The weighted$\ell _{r}-\ell _{1}$minimization with weight$\alpha$has been extensively employed to robustly estimate a high-dimensional sparse signal$x$coded by the underdetermined linear measurements$y=Ax+z$, where$A$and$z$are the measurement matrix and noise, respectively. In this paper, we demonstrate that if the restricted isometry constant (RIC)$\delta _{s}$of$A$fulfills\begin{align*} \delta _{s}< 1/\left(1+3t/\sqrt{5}\right), \end{align*}where$t$relies on sparsity level$s$for known model parameters$\alpha$and$r$, then any sparse signal$x$are ensured to be robustly reconstructed through solving the weighted$\ell _{r}-\ell _{1}$minimization in the noisy situation. The gained condition is testified to be much better that the state-of-art ones.

Existing blockchain systems can quickly respond to verifiable primary key queries based on authenticated indexes. However, many blockchain applications also require high-performance queries on non-primary keys. For example, traders query NFT or tokenized RWA with certain features, e.g., type and return. Therefore, it necessitates authenticated secondary indexes to support efficient verifiable queries on non-primary keys. However, the existing approach to authenticated index design that couples index and authenticated digest together does not adapt well to the phased nature of non-primary key queries, making the most time-consuming process of commitment generation severely block the query process. In this study, we propose the first authenticated secondary index MEST for verifiable non-primary key queries. MEST decouples the data index and authenticated digest, which can parallelize commitment generation on the secondary index and the query processing on the primary index, thus greatly reducing the latency of the non-primary key query. Furthermore, we adopt an Extendible Hash Table to index data and propose a Merkle Growth Tree to generate commitment, which can dynamically adapt to the rapid growth of data and the skew in data access pattern. Extensive experiments on both synthetic and real datasets demonstrate that MEST improves throughput by 3.17×, reduces latency by 59%, and exhibits better scalability than baselines.

A converging pattern represents the process in which a collection of moving objects gradually converges toward a target area from various directions and eventually forms a dense group. Unlike most existing group patterns, it indicates the early formation of group events, which has a significant application for predicting and detecting emergency events. Existing studies of the converging pattern merely discover patterns from historical trajectories in an offline manner. However, online mining over streaming trajectories has a more practical impact in some real-world scenarios like real-time traffic monitoring . In this paper, we investigate online algorithms that enable converging pattern mining over network-constrained streaming trajectories of moving objects. To achieve synchronization with the speed of trajectory updates, we propose an incremental density-based clustering algorithm in the road network called I D C R N and a converging monitoring method to detect converging patterns in real-time. To efficiently retrieve the constantly evolving spatial relationship among objects in road networks with a large search space and an intractable computation complexity for network distance, we propose a dual index called M O R N to support continuous neighborhood query and cluster pruning in the road network . Extensive experiments with real and synthetic datasets validate the efficiency of our proposed index and methods.

In this article, we bring forward a completely perturbed nonconvex Schatten p -minimization to address a model of completely perturbed low-rank matrix recovery (LRMR). This article based on the restricted isometry property (RIP) and the Schatten- p null space property (NSP) generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, and it gives the RIP condition and the Schatten- p NSP assumption that guarantee the recovery of low-rank matrix and the corresponding reconstruction error bounds. In particular, the analysis of the result reveals that in the case that p decreases 0 and for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition (Recht et al., 2010). In addition, we study the connection between RIP and Schatten- p NSP and discern that Schatten- p NSP can be inferred from the RIP. The numerical experiments are conducted to show better performance and provide outperformance of the nonconvex Schatten p -minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.

In this letter, we discuss the reconstruction of sparse signals from undersampled data, which belongs to the core content of compressed sensing. A new sufficient condition in terms of the restricted isometry constant (RIC) and restricted orthogonality constant (ROC) is first established for the performance guarantee of recently proposed non-convex weighted$\ell _{r}-\ell _{1}$minimization in recovering (approximately) sparse signals that may be polluted by noise. To be specific, it is shown that if the RIC$\delta _{s}$and ROC$\theta _{s,s}$of measurement matrix obey$\delta _{s}+\nu (s)\theta _{s,s}< 1$, where$\nu (s)$depends on$s$for given quantities, then any$s$-sparse signals in noiseless setting are guaranteed to be recovered accurately via solving the constrained weighted$\ell _{r}-\ell _{1}$minimization optimization problem and any (approximately)$s$-sparse signals can be estimated robustly in the noisy case. In addition, we provide several pivotal remarks which indicate the recovery guarantee is much less restricted than the existing one. The results obtained contribute to proving the fidelity of the excellent weighted$\ell _{r}-\ell _{1}$minimization method.

A distributed algorithm is presented in this article under directed communication networks, which is used to solve the economic dispatch problem in fixed time in smart grid systems. A new globally fixed-time stability theory (Lemma 3) is first given in this article, which contains a new upper bound for the estimation of the settling time. Moreover, the fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization theory, the new lemma, and Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, numerical simulations show the effectiveness and advantages of the distributed fixed-time optimization algorithm.

Group pattern mining from spatio-temporal trajectories of moving objects have gained significant attentions due to the prevalence of location-acquisition devices and tracking technologies. In this work, we propose a new group pattern, named converging, which is a group of moving objects that converge from different directions for a certain time period. Examples of convergings may include traffic jams, troop assembly, serious stampedes, and other public congregations. As a proof-of-concept, we implemented a visual analytic system CPM based on road-network constrained trajectories to detect converging events in road networks. A user-friendly interface is designed to help users gain insights into converging events from spatial and temporal aspects. Finally, we demonstrate the effectiveness and efficiency of our system by using a real dataset.