Topological Resilience Research Articles

Strength and resilience of developing brain circuits predict adolescent emotional and stress responses during the COVID-19 pandemic.

The COVID-19 pandemic has had profound but incompletely understood adverse effects on youth. To elucidate the role of brain circuits in how adolescents responded to the pandemic's stressors, we investigated their prepandemic organization as a predictor of mental/emotional health in the first ~15months of the pandemic. We analyzed resting-state networks from n = 2,641 adolescents [median age (interquartile range) = 144.0 (13.0) months, 47.7% females] in the Adolescent Brain Cognitive Development study, and longitudinal assessments of mental health, stress, sadness, and positive affect, collected every 2 to 3months from May 2020 to May 2021. Topological resilience and/or network strength predicted overall mental health, stress and sadness (but not positive affect), at multiple time points, but primarily in December 2020 and May 2021. Higher resilience of the salience network predicted better mental health in December 2020 (β = 0.19, 95% CI = [0.06, 0.31], P = 0.01). Lower connectivity of left salience, reward, limbic, and prefrontal cortex and its thalamic, striatal, amygdala connections, predicted higher stress (β = -0.46 to -0.20, CI = [-0.72, -0.07], P < 0.03). Lower bilateral robustness (higher fragility) and/or connectivity of these networks predicted higher sadness in December 2020 and May 2021 (β = -0.514 to -0.19, CI = [-0.81, -0.05], P < 0.04). These findings suggest that the organization of brain circuits may have played a critical role in adolescent stress and mental/emotional health during the pandemic.

Exploring the link between brain topological resilience and cognitive performance in the context of aging and vascular risk factors: A cross-ethnicity population-based study

Brain aging is typically associated with a significant decline in cognitive performance. Vascular risk factors (VRF) and subsequent atherosclerosis (AS) play a major role in this process. Brain resilience reflects the brain's ability to withstand external perturbations, but the relationship of brain resilience with cognition during the aging process remains unclear. Here, we investigated how brain topological resilience (BTR) is associated with cognitive performance in the face of aging and vascular risk factors. We used data from two cross-ethnicity community cohorts, PolyvasculaR Evaluation for Cognitive Impairment and Vascular Events (PRECISE, n = 2220) and Sydney Memory and Ageing Study (MAS, n = 246). We conducted an attack simulation on brain structural networks based on k-shell decomposition and node degree centrality. BTR was defined based on changes in the size of the largest subgroup of the network during the simulation process. Subsequently, we explored the negative correlations of BTR with age, VRF, and AS, and its positive correlation with cognitive performance. Furthermore, using structural equation modeling (SEM), we constructed path models to analyze the directional dependencies among these variables, demonstrating that aging, AS, and VRF affect cognition by disrupting BTR. Our results also indicated the specificity of this metric, independent of brain volume. Overall, these findings underscore the supportive role of BTR on cognition during aging and highlight its potential application as an imaging marker for objective assessment of brain cognitive performance.

An integrated resilience assessment model of urban transportation network: A case study of 40 cities in China

The transportation network is essential in providing daily accessibility and essential service to societies. An acceptable level of service needs to be maintained in critical infrastructures, even in the case of disruptions. We develop an integrated model to assess the resilience of urban transportation networks when exposed to different disruptions. Resilience is evaluated from perspectives of both traffic network topology and traffic flow. This model contains three parts: (1) a traffic flow simulation model to get flow distributed throughout the whole network, (2) different real-world disruptions are abstracted as random, localized, and flood disturbances, (3) functional and topological resilience are accessed by analyzing variations in travel time and connected components before and after a disruption occurs. 40 major cities are chosen to conduct resilience assessments. As the intensity of the disruption increases, common trends in the changes of functional and topological resilience values are observed and analyzed across all studied cities. In most cases, flood disruption is the least disruptive one of all three types of disruptions. Regression models are developed to estimate functional and topological resilience after random, localized, and flood disturbances. Possible resilience enhancement strategies are discussed based on analyses of regression models. This study could aid stakeholders in gaining a clear understanding of resilience not only topologically but also from the perspective of traffic flow and offer them practical strategies to enhance resilience in face of disruptions.

