Generalized network density matrices for analysis of multiscale functional diversity

Physical review. E, Journal Year: 2023, Volume and Issue: 107(4)

Published: April 20, 2023

The network density matrix formalism allows for describing the dynamics of information on top complex structures and it has been successfully used to analyze, e.g., a system's robustness, perturbations, coarse-graining multilayer networks, characterization emergent states, performing multiscale analysis. However, this framework is usually limited diffusion undirected networks. Here, overcome some limitations, we propose an approach derive matrices based dynamical systems theory, which encapsulating much wider range linear nonlinear richer classes structure, such as directed signed ones. We use our study response local stochastic perturbations synthetic empirical including neural consisting excitatory inhibitory links gene-regulatory interactions. Our findings demonstrate that topological complexity does not necessarily lead functional diversity, i.e., heterogeneous stimuli or perturbations. Instead, diversity genuine property cannot be deduced from knowledge features heterogeneity, modularity, presence asymmetries, properties system.

Language: Английский

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An integrative dynamical perspective for graph theory and the analysis of complex networks

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(4)

Published: April 1, 2024

Built upon the shoulders of graph theory, field complex networks has become a central tool for studying real systems across various fields research. Represented as graphs, different can be studied using same analysis methods, which allows their comparison. Here, we challenge widespread idea that theory is universal tool, uniformly applicable to any kind network data. Instead, show many classical metrics-including degree, clustering coefficient, and geodesic distance-arise from common hidden propagation model: discrete cascade. From this perspective, metrics are no longer regarded combinatorial measures but spatiotemporal properties dynamics unfolded at temporal scales. Once seen model-based (and not purely data-driven) freely or intentionally replace cascade by other canonical models define new metrics. This opens opportunity design-explicitly transparently-dedicated analyses types choosing model matches individual constraints. In way, take stand topology cannot always abstracted independently shall jointly studied, key interpretability analyses. The perspective here proposed serves integrate into context both more recent defined in literature were, directly indirectly, inspired phenomena on networks.

Language: Английский

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Diffusion capacity of single and interconnected networks

Nature Communications, Journal Year: 2023, Volume and Issue: 14(1)

Published: April 18, 2023

Improving the understanding of diffusive processes in networks with complex topologies is one main challenges today's complexity science. Each network possesses an intrinsic potential that depends on its structural connectivity. However, diffusion a process not only this topological but also dynamical itself. Quantifying will allow design more efficient systems which it necessary either to weaken or enhance diffusion. Here we introduce measure, {\em capacity}, quantifies, through concept paths, element system, and also, system itself, propagate information. Among other examples, study heat model SIR demonstrate value proposed measure. We found, last case, capacity can be used as predictor evolution spreading process. In general, show provides tool evaluate performance systems, identify quantify modifications could improve mechanisms.

Language: Английский

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Laplacian renormalization group: an introduction to heterogeneous coarse-graining

Journal of Statistical Mechanics Theory and Experiment, Journal Year: 2024, Volume and Issue: 2024(8), P. 084002 - 084002

Published: Aug. 2, 2024

Abstract The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into relatively small set universality classes. RG is most powerful tool for investigating organizational scales within dynamic systems. However, application techniques to complex networks has presented significant challenges, primarily due intricate interplay on multiple scales. Existing approaches have relied hypotheses involving hidden geometries based embedding metric spaces. Here, we present practical overview recently introduced Laplacian (LRG) heterogeneous networks. First, brief that justifies use as natural extension well-known field theories analyze spatial disorder. We then draw an analogy traditional real-space procedures, explaining how LRG generalizes concept ‘Kadanoff supernodes’ block nodes span These supernodes help mitigate effects cross-scale small-world properties. Additionally, rigorously define procedure momentum space spirit Wilson RG. Finally, show different analyses evolution network properties along flow following structural changes when properly reduced.

