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In many systems, from brain neural networks to epidemic transmission networks, pairwise interactions are insufficient to express complex relationships. Nodes sometimes cooperate and form groups to increase their robustness to risks, and each such group can be considered a “supernode”. Furthermore, previous studies of cascading failures in interdependent networks have typically concentrated on node coupling connections; however, in many realistic scenarios, interactions occur between the edges connecting nodes rather than between the nodes themselves. Networks of this type are called edge-coupled interdependent networks. To better reflect complex networks in the real world, in this paper, we construct a theoretical model of a two-layer partially edge-coupled interdependent network with groups, where all nodes in the same group are functionally dependent on each other. We identify several types of phase transitions, namely, discontinuous, hybrid and continuous, which are determined by the strength of the dependency and the distribution of the supernodes. We first apply our developed mathematical framework to ErdsRnyi and scale-free partially edge-coupled interdependent networks with equally sized groups to analytically and numerically calculate the phase transition thresholds and the critical dependency strengths that distinguish different types of transitions. We then investigate the influence of the group size distribution on cascading failures by presenting examples of two different heterogeneous group size distributions. Our theoretical predictions and numerical findings are in close agreement, demonstrating that decreasing the dependency strength and increasing group size heterogeneity can increase the robustness of interdependent networks. Our results have significant implications for the design and optimization of network security and fill a knowledge gap in the robustness of partially edge-coupled interdependent networks with different group size distributions.

New Simple Queue (NSQ) is a distributed messaging platform developed in Golang that can handle billions of daily messages. Its distributed architecture ensures high fault tolerance and availability. Given NSQ’s widespread application across various fields, it is crucial to focus on the system’s robustness and data transmission security. Therefore, a rigorous mathematical logic analysis of NSQ’s messaging mechanism is essential for verifying its reliability. This paper formalizes NSQ’s core components using Communicating Sequential Processes (CSP), resulting in a comprehensive formal model of the system. Furthermore, this paper utilizes the Process Analysis Toolkit (PAT) for practical implementation of the model, verifying five critical properties of the NSQ system. And the verification results demonstrate that the NSQ system successfully satisfies these essential properties, highlighting its flexibility, robustness and efficient messaging service capabilities. Moreover, this paper focuses on formalizing and verifying the security mechanisms in NSQ’s data transmission. By integrating the Transport Layer Security (TLS) protocol into the NSQ system and employing a man-in-the-middle model to simulate deception and interception attacks, it is demonstrated that the TLS protocol enhances the security of NSQ data transmission. This paper also proposes upgrading from one-way to two-way certificate authentication to further enhance TLS data security. Experimental results reveal that despite significant security improvements with the TLS protocol, producer and consumer processes remain vulnerable to spoofing attacks under specific insecure network conditions, leading to potential data leaks. Therefore, the TLS protocol can significantly improve the data security of the NSQ system.

This paper focuses on trajectory tracking, robustness and stabilization of a golf swing robot which has been recently developed to simulate the ultra-high-speed swing motions of a golfer. The proposed control strategies are based on the Lyapunov stability theory and include Backstepping and Sliding-Mode Control based techniques. To attenuate the chattering phenomena caused by a discontinuous switching function and improve the dynamic response of the manipulator, a fuzzy system is used in this research; a Backstepping Sliding-Mode Controller (BSMC), a Backstepping Fuzzy Sliding-Mode Controller (BFSMC) and a Super-twisting Backstepping Sliding-Mode Controller (STBSMC) are used to evaluate the proposed hybrid controller’s BFSMC performance. The Lyapunov stability theory is used to guarantee the stability of the proposed closed-loop robot technique. Numerical simulations show the effectiveness of the proposed strategy based on the fuzzy logic mechanism under different disturbances and uncertainties.

Visual-inertial odometry (VIO) has been found to have great value in robot positioning and navigation. However, the existing VIO algorithms rely heavily on excellent lighting environments and the accuracy of robot positioning and navigation is degraded largely in illumination-challenging scenes. A robust visual-inertial navigation method is developed in this paper. We construct an effective low-light image enhancement model using a deep curve estimation network (DCE) and a lightweight convolutional neural network to recover the texture information of dark images. Meanwhile, a brightness consistency inference method based on the Kalman filter is proposed to cope with illumination variations in image sequences. Multiple sequences obtained from UrbanNav and M2DRG datasets are used to test the proposed algorithm. Furthermore, we also conduct a real-world experiment for the proposed algorithm. Both experimental results demonstrate that our algorithm outperforms other state-of-art algorithms. Compared to the baseline algorithm VINS-mono, the tracking time is improved from 22.0% to 68.2% and the localization accuracy is improved from 0.489m to 0.258m on the darkest sequences.

