Search Results (1,932)

3D vision-based groove detection is playing a critical role in enabling autonomous recognition. However, most existing interference evaluation strategies rely on height-based statistics or handcrafted heuristics, which (i) confuse genuine groove geometries (e.g., deep gaps and rounded corners) with noise and (ii) are sensitive to measurement scale and scanning configurations, making parameter tuning unreliable across scenes. To address this challenge, this paper proposes a novel method for evaluating the degree of interference in groove detection data, providing a reliable basis for the adaptive adjustment of algorithm parameters. The method leverages the angles of reconstructed triangular patches to assess the interference level in groove 3D detection data and computes the eigenvalues of the covariance matrix of these angles, establishing a rotationally invariant model for interference quantification. Experimental results show that the proposed method outperforms traditional methods, identifying more regions of high dispersion and demonstrating better adaptability to common groove features, such as deep gaps and rounded corners. By exploiting geometric invariance as a form of symmetry, the proposed eigenvalue-based dispersion descriptor provides a robust and coordinate-independent criterion for interference evaluation. Quantitatively, across multiple real industrial datasets, the proposed descriptor achieves an average 30.99% improvement in identifying severely interfered regions compared with the mainstream height-difference-based evaluation baseline. Full article

High penetration of distributed photovoltaics (PV) makes hosting-capacity assessment and active distribution network operation challenging, primarily due to the need to accurately restore nonconvex branch-flow equalities rather than relying on relaxations that may produce physically inconsistent solutions. This paper develops an ADMM-coordinated framework with an exact spectral refinement for QP1QC subproblems, which converts the semidefinite characterization into a tractable one-dimensional refinement over a generalized-eigenvalue-defined interval and enables reliable primal recovery of the original equality constraints. Numerical tests on modified IEEE 33-, 792-, and 1137-bus feeders show that the proposed method substantially improves equality restoration: the normalized mismatch of nonconvex equalities is reduced from 82–108% under SOCP/SDP relaxations to 0.004% on the 33-bus system, and from 94–98% to 0.67% on the 792-bus system; on the 1137-bus system, the mismatch remains 6.4%, still far below the relaxation baselines. Compared with an SDP-based hidden-convex benchmark, the proposed approach preserves essentially the same optimization outcomes while achieving 7–16× lower runtime and converging in 8–13 ADMM iterations. Full article

In this paper, we consider a partial differential equation with mixed derivatives of first order in time and second order in the spatial variable. Such equations are usually referred to as one-dimensional pseudoparabolic equations. We prove the existence and uniqueness of a classical solution to problems for a pseudoparabolic equation with a second-order differential operator involving pure involution, under certain requirements imposed on the initial data. The possibility of applying the Fourier method is based on the Riesz basis property of the eigenfunctions of the considered non-self-adjoint second-order differential operator with pure involution. Bessel-type inequalities are established for new systems of functions. The presence of a Bessel inequality for Fourier coefficients facilitates the proof of the uniform convergence of differentiated Fourier series. The solutions are obtained explicitly in the form of a Fourier series. Such representations can be used for performing numerical computations. Full article

We study positive semi-definite (PSD) biquadratic forms and their sum-of-squares (SOS) representations. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definiteness and prove that every PSD partially symmetric biquadratic form is an SOS. This extends the known result for fully symmetric biquadratic forms. Furthermore, we describe an efficient computational procedure for constructing SOS decompositions, exploiting the Kronecker-product structure of the associated matrix representation. We introduce simple biquadratic forms. For $m\ge 2$, we provide a explicit example to show the lower bound for sos rank of $m\times 2$ biquadratic forms is $m+1$, and show that previously proved results indicating that a $2\times 2$ PSD biquadratic form can be expressed as the sum of three squares and a $3\times 2$ PSD biquadratic form can be expressed as the sum of four squares are tight. We also present an $3\times 3$ SOS biquadratic form, which can be expressed as the sum of six squares, but not the sum of five squares. Moreover, we establish a universal upper bound $mn-1$ for any $m\times n$ SOS biquadratic form, which improves the trivial bound $mn$. Full article