Topology-Based Resilience Metrics for Seismic Performance Evaluation and Recovery Analysis of Water Distribution Systems

Water distribution systems (WDSs) need to be resilient against seismic hazards to ensure rapid recovery of the community following an earthquake. Topology-based resilience metrics are often used to determine the system-level performance of WDSs. However, existing topology-based resilience metrics are unable to estimate seismic performance of WDSs accurately because they do not account for the vulnerability of pipelines in the metrics. This study tailored an existing topological metric and developed a new edge-betweenness-based topological metric for evaluating the seismic resilience of a complex water distribution network. System-level performance of WDSs is compared using four performance measures including minimum cut set (MCS)–based system reliability, topological resilience metric (TRM), modified TRM, and the newly developed edge-betweenness-based TRM. These metrics were applied for four WDSs (i.e., Anytown, New York Tunnel, Jilin, and Bellingham WDSs) with unique characteristics to validate their effectiveness in estimating the seismic performance of WDSs against seismic hazards. The outcomes of these applications show that the proposed TRM can be used to determine pipelines’ seismic performance and functionality after an earthquake with an acceptable accuracy compared with existing approaches. While the topology-based resilience analysis provides information about system-level functionality, it is also vital to determine an optimal recovery sequence for damaged WDSs to maximize the functionality during the recovery process. Therefore, an easy-to-use recovery strategy is proposed to determine the optimal recovery sequence based on a repair index. The optimal recovery strategy was tested for the recovery procedure for the damaged Anytown WDS due to an earthquake, and outcomes show the system functionality is restored quickest using the proposed optimal recovery strategy.

A robust core architecture of functional brain networks supports topological resilience and cognitive performance in middle- and old-aged adults

Aging is associated with gradual changes in cognition, yet some individuals exhibit protection against age-related cognitive decline. The topological characteristics of brain networks that promote protection against cognitive decline in aging are unknown. Here, we investigated whether the robustness and resilience of brain networks, queried via the delineation of the brain's core network structure, relate to age and cognitive performance in a cross-sectional dataset of healthy middle- and old-aged adults (n = 478, ages 40 to 90 y). First, we decomposed each subject's functional brain network using k-shell decomposition and found that age was negatively associated with robust core network structures. Next, we perturbed these networks, via attack simulations, and found that resilience of core brain network nodes also declined in relationship to age. We then partitioned our dataset into middle- (ages 40 to 65 y, n = 300) and old- (ages 65 to 90 y, n = 178) aged subjects and observed that older individuals had less robust core connectivity and resilience. Following these analyses, we found that episodic memory was positively related to robust connectivity and core resilience, particularly within the default node, limbic, and frontoparietal control networks. Importantly, we found that age-related differences in episodic memory were positively related to core resilience, which indicates a potential role for core resilience in protection against cognitive decline. Together, these findings suggest that robust core connectivity and resilience of brain networks could facilitate high cognitive performance in aging.

Resilience Analysis of Australian Electricity and Gas Transmission Networks

Given they are two critical infrastructure areas, the security of electricity and gas networks is highly important due to potential multifaceted social and economic impacts. Unexpected errors or sabotage can lead to blackouts, causing a significant loss for the public, businesses, and governments. Climate change and an increasing number of consequent natural disasters (e.g., bushfires and floods) are other emerging network resilience challenges. In this paper, we used network science to examine the topological resilience of national energy networks with two case studies of Australian gas and electricity networks. To measure the fragility and resilience of these energy networks, we assessed various topological features and theories of percolation. We found that both networks follow the degree distribution of power-law and the characteristics of a scale-free network. Then, using these models, we conducted node and edge removal experiments. The analysis identified the most critical nodes that can trigger cascading failure within the network upon a fault. The analysis results can be used by the network operators to improve network resilience through various mitigation strategies implemented on the identified critical nodes.