We present a novel approach to the automatic verification and falsification of LTL requirements of non-linear discrete-time hybrid systems. The verification tool uses an interval-based constraint solver for non-linear robust constraints to compute incrementally refined abstractions. Although the problem is in general undecidable, we prove termination of abstraction refinement based verification and falsification of such properties for the class of non-linear robust discrete-time hybrid systems. We argue, that—in industrial practice—safety critical control applications give rise to hybrid systems that are robust. We give first results on the application of this approach to a variant of an aircraft collision avoidance protocol.

We study a modelling framework and computational paradigm called Colonies of Synchronizing Agents (CSAs), which abstracts intracellular and intercellular mechanisms of biological tissues. The model is based on a multiset of agents (cells) in a common environment (a tissue). Each agent has a local contents, stored in the form of a multiset of atomic objects (e.g., representing molecules), updated by multiset rewriting rules which may act on individual agents (intracellular action) or synchronize the contents of pairs of agents (intercellular action).

In this paper we investigate dynamic properties of CSAs, by means of temporal logic, and we give a logical characterization of some notions inspired by biology such as robustness, mutants and species. We reveal the relation that exists between the concept of robustness for CSAs and the bisimulation relation on colonies. We also present some decidability results for particular cases of robustness.

Neural networks are powerful computation tools for mimicking the human brain to solve realistic problems. Since spiking neural networks are a type of brain-inspired network, called the novel spiking system, Monitor-based Spiking Recurrent network (MbSRN), is derived to learn and represent patterns in this paper. This network provides a computational framework for memorizing the targets using a simple dynamic model that maintains biological plasticity. Based on a recurrent reservoir, the MbSRN presents a mechanism called a ‘monitor’ to track the components of the state space in the training stage online and to self-sustain the complex dynamics in the testing stage. The network firing spikes are optimized to represent the target dynamics according to the accumulation of the membrane potentials of the units. Stability analysis of the monitor conducted by limiting the coefficient penalty in the loss function verifies that our network has good anti-interference performance under neuron loss and noise. The results of solving some realistic tasks show that the MbSRN not only achieves a high goodness-of-fit of the target patterns but also maintains good spiking efficiency and storage capacity.

Deep neural networks (DNNs) have emerged as a prominent model in medical image segmentation, achieving remarkable advancements in clinical practice. Despite the promising results reported in the literature, the effectiveness of DNNs necessitates substantial quantities of high-quality annotated training data. During experiments, we observe a significant decline in the performance of DNNs on the test set when there exists disruption in the labels of the training dataset, revealing inherent limitations in the robustness of DNNs. In this paper, we find that the neural memory ordinary differential equation (nmODE), a recently proposed model based on ordinary differential equations (ODEs), not only addresses the robustness limitation but also enhances performance when trained by the clean training dataset. However, it is acknowledged that the ODE-based model tends to be less computationally efficient compared to the conventional discrete models due to the multiple function evaluations required by the ODE solver. Recognizing the efficiency limitation of the ODE-based model, we propose a novel approach called the nmODE-based knowledge distillation (nmODE-KD). The proposed method aims to transfer knowledge from the continuous nmODE to a discrete layer, simultaneously enhancing the model’s robustness and efficiency. The core concept of nmODE-KD revolves around enforcing the discrete layer to mimic the continuous nmODE by minimizing the KL divergence between them. Experimental results on 18 organs-at-risk segmentation tasks demonstrate that nmODE-KD exhibits improved robustness compared to ODE-based models while also mitigating the efficiency limitation.

For a nonautonomous dynamics defined by a sequence of linear operators, we introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility in l^p spaces, both for the space of perturbations and the space of solutions. This allows unifying the notions of uniform and nonuniform exponential behavior. Moreover, we consider the general case of a noninvertible dynamics. As a nontrivial application we show that the conditional stability of a nonuniform exponential dichotomy persists under sufficiently small linear perturbations.

