Search Results (83)

The 32-bit floating-point (FP32) format has many useful applications, particularly in computing and neural network systems. The classic 32-bit fixed-point (FXP32) format often introduces lower quality of representation (i.e., precision), making it unsuitable for real deployment, despite offering faster computations and reduced computational cost, which positively impacts energy efficiency. In this paper, we propose a switched FXP32 format able to compete with or surpass the widely used FP32 format across a wide variance range. It actually proposes switching between the possible values of key parameters according to the variance level of the data modeled with the Laplacian distribution. Precision analysis is achieved using the signal-to-quantization noise ratio (SQNR) as a performance metric, introduced based on the analogy between digital formats and quantization. Theoretical SQNR results provided in a wide range of variance confirm the design objectives. Experimental and simulation results obtained using neural network weights further support the approach. The strong agreement between the experiment, simulation, and theory indicates the efficiency of this proposal in encoding Laplacian data, as well as its potential applicability in neural networks. Full article

To improve the surface morphology quality of ultra-precision optical components, particularly in the suppression of mid-spatial frequency (MSF) errors, this paper proposes a morphology gradient-aware spatiotemporal coupled smoothing model based on convolutional material removal. By introducing the Laplacian curvature into the surface evolution framework, a curvature-sensitive “peak-priority” mechanism is established to dynamically guide the local dwell time. A nonlinear spatiotemporal coupling equation is constructed, in which the dwell time is adaptively modulated by surface gradient magnitude, local curvature, and periodic fluctuation terms. The material removal process is modeled as the convolution of a spatially invariant removal function with a locally varying dwell time distribution. Moreover, analytical evolution expressions of PV, RMS, and PSD metrics are derived, enabling a quantitative assessment of smoothing performance. Simulation results and experimental validations demonstrate that the proposed model can significantly improve smoothing performance and enhance MSF error suppression. Full article

This paper studies the robust $H_{\infty }$ time-varying formation tracking (TVFT) problem for heterogeneous nonlinear multi-agent systems (MASs) with parameter uncertainties, external disturbances, and unknown leader inputs. The objective is to ensure that follower agents track the leader’s trajectory while achieving a desired time-varying formation, even under unmodeled dynamics and disturbances. Unlike existing methods that rely on global topology information or homogeneous system assumptions, an adaptive control protocol is proposed in full distribution, requiring no global topology information, and integrates nonlinear compensation terms to handle unknown leader inputs and parameter uncertainties. Based on the Lyapunov theory and laplacian matrix, a robust $H_{\infty }$ TVFT criterion is developed. Finally, a numerical example is given to verify the theory. Full article

The automation of the detection infrastructure in GPR imagery is a key issue, particularly in the context of the non-invasive acquisition of radargrams with a multi-antenna ground-penetrating radar. Due to the fact that the dataset acquired with a multi-antenna GPR is very large, in the context of automating the process of detecting hyperbolas, the authors have proposed an adaptive approach to the selection of GPR images. The aim of this project was to develop a method for the selection of GPR images by means of applying the appropriate quality indicators. The authors propose a new, adaptive approach to the selection of radargrams that were recorded during the route of a GPR in a single profile, where several radargrams were recorded. Depending on the obtained initial values of the standard indicators for the assessment of the quality and quality maps of the radargrams, those images from selected channels that will ensure the highest possible quality and efficiency of hyperbola detection were selected. The stage of image quality assessment is essential in the context of improving the effectiveness of the automated detection of underground infrastructure. The quality assessment was performed based on the entropy indicator, PIQE, and Laplacian variance. The selected quality indicators allowed the authors to assess the degree of blurring, noise, and the number of details representing the underground structures that are present in GPR images. An additional product of the quality assessment were the generated maps that present the distribution of entropy in the analyzed images. The image selection was verified based on the results of the parameters that assess the effectiveness of the detection of hyperbolas that represent underground networks. The proposed innovative adaptive approach to the selection of images acquired by GPR enabled a significant improvement in the efficiency of the detection of hyperbolas representing underground utility networks, by 15–40%, shortening data processing and infrastructure detection times. Full article

