Search Results (494)

This study advances the application of the generalized Halmos’ two projections theorem to idempotent operators on Hilbert $C^{*}$-modules through a comprehensive study of sums involving adjointable idempotents and their adjoints. We establish fundamental properties including the closedness, orthogonal complementability, Moore–Penrose inverses, and spectral norms of such sums. For arbitrary (not necessarily adjointable) idempotent operators that admit a decomposition into linear combinations or products of two idempotents, we derive explicit representations for all such decompositions. A numerical example is given to show how our main theorem allows for the decomposition of idempotent matrices into linear combinations of two idempotent matrices, and two concrete examples on Hilbert $C^{*}$-modules validate the theoretical significance of our framework. Full article

Recent studies report that gradient guidance extracted from a single-reference model can improve Limited-Sample regression. However, one reference model may not capture all relevant characteristics of the target function, which can restrict the capacity of the learner. To address this issue, we introduce the Multi-Gradient Guided Network (MGGN), an extension of single-gradient guidance that combines gradients from several reference models. The gradients are merged through an adaptive weighting scheme, and an orthogonal-projection step is applied to reduce potential conflicts between them. Experiments on sine regression are used to evaluate the method. The results indicate that MGGN achieves higher predictive accuracy and improved stability than existing single-gradient guidance and meta-learning baselines, benefiting from the complementary information provided by multiple reference models. Full article

Using the Dixmier angle between two closed subspaces of a complex Hilbert space $\mathcal{H}$, we establish the necessary and sufficient conditions for the operator norm of the sum of two orthogonal projections, $P_{{\mathcal{W}}_1}$ and $P_{{\mathcal{W}}_2}$, onto closed subspaces ${\mathcal{W}}_1$ and ${\mathcal{W}}_2$, to attain its maximum, namely $\parallel P_{{\mathcal{W}}_1}+P_{{\mathcal{W}}_2}\parallel =2.$ These conditions are expressed in terms of the geometric relationship and symmetry between the ranges of the projections. We apply these results to orthogonal projections associated with a closed-range operator via its Moore–Penrose inverse. Additionally, for any bounded operator T with closed range in $\mathcal{H}$, we derive sufficient conditions ensuring $\parallel T{T}^{†}+T^{†}T\parallel =2,$ where $T^{†}$ denotes the Moore–Penrose inverse of T. This work highlights how symmetry between operator ranges and their algebraic structure governs norm extremality and extends a recent finite-dimensional result to the general Hilbert space setting. Full article

In the real world, most data are unlabeled, which drives the development of semi-supervised learning (SSL). Among SSL methods, least squares regression (LSR) has attracted attention for its simplicity and efficiency. However, existing semi-supervised LSR approaches suffer from challenges such as the insufficient use of unlabeled data, low pseudo-label accuracy, and inefficient label propagation. To address these issues, this paper proposes dual label propagation-driven least squares regression with feature selection, named DLPLSR, which is a pseudo-label-free SSL framework. DLPLSR employs a fuzzy-graph-based clustering strategy to capture global relationships among all samples, and manifold regularization preserves local geometric consistency, so that it implements the dual label propagation mechanism for comprehensive utilization of unlabeled data. Meanwhile, a dual-feature selection mechanism is established by integrating orthogonal projection for maximizing feature information with an ℓ_2,1-norm regularization for eliminating redundancy, thereby jointly enhancing the discriminative power. Benefiting from these two designs, DLPLSR boosts learning performance without pseudo-labeling. Finally, the objective function admits an efficient closed-form solution solvable via an alternating optimization strategy. Extensive experiments on multiple benchmark datasets show the superiority of DLPLSR compared to state-of-the-art LSR-based SSL methods. Full article

