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In this paper, we study the Aubin property of the Karush-Kuhn-Tucker solution mapping for the nonlinear semidefinite programming (NLSDP) problem at a locally optimal solution. In the literature, it is known that the Aubin property implies the constraint nondegeneracy by Fusek [SIAM J. Optim. 23 (2013), pp. 1041-1061] and the second-order sufficient condition by Ding et al. [SIAM J. Optim. 27 (2017), pp. 67-90]. Based on the Mordukhovich criterion, here we further prove that the strong second-order sufficient condition is also necessary for the Aubin property to hold. Consequently, several equivalent conditions including the strong regularity are established for NLSDP's Aubin property. Together with the recent progress made by Chen et al. on the equivalence between the Aubin property and the strong regularity for nonlinear second-order cone programming [arXiv:2406.13798v1 (2024)], this paper constitutes a significant step forward in characterizing the Aubin property for general non-polyhedral $C^2$-cone reducible constrained optimization problems.

Dual quaternions and dual quaternion matrices have found widespread applications in robotic research, with their spectral theory been extensively studied in recent years. This paper delves into the realm of eigenvalue computation and related problems specific to dual quaternion Hermitian matrices. We establish the connection between dual quaternion matrices and their dual complex adjoint matrices, concerning eigenvalue problems and matrix rank-k approximations. By integrating the dual complex adjoint matrix, we refine the power method for eigenvalue computation for dual quaternion Hermitian matrices, achieving greater numerical efficiency. Furthermore, leveraging the eigen-decomposition of dual complex adjoint matrices, we introduce a novel approach for calculating all eigenpairs of dual quaternion Hermitian matrices. This method surpasses the power method in terms of accuracy and speed and addresses its limitations, as exemplified by its application to the eigenvalue computation of Laplacian matrices, where our algorithm demonstrates significant advantages. Additionally, we apply the improved power method and optimal rank-k approximations to pose graph optimization problem, enhancing efficiency and success rates, especially under low observation conditions., Comment: arXiv admin note: text overlap with arXiv:2407.12635

Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex adjoint matrices for dual quaternion matrices. We delve into exploring the properties of this matrix, utilizing it to study eigenvalues of dual quaternion matrices and defining the concept of standard right eigenvalues. Notably, we leverage the properties of the dual complex adjoint matrix to devise a direct solution to the Hand-Eye calibration problem. Additionally, we apply this matrix to solve dual quaternion linear equations systems, thereby advancing the Rayleigh quotient iteration method for computing eigenvalues of dual quaternion Hermitian matrices, enhancing its computational efficiency. Numerical experiments have validated the correctness of our proposed method in solving the Hand-Eye calibration problem and demonstrated the effectiveness in improving the Rayleigh quotient iteration method, underscoring the promising potential of dual complex adjoint matrices in tackling dual quaternion-related challenges.

This paper documents our characterization study and practices for serving text-to-image requests with stable diffusion models in production. We first comprehensively analyze inference request traces for commercial text-to-image applications. It commences with our observation that add-on modules, i.e., ControlNets and LoRAs, that augment the base stable diffusion models, are ubiquitous in generating images for commercial applications. Despite their efficacy, these add-on modules incur high loading overhead, prolong the serving latency, and swallow up expensive GPU resources. Driven by our characterization study, we present SwiftDiffusion, a system that efficiently generates high-quality images using stable diffusion models and add-on modules. To achieve this, SwiftDiffusion reconstructs the existing text-to-image serving workflow by identifying the opportunities for parallel computation and distributing ControlNet computations across multiple GPUs. Further, SwiftDiffusion thoroughly analyzes the dynamics of image generation and develops techniques to eliminate the overhead associated with LoRA loading and patching while preserving the image quality. Last, SwiftDiffusion proposes specialized optimizations in the backbone architecture of the stable diffusion models, which are also compatible with the efficient serving of add-on modules. Compared to state-of-the-art text-to-image serving systems, SwiftDiffusion reduces serving latency by up to 5x and improves serving throughput by up to 2x without compromising image quality.

