие.

arXiv (Cornell University), Год журнала: 2023, Номер unknown

Опубликована: Янв. 1, 2023

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

Complex quantum networks: a topical review DOI Creative Commons
Johannes Nokkala, Jyrki Piilo, Ginestra Bianconi

и другие.

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

Процитировано

15

A unified framework for simplicial Kuramoto models DOI Creative Commons
Marco Nurisso, Alexis Arnaudon, Maxime Lucas

и другие.

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

Процитировано

15

Topology shapes dynamics of higher-order networks DOI
Ana P. Millán, Hanlin Sun, Lorenzo Giambagli

и другие.

Nature Physics, Год журнала: 2025, Номер unknown

Опубликована: Фев. 19, 2025

Язык: Английский

Процитировано

2

Local Dirac Synchronization on networks DOI Open Access

Lucille Calmon,

Sanjukta Krishnagopal, Ginestra Bianconi

и другие.

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

Процитировано

20

Persistent Dirac for molecular representation DOI Creative Commons
JunJie Wee, Ginestra Bianconi, Kelin Xia

и другие.

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

Процитировано

20

Generalized Simplicial Attention Neural Networks DOI
Claudio Battiloro,

Lucia Testa,

Lorenzo Giusti

и другие.

IEEE Transactions on Signal and Information Processing over Networks, Год журнала: 2024, Номер 10, С. 833 - 850

Опубликована: Янв. 1, 2024

Язык: Английский

Процитировано

8

Robustness of interdependent hypergraphs: A bipartite network framework DOI Creative Commons
Xingyu Pan, Jie Zhou, Yinzuo Zhou

и другие.

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

Процитировано

7

Persistent Dirac of paths on digraphs and hypergraphs DOI Open Access
Faisal Suwayyid, Guo‐Wei Wei

Foundations of Data Science, Год журнала: 2024, Номер 6(2), С. 124 - 153

Опубликована: Янв. 1, 2024

This work introduces the development of path Dirac and hypergraph operators, along with an exploration their persistence. These operators excel in distinguishing between harmonic non-harmonic spectra, offering valuable insights into subcomplexes within these structures. The paper showcases functionality through a series examples various contexts. An essential facet this research involves examining operators' sensitivity to filtration, emphasizing capacity adapt topological changes. also explores significant application persistent molecular science, specifically analyzing study strict preorders derived from structures, which generate graphs digraphs intricate depth information complexes reflects complexity different preorder classes influenced by characteristic underscores effectiveness tools realm data analysis.

Язык: Английский

Процитировано

6

The mass of simple and higher-order networks DOI Creative Commons
Ginestra Bianconi

Journal of Physics A Mathematical and Theoretical, Год журнала: 2023, Номер 57(1), С. 015001 - 015001

Опубликована: Ноя. 24, 2023

Abstract We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology geometry. use discrete topological Dirac operator to define an action for massless self-interacting field inspired by Nambu–Jona-Lasinio model. The network is strictly speaking this defined on network; it results chiral symmetry breaking model satisfies self-consistent gap equation. Interestingly, shown depends its spectral properties, topology, Due matter–antimatter observed harmonic modes operator, two possible definitions can be given. For both definitions, comes equation with difference among encoded in value bare mass. Indeed, determined either Betti number β 0 or 1 network. provide numerical different networks, including random graphs, scale-free, real weighted collaboration networks. also discuss generalization these defining simplicial complexes. dependence considered geometry could lead interesting physics scenario which coupled dynamical evolution underlying structure.

Язык: Английский

Процитировано

13

Topology and dynamics of higher-order multiplex networks DOI Creative Commons
Sanjukta Krishnagopal, Ginestra Bianconi

Chaos Solitons & Fractals, Год журнала: 2023, Номер 177, С. 114296 - 114296

Опубликована: Ноя. 22, 2023

Higher-order networks are gaining significant scientific attention due to their ability encode the many-body interactions present in complex systems. However, higher-order have limitation that they only capture of same type. To address this limitation, we a mathematical framework determines topology multiplex and illustrates interplay between dynamics. Specifically, examine diffusion topological signals associated not nodes but also links higher-dimensional simplices simplicial complexes. We leverage on ubiquitous presence overlap couple dynamics among layers, introducing definition Hodge Laplacians Dirac operators. show spectral properties these operators determine Betti numbers. Our numerical investigation synthetic real (connectome, microbiome) complexes indicates coupling layers can either speed up or slow down signals. This is very general be applied study generic systems with multiple types. In particular, results might find applications brain which understood both multilayer higher-order.

Язык: Английский

Процитировано

12