As demand for plant-based beverages grows, analytical tools are needed to classify and understand their structural and compositional diversity. This study applied a multi-analytical approach to characterize 41 commercial almond-, oat-, rice- and soy-based beverages, evaluating attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy, protein secondary structure proportions, colorimetry, and microscopic image texture analysis. A total of 26 variables, derived from ATR-FTIR and protein secondary structure assessment, were employed in multivariate models, using partial least squares discriminant analysis (PLS-DA) and orthogonal PLS-DA (OPLS-DA) to evaluate classification performance. The results indicated clear group separation, with soy and rice beverages forming distinct clusters while almond and oat samples showing partial overlap. Variable importance in projection (VIP) scores revealed that β-turn and α-helix protein structures, along with carbohydrate-associated spectral bands, were the key features for beverages’ classification. Textural features derived from microscopy images correlated with sugar and carbohydrate content and color parameters were also employed to describe beverages’ differences related to sugar content and visual appearance in terms of homogeneity. These findings demonstrate that combining ATR-FTIR spectral data with protein secondary structure data enables the effective classification of plant-based beverages, while microscopic image textural and color parameters offer additional extended product characterization. Full article

The accurate measurement of a crack width in concrete infrastructure is essential for structural safety assessment and maintenance. However, existing image-based methods either suffer from overestimation in complex geometries or are computationally inefficient. This paper proposes a novel hybrid approach combining a fast skeleton-pruning algorithm and a crack-width measurement technique called edge-OrthoBoundary (EOB). The skeleton-pruning algorithm prunes the skeleton, viewed as the longest branch in a tree structure, using a depth-first search (DFS) approach. Additionally, an intersection removal algorithm based on dilation replaces the midpoint circle algorithm to segment the crack skeleton into computable parts. The EOB method combines the OrthoBoundary and edge shortest distance (ESD) techniques, effectively correcting the propagation direction of the skeleton points while accounting for their width. The validation of real cracks shows the skeleton-pruning algorithm’s effectiveness, eliminating the need for a specified threshold and reducing time complexity. Experimental results with both actual and synthetic cracks demonstrate that the EOB method achieves the smallest RMS, MAE, and R values, confirming its accuracy and stability compared to the orthogonal projection (OP), OrthoBoundary, and ESD methods. Full article

This paper provides a new proof of the operator norm identity $\parallel Q\parallel = \parallel I-Q\parallel$, where Q is a bounded idempotent operator on a complex Hilbert space, and I is the identity operator. We also derive explicit lower and upper bounds for the distance from an arbitrary idempotent operator to the set of orthogonal projections. Our approach simplifies existing proofs. Full article

The Automatic Modulation Classification (AMC) for underwater acoustic signals enables more efficient utilization of the acoustic spectrum. Deep learning techniques significantly improve classification performance. Hence, they can be applied in AMC work to improve the underwater acoustic (UWA) communication. This paper is based on the adoption of Hough Transform (HT) and Edge Detection (ED) to enhance modulation classification, especially for a small dataset. Deep neural models based on basic Convolutional Neural Network (CNN), Visual Geometry Group-16 (VGG-16), and VGG-19 trained on constellation diagrams transformed using HT are adopted. The objective is to extract features from constellation diagrams projected onto the Hough space. In addition, we use Orthogonal Frequency Division Multiplexing (OFDM) technology, which is frequently utilized in UWA systems because of its ability to avoid multipath fading and enhance spectrum utilization. We use an OFDM system with the Discrete Cosine Transform (DCT), Cyclic Prefix (CP), and equalization over the UWA communication channel under the effect of estimation errors. Seven modulation types are considered for classification, including Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM) (2/8/16-PSK and 4/8/16/32-QAM), with a Signal-to-Noise Ratio (SNR) ranging from −5 to 25 dB. Simulation results indicate that our CNN model with HT and ED at perfect channel estimation, achieves a 94% classification accuracy at 10 dB SNR, outperforming benchmark models by approximately 40%. Full article