This paper presents a comprehensive investigation into the phenomenon of gamut boundary distortion that occurs during the gamut conversion process in LED full-color display systems. This phenomenon is influenced by the electro-optical transfer function. First, a CIE-xyY colorimetric framework specifically designed for LEDs is developed and established as the foundation for gamut conversion in LED applications. Next, the principles of gamut conversion based on this model are detailed. Additionally, a set of indices, including the Laplacian operator, entropy function, and magnitude of deviation of distorted color points, is integrated to form a comprehensive descriptive methodology. This methodology enables a thorough quantification of distribution patterns and effectively illustrates the outcomes of distortion. The findings of this research are significant for improving color conversion strategies and enhancing the color performance of display devices, making meaningful contributions to related fields. Full article

The combined use of synthetic aperture radar (SAR) and optical images for surface observation is gaining increasing attention. Optical images, with their distinct edge features, can accurately classify different objects, while SAR images reveal deeper internal variations. To address the challenge of differing feature distributions in multi-source images, we propose an edge enhancement network, OSNet (network for optical and SAR images), designed to jointly extract features from optical and SAR images and enhance edge feature representation. OSNet consists of three core modules: a dual-branch backbone, a synergistic attention integration module, and a global-guided local fusion module. These modules, respectively, handle modality-independent feature extraction, feature sharing, and global-local feature fusion. In the backbone module, we introduce a differentiable Lee filter and a Laplacian edge detection operator in the SAR branch to suppress noise and enhance edge features. Additionally, we designed a multi-source attention fusion module to facilitate cross-modal information exchange between the two branches. We validated OSNet’s performance on segmentation tasks (WHU-OPT-SAR) and regression tasks (SNOW-OPT-SAR). The results show that OSNet improved PA and MIoU by 2.31% and 2.58%, respectively, in the segmentation task, and reduced MAE and RMSE by 3.14% and 4.22%, respectively, in the regression task. Full article

The combinatorial fusion cascade provides a surprisingly simple and complete explanation for the origin of the genetic code based on competing protocodes. Although its molecular basis is only beginning to be uncovered, it represents a natural pattern of information generation from initial signals and has potential applications in designing more-efficient neural networks. By utilizing the properties of the combinatorial fusion cascade, we demonstrate its embedding into deep neural networks with sequential fully connected layers using the dynamic matrix method and compare the resulting modifications. We observe that the Fiedler Laplacian eigenvector of a combinatorial cascade neural network does not reflect the cascade architecture. Instead, eigenvectors associated with the cascade structure exhibit higher Laplacian eigenvalues and are distributed widely across the network. We analyze a text classification model consisting of two sequential transformer layers with an embedded cascade architecture. The cascade shows a significant influence on the classifier’s performance, particularly when trained on a reduced dataset (approximately 3% of the original). The properties of the combinatorial fusion cascade are further examined for their application in training neural networks without relying on traditional error backpropagation. Full article

As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide the decomposition process, using fixed data graphs and feature graphs to capture relationships between data points and features. However, these fixed graphs may limit the model’s expressiveness. Additionally, many NMF variants face challenges when dealing with complex data distributions and are vulnerable to noise and outliers. To overcome these challenges, we propose a novel method called sparse feature-weighted double Laplacian rank constraint non-negative matrix factorization (SFLRNMF), along with its extended version, SFLRNMTF. These methods adaptively construct more accurate data similarity and feature similarity graphs, while imposing rank constraints on the Laplacian matrices of these graphs. This rank constraint ensures that the resulting matrix ranks reflect the true number of clusters, thereby improving clustering performance. Moreover, we introduce a feature weighting matrix into the original data matrix to reduce the influence of irrelevant features and apply an $L_{\mathrm{2,1}/2}$ norm sparsity constraint in the basis matrix to encourage sparse representations. An orthogonal constraint is also enforced on the coefficient matrix to ensure interpretability of the dimensionality reduction results. In the extended model (SFLRNMTF), we introduce a double orthogonal constraint on the basis matrix and coefficient matrix to enhance the uniqueness and interpretability of the decomposition, thereby facilitating clearer clustering results for both rows and columns. However, enforcing double orthogonal constraints can reduce approximation accuracy, especially with low-rank matrices, as it restricts the model’s flexibility. To address this limitation, we introduce an additional factor matrix R, which acts as an adaptive component that balances the trade-off between constraint enforcement and approximation accuracy. This adjustment allows the model to achieve greater representational flexibility, improving reconstruction accuracy while preserving the interpretability and clustering clarity provided by the double orthogonality constraints. Consequently, the SFLRNMTF approach becomes more robust in capturing data patterns and achieving high-quality clustering results in complex datasets. We also propose an efficient alternating iterative update algorithm to optimize the proposed model and provide a theoretical analysis of its performance. Clustering results on four benchmark datasets demonstrate that our method outperforms competing approaches. Full article

