Search Results (22,505)

Driven by rapid advancements in big data and Internet of Things (IoT) technologies, time series data are now extensively utilized across diverse industrial sectors. The precise identification of anomalies in time series data—especially within intricate and ever-changing environments—has emerged as a key focus in contemporary research. This paper proposes a multivariate anomaly detection framework that synergistically combines variational autoencoders with association discrepancy analysis. By incorporating prior knowledge of associations and sequence association mechanisms, the model can capture long-term dependencies in time series and effectively model the association discrepancy between different time points. Through reconstructing time series data, the model enhances the distinction between normal and anomalous points, learning the association discrepancy during reconstruction to strengthen its ability to identify anomalies. By combining reconstruction errors and association discrepancy, the model achieves more accurate anomaly detection. Extensive experimental validation demonstrates that the proposed methodological framework achieves statistically significant improvements over existing benchmarks, attaining superior F1 scores across diverse public datasets. Notably, it exhibits enhanced capability in modeling temporal dependencies and identifying nuanced anomaly patterns. This work establishes a novel paradigm for time series anomaly detection with profound theoretical implications and practical implementations. Full article

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow of Casson fluid along an inclined heated channel. The governing equations for the flow of velocity, temperature, and entropy generation are formulated based on the Casson constitutive relations and thermodynamics’ first and second laws. The exact solutions are constructed for the dimensionless equations and validated with previous results in the literature. The effects of various fluid parameters on the flow, heat transfer, and entropy production rate are conducted and reported graphically with adequate discussion. The impact of the Hartmann number parameter reveals a decrease in both flow velocity and entropy generation rate, meanwhile it also enhances the fluid temperature distribution across the inclined channel. An opposite trend is, however, observed with the Casson fluid parameter. Full article

In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. results, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions that may represent the interest themselves. Full article

This article presents the first theoretical analysis of the bending behavior of circular organic solar cells (COSCs). The solar cell under investigation is built on a flexible Kerr foundation and has five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. The cell is exposed to hygrothermal conditions. The related Kerr foundation lessens displacements and supports the cell. The principle of virtual work is used to generate the basic partial differential equations, which are then solved using the differential quadrature method (DQM). The results of the present theory are validated by comparing them with published ones. The effects of the temperature, humidity, elastic foundation factors, and geometric configuration characteristics on the deflection and stresses of the COSC are examined. Full article

Multi-label classification (MLC) plays a crucial role in various real-world scenarios. Prediction with nearest neighbors has achieved competitive performance in MLC. Hubness, a phenomenon in which a few points appear in the k-nearest neighbor (kNN) lists of many points in high-dimensional spaces, may significantly impact machine learning applications and has recently attracted extensive attention. However, it has not been adequately addressed in developing MLC algorithms. To address this issue, we propose a hubness-aware kNN-based MLC algorithm in this paper, named multi-label hubness information-based k-nearest neighbor (MLHiKNN). Specifically, we introduce a fuzzy measure of label relevance and employ a weighted kNN scheme. The hubness information is used to compute each training example’s membership in relevance and irrelevance to each label and calculate weights for the nearest neighbors of a query point. Then, MLHiKNN exploits high-order label correlations by training a logistic regression model for each label using the kNN voting results with respect to all possible labels. Experimental results on 28 benchmark datasets demonstrate that MLHiKNN is competitive among the compared methods, including nine well-established MLC algorithms and three commonly used hubness reduction techniques, in dealing with MLC problems. Full article

Aiming at the problems of poor image quality of traditional cameras and serious noise interference of event cameras under complex lighting conditions in coal mines, an event denoising algorithm fusing spatio-temporal information and a method of denoising event target pose estimation is proposed. The denoising algorithm constructs a spherical spatio-temporal neighborhood to enhance the spatio-temporal denseness and continuity of valid events, and combines event density and curvature to achieve event stream denoising. The attitude estimation framework adopts the noise reduction event and global optimal perspective-n-line (OPNL) methods to obtain the initial target attitude, and then establishes the event line correlation model through the robust estimation, and achieves the attitude tracking by minimizing the event line distance. The experimental results show that compared with the existing methods, the noise reduction algorithm proposed in this paper has a noise reduction rate of more than 99.26% on purely noisy data, and the event structure ratio (ESR) is improved by 47% and 5% on DVSNoise20 dataset and coal mine data, respectively. The maximum absolute trajectory error of the localization method is 2.365 cm, and the mean square error is reduced by 2.263% compared with the unfiltered event localization method. Full article

