Network analysis predicts failure of materials and structures

Moretti, Paolo; Zaiser, Michael

doi:10.1073/pnas.1911715116

Cited by 13 publications

(8 citation statements)

References 15 publications

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“…The network propagator, K = e −τ L, represents the discrete counterpart of the path-integral formulation of general diffusion processes 20,30 , and each matrix element K ij describes the sum of diffusion trajectories along all possible paths connecting nodes i and j at time τ (refs. [31][32][33]. We assume connected networks to fulfill the ergodic hypothesis.…”

Section: Statistical Physics Of Information Network Diffusionmentioning

confidence: 99%

Laplacian renormalization group for heterogeneous networks

et al. 2023

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The renormalization group is the cornerstone of the modern theory of universality and phase transitions and it is a powerful tool to scrutinize symmetries and organizational scales in dynamical systems. However, its application to complex networks has proven particularly challenging, owing to correlations between intertwined scales. To date, existing approaches have been based on hidden geometries hypotheses, which rely on the embedding of complex networks into underlying hidden metric spaces. Here we propose a Laplacian renormalization group diffusion-based picture for complex networks, which is able to identify proper spatiotemporal scales in heterogeneous networks. In analogy with real-space renormalization group procedures, we first introduce the concept of Kadanoff supernodes as block nodes across multiple scales, which helps to overcome detrimental small-world effects that are responsible for cross-scale correlations. We then rigorously define the momentum space procedure to progressively integrate out fast diffusion modes and generate coarse-grained graphs. We validate the method through application to several real-world networks, demonstrating its ability to perform network reduction keeping crucial properties of the systems intact.

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Section: Statistical Physics Of Information Network Diffusionmentioning

confidence: 99%

Laplacian renormalization group for heterogeneous networks

et al. 2023

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“…The evolution of information of a given initial specific state of the network, s(0), will evolve with time as s(τ ) = e −τ Ls(0). The network propagator, K = e −τ L, represents the discrete counterpart of the path-integral formulation of general diffusion processes [20,30], and each matrix element Kij describe the sum of diffusion trajectories along all possible paths connecting nodes i and j at time τ [31]. To fulfill the ergodic hypothesis, we assume the connected networks case.…”

Section: Statistical Physics Of Information Network Diffusionmentioning

confidence: 99%

Laplacian Renormalization Group for heterogeneous networks

Bolaños-Villegas¹,

Gili²,

Caldarelli³

et al. 2022

Preprint

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“…Interestingly, link-based centrality measures have received very little attention instead. A notable exception is the definition of edge betweenness (38) and its recent application to failure prediction in network models of materials and structures under mechanical load (39,40). Basic phenomena such as wave propagation, simple in Euclidean geometries, may need even more complex tools: The systematic advancement of a wave front implies the systematic usage of certain links, and systematically in one direction.…”

Section: Physicsmentioning

confidence: 99%

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

Moretti

Hütt

2020

Proc. Natl. Acad. Sci. U.S.A.

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In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of “link-usage asymmetry” are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.

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Network analysis predicts failure of materials and structures

Cited by 13 publications

References 15 publications

Laplacian renormalization group for heterogeneous networks

Laplacian renormalization group for heterogeneous networks

Laplacian Renormalization Group for heterogeneous networks

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

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