Dual quaternion matrices have various applications in robotic research and its spectral theory has been extensively studied in recent years. In this paper, we extend Jacobi method to compute all eigenpairs of dual quaternion Hermitian matrices and establish its convergence. The improved version with elimination strategy is proposed to reduce the computational time. Especially, we present a novel three-step Jacobi method to compute such eigenvalues which have identical standard parts but different dual parts. We prove that the proposed three-step Jacobi method terminates after at most finite iterations and can provide $\epsilon$-approximation of eigenvalue. To the best of our knowledge, both the power method and the Rayleigh quotient iteration method can not handle such eigenvalue problem in this scenario. Numerical experiments illustrate the proposed Jacobi-type algorithms are effective and stable, and also outperform the power method and the Rayleigh quotient iteration method.

Cardiac MRI, crucial for evaluating heart structure and function, faces limitations like slow imaging and motion artifacts. Undersampling reconstruction, especially data-driven algorithms, has emerged as a promising solution to accelerate scans and enhance imaging performance using highly under-sampled data. Nevertheless, the scarcity of publicly available cardiac k-space datasets and evaluation platform hinder the development of data-driven reconstruction algorithms. To address this issue, we organized the Cardiac MRI Reconstruction Challenge (CMRxRecon) in 2023, in collaboration with the 26th International Conference on MICCAI. CMRxRecon presented an extensive k-space dataset comprising cine and mapping raw data, accompanied by detailed annotations of cardiac anatomical structures. With overwhelming participation, the challenge attracted more than 285 teams and over 600 participants. Among them, 22 teams successfully submitted Docker containers for the testing phase, with 7 teams submitted for both cine and mapping tasks. All teams use deep learning based approaches, indicating that deep learning has predominately become a promising solution for the problem. The first-place winner of both tasks utilizes the E2E-VarNet architecture as backbones. In contrast, U-Net is still the most popular backbone for both multi-coil and single-coil reconstructions. This paper provides a comprehensive overview of the challenge design, presents a summary of the submitted results, reviews the employed methods, and offers an in-depth discussion that aims to inspire future advancements in cardiac MRI reconstruction models. The summary emphasizes the effective strategies observed in Cardiac MRI reconstruction, including backbone architecture, loss function, pre-processing techniques, physical modeling, and model complexity, thereby providing valuable insights for further developments in this field., Comment: 25 pages, 17 figures

Robust Principal Component Analysis (RPCA) and its associated non-convex relaxation methods constitute a significant component of matrix completion problems, wherein matrix factorization strategies effectively reduce dimensionality and enhance computational speed. However, some non-convex factorization forms lack theoretical guarantees. This paper proposes a novel strategy in non-convex quasi-norm representation, introducing a method to obtain weighted matrix quasi-norm factorization forms. Especially, explicit bilinear factor matrix factorization formulations for the weighted logarithmic norm and weighted Schatten-$q$ quasi norms with $q=1, 1/2, 2/3$ are provided, along with the establishment of corresponding matrix completion models. An Alternating Direction Method of Multipliers (ADMM) framework algorithm is employed for solving, and convergence results of the algorithm are presented.

Real-time prediction plays a vital role in various control systems, such as traffic congestion control and wireless channel resource allocation. In these scenarios, the predictor usually needs to track the evolution of the latent statistical patterns in the modern high-dimensional streaming time series continuously and quickly, which presents new challenges for traditional prediction methods. This paper is the first to propose a novel online algorithm (TOPA) based on tensor factorization to predict streaming tensor time series. The proposed algorithm TOPA updates the predictor in a low-complexity online manner to adapt to the time-evolving data. Additionally, an automatically adaptive version of the algorithm (TOPA-AAW) is presented to mitigate the negative impact of stale data. Simulation results demonstrate that our proposed methods achieve prediction accuracy similar to that of conventional offline tensor prediction methods, while being much faster than them during long-term online prediction. Therefore, TOPA-AAW is an effective and efficient solution method for the online prediction of streaming tensor time series.

