Search Results (203)

Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, including topology, convergence theory, and completeness, and handles both symmetric and asymmetric cases, generalising previous neutrosophic metric results. For this purpose, neutrosophic quadruple metric spaces were derived from neutrosophic metric spaces in order to better model situations involving uncertainty. Also, we generalised the findings obtained with the neutrosophic metric to the quadruple neutrosophic metric. Full article

Large language models (LLMs) have driven transformative progress in artificial intelligence, yet critical challenges persist in data management and privacy protection during model deployment and training. The approximate nearest neighbor (ANN) search, a core operation in LLMs, faces inherent trade-offs between efficiency and security when implemented through conventional locality-sensitive hashing (LSH)-based secure ANN (SANN) methods, which often compromise either query accuracy due to false positives. To address these limitations, this paper proposes a novel secure ANN scheme based on nearest neighbor graph (NNG-SANN), which is designed to ensure the security of approximate k-nearest neighbor queries for vector data commonly used in LLMs. Specifically, a secure indexing structure and subset partitioning method are proposed based on LSH and NNG. The approach utilizes neighborhood information stored in the NNG to supplement subset data, significantly reducing the impact of false positive points generated by LSH on query results, thereby effectively improving query accuracy. To ensure data privacy, we incorporate a symmetric encryption algorithm that encrypts the data subsets obtained through greedy partitioning before storing them on the server, providing robust security guarantees. Furthermore, we construct a secure index table that enables complete candidate set retrieval through a single query, ensuring our solution completes the search process in one interaction while minimizing communication costs. Comprehensive experiments conducted on two datasets of different scales demonstrate that our proposed method outperforms existing state-of-the-art algorithms in terms of both query accuracy and security, effectively meeting the precision and security requirements for nearest neighbor queries in LLMs. Full article

Recent advancements in deep learning have driven the rapid proliferation of deepfake generation techniques, raising substantial concerns over digital security and trustworthiness. Most current detection methods primarily focus on spatial or frequency domain features but show limited effectiveness when dealing with compressed videos and cross-dataset scenarios. Observing that mainstream generation methods use frame-by-frame synthesis without adequate temporal consistency constraints, we introduce the Spatiotemporal Attention 3D Network (STA-3D), a novel framework that combines a lightweight spatiotemporal attention module with a 3D convolutional architecture to improve detection robustness. The proposed attention module adopts a symmetric multi-branch architecture, where each branch follows a nearly identical processing pipeline to separately model temporal-channel, temporal-spatial, and intra-spatial correlations. Our framework additionally implements Spatial Pyramid Pooling (SPP) layers along the temporal axis, enabling adaptive modeling regardless of input video length. Furthermore, we mitigate the inherent asymmetry in the quantity of authentic and forged samples by replacing standard cross entropy with focal loss for training. This integration facilitates the simultaneous exploitation of inter-frame temporal discontinuities and intra-frame spatial artifacts, achieving competitive performance across various benchmark datasets under different compression conditions: for the intra-dataset setting on FF++, it improves the average accuracy by 1.09 percentage points compared to existing SOTA, with a more significant gain of 1.63 percentage points under the most challenging C40 compression level (particularly for NeuralTextures, achieving an improvement of 4.05 percentage points); while for the intra-dataset setting, AUC is enhanced by 0.24 percentage points on the DFDC-P dataset. Full article