Electroencephalogram (EEG) signals serve as a primary input for brain–computer interface (BCI) systems, and extensive research has been conducted on EEG-based emotion recognition. However, because EEG signals are inherently contaminated with various types of noise, the performance of emotion recognition is often degraded. Furthermore, the use of a Band Feature Extraction Neural Network (BFE-Net), a state-of-the-art (SOTA) method in this field, has limitations with respect to independent band-wise feature extraction and a simplistic band aggregation process to obtain final classification results. To address these problems, this study proposes the noise-robust band-attention BFE-Net framework, aiming to improve the conventional BFE-Net from two perspectives. First, we implement multiple-input, multiple-output (MIMO)-based preprocessing. Specifically, we utilize multichannel minima-controlled recursive averaging for precise non-stationary noise covariance estimation and generalized eigenvalue decomposition for subspace filtering to enhance the signal-to-noise ratio. Second, we propose an attention-based band aggregation mechanism. By integrating a band-wise self-attention mechanism, the model learns dynamic inter-band dependencies for more sophisticated feature fusion for classification. Experimental results on the SEED and SEED-IV datasets under a subject-independent protocol show that our model outperforms the SOTA BFE-Net by 3.27% and 3.34%, respectively. This confirms that rigorous MIMO noise reduction, combined with frequency-centric attention, significantly enhances the reliability and generalization of BCI systems. Full article

Theenergy of a graph is a classical spectral invariant defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. Recently, the notion of local energy was introduced to measure the contribution of vertices to the total energy via vertex deletion. In this paper, we first study the variation of graph energy under the deletion of a set of vertices and obtain general upper bounds in terms of vertex degrees, together with a characterization of the equality cases under natural structural conditions. These results provide the foundation for extending the concept of local energy to digraphs. Using the singular values of the adjacency matrix, we define the local energy of a digraph and derive sharp upper bounds in terms of the in-degree and out-degree of a vertex. The equality cases are characterized by introducing a special class of vertices, called star-vertices. Finally, we obtain sharp bounds for the total local energy of a digraph in terms of its energy and of the Randić index. Full article

Efficient target detection in hyperspectral images faces significant deployment challenges on resource-constrained edge platforms due to the large data volume and high computational complexity of detection algorithms. This paper proposes a CEM target detection method based on 1D-CNN feature dimensionality reduction. A lightweight 1D-CNN reduces spectral dimensions from L bands to 16 features, decreasing the core matrix inversion complexity from $O\left(L^3\right)$ to $O\left({16}^3\right)$. Unlike PCA-based dimensionality reduction requiring online eigenvalue decomposition, the proposed approach employs fixed pre-trained weights with simple convolution operations, enabling high parallelizability for FPGA implementation. A Zynq-based PS + PL collaborative acceleration scheme is designed, deploying CNN on the PL side through RTL implementation and CEM on the PS side using double-precision floating-point computation. Experimental validation on multiple hyperspectral datasets demonstrates that the proposed method achieves an AUC of 0.9953 with less than 1% difference compared to traditional CEM, processes 40,000 pixels in approximately 10.8 s, and consumes only 2.067 W, making it suitable for power-sensitive edge applications such as UAV reconnaissance and satellite on-board processing. The system achieves a processing rate of 3704 pixels/s. Full article

KANECS is a 3D multigroup neutronics code based on the Simplified Spherical Harmonics (SP_N) approximation and the Continuous Galerkin Finite Element Method (CGFEM). In this work, the code is extended to solve the time-dependent neutron kinetics by implementing a fully implicit backward Euler scheme for the neutron transport equation and an implicit exponential integration for delayed neutron precursors. These schemes ensure unconditional stability and minimize temporal discretization errors, making the method suitable for fast transients. The new formulation transforms each time step into a transient fixed-source problem, which is solved efficiently using the GMRES solver with ILU preconditioning. The kinetics module is validated against established benchmark problems, including TWIGL, the C5G2 MOX benchmark, and both 2D and 3D mini-core rod-ejection transients. KANECS shows close agreement with the reference solutions from well-known neutron transport codes, with consistent accuracy in normalized power evolution, spatial power distributions, and steady-state eigenvalues. The results confirm that KANECS provides a reliable and accurate framework for solving neutron kinetics problems. Full article

