Distributed formation tracking control with obstacle avoidance of multiagent systems (MASs) under random switching topologies and external disturbances is considered in this article. To achieve the complex objective, an effective control strategy is developed in three steps. First, under the transition probability (TP)-based mode-dependent average dwell-time (MDADT) switching topologies, a distributed objective trajectory achieves almost sure global exponential tracking of the desired formation trajectory. Second, a safe objective trajectory approach is designed by geometrically projecting the unsafe parts of the existing formation trajectory onto the boundary of the obstacle region. Finally, an integral-multiplicative barrier Lyapunov function (IMBLF) is proposed to allow agents to track the safe objective trajectory, where the IMBLF can further guarantee the safety of the MASs. One of the interesting merits of our results is that the impulsive increasing of Lyapunov function at switching instants which is necessary for classical analysis methods has been removed. The feasibility of the proposed formation control method with obstacle avoidance is verified by simulations.

Protein kinases regulate diverse cellular functions, including cell cycle progression, metabolism, differentiation, and survival, with their dysregulation implicated in multiple carcinogenic processes. Phosphatidylinositol 3-kinase alpha inhibitors (PI3K$ \alpha $is) have revolutionized breast cancer treatment, but acquired resistance remains a major clinical challenge, with around 40% of patients experiencing progression within 4-6 months. Current drug response prediction (DRP) methods typically rely on individual pathways or biomarkers, limiting their ability to capture complex cancer-specific molecular interactions and predict resistance mechanisms. To overcome these limitations, we present AdaSemb, an adaptive, knowledge-driven deep learning framework that uses a multi-protein assembly map to predict responses and resistance to PI3K$ \alpha $i. AdaSemb comprises two modules: the AdaSemb-PA module incorporates tumor genomic variations into a biological structural neural network, while the AdaSemb-DRP module uses conditional domain adversarial networks to enhance gene-drug distribution generalization. By combining genomic data with drug molecular structures, AdaSemb identifies critical protein combinations linked to drug resistance. In validation with 1244 cancer cell lines and patient-derived xenografts (PDX), AdaSemb outperformed existing DRP models. In a cohort of 116 breast cancer patients from the Cancer Genome Atlas (TCGA), it predicted significantly longer survival for sensitive patients, surpassing traditional biomarkers in precision. Furthermore, we identified seven key assemblages that integrate mutations from 93 genes, which distinguish alpelisib sensitive and resistant cell lines. These results are applicable to breast cancer patient samples and PDX models, demonstrating AdaSemb's significant clinical potential in personalized treatment and prediction of resistance for breast cancer.

Abstract Federated learning (FL) is widely used in edge‐cloud collaborative training due to its distributed architecture and privacy‐preserving properties without sharing local data. FLTrust, the most state‐of‐the‐art FL defense method, is a federated learning defense system with trust guidance. However, we found that FLTrust is not very robust. Therefore, in the edge collaboration scenario, we mainly study the poisoning attack on the FLTrust defense system. Due to the aggregation rule, FLTrust, with trust guidance, the model updates of participants with a significant deviation from the root gradient direction will be eliminated, which makes the poisoning effect on the global model not obvious. To solve this problem, under the premise of not being deleted by the FLTrust aggregation rules, we construct malicious model updates that deviate from the trust gradient to the greatest extent to achieve model poisoning attacks. First, we utilize the rotation of high‐dimensional vectors around axes to construct malicious vectors with fixed orientations. Second, the malicious vector is constructed by the gradient inversion method to achieve an efficient and fast attack. Finally, a method of optimizing random noise is used to construct a malicious vector with a fixed direction. Experimental results show that our attack method reduces the model accuracy by 20%, severely undermining the usability of the model. Attacks are also successful hundreds of times faster than the FLTrust adaptive attack method.

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popularpurely randomgeometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family ofsparserandom geometric graphs that are parametrized by a fractality parameter$\nu $which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We asymptotically characterize the expected number of edges, triangles, cliques and hub-and-spoke motifs in FGNs, unveiling a distinct pattern in their scaling with the size parameter of the network. We then examine the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data, in addition to fundamental properties of the FGN as a random graph model. We also explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs. Finally, we substantiate our results with phenomenological analysis of the FGN in the context of available scientific literature for fractality in networks, including applications to real-world massive network data.

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs.