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We propose a unified framework for time-varying convex optimization based on the prediction-correction paradigm, both in the primal and dual spaces. In this framework, a continuously varying optimization problem is sampled at fixed intervals, and each problem is approximately solved with a primal or dual correction step. The solution method is warm-started with the output of a prediction step, which solves an approximation of a future problem using past information. Prediction approaches are studied and compared under different sets of assumptions. Examples of algorithms covered by this framework are time-varying versions of the gradient method, splitting methods, and the celebrated alternating direction method of multipliers (ADMM).

Rate Splitting Multiple Access (RSMA) has emerged as an effective interference management scheme for applications that require high data rates. Although RSMA has shown advantages in rate enhancement and spectral efficiency, it has yet not to be ready for latency-sensitive applications such as virtual reality streaming, which is an essential building block of future 6G networks. Unlike conventional High-Definition streaming applications, streaming virtual reality applications requires not only stringent latency requirements but also the computation capability of the transmitter to quickly respond to dynamic users' demands. Thus, conventional RSMA approaches usually fail to address the challenges caused by computational demands at the transmitter, let alone the dynamic nature of the virtual reality streaming applications. To overcome the aforementioned challenges, we first formulate the virtual reality streaming problem assisted by RSMA as a joint communication and computation optimization problem. A novel multicast approach is then proposed to cluster users into different groups based on a Field-of-View metric and transmit multicast streams in a hierarchical manner. After that, we propose a deep reinforcement learning approach to obtain the solution for the optimization problem. Extensive simulations show that our framework can achieve the millisecond-latency requirement, which is much lower than other baseline schemes.

In recent years there has been a growing interest in reconfigurable intelligent surfaces (RISs) as enablers for the realization of smart radio propagation environments which can provide performance improvements with low energy consumption in future wireless networks. However, to reap the potential gains of RIS it is crucial to jointly design both the transmit precoder and the phases of the RIS elements. Within this context, in this paper we study the use of multiple RIS panels in a parallel or multi-hop configuration with the aim of assisting a multi-stream multiple-input multiple-output (MIMO) communication. To solve the nonconvex joint optimization problem of the precoder and RIS elements targeted at maximizing the achievable rate, we propose an iterative algorithm based on the monotone accelerated proximal gradient (mAPG) method which includes an extrapolation step for improving the convergence speed and monitoring variables for ensuring sufficient descent of the algorithm. Based on the sufficient descent property we then present a detailed convergence analysis of the algorithm which includes expressions for the step size. Simulation results in different scenarios show that, besides being effective, the proposed approach can often achieve higher rates than other benchmarked schemes.

Although generative facial prior and geometric prior have recently demonstrated high-quality results for blind face restoration, producing fine-grained facial details faithful to inputs remains a challenging problem. Motivated by the classical dictionary-based methods and the recent vector quantization (VQ) technique, we propose a VQ-based face restoration method - VQFR. VQFR takes advantage of high-quality low-level feature banks extracted from high-quality faces and can thus help recover realistic facial details. However, the simple application of the VQ codebook cannot achieve good results with faithful details and identity preservation. Therefore, we further introduce two special network designs. 1). We first investigate the compression patch size in the VQ codebook and find that the VQ codebook designed with a proper compression patch size is crucial to balance the quality and fidelity. 2). To further fuse low-level features from inputs while not "contaminating" the realistic details generated from the VQ codebook, we proposed a parallel decoder consisting of a texture decoder and a main decoder. Those two decoders then interact with a texture warping module with deformable convolution. Equipped with the VQ codebook as a facial detail dictionary and the parallel decoder design, the proposed VQFR can largely enhance the restored quality of facial details while keeping the fidelity to previous methods.

Reconfigurable intelligent surface (RIS)-aided terahertz (THz) communications have been regarded as a promising candidate for future 6G networks because of its ultra-wide bandwidth and ultra-low power consumption. However, there exists the beam split problem, especially when the base station (BS) or RIS owns the large-scale antennas, which may lead to serious array gain loss. Therefore, in this paper, we investigate the beam split and beamforming design problems in the THz RIS communications. Specifically, we first analyze the beam split effect caused by different RIS sizes, shapes and deployments. On this basis, we apply the fully connected time delayer phase shifter hybrid beamforming architecture at the BS and deploy distributed RISs to cooperatively mitigate the beam split effect. We aim to maximize the achievable sum rate by jointly optimizing the hybrid analog/digital beamforming, time delays at the BS and reflection coefficients at the RISs. To solve the formulated problem, we first design the analog beamforming and time delays based on different RISs physical directions, and then it is transformed into an optimization problem by jointly optimizing the digital beamforming and reflection coefficients. Next, we propose an alternatively iterative optimization algorithm to deal with it. Specifically, for given the reflection coefficients, we propose an iterative algorithm based on the minimum mean square error technique to obtain the digital beamforming. After, we apply LDR and MCQT methods to transform the original problem to a QCQP, which can be solved by ADMM technique to obtain the reflection coefficients. Finally, the digital beamforming and reflection coefficients are obtained via repeating the above processes until convergence. Simulation results verify that the proposed scheme can effectively alleviate the beam split effect and improve the system capacity.

Face clustering is a promising way to scale up face recognition systems using large-scale unlabeled face images. It remains challenging to identify small or sparse face image clusters that we call hard clusters, which is caused by the heterogeneity, \ie, high variations in size and sparsity, of the clusters. Consequently, the conventional way of using a uniform threshold (to identify clusters) often leads to a terrible misclassification for the samples that should belong to hard clusters. We tackle this problem by leveraging the neighborhood information of samples and inferring the cluster memberships (of samples) in a probabilistic way. We introduce two novel modules, Neighborhood-Diffusion-based Density (NDDe) and Transition-Probability-based Distance (TPDi), based on which we can simply apply the standard Density Peak Clustering algorithm with a uniform threshold. Our experiments on multiple benchmarks show that each module contributes to the final performance of our method, and by incorporating them into other advanced face clustering methods, these two modules can boost the performance of these methods to a new state-of-the-art. Code is available at: //github.com/echoanran/On-Mitigating-Hard-Clusters.

This paper studies queueing problems with an endogenous number of machines with and without an initial queue, the novelty being that coalitions not only choose how to queue, but also on how many machines. For a given problem, agents can (de)activate as many machines as they want, at a cost. After minimizing the total cost (processing costs and machine costs), we use a game theoretical approach to share to proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems with an endogenous number of machines, and examine how to share the total cost. We provide an upper bound and a lower bound on the cost of a machine to guarantee the non-emptiness of the core (the set of stable allocations). Next, we study requeueing problems with an endogenous number of machines, where there is an existing queue. We examine how to share the cost savings compared to the initial situation, when optimally requeueing/changing the number of machines. Although, in general, stable allocation may not exist, we guarantee the existence of stable allocations when all machines are considered public goods, and we start with an initial schedule that might not have the optimal number of machines, but in which agents with large waiting costs are processed first.

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase random field. The penalty term encourages the overall phase at a particular location to be similar to the spatially weighted average phase in its neighbourhood, and thus engenders a regularization that prevents over-alignment. Utility of the registration method, and its superior performance compared to methods that fail to account for the spatial correlation, is demonstrated through performance on simulated examples and two multivariate functional datasets pertaining to EEG signals and ozone concentrations. The generality of the framework opens up the possibility for extension to settings involving different forms of correlation between the component functions and their phases.

Intelligent reflecting surfaces (IRSs) have recently received significant attention for wireless communications because it reduces the hardware complexity, physical size, weight, and cost of conventional large arrays. However, deployment of IRS entails dealing with multiple channel links between the base station (BS) and the users. Further, the BS and IRS beamformers require a joint design, wherein the IRS elements must be rapidly reconfigured. Data-driven techniques, such as deep learning (DL), are critical in addressing these challenges. The lower computation time and model-free nature of DL makes it robust against the data imperfections and environmental changes. At the physical layer, DL has been shown to be effective for IRS signal detection, channel estimation and active/passive beamforming using architectures such as supervised, unsupervised and reinforcement learning. This article provides a synopsis of these techniques for designing DL-based IRS-assisted wireless systems.

We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues that are highly dependent on the inputs, as common sense would suggest. Our approach proposes instead to use a set of eigenvalues totally independent from the inputs and that encode the long-term averaging of the influence of the future on present eigenvalues. Such an influence can be the predominant factor in nonstationary systems. Using real and synthetic data, we show that our data-driven method outperforms optimal methods designed for stationary systems for the filtering of both covariance matrix and its inverse, as illustrated by financial portfolio variance minimization, which makes out method generically relevant to many problems of multivariate inference.