State evaluation of relay protection equipment constitutes a crucial component in ensuring the stable, secure, and symmetric operation of power systems. Current methodologies predominantly encompass fuzzy-rule-based control systems and data-driven machine learning approaches. The former relies on manual experience for designing fuzzy rules and membership functions and exhibits limitations in high-dimensional data integration and analysis. The latter predominantly formulates state evaluation as a classification task, which demonstrates its ineffectiveness in identifying equipment at boundary states and faces challenges in model parameter selection. To address these limitations, this paper proposes a quantitative state evaluation method for relay protection equipment based on a two-stage artificial protozoa optimizer (two-stage APO) optimized improved Conformer (two-stage APO-IConf) model. First, we modify the Conformer architecture by replacing pre-layer normalization (Pre-LN) in residual networks with post-batch normalization (post-BN) and introducing dynamic weighting coefficients to adaptively regulate the connection strengths between the first and second feed-forward network layers, thereby enhancing the capability of the model to fit relay protection state evaluation data. Subsequently, an improved APO algorithm with two-stage optimization is developed, integrating good point set initialization and elitism preservation strategies to achieve dynamic equilibrium between global exploration and local exploitation in the Conformer hyperparameter space. Experimental validation using operational data from a substation demonstrates that the proposed model achieves a RMSE of 0.5064 and a MAE of 0.2893, representing error reductions of 33.6% and 35.0% compared to the baseline Conformer, and 9.1% and 15.2% error reductions over the improved Conformer, respectively. This methodology can provide a quantitative state evaluation and guidance for developing maintenance strategies for substations. Full article

Aiming at the state estimation problem of nonlinear systems (NLSs), the traditional typical nonlinear filtering methods (e.g., Particle Filter, PF) have large errors in system state, resulting in low accuracy and high computational speed. To perfect the imperfections, a new Bayesian estimation method based on particle flow velocity (PFV-BEM) is proposed in this paper. Firstly, a symmetrical projection space based on the state information is selected, the basis function is determined by a set of Fourier series with symmetric properties, the state update is carried out according to the projection principle to calculate the prior information of the state, and select its particle points. Secondly, the particle flow velocity is defined, which describes the evolution process of random samples from the prior distribution to the posterior distribution. The posterior information of the state is calculated by solving the parameters related to the particle flow velocity. Finally, the estimated mean and standard deviation of the state are solved. Simulation experiments are carried out based on two instances of one-dimensional general nonlinear examples and multi-target motion tracking, The newly proposed algorithm is compared with the Particle Filter (PF), and the simulation results clearly indicate the feasibility of this novel Bayesian estimation algorithm. Full article

This paper presents a control framework for the image tracking of two-wheeled self-balancing carts, with the objective of achieving precise tracking control. Exploiting the remarkable memory capacity of the Long Short-Term Memory (LSTM) neural network for sequence signals, the framework conducts image memory judgment and memorization, aiming to enhance control accuracy. After the training phase, comprehensive simulations and real-world experiments are carried out based on the established model to verify the effectiveness and practicality of the proposed control strategy. The system utilizes the TSL1401 linear array CCD lens to detect black tapes on the ground and identify and memorize surrounding images. Through the establishment of a continuous set of training sample points, the LSTM network is trained using Python and TensorFlow. This training process optimizes the network’s weights and generates weight files, which can be readily converted into machine code for physical implementation. Initially, the effectiveness of the control law is verified through simulating the symmetrical steering control of the two-wheeled cart. The simulation results demonstrate the validity of the proposed design method and its superior performance. Finally, a physical two-wheeled self-balancing cart is developed to further validate the feasibility of the framework. Experimental results confirm that this method is highly effective, demonstrating robust image tracking capabilities and optimal tracking performance. Full article

This study addresses the challenging issues in 3D point cloud feature matching within the field of computer vision, where high data quality requirements and vulnerability to disturbances significantly impact performance. Existing methods are prone to outliers when generating feature correspondences due to noise, sampling deviations, symmetric structure, and other factors. To improve the robustness of point cloud feature matching, this paper proposes a novel 3D spatial encoding (3DSE) method that incorporates compact geometric constraints. Our method encodes the spatial layout of matching feature points by quantifying the order of appearance of matching points, and combines rigidity constraints to iteratively eliminate the least consistent matching pairs with the remaining point pairs, thereby sorting the initial matching set. The 3DSE algorithm was evaluated on multiple datasets, including simulated data, self-collected data, and public datasets, which cover data from both LiDAR and Kinect sensors. The comparison results with existing techniques demonstrate that 3DSE exhibits superior performance and robustness in handling noise, sparse point clouds, and changes in data modalities. The application of the proposed method significantly enhances the point cloud registration process, showing promising potential for 3D reconstruction, model-driven 3D object recognition, and pose estimation of non-cooperative targets. Full article

