Node-Level Resilience Loss in Dynamic Complex Networks

Comparative analysis of Ball Mapper and conventional Mapper in investigating air pollutants' behavior

This study investigates the effectiveness and efficiency of two topological data analysis (TDA) techniques, the conventional Mapper (CM) and its variant version, the Ball Mapper (BM), in analyzing the behavior of six major air pollutants (NO2, PM10, PM2.5, O3, CO, and SO2) across 60 air quality monitoring stations in Malaysia. Topological graphs produced by CM and BM reveal redundant monitoring stations and geographical relationships corresponding to air pollutant behavior, providing better visualization than traditional hierarchical clustering. Additionally, a comparative analysis of topological graph structures was conducted using node degree distribution, topological graph indices, and Dynamic Time Warping (DTW) to evaluate the sensitivity and performance of these TDA techniques. Both approaches yielded valuable insights in representing the air quality monitoring stations network; however, the complexity of CM, which requires multiple parameters, poses a challenge in graph construction. In contrast, the simplicity of BM, requiring only a single parameter, is preferable for representing air pollutant behavior. The findings suggest an alternative approach for assessing and identifying redundancies in air quality monitoring stations, which could contribute to improved air quality monitoring management and more effective regulatory policies.

Uncertainty in vulnerability of networks under attack

This study builds conceptual explanations and empirical examinations of the vulnerability response of networks under attack. Two quantities of "vulnerability" and "uncertainty in vulnerability" are defined by scrutinizing the performance loss trajectory of networks experiencing attacks. Both vulnerability and uncertainty in vulnerability quantities are a function of the network topology and size. This is tested on 16 distinct topologies appearing in infrastructure, social, and biological networks with 8 to 26 nodes under two percolation scenarios exemplifying benign and malicious attacks. The findings imply (i) crossing path, tree, and diverging tail are the most vulnerable topologies, (ii) complete and matching pairs are the least vulnerable topologies, (iii) complete grid and complete topologies show the most uncertainty for vulnerability, and (iv) hub-and-spoke and double u exhibit the least uncertainty in vulnerability. The findings also imply that both vulnerability and uncertainty in vulnerability increase with an increase in the size of the network. It is argued that in networks with no undirected cycle and one undirected cycle, the uncertainty in vulnerability is maximal earlier in the percolation process. With an increase in the number of cycles, the uncertainty in vulnerability is accumulated at the end of the percolation process. This emphasizes the role of tailoring preparedness, response, and recovery phases for networks with different topologies when they might experience disruption.

Uncertainty quantification of multi-scale resilience in networked systems with nonlinear dynamics using arbitrary polynomial chaos

Complex systems derive sophisticated behavioral dynamics by connecting individual component dynamics via a complex network. The resilience of complex systems is a critical ability to regain desirable behavior after perturbations. In the past years, our understanding of large-scale networked resilience is largely confined to proprietary agent-based simulations or topological analysis of graphs. However, we know the dynamics and topology both matter and the impact of model uncertainty of the system remains unsolved, especially on individual nodes. In order to quantify the effect of uncertainty on resilience across the network resolutions (from macro-scale network statistics to individual node dynamics), we employ an arbitrary polynomial chaos (aPC) expansion method to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk on a single node. We test this using both a generic networked bi-stable system and also established ecological and work force commuter network dynamics to demonstrate applicability. This framework will aid practitioners to both understand macro-scale behavior and make micro-scale interventions.