Sandbox fixed-mass algorithm for multifractal unweighted complex networks

Pavón-Domínguez, Pablo; Moreno-Pulido, Soledad

doi:10.1016/j.chaos.2022.111836

Cited by 8 publications

(8 citation statements)

References 52 publications

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“…87 Higher values of p r were shown to reduce the characteristic length scale in WS networks, which increases d f . 88 In the random limit (p r = 1), d f increases with the number of nodes, n. 89 Similarly, in this work, the fractal dimension, d f , of WS, LNP-R, and LP-R networks increases with larger p r as shown for LNP-R and LP-R networks in Figure 5. The initial increase of d f with p r is quite steep but becomes shallower at p r ≥ 0.2, as shown in Figure 5.…”

Section: Comparisons To Generative Network Modelssupporting

confidence: 72%

“…The existing body of work has demonstrated that randomness increases fractal dimension, d f , reduces average shortest path length, l, and suppresses local clustering. 25,80,[86][87][88][89][90][91][92][93][94] Consequently, the size-matched random ER and BR networks have values of d f higher by 0.6 to 1.1 units and values of C 4 smaller by one to three orders of magnitude in comparison to the RNs. BR networks show higher local clustering but are still much less ordered than RNs.…”

Section: Comparisons To Generative Network Modelsmentioning

confidence: 97%

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Reaction Networks Resemble Low-Dimensional Regular Lattices

Stulajter,

Rappoport

2024

Preprint

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The computational exploration, manipulation, and design of complex chemical reactions face fundamental challenges related to the high-dimensional nature of potential energy surfaces (PESs) that govern reactivity. Accurately modeling complex reactions is crucial for understanding the chemical processes involved in, for example, organocatalysis, autocatalytic cycles, and one-pot molecular assembly. Our prior research demonstrated that discretizing PESs using heuristics based on bond breaking and bond formation produces a reaction network representation with a low-dimensional structure (metric space). We now find that these reaction networks possess additional, though approximate, structure and resemble low-dimensional regular lattices with a small amount of random edge rewiring. The heuristics-based discretization thus generates a nonlinear dimensionality reduction by a factor of ten with an a posteriori error measure (probability of random rewiring). The structure becomes evident through a comparative analysis of CHNO reaction networks of varying stoichiometries against a panel of size-matched generative network models, taking into account their local, metric, and global properties. The generative models include random networks (Erdős-Rényi and bipartite random networks), regular lattices (periodic and non-periodic), and network models with a tunable level of "randomness" (Watts-Strogatz graphs and regular lattices with random rewiring). The CHNO networks are simultaneously closely matched in all these properties by 3-4-dimensional regular lattices with 10% or less of edges randomly rewired. The effective dimensionality reduction is found to be independent of the system size, stoichiometry, and rule set, suggesting that search and sampling algorithms for PESs of complex chemical reactions can be effectively leveraged.

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Section: Comparisons To Generative Network Modelssupporting

confidence: 72%

Section: Comparisons To Generative Network Modelsmentioning

confidence: 97%

Reaction Networks Resemble Low-Dimensional Regular Lattices

Stulajter,

Rappoport

2024

Preprint

View full text Add to dashboard Cite

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“…We plot in Figure 5 the evolution with L of the ratio of the proportion of "wet" sections-i.e., number of sections that have at least one inflow divided by the total number of sections-with scale. This ratio, hereafter called the wetting ratio r w , controls the evolution of K a (L) (see discussion above and (5)) and it can be used to identify a potential fractal nature of the flowing structure as it is classically done in box-counting methods [Mandelbrot, 1982, Pavón-Domínguez andMoreno-Pulido, 2022]. In a fractal of dimension D 1D in 1D, the number of wet sections decreases as (L/H ) D 1D with H the investigated borehole length (here 300 m), and the wetting ratio increases as r w ∼ (L/H ) 1−D 1D .…”

Section: Flow Structure Organizationmentioning

confidence: 99%

Scaling of fractured rock flow. Proposition of indicators for selection of DFN based flow models