This paper introduces a novel kind of factorial hidden Markov model (FHMM), specifically the feedforward FHMM (FFHMM). In contrast to traditional FHMMs, the FFHMM is capable of directly utilizing supplementary information from observations through predefined states, which are derived using an automatic feature filter (AFF). We investigate two variations of FFHMM models that integrate predefined states with the FHMM: the direct FFHMM and the embedded FFHMM. In the direct FFHMM, alterations to one sub-hidden Markov model (HMM) do not affect the others, enabling individual improvements in HMM estimation. On the other hand, the sub-HMM chains within the embedded FFHMM are interconnected, suggesting that adjustments to one HMM chain may enhance the estimations of other HMM chains. Consequently, we propose two algorithms for these FFHMM models to estimate their respective hidden states. Ultimately, experiments conducted on two real-world datasets validate the efficacy of the proposed models and algorithms. Full article

The Kohn–Nirenberg domains are unbounded domains in ${\mathbb{C}}^n$. In this article, we modify the Kohn–Nirenberg domain ${\mathrm{\Omega }}_{K,L}=\left\{(z_1,\dots ,z_n)\right.\in {\mathbb{C}}^n:Re{z}_n+g\mid z_n{\mid }^2+{\sum }_{j=1}^{n-1}(\mid z_j{\mid }^p+K_j\mid z_j{\mid }^{p-q}Re{z}_j^q+L_j\mid z_j{\mid }^{p-2q}Im{z}_j^{2q})<0\}$ and discuss the existence of supporting surface and peak functions at the origin. Full article

This paper investigates a generalization of the spherical numerical radius for a pair $(B,C)$ of bounded linear operators on a complex Hilbert space H. The generalized spherical numerical radius is defined as $w_p(B,C):={\displaystyle \underset{x\in H,\parallel x\parallel =1}{\sup }}{\left({\left|⟨Bx,x⟩\right|}^p+{\left|⟨Cx,x⟩\right|}^p\right)}^{{\displaystyle \frac{1}{p}}}$, $p\ge 1$. We derive lower bounds for $w_p^2(B,C)$ involving combinations of B and C, where $p>1$. Additionally, we establish upper bounds in terms of operator norms. Applications include the cases where $(B,C)=(A,A^{*})$, with $A^{*}$ denoting the adjoint of a bounded linear operator A, and $(B,C)=\left(\mathfrak{R}\right(A),\mathfrak{I}(A\left)\right)$, representing the real and imaginary parts of A, respectively. We also explore applications to the so-called Davis–Wielandt p-radius for $p\ge 1$, which serves as a natural generalization of the classical Davis–Wielandt radius for Hilbert-space operators. Full article

In this study, a PID-nested nonsingular terminal sliding controller is proposed to minimize the chattering phenomenon. By adding both integral and derivative errors of states into the nonsingular terminal sliding manifolds, a composite sliding manifold was created. Compared to nonsingular terminal sliding mode (NTSM) techniques, this sliding manifold can handle higher-order derivatives. The speed of the motor is controlled by a sliding control law determined through a higher-order integral, making the signal continuous, and the sliding manifold is achieved in finite time. A special full-order terminal sliding mode manifold is introduced, which allows the system to converge in finite time while being chattering-free and avoiding the singularity phenomenon of conventional and terminal sliding modes. The controller’s efficiency is demonstrated with faster convergence time and fewer errors than state-of-the-art controllers, which is demonstrated through both simulation and experiment. Full article

This paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number. These Ramsey numbers play a crucial role in combinatorial mathematics, determining the minimum number of vertices required to guarantee specific monochromatic substructures. We establish upper and lower bounds for each of these numbers, providing new insights into their behavior for cycles with pendant edges—graphs formed by attaching additional edges to one or more vertices of a cycle. The results presented contribute to the broader understanding of Ramsey theory and serve as a foundation for future research on generalized Ramsey numbers in complex graph structures. Full article

Defining an adequate unit size is often crucial in brain imaging analysis, where datasets are complex, high-dimensional, and computationally demanding. Unit size refers to the spatial resolution at which brain data is aggregated for analysis. Optimizing unit size in data aggregation requires balancing computational efficiency in handling large-scale data sets with the preservation of brain activity patterns, minimizing signal dilution. We propose using the Calinski–Harabasz index, demonstrating its invariance to sample size changes due to varying image resolutions when no distributional differences are present, while the index effectively identifies an appropriate unit size for detecting suspected regions in image comparisons. The resolution-independent metric can be used for unit size evaluation, ensuring adaptability across different imaging protocols and modalities. This study enhances the scalability and efficiency of brain imaging research by providing a robust framework for unit size optimization, ultimately strengthening analytical tools for investigating brain function and structure. Full article