Unsupervised feature selection has drawn wide attention in the era of big data since it is a primary technique for dimensionality reduction. However, many existing unsupervised feature selection models and solution methods were presented for the purpose of application, and lack of theoretical support, e.g., without convergence analysis. In this paper, we first establish a novel unsupervised feature selection model based on regularized minimization with nonnegative orthogonal constraints, which has advantages of embedding feature selection into the nonnegative spectral clustering and preventing overfitting. An effective inexact augmented Lagrangian multiplier method is proposed to solve our model, which adopts the proximal alternating minimization method to solve subproblem at each iteration. We show that the sequence generated by our method globally converges to a Karush-Kuhn-Tucker point of our model. Extensive numerical experiments on popular datasets demonstrate the stability and robustness of our method. Moreover, comparison results of algorithm performance show that our method outperforms some existing state-of-the-art methods.

The previous support vector machine(SVM) including $0/1$ loss SVM, hinge loss SVM, ramp loss SVM, truncated pinball loss SVM, and others, overlooked the degree of penalty for the correctly classified samples within the margin. This oversight affects the generalization ability of the SVM classifier to some extent. To address this limitation, from the perspective of confidence margin, we propose a novel Slide loss function ($\ell_s$) to construct the support vector machine classifier($\ell_s$-SVM). By introducing the concept of proximal stationary point, and utilizing the property of Lipschitz continuity, we derive the first-order optimality conditions for $\ell_s$-SVM. Based on this, we define the $\ell_s$ support vectors and working set of $\ell_s$-SVM. To efficiently handle $\ell_s$-SVM, we devise a fast alternating direction method of multipliers with the working set ($\ell_s$-ADMM), and provide the convergence analysis. The numerical experiments on real world datasets confirm the robustness and effectiveness of the proposed method.

Recently, a quaternion tensor product named Qt-product was proposed, and then the singular value decomposition and the rank of a third-order quaternion tensor were given. From a more applicable perspective, we extend the Qt-product and propose a novel multiplication principle for third-order quaternion tensor named gQt-product. With the gQt-product, we introduce a brand-new singular value decomposition for third-order quaternion tensors named gQt-SVD and then define gQt-rank and multi-gQt-rank. We prove that the optimal low-rank approximation of a third-order quaternion tensor exists and some numerical experiments demonstrate the low-rankness of color videos. So, we apply the low-rank quaternion tensor completion to color video inpainting problems and present alternating least-square algorithms to solve the proposed low gQt-rank and multi-gQt-rank quaternion tensor completion models. The convergence analyses of the proposed algorithms are established and some numerical experiments on various color video datasets show the high recovery accuracy and computational efficiency of our methods.

Recently, tensor time-series forecasting has gained increasing attention, whose core requirement is how to perform dimensionality reduction. Among all multidimensional data, third-order tensor is the most prevalent structure in real-world scenarios, such as RGB images and network traffic data. Previous studies in this field are mainly based on tensor Tucker decomposition and such methods have limitations in terms of computational cost, with iteration complexity of approximately $O(2n^3r)$, where $n$ and $r$ are the dimension and rank of original tensor data. Moreover, many real-world data does not exhibit the low-rank property under Tucker decomposition, which may fail the dimensionality reduction. In this paper, we pioneer the application of tensor singular value decomposition (t-SVD) to third-order time-series, which builds an efficient forecasting algorithm, called Low-rank Tensor Autoregressive Predictor (LOTAP). We observe that tensor tubal rank in t-SVD is always less than Tucker rank, which leads to great benefit in computational complexity. By combining it with the autoregressive (AR) model, the forecasting problem is formulated as a least squares optimization. We divide such an optimization problem by fast Fourier transformation into four decoupled subproblems, whose variables include regressive coefficient, f-diagonal tensor, left and right orthogonal tensors. The alternating minimization algorithm is proposed with iteration complexity of about $O(n^3 + n^2r^2)$, in which each subproblem has a closed-form solution. Numerical experiments show that, compared to Tucker-decomposition-based algorithms, LOTAP achieves a speed improvement ranging from 2 to 6 times while maintaining accurate forecasting performance in all four baseline tasks. In addition, LOTAP is applicable to a wider range of tensor forecasting tasks due to its more effective dimensionality reduction ability., Comment: 11 pages