This paper generalizes the efficient matrix decomposition method for solving the finite-difference (FD) discretized three-dimensional (3D) Poisson’s equation using symmetric 27-point, 4th-order accurate stencils to adapt more boundary conditions (BCs), i.e., Dirichlet, Neumann, and Periodic BCs. It employs equivalent Dirichlet nodes to streamline source term computation due to BCs. A generalized eigenvalue formulation is presented to accommodate the flexible 4th-order stencil weights. The proposed method significantly enhances computational speed by reducing the 3D problem to a set of independent 1D problems. As compared to the typical matrix inversion technique, it results in a speed-up ratio proportional to $n^4$, where $n$ is the number of nodes along one side of the cubic domain. Accuracy is validated using Gaussian and sinusoidal source fields, showing 4th-order convergence for Dirichlet and Periodic boundaries, and 2nd-order convergence for Neumann boundaries due to extrapolation limitations—though with lower errors than traditional 2nd-order schemes. The method is also applied to vortex-in-cell flow simulations, demonstrating its capability to handle outer boundaries efficiently and its compatibility with immersed boundary techniques for internal solid obstacles. Full article

This study presents a topological design and modeling framework for 3D-printed robotic grippers, tailored for combined precision and coarse robotics assembly. The proposed methodology leverages topology optimization to develop multi-scale-compliant mechanisms, comprising a symmetrical continuum structure of five beams. The proposed methodology centers on the hybrid kinematics for precision and coarse operations of the gripper, parametrizing beam deformations in response to a defined set of boundary conditions and varying input loads. The research employs topology analysis to draw a clear correlation between input load and resultant motion, with a particular emphasis on the mechanism’s capacity to integrate both fine and coarse movements efficiently. Additionally, the paper pioneers an innovative solution to the ubiquitous point-contact problem encountered in grasping, intricately weaving it with the stiffness matrix. The overarching aim remains to provide a streamlined design methodology, optimized for manufacturability, by harnessing the capabilities of contemporary 3D fabrication techniques. This multifaceted approach, underpinned by the multiscale grasping method, promises to significantly advance the domain of robotic gripping and manipulation across applications such as micro-assembly, biomedical manipulation, and industrial robotics. Full article

The present article presents a system of symmetric equations defining multi-cubic mappings (M-CMs). Next, we describe how these mappings are structured and obtain an equation for describing them. Moreover, we Address the Hyers-Ulam stability (H-UStab) in the sense of Găvruţa for a symmetric multi-cubic equation through the application of the so-called Hyers (direct) method in the setting of 2-Banach spaces. For a typical case, by means of a norm, induced from a 2-norm of ${\mathbb{R}}^d$, we examine the stability and hyperstability of a mapping $f:{\mathbb{R}}^{dn}⟶{\mathbb{R}}^d$ by using a fixed point (FP) result. Full article

