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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.

Bioluminescent tomography (BLT) is a noninvasive imaging technology that uses optical methods to study physiological and pathological processes at the cellular and molecular levels. It is a powerful tool for early diagnosis and treatment of tumors, as well as drug development. However, the simplified optical transmission models and the ill-posed inverse reconstruction limit its wide applications. The development of deep learning has provided new potential for extending the applications of optical BLT. Researchers have introduced various methods such as neural networks and self-attention mechanisms to improve reconstruction accuracy. Despite these efforts, weak energy points around the reconstructed light source center still impact the accuracy of restoration. In this study, we propose a dual-branch network based on a combination of attention mechanism and fully connected layers (FC-AM) to reduce centroid error and improve reconstruction performance. The network architecture consists of a fully connected (FC) subnetwork and an attention mechanism-based dual-branch (AMDB) subnetwork. The FC subnetwork is used to process input data. AMDB subnetwork is used for deep feature extraction, and captures feature information from different perspectives in parallel. Each branch of the AMDB subnetwork is composed of four AM subnets, which extract features through multilayer linear transformations and attention mechanisms. The outputs of the AMDB are combined through feature fusion to produce the final result. Numerical simulations and experimental results demonstrate that the FC-AM network significantly improves BLT reconstruction performance compared to existing methods (KNN_LC and AMLC networks), offering enhanced stability and accuracy.

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.

Current researches on the network characteristics of metro networks are generally carried out on topology networks without passenger flows running on it, thus more complex features of the networks with ridership loaded on it cannot be captured. In this study, we incorporated the load of metro networks, passenger volume, into the exploration of network features. Thus, the network can be examined in the context of operation, which is the ultimate purpose of the existence of a metro network. To this end, section load was selected as an edge weight to demonstrate the influence of ridership on the network, and a weighted calculation method for complex network indicators and robustness were proposed to capture the unique behaviors of a metro network with passengers flowing in it. The proposed method was applied on Beijing Subway. Firstly, the passenger volume in terms of daily origin and destination matrix was extracted from exhausted transit smart card data. Using the established approach and the matrix as weighting, common indicators of complex network including clustering coefficient, betweenness and degree were calculated, and network robustness were evaluated under potential attacks. The results were further compared to that of unweighted networks, and it suggests indicators of the network with consideration of passenger volumes differ from that without ridership to some extent, and networks tend to be more vulnerable than that without load on it. The significance sequence for the stations can be changed. By introducing passenger flow weighting, actual operation status of the network can be reflected more accurately. It is beneficial to determine the crucial stations and make precautionary measures for the entire network’s operation security.

Systematic studies have revealed that single gene deletions often display little phenotypic effects under laboratory conditions and that in many cases gene dispensability depends on the experimental conditions. To elucidate the environmental dependency of genes, we analyzed the effects of gene deletions by Phenotype MicroArray™ (PM), a system for quantitative screening of thousands of phenotypes in a high-throughput manner. Here, we proposed a new statistical approach to minimize error inherent in measurements of low respiration rates and find which mutants showed significant phenotypic changes in comparison to the wild-type. We show analyzing results from comprehensive PM assays of 298 single-gene knockout mutants in the Keio collection and two additional mutants under 1,920 different conditions. We focused on isozymes of these genes as simple duplications and analyzed correlations between phenotype changes and protein expression levels. Our results revealed divergence of the environmental dependency of the gene among the knockout genes and have also given some insights into possibilities of alternative pathways and availabilities of information on protein synthesis patterns to classify or predict functions of target genes from systematic phenotype screening.

This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic $p$-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain ${ℝ}^N$. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in $L^2({ℝ}^N)$. This attractor is further proved to be a bi-spatial $(L^2({ℝ}^N),L^r({ℝ}^N))$-attractor for any $r\in [2,\infty )$, which is compact, measurable in $L^r({ℝ}^N)$ and attracts all random subsets of $L^2({ℝ}^N)$ with respect to the norm of $L^r({ℝ}^N)$. Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in $L^r({ℝ}^N)$ for $r\in [2,\infty )$ in order to overcome the non-compactness of Sobolev embeddings on ${ℝ}^N$ and the nonlinearity of the fractional $p$-Laplace operator.