Multilayer perception (MLP) has permeated various disciplinary domains, ranging from bioinformatics to financial analytics, where their application has become an indispensable facet of contemporary scientific research endeavors. However, MLP has obvious drawbacks. 1), The type of activation function is single and relatively fixed, which leads to poor `representation ability' of the network, and it is often to solve simple problems with complex networks; 2), the network structure is not adaptive, it is easy to cause network structure redundant or insufficient. In this work, we propose a novel neural network paradigm X-Net promising to replace MLPs. X-Net can dynamically learn activation functions individually based on derivative information during training to improve the network's representational ability for specific tasks. At the same time, X-Net can precisely adjust the network structure at the neuron level to accommodate tasks of varying complexity and reduce computational costs. We show that X-Net outperforms MLPs in terms of representational capability. X-Net can achieve comparable or even better performance than MLP with much smaller parameters on regression and classification tasks. Specifically, in terms of the number of parameters, X-Net is only 3% of MLP on average and only 1.1% under some tasks. We also demonstrate X-Net's ability to perform scientific discovery on data from various disciplines such as energy, environment, and aerospace, where X-Net is shown to help scientists discover new laws of mathematics or physics., Comment: 35 pages

This paper studies the consensus problem of heterogeneous multi-agent systems by the feedforward control and linear quadratic (LQ) optimal control theory. Different from the existing consensus control algorithms, which require to design an additional distributed observer for estimating the leader's information and to solve a set of regulator equations. In this paper, by designing a distributed feedforward controller, a non-standard neighbor error system is transformed into a standard linear system, and then an optimal consensus controller is designed by minimizing a combined state error with neighbour agents. The proposed optimal controller is obtained by solving Riccati equations, and it is shown that the corresponding cost function under the proposed distributed controllers is asymptotically optimal. The proposed consensus algorithm can be directly applicable to solve the consensus problem of homogeneous systems. Simulation example indicates the effectiveness of the proposed scheme and a much faster convergence speed than the existing algorithm., Comment: arXiv admin note: substantial text overlap with arXiv:2309.12577

In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning techniques have achieved great success in processing regular structured 2D grid image data, there are still great challenges in processing irregular, unstructured point cloud data. Point cloud classification is the basis of point cloud analysis, and many deep learning-based methods have been widely used in this task. Therefore, the purpose of this paper is to provide researchers in this field with the latest research progress and future trends. First, we introduce point cloud acquisition, characteristics, and challenges. Second, we review 3D data representations, storage formats, and commonly used datasets for point cloud classification. We then summarize deep learning-based methods for point cloud classification and complement recent research work. Next, we compare and analyze the performance of the main methods. Finally, we discuss some challenges and future directions for point cloud classification.

In this paper, a classical deflation process raised by Dayton, Li and Zeng is realized for the Brent equations, which provides new bounds for local dimensions of the solution set. Originally, this deflation process focuses on isolated solutions. We generalize it to the case of irreducible components and a related conjecture is given. We analyze its realization and apply it to the Brent equations. The decrease of the nullities is easily observed. So the deflation process can be served as a useful tool for determining the local dimensions. In addition, our result implies that along with the decrease of the tensor rank, the singular solutions will become more and more., Comment: The previous Remark 5.1 is clarified

Cardiac magnetic resonance imaging (CMR) has been widely used in clinical practice for the medical diagnosis of cardiac diseases. However, the long acquisition time hinders its development in real-time applications. Here, we propose a novel self-consistency guided multi-prior learning framework named $k$-$t$ CLAIR to exploit spatiotemporal correlations from highly undersampled data for accelerated dynamic parallel MRI reconstruction. The $k$-$t$ CLAIR progressively reconstructs faithful images by leveraging multiple complementary priors learned in the $x$-$t$, $x$-$f$, and $k$-$t$ domains in an iterative fashion, as dynamic MRI exhibits high spatiotemporal redundancy. Additionally, $k$-$t$ CLAIR incorporates calibration information for prior learning, resulting in a more consistent reconstruction. Experimental results on cardiac cine and T1W/T2W images demonstrate that $k$-$t$ CLAIR achieves high-quality dynamic MR reconstruction in terms of both quantitative and qualitative performance., Comment: 12 pages, 3 figures, 4 tables. CMRxRecon Challenge, MICCAI 2023