The integration of new energy into the grid has significantly intensified power grid operational pressure, posing higher demands on hydropower system regulation. As a key unit for power grid load tracking and stability maintenance, parameter mismatch of the PID governor is prone to inducing system bifurcation, thus leading to oscillatory instability, which has emerged as a critical challenge affecting the reliable consumption and sustainable supply of new energy. To address this challenge, a hydroelectric power generation system (HPGS) model in the infinite-bus power system is established. Bifurcation analysis is employed to quantitatively identify the critical thresholds of PID parameters that cause HPGS instability. Based on this, system dynamic response processes under critical thresholds are clarified using time-domain analysis. Furthermore, the potential oscillation instability mechanism is revealed using eigenvalue analysis, and suggestions for PID parameter selection are provided. Key quantitative results indicate that variations in proportional gain, kp, induce five limit point bifurcations. The system enters an unstable region when k_p exceeds 2.467, whereas operation within the range below 0.891 is conducive to system stability. A supercritical Hopf bifurcation arises when integral gain k_i reaches 0.925, so strict restrictions should be imposed on k_i to avoid operating around this critical value. Two supercritical Hopf bifurcations that may trigger system oscillatory instability are identified during differential gain k_d changing, and it should be regulated to a level below 5.188 to ensure system stability. By integrating bifurcation analysis, time-domain analysis, and eigenvalue analysis, this study effectively improves the accuracy of characterizing system dynamic behaviors, providing a clear quantitative basis for PID parameter optimization and bifurcation suppression, as well as laying a theoretical foundation for hydropower system stable operation and the efficient absorption of new energy. Full article

To provide deeper insights into the complex and multidimensional nature of swimming start performance, the present study aimed to determine its key performance indicators (KPIs) and provide percentile-based reference values for elite junior and adult swimmers. Hence, routine performance analysis data of Swiss junior and senior national team members were analyzed, including multiple European champions, World champions, Olympic medalists and a World record holder (n = 136, age: 18.3 ± 3.6 [13–32] years, World Aquatics swimming points: 761 ± 73 [609–1061]). All kinetic and kinematic variables measured by the instrumented starting block were analyzed, and variables with pairwise correlation > 0.80 were clustered using principal component analysis with orthogonal Varimax rotation, retaining components with Eigenvalue > 1.0 and factor loadings > 0.6. The highest loaded variables of each component were used as independent variables, alongside the variables with low co-variance, to determine KPIs with multiple linear regression analysis. As such, peak and average power (p ≤ 0.05), front horizontal and total vertical peak forces (p ≤ 0.04), timing of peak power and rear horizontal forces (p ≤ 0.02), resultant grab forces and their timing (p ≤ 0.05), center-of-gravity height at take-off (p = 0.03), take-off horizontal and vertical velocity (p = 0.02), resultant entry velocity (p = 0.01), entry time (p < 0.01), distance before the first kick (p < 0.01), maximal swimming depth (p = 0.02) and distance before breaking through the water surface (p < 0.01) showed a significant effect on the dependent variables (15 m start time). In conclusion, swimmers should maximize power and force production peaking earlier and grab forces peaking later during the block phase. They should increase take-off and entry velocities, distance before the first undulating kick, maximal swimming depth and underwater distance. Full article

The well-known shooting algorithm has produced important results in solving various linear as well as nonlinear BVPs, defined on unbounded intervals, but has become obsolete. The main difficulty lies in the numerical handling of the domain’s infiniteness. This paper presents a three-step strategy that significantly improves the traditional truncation algorithm. It consists of Chebyshev collocation, implemented as Chebfun, in conjunction with rational AAA interpolation and analytic continuation. Furthermore, and more importantly, this approach enables us to provide a thorough analysis of both possible errors in dealing with and the hidden singularities of some BVPs of real interest. A singular second-order eigenvalue problem and a fourth-order nonlinear degenerate parabolic equation, all defined on the real axis, are considered. For the latter, Chebfun provides properties-preserving solutions. Travelling wave solutions are also studied. They are highly nonlinear BVPs. The problem arises from the analysis of thin viscous film flows down an inclined plane under the competing stress due to the surface tension gradients and gravity, a long-standing concern of ours. By extending the solutions to these problems in the complex plane, we observe that the complex poles do not influence their behaviour. On the other hand, the real ones involve singularities and indicate how long solutions can be extended through continuity. Full article