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. Based on the theory of complex networks and computer simulation, we analyze the robustness to time-delay in linear consensus problem with different network topologies, such as global coupled network, star network, nearest-neighbor coupled network, small-world network, and scale-free network. It is found that global coupled network, star network, and scale-free network are vulnerable to time-delay, while nearest-neighbor coupled network and small-world network are robust to time-delay. And it is found that the maximum node degree of the network is a good predictor for time-delay robustness. And it is found that the robustness to time-delay can be improved significantly by a decoupling process to a small part of edges in scale-free network.

Transmission efficiency and robustness are two important properties of various networks and a number of optimization strategies have been proposed recently. We propose a scheme to enhance the network performance by adding a small fraction of links (or edges) to the currently existing network topology, and we present four edge addition strategies for adding edges efficiently. We aim at minimizing the maximum node betweenness of any node in the network to improve its transmission efficiency, and a number of experiments on both Barabási–Albert (BA) and Erdös–Rényi (ER) networks have confirmed the effectiveness of our four edge addition strategies. Also, we evaluate the effect of some other measure metrics such as average path length, average betweenness, robustness, and degree distribution. Our work is very valuable and helpful for service providers to optimize their network performance by adding a small fraction of edges or to make good network planning on the existing network topology incrementally.

According to the dynamical characteristics of the local redistribution of the load on a removal node, by the reconnection of the neighboring edge of the most vulnerable node, we propose an effective method to improve the network robustness against cascading failures. Under two constraints, i.e. keeping the degree of each node unchanged and fixing the total protective cost of a network, we investigate the efficiency of the swap method on scale-free networks and analyze the correlation between the optimized network and the Pearson correlation coefficient. We numerically show that effective swapping of the small part of connections can dramatically improve the network robust level against cascading failures and find that the optimized networks obtained by the swap method exhibit an extremely disassortative degree–degree correlation, that is, the disassortativity decreases the robustness of the optimized network against cascading failures. While the extent of the disassortative mixing is decided by the parameters in the cascading model. In addition, we also compare the average path length and the diameter of the optimized and the original networks.

Many real-world networks interact with other networks by only several links, for example, transportation networks and aviation networks among cities, internet router network among the different regions, power supply network among cities and so on. Understanding how to protect these coupled networks and improve their robustness against cascading failures is very important. By protecting the edges between coupled networks, we investigate its efficiency on improving the robustness of coupled networks against cascading failures. Fixing the total protective cost of coupled networks, we find that adjusting the capacities of the edges among coupled networks can better improve the robustness of coupled networks against cascading failures and observe that the more uniform the distribution of the edge load, the more effective the protection strategy. In addition, by immunizing the edges among coupled networks, we compare two protecting methods and find that the immunization strategy can better protect coupled networks. Our results are useful not only for how to protect coupled networks from the local perspective, but also for significantly improving the robustness of a single network by protecting some key edges.

The methodology of open-plus-close-loop (OPCL), which is up till now mainly used for the case of ordinary dynamical systems is extended for the first time to the case of delay dynamical process, to achieve complete, lag synchronization. Both the one and two way couplings are examined in detail, with the help of delay logistics, Ikeda and Mackey–Glass system. Robustness of the process is exhibited when the same analysis is done in presence of Gaussian noise. Influence of the strength of such a noise is shown. Our procedure opens up a potentially new approach for the synchronization study of delay dynamical systems.

To control counterparty risk, financial regulations such as the Dodd Frank Act are increasingly requiring standardized derivatives trades to be cleared by central counterparties (CCPs). It is anticipated that in the near-term future, CCPs across the world will be linked through interoperability agreements that facilitate risk-sharing but also serve as a conduit for transmitting shocks. This paper theoretically studies a network with CCPs that are linked through interoperability arrangements, and studies the properties of the network that contribute to cascading failures. The magnitude of the cascading is theoretically related to the strength of network linkages, the size of the network, the logistic mapping coefficient, a stochastic effect and CCP's defense lines. Simulations indicate that larger network effects increase systemic risk from cascading failures. The size of the network N raises the threshold value of shock sizes that are required to generate cascades. Hence, the larger the network, the more robust it will be.