This paper develops a novel approach to the consensus problem of multi-agent systems by minimizing a weighted state error with neighbor agents via linear quadratic (LQ) optimal control theory. Existing consensus control algorithms only utilize the current state of each agent, and the design of distributed controller depends on nonzero eigenvalues of the communication topology. The presented optimal consensus controller is obtained by solving Riccati equations and designing appropriate observers to account for agents' historical state information. It is shown that the corresponding cost function under the proposed controllers is asymptotically optimal. Simulation examples demonstrate the effectiveness of the proposed scheme, and a much faster convergence speed than the conventional consensus methods. Moreover, the new method avoids computing nonzero eigenvalues of the communication topology as in the traditional consensus methods.

Very recently, Qi and Cui extended the Perron-Frobenius theory to dual number matrices with primitive and irreducible nonnegative standard parts and proved that they have Perron eigenpair and Perron-Frobenius eigenpair. The Collatz method was also extended to find Perron eigenpair. Qi and Cui proposed two conjectures. One is the k-order power of a dual number matrix tends to zero if and only if the spectral radius of its standard part less than one, and another is the linear convergence of the Collatz method. In this paper, we confirm these conjectures and provide theoretical proof. The main contribution is to show that the Collatz method R-linearly converges with an explicit rate., Comment: arXiv admin note: text overlap with arXiv:2306.16140 by other authors

Cloud-native architecture is becoming increasingly crucial for today's cloud computing environments due to the need for speed and flexibility in developing applications. It utilizes microservice technology to break down traditional monolithic applications into light-weight and self-contained microservice components. However, as microservices grow in scale and have dynamic inter-dependencies, they also pose new challenges in resource provisioning that cannot be fully addressed by traditional resource scheduling approaches. The various microservices with different resource needs and latency requirements can create complex calling chains, making it difficult to provide fine-grained and accurate resource allocation to each component while maintaining the overall quality of service in the chain. In this work, we aim to address the research problem on how to efficiently provision resources for the growing scale of microservice platform and ensure the performance of latency-critical microservices. To address the problem, we present in-depth analyses of Alibaba's microservice cluster and propose optimized resource provisioning algorithms to enhance resource utilization while ensuring the latency requirement. First, we analyze the distinct features of microservices in Alibaba's cluster compared to traditional applications. Then we present Alibaba's resource capacity provisioning workflow and framework to address challenges in resource provisioning for large-scale and latency-critical microservice clusters. Finally, we propose enhanced resource provisioning algorithms over Alibaba's current practice by making both proactive and reactive scheduling decisions based on different workloads patterns, which can improve resource usage by 10-15% in Alibaba's clusters, while maintaining the necessary latency for microservices., Comment: 19 pages

In the undetermined linear system $\bm{b}=\mathcal{A}(\bm{X})+\bm{s}$, vector $\bm{b}$ and operator $\mathcal{A}$ are the known measurements and $\bm{s}$ is the unknown noise. In this paper, we investigate sufficient conditions for exactly reconstructing desired matrix $\bm{X}$ being low-rank or approximately low-rank. We use the difference of nuclear norm and Frobenius norm ($L_{*-F}$) as a surrogate for rank function and establish a new nonconvex relaxation of such low rank matrix recovery, called the $L_{*-F}$ minimization, in order to approximate the rank function closer. For such nonconvex and nonsmooth constrained $L_{*-F}$ minimization problems, based on whether the noise level is $0$, we give the upper bound estimation of the recovery error respectively. Particularly, in the noise-free case, one sufficient condition for exact recovery is presented. If linear operator $\mathcal{A}$ satisfies the restricted isometry property with $\delta_{4r}<\frac{\sqrt{2r}-1}{\sqrt{2r}-1+\sqrt{2}(\sqrt{2r}+1)}$, then $r$-\textbf{rank} matrix $\bm{X}$ can be exactly recovered without other assumptions. In addition, we also take insights into the regularized $L_{*-F}$ minimization model since such regularized model is more widely used in algorithm design. We provide the recovery error estimation of this regularized $L_{*-F}$ minimization model via RIP tool. To our knowledge, this is the first result on exact reconstruction of low rank matrix via regularized $L_{*-F}$ minimization.