The analysis of multivariate data is a central issue in biomedical research, where the accurate classification of patients and the extraction of reliable conclusions are of critical importance. Linear Discriminant Analysis (LDA) remains one of the most established methods for both dimensionality reduction and classification of data. In this paper, we examine in detail the theoretical foundations, assumptions, and statistical properties of LDA, and apply the method step by step to real data from the Breast Cancer Wisconsin (Diagnostic) database, which includes cellular features from breast biopsy samples with the aim of distinguishing benign from malignant tumors. Emphasis is placed on the importance of the method’s assumptions, such as multivariate normality, equality of covariance matrices, and absence of multicollinearity, demonstrating that their fulfillment leads to significant improvements in model performance. Specifically, careful preprocessing and strict adherence to these assumptions increase classification accuracy from $95.6\%$ ($94.7\%$ cross-validated) to $97.8\%$ ($97.4\%$ cross-validated). To our knowledge, this study is the first to demonstrate the dual use of LDA as both a dimensionality-reduction tool and a predictive classification model for this medical database within the same biomedical analysis framework. Moreover, we provide, for the first time, a systematic comparison between our assumption-aware LDA model and related studies employing the most accurate machine-learning classifiers reported in the literature for this dataset, showing that classical LDA achieves accuracy comparable to these more complex methods. The resulting discriminant model, which uses 13 variables out of the original 30, can be applied easily by clinical researchers to classify new cases as benign or malignant, while simultaneously providing interpretable coefficients that reveal the underlying relationships among variables. The implementation is carried out in the SPSS environment, following the theoretical steps described in the paper, thus offering a user-friendly and reproducible framework for reliable application. In addition, the study establishes a structured and transparent workflow for the proper application of LDA in biomedical research by explicitly linking assumption verification, preprocessing, dimensionality reduction, and classification. Full article

The Generalized Eigenvalue Proximal Support Vector Machine (GEPSVM) introduces a novel large-margin classifier that improves upon standard SVMs by constructing a pair of non-parallel hyperplanes derived from a generalized eigenvalue problem. However, the GEPSVM suffers from severe misclassification in the overlapped hyperplane region, known as the underdetermined hyperplane problem (UHP). A localized GEPSVM (LGEPSVM) alleviates this issue by building convex hulls on the hyperplanes for classification, but it still faces notable drawbacks: (1) an inability to integrate both local and global information, (2) a lack of consideration of the data’s statistical characteristics, and (3) high computational and storage costs. To address these limitations, we propose the Ellipsoid-structured Localized GEPSVM (EL-GEPSVM), which extends the GEPSVM by constructing ellipsoid-structured convex hulls under the Mahalanobis metric. This design incorporates statistical data characteristics and enables a classification scheme that simultaneously considers local and global information. Extensive theoretical analyses and experiments demonstrate that the proposed EL-GEPSVM achieves improved effectiveness and efficiency compared with existing methods. Full article

We explore how easy it is to enforce the advent of exceptional points starting from random matrices of non-Hermitian nature. We use the Petermann factor, whose mathematical version is called “overlap”, for guidance, as well as simple pseudo-spectral tools. We attempt to proceed in the most agnostic way, by adding random perturbation and checking basic metrics such as the sum of all vectors’ Petermann factors, equivalently the sum of diagonal overlaps. Issues such as the location of high Petermann factors vs. the modulus of eigenvalue are addressed. We contrast the fate of exploratory approaches in the Ginibre set (real matrices) and complex matrices, noting the special role of exceptional points on the real axis for the Ginibre matrices, completely absent in complex matrices. Full article

An Improved Two-Stage Rank Reduction (ITS-RARE) algorithm is proposed for the localization of mixed far-field (FF) and near-field (NF) sources under unknown mutual coupling with the uniform linear sensor array. Our algorithm includes two steps: in the first step, the eigenvectors are exploited when the rank reduction occurs at the right DOAs in our method. The eigenvectors corresponding to the smallest eigenvalues inherently represent the mutual coupling coefficient vectors. Based on it, the joint estimation of FF source DOAs and mutual coupling factors is achieved without pre-calibration. In the second step, after the DOA estimation of NF sources (NFSs), the ranges are estimated in closed form. As a result, the computational complexity is significantly reduced compared to existing methods. Furthermore, the full array aperture is preserved through the covariance matrix reconstruction (CMR) method during the FF/NF source classification. The simulation results demonstrate that the proposed algorithm is not only computationally efficient and effective in source classification but also preserves a larger effective aperture, thereby improving estimation accuracy. Full article