Eigenvector overlaps in large sample covariance matrices and nonlinear shrinkage estimators

Consider a data matrix $Y = [\mathbf{y}_1, \cdots, \mathbf{y}_N]$ of size $M \times N$, where the columns are independent observations from a random vector $\mathbf{y}$ with zero mean and population covariance $\Sigma$. Let $\mathbf{u}_i$ and $\mathbf{v}_j$ denote the left and right singular vectors of $Y$, respectively. This study investigates the eigenvector/singular vector overlaps $\langle {\mathbf{u}_i, D_1 \mathbf{u}_j} \rangle$, $\langle {\mathbf{v}_i, D_2 \mathbf{v}_j} \rangle$ and $\langle {\mathbf{u}_i, D_3 \mathbf{v}_j} \rangle$, where $D_k$ are general deterministic matrices with bounded operator norms. We establish the convergence in probability of these eigenvector overlaps toward their deterministic counterparts with explicit convergence rates, when the dimension $M$ scales proportionally with the sample size $N$. Building on these findings, we offer a more precise characterization of the loss for Ledoit and Wolf's nonlinear shrinkage estimators of the population covariance $\Sigma$

Electrode with Tip Life Improvement and Related Methods

A resistance spot welding system includes an electrode with a cap that includes a cap body having a tip, a body cavity defined within the cap body, and a tip cavity defined within the cap body that extends from the body cavity towards the tip. A method of manufacturing the electrode includes forming a body cavity within a cap body of the electrode, and forming a tip cavity within the cap body of the electrode such that the tip cavity extends from the body cavity towards a tip of the cap body. In other aspects, a resistance spot welding system includes a first electrode, a second electrode, and an external cooling unit that is configured to inject a coolant adjacent to at least one of the first electrode and the second electrode during welding

The Impact Of 3d Printing Technology On Traditional Jun Porcelain Shaping Techniques

The purpose of this study is to investigate 3D printing technology and the traditional forming technique of Jun porcelain, with a view to exploring how 3D printers can be integrated into its original mold system through modernization instead of enhancing production efficiency at the manufacturing level while preserving the essence of authenticity in tradition. This study investigates the synergy of digital modeling and manual production with a novel design methodology balancing both tradition and innovation through literature review, case analysis, as well as experimental validation. An historical overview of Jun porcelain and traditional shaping prescribed by distinctive manual throwing and carving technologies The paper additionally highlights the advantages of 3D printing technology in ceramics: The advantages of 3D printing technology in ceramics include high-accuracy digital modeling, the ability to realize complex shapes, and the use of new materials. The findings indicate that 3D printing technology and traditional craftsmanship can enhance production efficiency without compromising artistic value. Additionally, digital design and rapid prototyping technology offer more efficient processes for the production of Jun porcelain, resulting in significant time and cost savings. This article also explores the preservation of Jun porcelain's cultural characteristics and artistic value through the application of modern technology. These results demonstrated the potential application of 3D printing technology in the molding of Jun porcelain, and they provided programmatic guidance for its innovation in unconventional expression forms

Quality Improvement of Self-Piercing Riveting of High Strength Aluminum Alloys

Described are metal products including metal alloy substrates joined by self-piercing rivets, and methods and apparatus for joining metal alloy substrates using self-piercing rivets. For high-strength metal alloy substrates, the disclosed joining techniques involve retrogressing portions of the metal alloy substrates, such as by heating using a laser heating source, a conductive heating source, or an inductive heating source, to produce crack-free joined metal products

