arXiv subjects

Marcus Engsig

Publications and source records attributed to Marcus Engsig.

5 recordsLinked to original sources

arXiv2025

Identifying Central Nodes in Multiplex Networks by Embracing Layer-Specific Heterogeneity via DomiRank

The robustness and resilience of complex systems are crucial for maintaining functionality amid disruptions or intentional attacks. Many such systems can be modeled as networks, where identifying structurally central nodes is essential for assessing their robustness and susceptibility to failure. Traditional centrality metrics often face challenges in identifying structurally important nodes in networks exhibiting heterogeneity at the network scale, with multilayer networks being a prime example of such networks. These metrics typically fail to balance the trade-off between capturing local layer-specific structures and integrating global multiplex connectivity. In this study, we extend DomiRank centrality, a metric that has been shown to effectively assess nodal importance across diverse monoplex topologies, to multiplex networks. Our approach combines layer-specific DomiRank calculations with a global contextualization step, incorporating multiplex-wide DomiRank scores to combine rankings. Through synthetic and real-world network studies, we demonstrate that our generalized DomiRank framework significantly improves the identification of key nodes in highly heterogeneous multiplex networks. This work advances centrality-based robustness assessments by addressing the fundamental trade-off between layer adaptability and multiplex-wide coherence.

physics.soc-ph↗

arXiv2023

DomiRank Centrality: revealing structural fragility of complex networks via node dominance

Determining the key elements of interconnected infrastructure and complex systems is paramount to ensure system functionality and integrity. This work quantifies the dominance of the networks' nodes in their respective neighborhoods, introducing a novel centrality metric, DomiRank, that integrates local and global topological information via a tunable parameter. We present an analytical formula and an efficient parallelizable algorithm for DomiRank centrality, making it applicable to massive networks. From the networks' structure and function perspective, nodes with high values of DomiRank highlight fragile neighborhoods whose integrity and functionality are highly dependent on those dominant nodes. Underscoring this relation between dominance and fragility, we show that DomiRank systematically outperforms other centrality metrics in generating targeted attacks that effectively compromise network structure and disrupt its functionality for synthetic and real-world topologies. Moreover, we show that DomiRank-based attacks inflict more enduring damage in the network, hindering its ability to rebound and, thus, impairing system resilience. DomiRank centrality capitalizes on the competition mechanism embedded in its definition to expose the fragility of networks, paving the way to design strategies to mitigate vulnerability and enhance the resilience of critical infrastructures.

physics.soc-ph↗

arXiv2022

Numerical Fr\'echet derivatives of the displacement tensor for 2.5-D frequency-domain seismic full-waveform inversion in viscoelastic TTI media

Derivatives of the displacement tensor with respect to the independent model parameters of the subsurface, also called Fr\'echet derivatives (or sensitivity kernels), are a key ingredient for seismic full-waveform inversion with a local-search optimization algorithm. They provide a quantitative measure of the expected changes in the seismograms due to perturbations of the subsurface model parameters for a given survey geometry. Since 2.5-D wavefield modeling involves a real point source in a 2-D geological model with 3D (spherical) wave properties, it yields synthetic data much closer to the actual practical field data than the commonly used 2-D wave simulation does, which uses an unrealistic line source in which the waves spread cylindrically. Based on our recently developed general 2.5-D wavefield modeling scheme, we apply the perturbation method to obtain explicit analytic expressions for the derivatives of the displacement tensor for 2.5-D/2-D frequency-domain seismic full-waveform inversion in general viscoelastic anisotropic media. We then demonstrate the numerical calculations of all these derivatives in two common cases: (i) viscoelastic isotropic and (ii) viscoelastic tilted transversely isotropic (TTI) solids. Examples of the differing sensitivity patterns for the various derivatives are investigated and compared for four different homogeneous models involving 2-D and 2.5-D modeling.

physics.geo-ph↗

arXiv2022

Generalization of Higher Order Methods for Fast Iterative Matrix Inversion Suitable for GPU Acceleration

Recent technological developments have led to big data processing, which resulted in significant computational difficulties when solving large-scale linear systems or inverting matrices. As a result, fast approximate iterative matrix inversion methodologies via Graphical Processing Unit (GPU) acceleration has been a subject of extensive research, to find solutions where classic and direct inversion are too expensive to conduct. Some currently used methods are Neumann Series (NS), Newton iteration (NI), Chebyshev Iteration (CI), and Successive Over-Relaxation, to cite a few. In this work, we develop a new iterative algorithm based off the NS, which we named 'Nested Neumann' (NN). This new methodology generalizes higher orders of the NI (or CI), by taking advantage of a computationally free iterative update of the preconditioning matrix as a function of a given 'inception depth'. It has been mathematically demonstrated that the NN: (i) convergences given the preconditioning satisfies the spectral norm condition of the NS, (ii) has an order of rate of convergence has been shown to be equivalent to the order (inception depth plus one), and (iii) has an optimal inception depth is an inception depth of one or preferably two, depending on RAM constraints. Furthermore, we derive an explicit formula for the NN, which is applicable to massive sparse matrices, given an increase in computational cost. Importantly, the NN finds an analytic equivalancy statement between the NS and the the NN (NI, CI, and higher orders), which is of importance for mMIMO systems. Finally, the NN method is applicable positive semi-definite matrices for matrix inversion, and applicable to any linear system (sparse, non-sparse, complex, etc.).

cs.OH↗

arXiv2022

Robustness Assessment of Complex Networks using the Idle Network

Network robustness is an essential system property to sustain functionality in the face of failures or targeted attacks. Currently, only the connectivity of the nodes unaffected by an attack is utilized to assess robustness. We propose to incorporate the properties of the emerging connectivity of the nodes affected by the attack (Idle Network), which is demonstrated to contain pertinent information about network robustness, improving its assessment accuracy. The Idle network information offers the potential to generalize models, enabling them to estimate robustness for unseen attacks.

physics.soc-ph↗