In this paper, a distributed algorithm for reaching average consensus is proposed for multi-agent systems with tree communication graph, when the edge weight distribution is unbalanced. First, the problem is introduced as a key topic of core algorithms for several modern scenarios. Then, the relative solution is proposed as a finite-time algorithm, which can be included in any application as a preliminary setup routine, and it is well-suited to be integrated with other adaptive setup routines, thus making the proposed solution useful in several practical applications. A special focus is devoted to the integration of the proposed method with a recent Laplacian eigenvalue allocation algorithm, and the implementation of the overall approach in a wireless sensor network framework. Finally, a worked example is provided, showing the significance of this approach for reaching a more precise average consensus in uncertain scenarios. Full article

Federated learning is a widely applied distributed machine learning method that effectively protects client privacy by sharing and computing model parameters on the server side, thus avoiding the transfer of data to third parties. However, information such as model weights can still be analyzed or attacked, leading to potential privacy breaches. Traditional federated learning methods often disturb models by adding Gaussian or Laplacian noise, but under smaller privacy budgets, the large variance of the noise adversely affects model accuracy. To address this issue, this paper proposes a Symmetric Partition Mechanism (SPM), which probabilistically perturbs the sign of local model weight parameters before model aggregation. This mechanism satisfies strict $ϵ$-differential privacy, while introducing a variance constraint mechanism that effectively reduces the impact of noise interference on model performance. Compared with traditional methods, SPM generates smaller variance under the same privacy budget, thereby improving model accuracy and being applicable to scenarios with varying numbers of clients. Through theoretical analysis and experimental validation on multiple datasets, this paper demonstrates the effectiveness and privacy-protection capabilities of the proposed mechanism. Full article

Currently, with the increasing scale of industrial systems, multisensor monitoring data exhibit large-scale dynamic Gaussian and non-Gaussian concurrent complex characteristics. However, the traditional principal component analysis method is based on Gaussian distribution and uncorrelated assumptions, which are greatly limited in practice. Therefore, developing a new fault detection method for large-scale Gaussian and non-Gaussian concurrent dynamic systems is one of the urgent challenges to be addressed. To this end, a double-layer distributed and integrated data-driven strategy based on Laplacian score weighting and integrated Bayesian inference is proposed. Specifically, in the first layer of the distributed strategy, we design a Jarque–Bera test module to divide all multisensor monitoring variables into Gaussian and non-Gaussian blocks, successfully solving the problem of different data distributions. In the second layer of the distributed strategy, we design a dynamic augmentation module to solve dynamic problems, a K-means clustering module to mine local similarity information of variables, and a Laplace scoring module to quantitatively evaluate the structural retention ability of variables. Therefore, this double-layer distributed strategy can simultaneously combine the different distribution characteristics, dynamism, local similarity, and importance of variables, comprehensively mining the local information of the multisensor data. In addition, we develop an integrated Bayesian inference strategy based on detection performance weighting, which can emphasize the differential contribution of local models. Finally, the fault detection results for the Tennessee Eastman production system and a diesel engine working system validate the superiority of the proposed method. Full article

