The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

Zhukov, Dmitry; Andrianova, Elena; Lesko, S. A.

doi:10.3390/sym11070920

Cited by 5 publications

(6 citation statements)

References 42 publications

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“…Such a percolation is expected to have a strong effect on the bulk modulus of the system (Oliveira et al, 2014). The percolation threshold, p c , for irregular 3D networks can be estimated as (Zhukov et al, 2019)…”

Section: Agent-based Modeling Of Pulmonary Fibrosismentioning

confidence: 99%

Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

Hall

Bates²,

Casey³

et al. 2023

Front. Netw. Physiol.

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Pulmonary Fibrosis (PF) is a deadly disease that has limited treatment options and is caused by excessive deposition and cross-linking of collagen leading to stiffening of the lung parenchyma. The link between lung structure and function in PF remains poorly understood, although its spatially heterogeneous nature has important implications for alveolar ventilation. Computational models of lung parenchyma utilize uniform arrays of space-filling shapes to represent individual alveoli, but have inherent anisotropy, whereas actual lung tissue is isotropic on average. We developed a novel Voronoi-based 3D spring network model of the lung parenchyma, the Amorphous Network, that exhibits more 2D and 3D similarity to lung geometry than regular polyhedral networks. In contrast to regular networks that show anisotropic force transmission, the structural randomness in the Amorphous Network dissipates this anisotropy with important implications for mechanotransduction. We then added agents to the network that were allowed to carry out a random walk to mimic the migratory behavior of fibroblasts. To model progressive fibrosis, agents were moved around the network and increased the stiffness of springs along their path. Agents migrated at various path lengths until a certain percentage of the network was stiffened. Alveolar ventilation heterogeneity increased with both percent of the network stiffened, and walk length of the agents, until the percolation threshold was reached. The bulk modulus of the network also increased with both percent of network stiffened and path length. This model thus represents a step forward in the creation of physiologically accurate computational models of lung tissue disease.

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Section: Agent-based Modeling Of Pulmonary Fibrosismentioning

confidence: 99%

Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

Hall

Bates²,

Casey³

et al. 2023

Front. Netw. Physiol.

View full text Add to dashboard Cite

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“…In order to build a planar network with an accidental number of links for each junction (network density), we may use the following algorithm [24]:…”

Section: Algorithm Of Planar Network With Accidental Structuresmentioning

confidence: 99%

“…In Figure 5, the dependencies of percolation threshold values of planar networks on the average number of network links per single junction (in junction blocking tasks [24] and in link blocking tasks) are presented. To calculate the influence of the network's structure density on the value of its percolation limits, it is necessary to analyze the data, shown in Table 1 and in Figure 5, and to calculate a functional dependency which may describe the influence of the network density on the value of its percolation limit.…”

Section: Calculating the Dependency Of The Percolation Threshold Dependency On The Network Density (Average Number Of Links Per Crossroadmentioning

confidence: 99%

The Influence of Transport Link Density on Conductivity If Junctions and/or Links Are Blocked

Aleshkin¹

2021

Mathematics

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This paper examines some approaches to modeling and managing traffic flows in modern megapolises and proposes using the methods and approaches of the percolation theory. The author sets the task of determining the properties of the transport network (percolation threshold) when designing such networks, based on the calculation of network parameters (average number of connections per crossroads, road network density). Particular attention is paid to the planarity and nonplanarity of the road transport network. Algorithms for building a planar random network (for modeling purposes) and calculating the percolation thresholds in the resulting network model are proposed. The article analyzes the resulting percolation thresholds for road networks with different relationship densities per crossroad and analyzes the effect of network density on the percolation threshold for these structures. This dependence is specified mathematically, which allows predicting the qualitative characteristics of road network structures (percolation thresholds) in their design. The conclusion shows how the change in the planar characteristics of the road network (with adding interchanges to it) can improve its quality characteristics, i.e., its overall capacity.

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“…In the above example networks were not used, but in general our ability to carry or block information through a network depends on its topology. Especially when the conductivity or information transfer is considered then spatial symmetry becomes central together with its density or average number of links per node and topological dimension [38]. Therefore, an alternative method of classification ideally fitting the experiments in would involve encoding equivariance in learning [39].…”

Section: Image Network and Role Of Symmetrymentioning

confidence: 99%

Inference From Complex Networks: Role of Symmetry and Applicability to Images

Capobianco

2020

Front. Appl. Math. Stat.

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Symmetry is a mathematical concept only partially explored in networks, especially at the applicative level. One reason is a certain lack of interpretable inference obtained from networks. While the network systemic associations (links) between entities (nodes) emerge from the underlying dependence structure, this latter is only partially explicit via the established direct interactors and remains to a certain extent latent (distant node predicted paths). Verifiability of significant hubs, connectors, paths, and modules allows to build a knowledge base useful to infer latencies and/or validate complex associations. When symmetry is searched in images, reflection, translation and rotation are applicable transformations in n-dimensional Euclidean space that computational algorithms target. There is symmetry when original and transformed images cannot be distinguished. Once collected together, such transformations form an automorphism group, indicating a stable and robust global characteristic. It is common to step from images to quantifiable features for conducting inference. Deep learning is typically used to classify whole images reconstructed from the myriads of features in which these images are decomposed. However, with images considered at multiple scales and locations, symmetries are valuable for describing local characteristics. Casting local features into a network framework enables their associations to be explored by similarity or dissimilarity criteria. This is quite intriguing because network configurations may display topological features and connectivity patterns associated with synchronization and symmetry that reduce the redundancy of features to more compact functional descriptions. Then, identifying anomalies from unusual events, behaviors, patterns would spot network vulnerabilities and signs of symmetry breaking.

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The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

Cited by 5 publications

References 42 publications

Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

Predicting alveolar ventilation heterogeneity in pulmonary fibrosis using a non-uniform polyhedral spring network model

The Influence of Transport Link Density on Conductivity If Junctions and/or Links Are Blocked

Inference From Complex Networks: Role of Symmetry and Applicability to Images

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