Search Results (22)

Manifold learning is a significant computer vision task used to describe high-dimensional visual data in lower-dimensional manifolds without sacrificing the intrinsic structural properties required for 3D reconstruction. Isomap, Locally Linear Embedding (LLE), Laplacian Eigenmaps, and t-SNE are helpful in data topology preservation but are typically indifferent to the intrinsic differential geometric characteristics of the manifolds, thus leading to deformation of spatial relations and reconstruction accuracy loss. This research proposes an Optimization of Manifold Learning using Differential Geometry Framework (OML-DGF) to overcome the drawbacks of current manifold learning techniques in 3D reconstruction. The framework employs intrinsic geometric properties—like curvature preservation, geodesic coherence, and local–global structure correspondence—to produce structurally correct and topologically consistent low-dimensional embeddings. The model utilizes a Riemannian metric-based neighborhood graph, approximations of geodesic distances with shortest path algorithms, and curvature-sensitive embedding from second-order derivatives in local tangent spaces. A curvature-regularized objective function is derived to steer the embedding toward facilitating improved geometric coherence. Principal Component Analysis (PCA) reduces initial dimensionality and modifies LLE with curvature weighting. Experiments on the ModelNet40 dataset show an impressive improvement in reconstruction quality, with accuracy gains of up to 17% and better structure preservation than traditional methods. These findings confirm the advantage of employing intrinsic geometry as an embedding to improve the accuracy of 3D reconstruction. The suggested approach is computationally light and scalable and can be utilized in real-time contexts such as robotic navigation, medical image diagnosis, digital heritage reconstruction, and augmented/virtual reality systems in which strong 3D modeling is a critical need. Full article

Underground coal mines face increasing challenges in the scheduling of Electric Rubber-Tired Vehicles (ERTVs) due to confined spaces, dynamic production demands, and the need to coordinate multiple constraints such as complex roadway topologies, strict time windows, and limited charging resources in the context of clean energy transitions. This study presents a Constraint Programming (CP)-based optimization framework that integrates Virtual Charging Station Mapping (VCSM) and sensor fusion positioning to decouple spatiotemporal charging conflicts and applies a dynamic topology adjustment algorithm to enhance computational efficiency. A novel RFID–vision fusion positioning system, leveraging multi-source data to mitigate signal interference in underground environments, provides real-time, reliable spatiotemporal coordinates for the scheduling model. The proposed multi-objective model systematically incorporates hard time windows, load limits, battery endurance, and roadway regulations. Case studies conducted using real-world data from a large-scale Chinese coal mine demonstrate that the method achieves a 17.6% reduction in total transportation mileage, decreases charging events by 60%, and reduces vehicle usage by approximately 33%, all while completely eliminating time window violations. Furthermore, the computational efficiency is improved by 54.4% compared to Mixed-Integer Linear Programming (MILP). By balancing economic and operational objectives, this approach provides a robust and scalable solution for sustainable ERTV scheduling in confined underground environments, with broader applicability to industrial logistics and clean mining practices. Full article

Aiming at the limitations of existing multisensor fault diagnosis methods for rolling bearings in real industrial scenarios, this paper proposes an innovative intuitionistic fuzzy weighted least squares twin support higher-order tensor machine (IFW-LSTSHTM) model, which realizes a breakthrough in the noise robustness, adaptability to the working conditions, and the class imbalance processing capability. First, the multimodal feature tensor is constructed: the fourier synchro-squeezed transform is used to convert the multisensor time-domain signals into time–frequency images, and then the tensor is reconstructed to retain the three-dimensional structural information of the sensor coupling relationship and time–frequency features. The nonlinear feature mapping strategy combined with Tucker decomposition effectively maintains the high-order correlation of the feature tensor. Second, the adaptive sample-weighting mechanism is developed: an intuitionistic fuzzy membership score assignment scheme with global–local information fusion is proposed. At the global level, the class contribution is assessed based on the relative position of the samples to the classification boundary; at the local level, the topological structural features of the sample distribution are captured by K-nearest neighbor analysis; this mechanism significantly improves the recognition of noisy samples and the handling of class-imbalanced data. Finally, a dual hyperplane classifier is constructed in tensor space: a structural risk regularization term is introduced to enhance the model generalization ability and a dynamic penalty factor is set to set adaptive weights for different categories. A linear equation system solving strategy is adopted: the nonparallel hyperplane optimization is converted into matrix operations to improve the computational efficiency. The extensive experimental results on the two rolling bearing datasets have verified that the proposed method outperforms existing solutions in diagnostic accuracy and stability. Full article

Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exponential monomials in the space; in other words, the locally compact abelian group of the reals is synthesizable. This result does not hold for continuous functions in several real variables, as was shown by D.I. Gurevich’s counterexamples. On the other hand, if two discrete abelian groups have this synthesizability property, then so does their direct sum, as well. In this paper, we show that if two locally compact abelian groups have this synthesizability property and at least one of them is discrete, then their direct sum is synthesizable. In fact, more generally, we show that any extension of a synthesizable locally compact abelian group by a synthesizable discrete abelian group is synthesizable. This is an important step toward the complete characterization of synthesizable locally compact abelian groups. Full article

In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers ${\mathbb{R}}_0^{+}$. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topological properties of semi-vector spaces, such as completeness and separability, are also investigated here. New families of semi-vector spaces derived from the semi-metric, semi-norm and semi-inner product, among others, are exhibited. Furthermore, we show several new results concerning semi-algebras. After this theoretical approach, we apply such a theory in fuzzy automata. More precisely, we describe the semi-algebra of A-fuzzy regular languages and we apply the theory of fuzzy automata for counting patterns in DNA sequences. Full article

