This article focuses on training a robust global model under the dynamic participating client scenario in federated learning (FL). Unlike the static FL scenario, this scenario emphasizes that new clients participate into modeling process at specific training round, a situation commonly encountered in Internet of Things (IoT) networks. Particularly, new participating clients may introduce irrelevant data (e.g., label noise, outliers, and distinct data distributions), posing the challenge for training a robust global model. To tackle this challenge, we introduce a novel FL framework called Fed-TS. This framework incorporates the Thompson sampling (TS) policy, a reinforcement learning (RL) approach, to enable biased client participation for both relevant and irrelevant clients during modeling process. Specifically, new clients can participate into modeling process based on their successful probability of causing “small path drift" in the global model. In addition, our framework employs an adaptive threshold using the K-means algorithm to assess “small path drift" in the global model. During the experiments, we investigate the impact of hyper-parameters on the performance of biased client participation for both relevant and irrelevant clients. Compared to other schemes or frameworks, our framework ensures a robust global model with high accuracy.

Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon (TGRS) codes may not necessarily be MDS. It is meaningful to study the conditions under which TGRS codes are MDS. In this paper, we study a general class of TGRS (ATGRS) codes which include all the known special ones. First, we obtain another expression of the inverse of the Vandermonde matrix. Based on this, we further derive an equivalent condition under which an A-TGRS code is MDS. According to this, the A-TGRS MDS codes include nearly all the known related results in the previous literatures. More importantly, we also give three constructions to obtain many other classes of MDS TGRS codes with new parameter matrices. In addition, we present a new method to compute the inverse of the lower triangular Toplitz matrix by a linear feedback shift register, which will be very useful in many research fields.

This letter focuses on the robust low-rank matrix recovery (RLRMR) in the presence of gross sparse outliers. Instead of using$\ell _{1}$-norm to reduce or suppress the influence of anomalies, we aim to eliminate their impact. To this end, we model the RLRMR as a mixed integer programming (MIP) problem based on the$\ell _{0}$-norm. Then, a block coordinate descent (BCD) algorithm is developed to iteratively solve the resultant MIP. At each iteration, the proposed approach first utilizes the$\ell _{0}$-norm optimization theory to assign binary weights to all entries of the residual between the known and estimated matrices. With these binary weights, the optimization over the bilinear term is reduced to a weighted extension of the Frobenius norm. As a result, the optimization problem is decomposed into a group of row-wise and column-wise subproblems with closed-form solutions. Additionally, the convergence of the proposed algorithm is studied. Simulation results demonstrate that the proposed method is superior to five state-of-the-art RLRMR algorithms.

This correspondence contributes to construct some difference-balanced d-form functions. A modification of Klapper and No's theorem are given, from which some new d-form sequences with ideal correlation and new difference-balanced d-form functions are obtained.