Localized recovery of complex networks against failure

The recovery strategy of interdependent networks under targeted attacks

To effectively mitigate failures in interdependent systems during targeted-attack scenarios, a common approach is to pre-store repair resources. The question arises: what constitutes an appropriate quantity of these pre-stored repair resources? The paper introduces a novel recovery strategy aimed at providing guidance for this issue. Current recovery strategies frequently emphasize the dynamic interplay between cascading failures and recovery processes, indicating that interventions during the recovery phase are permissible. In this context, the recovery strategy focus on recovering a predetermined number of failed nodes that are adjacent to the largest connected component of each individual network, along with their dependent nodes, at each recovery stage. Simulation results demonstrate that this strategy significantly enhances the capacity to prevent system breakdowns for interdependent networks subjected to targeted attacks. Therefore, by determining the necessary recovery steps to prevent system failures and the appropriate repair resources required for each step, this novel strategy can serve as a valuable reference for the pre-storage of repair resources. Significantly, the strategy can be effectively applied to interdependent networks associated with critical infrastructure, such as power grids and communication networks.

Focus on the disruption of networks and system dynamics

Networks are designed to ensure proper functioning and sustained operability of the underlying systems. However, disruptions are generally unavoidable. Internal interactions and external environmental effects can lead to the removal of nodes or edges, resulting in unexpected collective behavior. For instance, a single failing node or removed edge may trigger a cascading failure in an electric power grid. This Focus Issue delves into recent advances in understanding the impacts of disruptions on networks and their system dynamics. The central theme is the disruption of networks and their dynamics from the perspectives of both data-driven analysis as well as modeling. Topics covered include disruptions in the dynamics of empirical systems such as nuclear reaction networks, infrastructure networks, social networks, epidemics, brain dynamics, and physiology. Emphasis is placed on various phenomena in collective behavior, including critical phase transitions, irregular collective dynamics, complex patterns of synchrony and asynchrony, chimera states, and anomalous oscillations. The tools used for these studies include control theory, diffusion processes, stochastic processes, and network theory. This collection offers an exciting addition to the evolving landscape of network disruption research.

A data-driven analysis of the aviation recovery from the COVID-19 pandemic

In Summer 2022, after a lean COVID-19 spell of almost three years, many airlines reported profits and some airlines even outperformed their pre-pandemic records. In context of the perceived recovery, it is interesting to understand how different markets have gone through the pandemic challenges. In this study, we perform a spatial and temporal dissection of the recovery process the global aviation system went through since May 2020. At the heart of this study, we investigate the patterns underlying market entry decisions during the recovery phase. We identify a rather heterogeneous type of recovery as well as its underlying drivers. We believe that our work is a timely contribution to the research on COVID-19 and aviation, complementary to the existing studies in the literature.

Fragmentation of outage clusters during the recovery of power distribution grids

The understanding of recovery processes in power distribution grids is limited by the lack of realistic outage data, especially large-scale blackout datasets. By analyzing data from three electrical companies across the United States, we find that the recovery duration of an outage is connected with the downtime of its nearby outages and blackout intensity (defined as the peak number of outages during a blackout), but is independent of the number of customers affected. We present a cluster-based recovery framework to analytically characterize the dependence between outages, and interpret the dominant role blackout intensity plays in recovery. The recovery of blackouts is not random and has a universal pattern that is independent of the disruption cause, the post-disaster network structure, and the detailed repair strategy. Our study reveals that suppressing blackout intensity is a promising way to speed up restoration.

Target recovery of the economic system based on the target reinforcement path method

An effective and stable operation of an economic system leads to a prosperous society and sustainable world development. Unfortunately, the system faces inevitable perturbations of extreme events and is frequently damaged. To maintain the system's stability, recovering its damaged functionality is essential and is complementary to strengthening its resilience and forecasting extreme events. This paper proposes a target recovery method based on network and economic equilibrium theories to defend the economic system against perturbations characterized as localized attacks. This novel method stimulates a set of economic sectors that mutually reinforce damaged economic sectors and is intuitively named the target reinforcement path (TRP) method. Developing a nonlinear dynamic model that simulates the economic system's operation after being perturbed by a localized attack and recovering based on a target recovery method, we compute the relaxation time for this process to quantify the method's efficiency. Furthermore, we adopt a rank aggregation method to comprehensively measure the method's efficiency by studying the target recovery of three country-level economic systems (China, India, and Japan) for 73 different regional attack scenarios. Through a comparative analysis of the TRP method and three other classic methods, the TRP method is shown to be more effective and less costly. Applicatively, the proposed method exhibits the potential to recover other vital complex systems with spontaneous recovery ability, such as immune, neurological, and ecological systems.