Attempts to simulate compressible flows with moderate Mach number to relatively high ones using Lattice Boltzmann Method (LBM) have been made by numerous researchers in the recent decade. The stability of the LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. The present study proposes an approach for simulation of inviscid flows by a compressible LB model in order to enhance the robustness using a combination of Essentially NonOscillatory (ENO) scheme and Shock-Detecting Sensor (SDS) procedure. A sensor is introduced with adjustable parameters which is active near the discontinuities and affects less on smooth regions. The validity of the improved model to capture shocks and to resolve contact discontinuity and rarefaction waves in the well-known benchmarks such as, Riemann problem, and shock reflection is investigated. In addition, the problem of supersonic flow in a channel with ramp is simulated using a skewed rectangular grid generated by an algebraic grid generation method. The numerical results are compared with analytical ones and those obtained by solving the original model. The numerical results show that the presented scheme is capable of generating more robust solutions in the simulation of compressible flows and is almost free of oscillations for high Mach numbers. Good agreements are obtained for all problems.

In the modeling, controlling, and monitoring of complex networks, a fundamental problem concerns the determination and observation of the system's states by using measurements or sensors as few as possible, defined as network observation. This work aims to investigate the robustness of network observation when an approach of minimum dominating set is considered in observing a network. We first investigate the structural properties of the minimum dominating sets, e.g. how the size depends on the degree–degree correlations and how to assess the nodes' importance in the malicious attacks. Then, we introduce a new measurement of robustness for network observation, and implement a hill-climbing algorithm to improve its robustness by edge rewiring. Furthermore, we propose a novel rewiring strategy, called smart rewiring, which could speed up the increment of robustness index. In comparison with previous strategy of edge rewiring, the smart rewiring has been found to be successfully useful on real-world and synthetic networks.

The hierarchical structure, $k$-core, is common in various complex networks, and the actual network always has successive layers from 1-core layer (the peripheral layer) to $k_m$-core layer (the core layer). The nodes within the core layer have been proved to be the most influential spreaders, but there is few work about how the depth of $k$-core layers (the value of $k_m$) can affect the robustness against cascading failures, rather than the interdependent networks. First, following the preferential attachment, a novel method is proposed to generate the scale-free network with successive $k$-core layers (KCBA network), and the KCBA network is validated more realistic than the traditional BA network. Then, with KCBA interdependent networks, the effect of the depth of $k$-core layers is investigated. Considering the load-based model, the loss of capacity on nodes is adopted to quantify the robustness instead of the number of functional nodes in the end. We conduct two attacking strategies, i.e. the RO-attack (Randomly remove only one node) and the RF-attack (Randomly remove a fraction of nodes). Results show that the robustness of KCBA networks not only depends on the depth of $k$-core layers, but also is slightly influenced by the initial load. With RO-attack, the networks with less $k$-core layers are more robust when the initial load is small. With RF-attack, the robustness improves with small $k_m$, but the improvement is getting weaker with the increment of the initial load. In a word, the lower the depth is, the more robust the networks will be.

Cascading failures in networked systems often lead to catastrophic consequence. Defending cascading failure propagation by employing local load redistribution method is an efficient way. Given initial load of every node, the key of improving network robustness against cascading failures is to maximally defend cascade propagation with minimum total extra capacity of all nodes. With finite total extra capacity of all nodes, we first discuss three general extra capacity distributions including degree-based distribution (DD), average distribution (AD) and random distribution (RD). To sufficiently use the total spare capacity (SC) of all neighboring nodes of a failed node, then we propose a novel SC-based local load redistribution mechanism to improve the cascade defense ability of network. We investigate the network robustness against cascading failures induced by a single node failure under the three extra capacity distributions in both scale-free networks and random networks. Compared with the degree-based (DB) local load redistribution method, our SC method achieves higher robustness under all of the three extra capacity distributions. The extensive simulation results can well confirm the effectiveness of the SC local load redistribution method.

Recently the robustness of coupled network under cascading failure has attracted a lot of attention. In this paper, we investigate the cascading failure of the interconnected weighted networks based on the state of link. The load on one link is defined by a function of the strength of the two nodes at the ends of that link, using four intentional attack strategies, we study the invulnerability of the interconnected weighted networks when cascading failure occurs. Our studies show that when the link with highest load is attacked, the damage to the network will be more serious by attacking the inner-link with highest load than that caused by attacking the coupling link with highest load, and no matter how the coupling links distribute, there are two thresholds. In addition, we find that the larger the weight increment in the model or the smaller the network’s mean clustering coefficient, the stronger the ability of the network to resist cascading failure when the inner-link with highest load is attacked, while the weaker the ability of the network to suppress the cascading failure when the inner-link with lowest load is attacked.