Fluid dynamic noise produced by eddy disturbances and friction along pipe walls poses a significant challenge in natural gas transmission and distribution stations. (K)TS control valves are widely used in natural gas transmission and distribution stations across Southwest China and are among the primary sources of noise in these facilities. In this study, a 3D geometric model of the (K)TS valve was developed, and the gas flow characteristics were simulated to analyze the gas flow field and sound field within the valve under varying pipeline flow velocities, outlet pressures, and valve openings. The results demonstrate that accurate calculations of the 3D valve model can be achieved with a grid cell size of 3.6 mm and a boundary layer set to 3. The noise-generating regions of the valve are concentrated around the throttle port, valve chamber, and valve inlet. The primary factors contributing to the aerodynamic noise include high gas flow velocity gradients, intense turbulence, rapid turbulent energy dissipation, and vortex formation and shedding within the valve. An increase in inlet flow velocity intensifies turbulence and energy dissipation inside the valve, while valve opening primarily influences the size of vortex rings in the valve chamber and throttle outlet. In contrast, outlet pressure exerts a relatively weak effect on the flow field characteristics within the valve. Under varying operating conditions, the noise directivity distribution remains consistent, exhibiting symmetrical patterns along the central axis of the flow channel and forming six-leaf or four-leaf flower shapes. As the distance from the monitoring point to the valve increases, noise propagation becomes more concentrated in the vertical direction of the valve. These findings provide a theoretical basis for understanding the mechanisms of aerodynamic noise generation within (K)TS control valves during natural gas transmission, and can also offer guidance for designing noise reduction solutions for valves. Full article

In this paper, we present the concept of $(\mathrm{{\rm Y}},\mathrm{\Omega })$-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement regardless of the order in which the elements are considered. Furthermore, we prove several best proximity point results by utilizing $(\mathrm{{\rm Y}},\mathrm{\Omega })$-fuzzy bipolar proximal contraction, $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Reich–Rus–Ciric type proximal contraction, $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Kannan type proximal contraction and $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Hardy–Rogers type contraction. Furthermore, we provide some non-trivial examples to show the comparison with the existing results in the literature. At the end, we present an application to find the existence and uniqueness of a solution of an integral equation by applying the main result. Full article

In 1965, H. Retkin and E. Stein defined a symmetric point set as a set of points with the same intersection numbers. In this paper, we perform a detailed analysis of symmetric point sets of the finite projective space which shows that the class of symmetric sets is very broad including caps, two-character sets and transitive sets. We derive necessary conditions for the existence of such sets. Since the most studied sets are caps and two-character sets and not much seems to be known in the general case of sets, which are different from caps, with more than two intersection numbers, by using incidence-preserving group actions, symmetric point sets with few intersection numbers are provided. The results indicate that any finite projective space contains symmetric sets with few intersection numbers. Full article

In this paper, we present Proinov-type fixed point theorems in the setting of bi-polar metric spaces and fuzzy bi-polar metric spaces. Fuzzy bi-polar metric spaces with symmetric property extend classical metric spaces to address dual structures and uncertainty, ensuring consistency and balance. We provide different concrete conditions on the real-valued functions $\Omega ,\Pi :\left(0,\infty \right)\to \mathbb{R}$ for the existence of fixed points via the $(\Omega ,\Pi )$-contraction in bi-polar metric spaces. Further, we define real-valued functions $\Omega ,\Pi :(0,1]\to \mathbb{R}$ to obtain fixed point theorems in fuzzy bi-polar metric spaces. We apply $\left(\Omega ,\Pi \right)$ fuzzy bi-polar version of a Banach fixed point theorem to show the existence of solutions. Furthermore, we provide some non-trivial examples to show the validity of our results. In the end, we find the existence and uniqueness of a solution of integral equations and boundary value problem used in chemical sciences by applying main results. Full article

In this paper, we give examples that improve the lower bound on the maximum number of halving lines for sets in the plane with 35, 59, 95, and 97 points and, as a consequence, we improve the current best upper bound of the rectilinear crossing number for sets in the plane with 35, 59, 95, and 97 points, provided that a conjecture included in the literature is true. As another consequence, we also improve the lower bound on the maximum number of halving pseudolines for sets in the plane with 35 points. These examples, and the recursive bounds for the maximum number of halving lines for sets with an odd number of points achieved, give a new insight in the study of the rectilinear crossing number problem, one of the most challenging tasks in Discrete Geometry. With respect to this problem, it is conjectured that, for all n multiples of 3, there are 3-symmetric sets of n points for which the rectilinear crossing number is attained. Full article