Davy¹,

Goc²,

Darcel³

et al. 2024

Comptes Rendus. Géoscience

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The objective of the paper is to better understand and quantify the flow structure in fractured rocks from flow logs, and to propose relevant indicators for validating, calibrating or even rejecting hydrogeological models. We first studied what the inflow distribution tells us about the permeability structure from a series of analyses: distribution of transmissivities as a function of depth, proportion of flowing sections as a function of section scale, and scaling of the arithmetically-averaged and geometrically-averaged permeability. We then define three indicators that describe few fundamental characteristics of the flow/permeability, whatever the scale: a percolation scale l s , the way permeability increases with scale above l s , and the variability of permeability. A 4th indicator on the representative elemental volume could in principle be defined but the data show that this volume/scale is beyond the 300 m investigated. We tested a series of numerical models built in three steps: the geo-DFN based on the observed fracture network, the open-DFN which is the part of the geo-DFN where fractures are open, and a transmissivity model applying on each fracture of the open-DFN (Discrete Fracture Network). The analysis of the models showed that the percolation scale is controlled by the open-DFN structure and that the percolation scale can be predicted from a scale analysis of the percolation parameter (basically, the third moment of the fracture size distribution that provides a measure of the network connectivity). The way permeability increases with scale above the percolation threshold is controlled by the transmissivity model and in particular by the dependence of the fracture transmissivity on either the orientation of the fractures via a stresscontrolled transmissivity or their size or both. The comparison with data on the first two indicators shows that a model that matches the characteristics of the geo-DFN with an open fraction of 15% as measured adequately fits the data provided that the large fractures remain open and that the fracture transmissivity model is well selected. Most of the other models show unacceptable differences with data but other models or model combinations has still to be explored beforerejecting them.

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“…Immediately following, Liu et al [22] adapted the Sandbox algorithm [23] for signal fractal analysis to multifractals of complex networks with a lower time complexity compared to previous algorithms. Pavón-Domínguez et al [24,25] analyzed multifractals of networks with another fixed-quality approach. The existing network multifractal studies only concern to limited scales that may loss some details.…”

Section: Introductionmentioning

confidence: 99%

Detection of EEG signals in normal and epileptic seizures with multiscale multifractal analysis approach via weighted horizontal visibility graph

Ren

et al. 2023

Chinese Phys. B

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Electroencephalogram (EEG) signals contain important information about the regulation of brain system. Thus, automatic detection of epilepsy by analyzing the characteristics obtained from EEG signals has important research implications in the field of clinical medicine. In this paper, the Horizontal Visibility Graph (HVG) algorithm is used to map multifractal EEG signals into complex networks. Then, we study the structure of the networks and explore the nonlinear dynamics properties of the EEG signals inherited from these networks. In order to better describe complex brain behaviors, we use the angle between two connected nodes as the edge weight of the network and construct the Weighted Horizontal Visibility Graph (WHVG). In our studies, fractality and multifractality of WHVG are innovatively used to analyze the structure of related networks. However, these methods only analyze the reconstructed dynamical system in general characterizations, they are not sufficient to describe the complex behavior and cannot provide a comprehensive picture of the system. To this effect, we propose an improved multiscale multifractal analysis (MMA) for network, which extends the description of the network dynamics features by focusing on the relationship between the multifractality and the measured scale-free intervals. Furthermore, neural networks are applied to train the above-mentioned parameters for the classification and identification of three kinds of EEG signals, i.e., health, interictal phase and ictal phase. By evaluating our experimental results, the classification accuracy is 99.0%, reflecting the effectiveness of WHVG algorithm in extracting the potential dynamic characteristics of EEG signals.

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Sandbox fixed-mass algorithm for multifractal unweighted complex networks

Cited by 8 publications

References 52 publications

Reaction Networks Resemble Low-Dimensional Regular Lattices

Reaction Networks Resemble Low-Dimensional Regular Lattices

Scaling of fractured rock flow. Proposition of indicators for selection of DFN based flow models

Detection of EEG signals in normal and epileptic seizures with multiscale multifractal analysis approach via weighted horizontal visibility graph

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