Language: Английский

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Low-dimensional controllability of brain networks

PLoS Computational Biology, Journal Year: 2025, Volume and Issue: 21(1), P. e1012691 - e1012691

Published: Jan. 7, 2025

Identifying the driver nodes of a network has crucial implications in biological systems from unveiling causal interactions to informing effective intervention strategies. Despite recent advances control theory, results remain inaccurate as number drivers becomes too small compared size, thus limiting concrete usability many real-life applications. To overcome this issue, we introduced framework that integrates principles spectral graph theory and output controllability project state into smaller topological space formed by Laplacian structure. Through extensive simulations on synthetic real networks, showed relatively low projected components can significantly improve accuracy. By introducing new low-dimensional metric experimentally validated our method N = 6134 human connectomes obtained UK-biobank cohort. Results revealed previously unappreciated influential brain regions, enabled draw directed maps between differently specialized cerebral systems, yielded insights hemispheric lateralization. Taken together, offered theoretically grounded solution deal with provided brain.

Language: Английский

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Hybrid universality classes of systemic cascades

Nature Communications, Journal Year: 2025, Volume and Issue: 16(1)

Published: Feb. 6, 2025

Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding universal aspects these phenomena is fundamental interest, yet typically bound to numerical observations in ad-hoc models and limited insights. Here, we develop a unifying approach that reveals two distinct universality classes cascades determined by global symmetry cascading process. We provide hyperscaling arguments predicting hybrid critical characterized combination both mean-field spinodal exponents d-dimensional corrections, show how parity invariance influences geometry lifetime avalanches. Our theory applies wide range networked systems arbitrary dimensions, as demonstrate simulations encompassing classic novel cascade models, revealing principles amenable experimental validation. Cascading accompanied mixed-order transitions characteristic for ecological, financial, earth, climate, social To better understand mechanisms behind, authors uncover cascades, symmetries

Language: Английский

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Strange attractors in complex networks

Physical review. E, Journal Year: 2025, Volume and Issue: 111(4)

Published: April 15, 2025

Language: Английский

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Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system

Journal of Mathematical Physics, Journal Year: 2025, Volume and Issue: 66(4)

Published: April 1, 2025

Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and corresponding network dynamics theories been continuously enriched with advancement of science. Recently, time-varying feature many-body interactions discovered various numerous networks real world like biological social systems, study contemporary science has gradually moved away from historically static frameworks that are based pairwise interactions. We aimed to propose a general rudimentary framework for Turing instability reaction-diffusion higher-order temporal networks. Firstly, we define brand Laplacian depict diffusion behaviors Furthermore, form frequency oscillation is defined, time-independent concise obtained by equivalent substitution method averaging. Next, discuss cases homogeneous heterogeneous give conditions through linear stability analysis. Finally, numerical simulation part, verify validity above theoretical effect processes. Our revealed reaction-diffusion, which takes into account both interactions, can formulate innovative diversified patterns. Moreover, these significantly differences patterns continuous space traditional

Language: Английский

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A simplex path integral and a simplex renormalization group for high-order interactions ^*

Reports on Progress in Physics, Journal Year: 2024, Volume and Issue: 87(8), P. 087601 - 087601

Published: July 30, 2024

Modern theories of phase transitions and scale invariance are rooted in path integral formulation renormalization groups (RGs). Despite the applicability these approaches simple systems with only pairwise interactions, they less effective complex undecomposable high-order interactions (i.e. among arbitrary sets units). To precisely characterize universality interacting systems, we propose a simplex RG (SRG) as generalizations classic to heterogeneous interactions. We first formalize trajectories units governed by define integrals on corresponding simplices based propagator. Then, develop method integrate out short-range momentum space, accompanied coarse graining procedure functioning structure generated The proposed SRG, equipped divide-and-conquer framework, can deal absence ergodicity arising from sparse distribution renormalize system intertwined at

Language: Английский

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Multi-scale representation learning for heterogeneous networks via Hawkes point processes

Knowledge-Based Systems, Journal Year: 2025, Volume and Issue: unknown, P. 113150 - 113150

Published: Feb. 1, 2025

Language: Английский

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