Improve the Resilience of Multilayer Supply Chain Networks

Due to the increasingly complex and dynamic features of global supply chain networks, it is challenging to provide high supply availability and network connectivity under unexpected disruptions. In this paper, we investigate how to improve the topology resilience of the supply chain network from its multilayer nature. We firstly conduct the study on the connectedness in the supply chain network from a topological perspective and adopt the t-core method to decompose the network into multiple layers. Then, we propose a layer-based rewiring algorithm to recover the network from disruptions. The experimental results in the real supply chain network show that our design greatly improves the network resilience under both random and targeted disruptions.

Modelling cascading failure of a CPS for topological resilience enhancement

This study focuses on the cyber-physical system (CPS) consisting of interdependent electrical distribution and communication networks, where the two networks are mutually dependent. A small disturbance in either of them can trigger a cascade of faults within the entire network. To investigate the failure mechanism, first, two features that affect topological resilience (TR) are defined in this study: adaptation and recovery abilities. Second, the authors model the process of cascading failures that occur in this coupled system by introducing and developing the infrastructure interdependencies simulator. The process of cascading failures is based on percolation theory, and they present a detailed analysis of cascading failure in a standard IEEE 33-bus system coupled with the 33-node communication system. This study proves that the adaptation ability of a coupled system is even lower than a single system. This is due to the interdependencies between systems, and the study of the failure mechanisms helps planers to make a better decision in the recovery process. Finally, the modified shortest path search is used to optimise the repair sequence. Their numerical results validate that the recovery ability of the coupled system is increased through the optimisation, which contributes to the TR enhancement.

Multiple scattering theory of non-Hermitian sonic second-order topological insulators

Topological phases of sound enable unconventional confinement of acoustic energy at the corners in higher-order topological insulators. These unique states which go beyond the conventional bulk-boundary correspondence have recently been extended to non-Hermitian wave physics comprising finite crystal structures including loss and gain units. We use a multiple scattering theory to calculate these topologically trapped complex states that agree very well to finite element predictions. Moreover, our semi-numerical tool allows us to compute the spectral dependence of corner states in the presence of defects, illustrating the limits of the topological resilience of these confined non-Hermitian acoustic states.

Capacity-Aware Topology Resilience in Software-Defined Networks

Network resilience against failures due to natural disasters, equipment malfunction, and malicious attacks has become important for software-defined networks. The current state of the art focuses on two directions: controller redundancy and related recovery mechanisms for resilience in the control plane, and reactive or proactive strategies for resilience against failure of switches or links in the data plane. However, proactive network topology resilience against multiswitch failure by installing backup switches at key locations has been overlooked. We propose a proactive network-topology resilience scheme against worst case adversarial multiswitch failures by installing backup switches at key locations to maximize long-term traffic demands. We formulate this problem as a trilevel optimization, which helps the network operator identify the key N positions for installing backup switches. We develop mixed integer linear programming formulations to maximize aggregate demand satisfaction and maximize the minimum fair demand satisfaction while satisfying constraints such as connectivity, control-plane latency limits, and association capacity of controllers. The proposed models are NP-hard; therefore, we propose efficient heuristic-based greedy algorithms to solve large instances of the above-mentioned problems. We implement the proposed solutions and present the numerical results, which show optimality of the exact formulations and efficiency of the greedy algorithms.

Road Network Resilience: How to Identify Critical Links Subject to Day-to-Day Disruptions

Disruptive events occur on road networks on a daily basis and affect traffic flow. Resilience analysis aims to assess the consequences of such disruptions by quantifying the ability of a network to absorb and react to adverse events. In this paper, we advance a methodological approach based on resilience stress testing and a dynamic mesoscopic simulator. We aim to identify and rank the links most critical to the overall performance of the road network, taking into account the dynamic properties of road traffic and focusing on day-to-day disruptions. As a metric to quantify road network performance in the presence of such disruptions, we use the increase in overall travel cost. We then compare our approach with purely topological approaches. We discuss the advantages and drawbacks of the different analyzed metrics. We prove that link ranking varies greatly depending on the metric. Specifically, the proposed stress testing methodology can produce very accurate results by taking into account demand and congestion, but requires computationally intensive simulations, being therefore prohibitive even on medium-sized networks. Conversely, purely static topological metrics can be inaccurate if they do not take into account traffic demand and network dynamics. Our study highlights the need for joining traditional traffic-agnostic topological resilience analysis with demand-aware dynamic stress testing techniques.