Optical molecular tomography (OMT) is a potential pre-clinical molecular imaging technique with applications in a variety of biomedical areas, which can provide non-invasive quantitative three-dimensional (3D) information regarding tumor distribution in living animals. The construction of optical transmission models and the application of reconstruction algorithms in traditional model-based reconstruction processes have affected the reconstruction results, resulting in problems such as low accuracy, poor robustness, and long-time consumption. Here, a gates joint locally connected network (GLCN) method is proposed by establishing the mapping relationship between the inside source distribution and the photon density on surface directly, thus avoiding the extra time consumption caused by iteration and the reconstruction errors caused by model inaccuracy. Moreover, gates module was composed of the concatenation and multiplication operators of three different gates. It was embedded into the network aiming at remembering input surface photon density over a period and allowing the network to capture neurons connected to the true source selectively by controlling three different gates. To evaluate the performance of the proposed method, numerical simulations were conducted, whose results demonstrated good performance in terms of reconstruction positioning accuracy and robustness.

We comprehensively investigate the robustness of well-known factor models to altered factor formation breakpoints. Deviating from the standard 30th and 70th percentile selection, we use an extensive set of anomaly test portfolios to uncover two main findings: First, there is a trade-off between specification and diversification. More centered breakpoints tend to result in less (idiosyncratic) risk. More extreme sorts lead to greater exposure to the underlying anomalies and thus to higher average returns. Second, the models are robust to varying degrees. Hou et al.’s model [2015, Digesting Anomalies: An Investment Approach, Review of Financial Studies 28, 650–705] is much more sensitive to changes in breakpoints than the Fama–French models.

Transfer-based attacks, a type of adversarial attack, have become a growing threat in recent years with the proliferation of cloud services. Deep neural networks that exploit human cognitive bias (Loosely Symmetric-Deep Neural Network, LS-DNN) are known as a defensive technique against transfer-based attacks. LS-DNN can prevent malfunctions caused by adversarial examples with a high probability by incorporating human learning characteristics into the neural network’s nodes. However, maintaining accuracy against normal data and reducing Training Time is challenging. This paper proposes a new model called “LS⁺-DNN” inspired by the Dropout method to solve this problem. Evaluation experiments on two datasets show that the proposed model can achieve both in high dimensions. In addition, we analyze the proposed model focusing on the variance and confidence score of the training parameters of the proposed model. As a result, we point out that the confidence score is an important indicator of robust models against transfer-based attacks.

Addressing the issues of nonlinearity, control redundancy and coupling, and system uncertainties in the deceleration transition process from level flight to hover in short takeoff and vertical landing (STOVL) aircraft, this paper establishes a six-degree-of-freedom nonlinear mathematical model for the STOVL deceleration transition process. An augmented control method based on $L_1$ adaptive control is proposed for the deceleration transition process: dynamic inversion (DI) method is used to design the fundamental control laws for the inner and the outer loops, while an $L_1$ adaptive controller is employed as the augmented controller to enhance performance and robustness under system uncertainties. Simulation results validate that this method effectively suppresses system uncertainties and improves the transition control performance.

In this paper, the formation control problem for unicycle multi-agent systems is considered. The design of a generalized homogeneous leader–follower formation control protocol is studied which shows that such a control protocol can be obtained by “upgrading” from the classical linear control. With this proposed control protocol, a finite-time stability of the formation error is ensured if the acceleration of the leader is bounded by some known value. In addition, if the leader acceleration is unknown but bounded, the robust formation is achieved by ensuring the formation error’s input-to-state stability. Simulations are carried out to verify the effectiveness of the proposed control protocol.

The $\epsilon$-insensitive-Least Squares Support Vector Regression ($\epsilon$-LSSVR) optimization problem with $\epsilon$-insensitive quadratic loss function is a non-smooth, piecewise quadratic complex problem. Therefore, the optimal solution of $\epsilon$-LSSVR takes longer than Classic LSSVR. Additionally, due to its unbounded influence function, $\epsilon$-LSSVR, like classical LSSVR, shows poor generalization ability in the presence of outliers. To overcome the above-mentioned drawbacks, this paper presents an $\epsilon$-insensitive Weighted Least Squares Support Vector Regression ($\epsilon$-WLSSVR) with equality constraints to increase robustness against outliers. To reduce the computational complexity and time, the optimization problem of $\epsilon$-WLSSVR is solved by the Sequential Minimal Optimization (SMO) algorithm. Extensive simulations have shown that the presented $\epsilon$-WLSSVR model combined with the SMO algorithm is more effective and efficient than LSSVR and its known sparse variants.