We introduce CartiMorph, a framework for automated knee articular cartilage morphometrics. It takes an image as input and generates quantitative metrics for cartilage subregions, including the percentage of full-thickness cartilage loss (FCL), mean thickness, surface area, and volume. CartiMorph leverages the power of deep learning models for hierarchical image feature representation. Deep learning models were trained and validated for tissue segmentation, template construction, and template-to-image registration. We established methods for surface-normal-based cartilage thickness mapping, FCL estimation, and rule-based cartilage parcellation. Our cartilage thickness map showed less error in thin and peripheral regions. We evaluated the effectiveness of the adopted segmentation model by comparing the quantitative metrics obtained from model segmentation and those from manual segmentation. The root-mean-squared deviation of the FCL measurements was less than 8%, and strong correlations were observed for the mean thickness (Pearson's correlation coefficient $\rho \in [0.82,0.97]$), surface area ($\rho \in [0.82,0.98]$) and volume ($\rho \in [0.89,0.98]$) measurements. We compared our FCL measurements with those from a previous study and found that our measurements deviated less from the ground truths. We observed superior performance of the proposed rule-based cartilage parcellation method compared with the atlas-based approach. CartiMorph has the potential to promote imaging biomarkers discovery for knee osteoarthritis., Comment: This preprint is an proofread version of a paper published in Medical Image Analysis (2023), which can be found at https://doi.org/10.1016/j.media.2023.103035

Mid-term electricity load forecasting (LF) plays a critical role in power system planning and operation. To address the issue of error accumulation and transfer during the operation of existing LF models, a novel model called error correction based LF (ECLF) is proposed in this paper, which is designed to provide more accurate and stable LF. Firstly, time series analysis and feature engineering act on the original data to decompose load data into three components and extract relevant features. Then, based on the idea of stacking ensemble, long short-term memory is employed as an error correction module to forecast the components separately, and the forecast results are treated as new features to be fed into extreme gradient boosting for the second-step forecasting. Finally, the component sub-series forecast results are reconstructed to obtain the final LF results. The proposed model is evaluated on real-world electricity load data from two cities in China, and the experimental results demonstrate its superior performance compared to the other benchmark models., Comment: 8 pages, 3 figures

Undersampling k-space data in MRI reduces scan time but pose challenges in image reconstruction. Considerable progress has been made in reconstructing accelerated MRI. However, restoration of high-frequency image details in highly undersampled data remains challenging. To address this issue, we propose CAMP-Net, an unrolling-based Consistency-Aware Multi-Prior Network for accelerated MRI reconstruction. CAMP-Net leverages complementary multi-prior knowledge and multi-slice information from various domains to enhance reconstruction quality. Specifically, CAMP-Net comprises three interleaved modules for image enhancement, k-space restoration, and calibration consistency, respectively. These modules jointly learn priors from data in image domain, k-domain, and calibration region, respectively, in data-driven manner during each unrolled iteration. Notably, the encoded calibration prior knowledge extracted from auto-calibrating signals implicitly guides the learning of consistency-aware k-space correlation for reliable interpolation of missing k-space data. To maximize the benefits of image domain and k-domain prior knowledge, the reconstructions are aggregated in a frequency fusion module, exploiting their complementary properties to optimize the trade-off between artifact removal and fine detail preservation. Additionally, we incorporate a surface data fidelity layer during the learning of k-domain and calibration domain priors to prevent degradation of the reconstruction caused by padding-induced data imperfections. We evaluate the generalizability and robustness of our method on three large public datasets with varying acceleration factors and sampling patterns. The experimental results demonstrate that our method outperforms state-of-the-art approaches in terms of both reconstruction quality and $T_2$ mapping estimation, particularly in scenarios with high acceleration factors.