Topics in spectral analysis of large sample covariance matrices

This thesis addresses two topics concerning spectral properties of sample covariance matrices when the data dimensionality M scales proportionally with the sample size N. In the first part, we consider the left and right singular vectors u_i and v_i of an M×N data matrix Y=Σ^(1/2) X. We establish the convergence in probability of the singular vector overlaps ⟨u_i,D_1 u_j⟩, ⟨v_i,D_2 v_j⟩ and ⟨u_i,D_3 v_j⟩ towards their deterministic counterparts, where the D_k's are general deterministic matrices with bounded operator norms. Building on these findings, we offer a more precise characterization of the loss associated with Ledoit and Wolf's nonlinear shrinkage estimators. The second part examines large signal-plus-noise data matrices of the form S+Σ^(1/2) X, where S is an M×N low-rank deterministic signal matrix and Σ^(1/2) X represents the noise matrix. Under general assumptions concerning the structure of (S,Σ) and the distribution of X, we establish the asymptotic joint distribution of the spiked singular values of the model when the signals are supercritical. It turns out that the asymptotic distributions exhibit nonuniversality in the sense of dependence on the distributions of X. As a corollary, we obtain the asymptotic distribution of the spiked eigenvalues associated with mixture models.Doctor of Philosoph

Robust Visual Place Recognition Method for Robot Facing Drastic Illumination Changes

Abstract The robustness of visual place recognition determines the accuracy of the SLAM to construct the environmental map. However, when the robot moves in the outdoor environment for a long time, it must face the challenge of drastic illumination changes (time shift, season or rain and fog weather factors), which leads to the robot’s ability to identify places is greatly restricted. This paper proposes a method for visual place recognition that is more robust to severe illumination changes. First, a generative adversarial network is introduced into visual SLAM to enhance the quality of candidate keyframes, and consistency of geographic locations corresponding to images before and after quality enhancement is evaluated, and then the image descriptor with illumination invariance is established for the robot's new observation image and keyframes of the map. Finally, the performance of the method in this paper is tested on the public dataset. The experimental results show that this method is conducive to improving the quality of environmental map nodes, and enables the robot to show a highly robust ability for visual place recognition in the face of severe illumination changes, which provides a powerful tool for robot to build an accurate environmental map.</jats:p

Dam Deformation Interpretation and Prediction Based on a Long Short-Term Memory Model Coupled with an Attention Mechanism

An accurate dam deformation prediction model is vital to a dam safety monitoring system, as it helps assess and manage dam risks. Most traditional dam deformation prediction algorithms ignore the interpretation and evaluation of variables and lack qualitative measures. This paper proposes a data processing framework that uses a long short-term memory (LSTM) model coupled with an attention mechanism to predict the deformation response of a dam structure. First, the random forest (RF) model is introduced to assess the relative importance of impact factors and screen input variables. Secondly, the density-based spatial clustering of applications with noise (DBSCAN) method is used to identify and filter the equipment based abnormal values to reduce the random error in the measurements. Finally, the coupled model is used to focus on important factors in the time dimension in order to obtain more accurate nonlinear prediction results. The results of the case study show that, of all tested methods, the proposed coupled method performed best. In addition, it was found that temperature and water level both have significant impacts on dam deformation and can serve as reliable metrics for dam management.</jats:p

Dam Deformation Interpretation and Prediction Based on a Long Short-Term Memory Model Coupled with an Attention Mechanism

An accurate dam deformation prediction model is vital to a dam safety monitoring system, as it helps assess and manage dam risks. Most traditional dam deformation prediction algorithms ignore the interpretation and evaluation of variables and lack qualitative measures. This paper proposes a data processing framework that uses a long short-term memory (LSTM) model coupled with an attention mechanism to predict the deformation response of a dam structure. First, the random forest (RF) model is introduced to assess the relative importance of impact factors and screen input variables. Secondly, the density-based spatial clustering of applications with noise (DBSCAN) method is used to identify and filter the equipment based abnormal values to reduce the random error in the measurements. Finally, the coupled model is used to focus on important factors in the time dimension in order to obtain more accurate nonlinear prediction results. The results of the case study show that, of all tested methods, the proposed coupled method performed best. In addition, it was found that temperature and water level both have significant impacts on dam deformation and can serve as reliable metrics for dam management