Satellite multi-view stereo (MVS) is a fundamental task in large-scale Earth surface reconstruction. Recently, learning-based multi-view stereo methods have shown promising results in this field. However, these methods are mainly developed by transferring the general learning-based MVS framework to satellite imagery, which lacks consideration of the specific terrain features of the Earth’s surface and results in inadequate accuracy. In addition, mainstream learning-based methods mainly use equal height interval partition, which insufficiently utilizes the height hypothesis surface, resulting in inaccurate height estimation. To address these challenges, we propose an end-to-end terrain feature-aware height estimation network named SA-SatMVS for large-scale Earth surface multi-view stereo, which integrates information across different scales. Firstly, we transform the Sobel operator into slope feature-aware kernels to extract terrain features, and a dual encoder–decoder architecture with residual blocks is applied to incorporate slope information and geometric structural characteristics to guide the reconstruction process. Secondly, we introduce a pixel-wise unequal interval partition method using a Laplacian distribution based on the probability volume obtained from other scales, resulting in more accurate height hypotheses for height estimation. Thirdly, we apply an adaptive spatial feature extraction network to search for the optimal fusion method for feature maps at different scales. Extensive experiments on the WHU-TLC dataset also demonstrate that our proposed model achieves the best MAE metric of 1.875 and an RMSE metric of 3.785, which constitutes a state-of-the-art performance. Full article

Actuator faults and external disturbances, which are inevitable due to material fatigue, operational wear and tear, and unforeseen environmental impacts, cause significant threats to the control reliability and performance of networked systems. Therefore, this paper primarily focuses on the distributed adaptive bipartite consensus tracking control problem of networked Euler–Lagrange systems (ELSs) subject to actuator faults and external disturbances. A robust distributed control scheme is developed by combining the adaptive distributed observer and neural-network-based tracking controller. On the one hand, a new positive definite diagonal matrix associated with an asymmetric Laplacian matrix is constructed in the distributed observer, which can be used to estimate the leader’s information. On the other hand, neural networks are adopted to approximate the lumped uncertainties composed of unknown matrices and external disturbances in the follower model. The adaptive update laws are designed for the unknown parameters in neural networks and the actuator fault factors to ensure the boundedness of estimation errors. Finally, the proposed control scheme’s effectiveness is validated through numerical simulations using two types of typical ELS models: two-link robot manipulators and quadrotor drones. The simulation results demonstrate the robustness and reliability of the proposed control approach in the presence of actuator faults and external disturbances. Full article

We define a new family of random geometric graphs which we call random covering graphs and study its statistical properties. To the best of our knowledge, this family of graphs has not been explored in the past. Our experimental results suggest that there are striking deviations in the expected number of edges, degree distribution, spectrum of adjacency/normalized Laplacian matrix associated with the new family of graphs as compared to both the well-known Erdos–Renyi random graphs and the general random geometric graphs as originally defined by Gilbert. Particularly, degree distribution of the graphs shows some interesting features in low dimensions. To the more applied end, we believe that our random graph family might be effective in modelling some practically useful networks (world wide web, social networks, railway or road networks, etc.). It is observed that the degree distribution of some complex networks arising in practice follow power law distribution or log power distribution; they tend to be right skewed, having a heavy tail unlike the degree distribution of Erdos–Renyi graphs or general geometric random graphs (which follow exponential distribution with a sharp tail). The degree distribution of our random graph family significantly deviates from that of Erdos–Renyi graphs or general geometric random graphs and is closer to a right-skewed power law distribution with a heavy tail. Thus, we believe that this new family of graphs might be more effective in modelling the typical real-world networks mentioned above. The key contribution of the paper is introducing this new random graph family and studying some of its properties experimentally, further investigation into which would be interesting from a purely mathematical perspective. Also, it might be of practical interest in terms of modelling real-world networks. Full article

In this paper, a fully distributed strategy for the economic dispatch problem (EDP) in the smart grid is proposed. The economic dispatch model considers both traditional thermal generators and wind turbines (WTs), integrating generation costs, carbon trading expenses, and the expected costs associated with the unpredictability of wind power. The EDP is transformed into an equivalent optimization problem with only an equality constraint and thus can be solved by an alternating-direction method of multipliers (ADMM). Then, to tackle this problem in a distributed manner, the outer-layer framework of the proposed strategy adopts a parallel ADMM, where different variables can be calculated simultaneously. And the inner-layer framework adopts a finite-step consensus algorithm. Convergence to the optimal solution is achieved within a finite number of communication iterations, which depends on the scale of the communication network. In addition, leveraging local and neighbor information, a distributed algorithm is designed to compute the eigenvalues of the Laplacian matrix essential for the finite-step algorithm. Finally, several numerical examples are presented to verify the correctness and effectiveness of the proposed strategy. Full article