Modelling the resilience of rail passenger transport networks affected by large-scale disruptive events: the case of HSR (high speed rail)

This paper deals with modelling the dynamic resilience of rail passenger transport networks affected by large-scale disruptive events whose impacts deteriorate the networks’ planned infrastructural, operational, economic, and social-economic performances represented by the selected indicators. The indicators of infrastructural performances refer to the physical and operational conditions of the networks’ lines and stations, and supportive facilities and equipment. Those of the operational performances include transport services scheduled along particular routes, their seating capacity, and corresponding transport work/capacity. The indicators of economic performances include the costs of cancelled and long-delayed transport services imposed on the main actors/stakeholder involved—the rail operator(s) and users/passengers. The indicators of social-economic performances reflect the compromised accessibility and consequent prevention of the user/passenger trips and their contribution to the local/regional/national Gross Domestic Product. Modeling resulted in developing a methodology including two sets of analytical models for: (1) assessing the dynamic resilience of a given rail network, i.e., before, during, and after the impacts of disruptive event(s); and (2) estimation of the indicators of particular performances as the figures-of-merit for assessing the network’s resilience under the given conditions. As such, the methodology could be used for estimating the resilience of different topologies of rail passenger networks affected by past, current, and future disruptive events, the latest according to the “what-if” scenario approach and after introducing the appropriate assumptions. The methodology has been applied to a past case—the Japanese Shinkansen HSR network affected by a large-scale disruptive event—the Great East Japan Earthquake on 11 March 2011.

Topological resilience in non-normal networked systems.

The network of interactions in complex systems strongly influences their resilience and the system capability to resist external perturbations or structural damages and to promptly recover thereafter. The phenomenon manifests itself in different domains, e.g., parasitic species invasion in ecosystems or cascade failures in human-made networks. Understanding the topological features of the networks that affect the resilience phenomenon remains a challenging goal for the design of robust complex systems. We hereby introduce the concept of non-normal networks, namely networks whose adjacency matrices are non-normal, propose a generating model, and show that such a feature can drastically change the global dynamics through an amplification of the system response to exogenous disturbances and eventually impact the system resilience. This early stage transient period can induce the formation of inhomogeneous patterns, even in systems involving a single diffusing agent, providing thus a new kind of dynamical instability complementary to the Turing one. We provide, first, an illustrative application of this result to ecology by proposing a mechanism to mute the Allee effect and, second, we propose a model of virus spreading in a population of commuters moving using a non-normal transport network, the London Tube.

Improving measures of topological robustness in networks of networks and suggestion of a novel way to counter both failure propagation and isolation

The study of interdependent complex networks in the last decade has shown how cascading failure can result in the recursive and complete fragmentation of all connected systems from the destruction of a comparatively small number of nodes. Existing “network of networks” approaches are still in infancy and have shown limits when trying to model the robustness of real-world systems, due to simplifying assumptions regarding network interdependencies and post-attack viability. In order to increase the realism of such models, we challenge such assumptions by validating the following four hypotheses trough experimental results obtained from computer based simulations. Firstly, we suggest that, in the case of network topologies vulnerable to fragmentation, replacing the standard measure of robustness based on the size of the one largest remaining connected component by a new measure allowing secondary components to remain viable when measuring post-attack viability can make a significant improvement to the model. Secondly, we show that it is possible to influence the way failure propagation is balanced between coupled networks while keeping the same overall robustness score by allowing nodes in a given network to have multiple counter parts in another network. Thirdly, we challenge the generalised assumption that partitioning between networks is a good way to increase robustness and find that isolation is a force as equally destructive as the iterative propagation of cascading failure. This result significantly alters where the optimum robustness lies in the balance between isolation and inter-network coupling in such interconnected systems. Finally, we propose a solution to the consequent problem of seemingly ever increasing vulnerability of interdependent networks to both cascading failure and isolation: the use of permutable nodes that would give such systems rewiring capabilities. This last concept could have wide implications when trying to improve the topological resilience of natural or engineered interdependent networks.