The Yellow River Basin features a unique geographical environment with challenges like seawater erosion and soft soil. In this context, the construction of foundation pits can significantly impact the settlement of adjacent structures. Grounded in a real-world project, this study employs the finite element software Midas GTS to construct a 3D interaction model between foundation pit excavation and nearby buildings. Through this model, we analyze the settlement patterns of adjacent buildings influenced by variables such as foundation soil strength, slope gradient, and construction sequence. By integrating orthogonal experimental design and range analysis, we identify the sensitive factors affecting the settlement deformation and stability of foundation pits. Our analysis reveals that among the factors significantly influencing settlement deformation at the foundation pit base, groundwater levels and internal friction angles are the most critical. Slope gradient and soil cohesion also play substantial roles, whereas the compressive modulus of soil shows relatively less impact. However, a comparison with actual engineering data indicates that groundwater factors considerably affect slope deformation, underscoring the necessity for stringent control of groundwater level fluctuations. Full article

This study presents a bilateral control architecture that links fluoroscopic image feedback directly to the kinematics of a tendon-driven, three-joint robotic catheter and a 3-DoF motorised C-arm, intending to preserve optimal imaging geometry during autonomous catheter insertion and thereby mitigating radiation exposure. Forward and inverse kinematics for both manipulators were derived via screw theory and geometric analysis, while a calibrated projection model generated synthetic X-ray images whose catheter bending angles were extracted through intensity thresholding, segmentation, skeletonisation, and least-squares circle fitting. The estimated angle fed a one-dimensional extremum-seeking routine that rotated the C-arm about its third axis until the apparent bending angle peaked, signalling an orthogonal view of the catheter’s bending plane. Implemented in a physics-based simulator, the framework achieved inverse-kinematic errors below 0.20% for target angles between ${20}^{°}$ and ${90}^{°}$, with accuracy decreasing to 3.00% at ${10}^{°}$. The image-based angle estimator maintained a root-mean-square error $\le 3$% across most of the same range, rising to 6.4% at ${10}^{°}$. The C-arm search consistently located the optimal perspective, and the combined controller steered the catheter tip along a predefined aortic path without collision. These results demonstrate sub-degree angular accuracy under idealised, noise-free conditions and validate real-time coupling of image guidance to dual-manipulator motion; forthcoming work will introduce realistic image noise, refined catheter mechanics, and hardware-in-the-loop testing to confirm radiation-dose and workflow benefits. Full article

The excavation of upper shallow foundation pits may cause the uneven deformation of existing tunnels buried below a shallow depth. Improper control measures may lead to a series of diseases, such as local cracking or breakage of the tunnel lining, which threaten the safety of tunnel operations. Regarding the safety of the existing tunnel affected by the construction of the foundation pit, cases of the application of portal frame anti-heave structures in upper foundation pit projects of existing tunnels in Shenzhen have been documented, and the main influencing factors have been analyzed and summarized. Taking the Qianhai Ring Water Corridor Project as an example, numerical orthogonal experiments were conducted to analyze the deformation response patterns in the depth of existing tunnels and the effectiveness of control measures in the upper shallow of foundation pit engineering. The roles of portal frame anti-heave structures are analyzed in detail using measured data. Studies indicate that the deformation of the existing tunnels mainly occurs during the top and immediately adjacent block excavation stages, and stabilizes after the uplift-resisting piles and anti-floating slabs form an effective frame structure. The portal frame anti-heave structures, combined with measures such as block excavation, jet grouting interlocking reinforcement, backfilling, and surcharge loading, have extremely strong deformation control capabilities. However, the construction costs are relatively high, leaving room for optimization. Full article