Dynamical Recovery of Complex Networks under a Localised Attack

In real systems, some damaged nodes can spontaneously become active again when recovered from themselves or their active neighbours. However, the spontaneous dynamical recovery of complex networks that suffer a local failure has not yet been taken into consideration. To model this recovery process, we develop a framework to study the resilience behaviours of the network under a localised attack (LA). Since the nodes’ state within the network affects the subsequent dynamic evolution, we study the dynamic behaviours of local failure propagation and node recoveries based on this memory characteristic. It can be found that the fraction of active nodes switches back and forth between high network activity and low network activity, which leads to the spontaneous emergence of phase-flipping phenomena. These behaviours can be found in a random regular network, Erdős-Rényi network and Scale-free network, which shows that these three types of networks have the same or different resilience behaviours under an LA and random attack. These results will be helpful for studying the spontaneous recovery real systems under an LA. Our work provides insight into understanding the recovery process and a protection strategy of various complex systems from the perspective of damaged memory.

Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application

A generalized form of the Mittag-Leffler function denoted by p E q ; δ λ , μ ; ν x is established and studied in this paper. The fractional integrals involving the newly defined function are investigated. As an application, the solutions of a generalized fractional kinetic equation containing this function are derived and the nature of the solution is studied with the help of graphical analysis.

A Note on Some Identities of New Type Degenerate Bell Polynomials

Recently, the partially degenerate Bell polynomials and numbers, which are a degenerate version of Bell polynomials and numbers, were introduced. In this paper, we consider the new type degenerate Bell polynomials and numbers, and obtain several expressions and identities on those polynomials and numbers. In more detail, we obtain an expression involving the Stirling numbers of the second kind and the generalized falling factorial sequences, Dobinski type formulas, an expression connected with the Stirling numbers of the first and second kinds, and an expression involving the Stirling polynomials of the second kind.

Competitive percolation strategies for network recovery

Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem of finding the optimal order of repairing elements in power grids and similar infrastructure. Most existing methods either only consider system network structure, potentially ignoring important features, or incorporate component level details leading to complex optimization problems with limited scalability. We aim to narrow the gap between the two approaches. Analyzing realistic recovery strategies, we identify over- and undersupply penalties of commodities as primary contributions to reconstruction cost, and we demonstrate traditional network science methods, which maximize the largest connected component, are cost inefficient. We propose a novel competitive percolation recovery model accounting for node demand and supply, and network structure. Our model well approximates realistic recovery strategies, suppressing growth of the largest connected component through a process analogous to explosive percolation. Using synthetic power grids, we investigate the effect of network characteristics on recovery process efficiency. We learn that high structural redundancy enables reduced total cost and faster recovery, however, requires more information at each recovery step. We also confirm that decentralized supply in networks generally benefits recovery efforts.

A Multi-Objective Optimization Model for the Design of Biomass Co-Firing Networks Integrating Feedstock Quality Considerations

The growth in energy demand, coupled with declining fossil fuel resources and the onset of climate change, has resulted in increased interest in renewable energy, particularly from biomass. Co-firing, which is the joint use of coal and biomass to generate electricity, is seen to be a practical immediate solution for reducing coal use and the associated emissions. However, biomass is difficult to manage because of its seasonal availability and variable quality. This study proposes a biomass co-firing supply chain optimization model that simultaneously minimizes costs and environmental emissions through goal programming. The economic costs considered include retrofitting investment costs, together with fuel, transport, and processing costs, while environmental emissions may come from transport, treatment, and combustion activities. This model incorporates the consideration of feedstock quality and its impact on storage, transportation, and pre-treatment requirements, as well as conversion yield and equipment efficiency. These considerations are shown to be important drivers of network decisions, emphasizing the importance of managing biomass and coal blend ratios to ensure that acceptable fuel properties are obtained.

Resilience-Based Recovery Assessments of Networked Infrastructure Systems under Localized Attacks

To reduce unforeseen disaster risks, infrastructure systems are expected to be resilient. The impact of many natural disasters on networked infrastructures is often observed to follow a localized attack pattern. The localized attack can be demonstrated by the failures of a group of links concentrated in a particular geographical domain which result in adjacent isolated nodes. In this paper, a resilience-based recovery assessment framework is proposed. The framework aims to find the most effective recovery strategy when subjected to localized attacks. The proposed framework was implemented in a lattice network structure inspired by a water distribution network case study. Three different recovery strategies were studied with cost and time constraints incorporated: preferential recovery based on nodal weight (PRNW), periphery recovery (PR), and localized recovery (LR). The case study results indicated that LR could be selected as the most resilient and cost-effective recovery strategy. This paper hopes to aid in the decision-making process by providing a strategic baseline for finding an optimized recovery strategy for localized attack scenarios.

Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically.

Random domain name and address mutation (RDAM) for thwarting reconnaissance attacks

Network address shuffling is a novel moving target defense (MTD) that invalidates the address information collected by the attacker by dynamically changing or remapping the host’s network addresses. However, most network address shuffling methods are limited by the limited address space and rely on the host’s static domain name to map to its dynamic address; therefore these methods cannot effectively defend against random scanning attacks, and cannot defend against an attacker who knows the target’s domain name. In this paper, we propose a network defense method based on random domain name and address mutation (RDAM), which increases the scanning space of the attacker through a dynamic domain name method and reduces the probability that a host will be hit by an attacker scanning IP addresses using the domain name system (DNS) query list and the time window methods. Theoretical analysis and experimental results show that RDAM can defend against scanning attacks and worm propagation more effectively than general network address shuffling methods, while introducing an acceptable operational overhead.