Resilience of developing brain networks to interictal epileptiform discharges is associated with cognitive outcome.

The effects of interictal epileptiform discharges on neurocognitive development in children with medically-intractable epilepsy are poorly understood. Such discharges may have a deleterious effect on the brain's intrinsic connectivity networks, which reflect the organization of functional networks at rest, and in turn on neurocognitive development. Using a combined functional magnetic resonance imaging-magnetoencephalography approach, we examine the effects of interictal epileptiform discharges on intrinsic connectivity networks and neurocognitive outcome. Functional magnetic resonance imaging was used to determine the location of regions comprising various intrinsic connectivity networks in 26 children (7-17 years), and magnetoencephalography data were reconstructed from these locations. Inter-regional phase synchronization was then calculated across interictal epileptiform discharges and graph theoretical analysis was applied to measure event-related changes in network topology in the peri-discharge period. The magnitude of change in network topology (network resilience/vulnerability) to interictal epileptiform discharges was associated with neurocognitive outcomes and functional magnetic resonance imaging networks using dual regression. Three main findings are reported: (i) large-scale network changes precede and follow interictal epileptiform discharges; (ii) the resilience of network topologies to interictal discharges is associated with stronger resting-state network connectivity; and (iii) vulnerability to interictal discharges is associated with worse neurocognitive outcomes. By combining the spatial resolution of functional magnetic resonance imaging with the temporal resolution of magnetoencephalography, we describe the effects of interictal epileptiform discharges on neurophysiological synchrony in intrinsic connectivity networks and establish the impact of interictal disruption of functional networks on cognitive outcome in children with epilepsy. The association between interictal discharges, network changes and neurocognitive outcomes suggests that it is of clinical importance to suppress discharges to foster more typical brain network development in children with focal epilepsy.

Localized Algorithm to Improve Connectivity and Topological Resilience of Multi-hop Wireless Networks

Maintaining connectivity is essential in multi-hop wireless networks since the network topology cannot be pre-determined due to mobility and environmental effects. To maintain the connectivity, a critical point in the network topology should be identified where the critical point is the link or node that partitions the network when it fails. In this paper, we propose a new critical point identification algorithm and also present numerical results that compare the critical points of the network and H-hop sub-network illustrating how effectively sub-network information can detect the network-wide critical points. Then, we propose two localized topological control resilient schemes that can be applied to both global and local H-hop sub-network critical points to improve the network connectivity and the network resilience. Numerical studies to evaluate the proposed schemes under node and link failure network conditions show that our proposed resilient schemes increase the probability of the network being connected in variety of link and node failure conditions.

Synchronous and asynchronous Mott transitions in topological insulator ribbons

We address how the nature of linearly dispersing edge states of two dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion $U$ in finite ribbons of two models of topological band insulators. Using an inhomogeneous cluster slave rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical $U$ that depends weakly on the width of the ribbon. In the second, asynchronous route, Mott localization first occurs on the edge layers at a smaller critical value of electronic interaction which then propagates into the bulk as $U$ is further increased until all layers of the ribbon become Mott localized. We show that the kind of Mott transition that takes place is determined by certain properties of the linearly dispersing edge states which characterize the topological resilience to Mott localization.

When Evidence Is Scant, Mathematical Modeling Offers a Roadmap for Discovery

When Evidence Is Scant, Mathematical Modeling Offers a Roadmap for Discovery

Modeling cascading failures in the North American power grid

The North American power grid is one of the most complex technological networks, and its interconnectivity allows both for long-distance power transmission and for the propagation of disturbances. We model the power grid using its actual topology and plausible assumptions about the load and overload of transmission substations. Our results indicate that the loss of a single substation can result in up to $25\%$ loss of transmission efficiency by triggering an overload cascade in the network. The actual transmission loss depends on the overload tolerance of the network and the connectivity of the failed substation. We systematically study the damage inflicted by the loss of single nodes, and find three universal behaviors, suggesting that $40\%$ of the transmission substations lead to cascading failures when disrupted. While the loss of a single node can inflict substantial damage, subsequent removals have only incremental effects, in agreement with the topological resilience to less than $1\%$ node loss.