This paper proposes a model identification method based on the auxiliary variable closed-loop subspace identification algorithm to address the problem of modeling difficulties caused by various complex factors affecting permanent magnet brushless DC motors in practical working conditions. This method breaks through the limitations caused by the correlation between input signals and noise in traditional subspace identification algorithms. By introducing auxiliary variables, it effectively avoids the projection process, simplifies the complex calculations of principal component analysis, and improves the practicality and efficiency of the algorithm. When constructing a data-driven identification model, the actual situation of measurement data being contaminated by noise has to be fully considered. Orthogonal compensation matrices and auxiliary variables were used to construct uncorrelated terms for noise, thereby eliminating the negative impact of noise on the model’s identification accuracy. The effectiveness of the proposed identification algorithm was verified by collecting data through a chassis dynamometer simulation test of a vehicle-mounted permanent magnet brushless DC motor. The results show that compared with the traditional N4SID algorithm, the proposed closed-loop subspace identification algorithm based on auxiliary variable principal component analysis exhibits higher model identification accuracy, stronger anti-interference ability, and better stability in both noise-free and noise-contaminated conditions, providing a more reliable model basis for motor performance evaluation and control strategy design. Full article

Structural cracks can critically undermine infrastructure integrity, driving the need for precise, scalable inspection methods beyond conventional visual or 2D image-based approaches. This study presents an automated system integrating photogrammetric 3D reconstruction with deep learning to quantify crack dimensions in a spatial context. Multiple images are processed via Agisoft Metashape to generate high-fidelity 3D meshes. Then, a subset of images are automatically selected based on camera orientation and distance, and a deep learning algorithm is applied to detect cracks in 2D images. The detected crack edges are projected onto a 3D mesh, enabling width measurements grounded in the structure’s true geometry rather than perspective-distorted 2D approximations. This methodology addresses the key limitations of traditional methods (parallax, occlusion, and surface curvature errors) and shows how these limitations can be mitigated by spatially anchoring measurements to the 3D model. Laboratory validation confirms the system’s robustness, with controlled tests highlighting the importance of near-orthogonal camera angles and ground sample distance (GSD) thresholds to ensure crack detectability. By synthesizing photogrammetry and a convolutional neural network (CNN), the framework eliminates subjectivity in inspections, enhances safety by reducing manual intervention, and provides engineers with dimensionally accurate data for maintenance decisions. Full article

Radar target detection in a sea clutter environment is of significant importance in both civilian and military applications, with the detection of small maneuvering targets being particularly challenging. To address this issue, this paper introduces the autocorrelation characteristics of sea clutter into orthogonal projection operations to suppress sea clutter and enhance the detection capability of small maneuvering targets on the sea surface. The proposed method first generates speckle components that are consistent with the correlation characteristics of the observed sea clutter. Then, it uses these speckle components to derive the feature subspace of the sea clutter and applies this subspace in an orthogonal projection suppression algorithm, thereby achieving effective suppression of the sea clutter. This method does not rely on the covariance matrix estimation of sea clutter from reference cells but instead directly utilizes the autocorrelation characteristics of the observed sea clutter data to obtain the feature subspace, making it more adaptable to different environments. Simulation and experimental results demonstrate that this method significantly suppresses sea clutter and effectively improves the performance of target detection on the sea surface. Full article

This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual loss, bridging the gap between traditional projection-based ROMs and physics-informed neural networks (PINNs). Unlike conventional PINNs that rely on analytical PDEs, our approach leverages FEM residuals to guide the learning of the ROM approximation manifold. Our key contributions include the following: (1) a parameter-agnostic, discrete residual loss applicable to nonlinear problems, (2) an architectural modification to PROM-ANN improving accuracy for fast-decaying singular values, and (3) an empirical study on the proposed physics-informed training process for ROMs. The method is demonstrated on a nonlinear hyperelasticity problem, simulating a rubber cantilever under multi-axial loads. The main accomplishment in regards to the proposed residual-based loss is its applicability on nonlinear problems by interfacing with FEM software while maintaining reasonable training times. The modified PROM-ANN outperforms POD by orders of magnitude in snapshot reconstruction accuracy, while the original formulation is not able to learn a proper mapping for this use case. Finally, the application of physics-informed training in ANN-PROM modestly narrows the gap between data reconstruction and ROM accuracy; however, it highlights the untapped potential of the proposed residual-driven optimization for future ROM development. This work underscores the critical role of FEM residuals in ROM construction and calls for further exploration on architectures beyond PROM-ANN. Full article