A real topological vector space is said to have the Krein–Milman property if every bounded, closed, convex subset has an extreme point. In the case of every bounded, closed, convex subset is the closed convex hull of its extreme points, then we say that the topological vector space satisfies the strong Krein–Milman property. The strong Krein–Milman property trivially implies the Krein–Milman property. We provide a sufficient condition for these two properties to be equivalent in the class of Hausdorff locally convex real topological vector spaces. This sufficient condition is the Bishop–Phelps property, which we introduce for real topological vector spaces by means of uniform convergence linear topologies. We study the inheritance of the Bishop–Phelps property. Nontrivial examples of topological vector spaces failing the Krein–Milman property are also given, providing us with necessary conditions to assure that the Krein–Milman property is satisfied. Finally, a sufficient condition to assure the Krein–Milman property is discussed. Full article

In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions. Full article

The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics. Full article

This paper introduces a sensorless nonlinear control scheme based on feedback linearization control (FLC) of an open-end winding five-phase induction motor (OeW-5PIM) topology fed by a dual neutral point clamped (NPC) inverter. The suggested sensorless control is combined with the sliding mode (SM) controller to improve the dynamic performance (i.e., rising time, overshoot, etc.) of the studied motor. Furthermore, a stator-current-based model reference adaptive system (SC-MRAS) estimator is designed for the estimation of the rotor flux and the motor speed. In parallel, to enhance the robustness of the designed sensorless control against motor parameter changes, an adaptive estimation method is suggested to estimate the rotor and stator resistances during low-speed ranges. The estimation method of motor resistances is associated with the suggested sensorless control to further improve the speed estimation accuracy and minimize the speed estimation error. Finally, the effectiveness and correctness of the suggested control with the examined estimators are validated in real-time implementation using a hardware-in-the-loop (HIL) based on the dSpace 1103 board. Full article

Topological spaces can be induced by various algebraic ordering relations such as, linear, partial and the inclusion-ordering of open sets forming chains and chain complexes. In general, the classifications of covering spaces are made by using fundamental groups and lifting. However, the Riesz ordered n-spaces and Urysohn interpretations of real-valued continuous functions as ordered chains provide new perspectives. This paper proposes the formulation of covering spaces of n-space charts of a foliated n-manifold containing linearly ordered chains, where the chains do not form topologically separated components within a covering section. The chained subspaces within covering spaces are subjected to algebraic split–join operations under a bijective function within chain-subspaces to form simply directed chains and twisted chains. The resulting sets of chains form simply directed chain-paths and oriented chain-paths under the homotopy path-products involving the bijective function. It is shown that the resulting embedding of any chain in a leaf of foliated n-manifold is homogeneous and unique. The finite measures of topological subspaces containing homotopies of chain-paths in covering spaces generate multiplicative and cyclic group varieties of different orders depending upon the types of measures. As a distinction, the proposed homotopies of chain-paths in covering spaces and the homogeneous chain embedding in a foliated n-manifold do not consider the formation of circular nerves and the Nachbin topological preordering, thereby avoiding symmetry/asymmetry conditions. Full article

Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly imply an optimal selection of spreaders used to diffuse and indoctrinate neighboring peers, often overlooking realistic limitations of time, space, and budget. Thus, finding trade-offs between a minimal number of influential nodes and maximizing opinion coverage is a relevant scientific problem. Therefore, we study the relationship between specific parameters that influence the effectiveness of opinion diffusion, such as the underlying topology, the number of active spreaders, the periodicity of spreader activity, and the injection strategy. We introduce an original benchmarking methodology by integrating time and cost into an augmented linear threshold model and measure indoctrination expense as a trade-off between the cost of maintaining spreaders’ active and real-time opinion coverage. Simulations show that indoctrination expense increases polynomially with the number of spreaders and linearly with the activity periodicity. In addition, keeping spreaders continuously active instead of periodically activating them can increase expenses by 69–84% in our simulation scenarios. Lastly, we outline a set of general rules for cost-effective opinion injection strategies. Full article

Feature matching is a key method of feature-based image registration, which refers to establishing reliable correspondence between feature points extracted from two images. In order to eliminate false matchings from the initial matchings, we propose a simple and efficient method. The key principle of our method is to maintain the topological and affine transformation consistency among the neighborhood matches. We formulate this problem as a mathematical model and derive a closed solution with linear time and space complexity. More specifically, our method can remove mismatches from thousands of hypothetical correspondences within a few milliseconds. We conduct qualitative and quantitative experiments on our method on different types of remote-sensing datasets. The experimental results show that our method is general, and it can deal with all kinds of remote-sensing image pairs, whether rigid or non-rigid image deformation or image pairs with various shadow, projection distortion, noise, and geometric distortion. Furthermore, it is two orders of magnitude faster and more accurate than state-of-the-art methods and can be used for real-time applications. Full article

Emerging wide bandgap (WBG) semiconductors, such as silicon carbide (SiC), will enable chargers to operate at higher switching frequencies, which grants the ability to deliver high power and enhances efficiency. This paper addresses the modeling of a double-sided cooling (DSC) SiC technology-based off-board charger for battery electric buses (BEBs) and the design of its control and real-time (RT) implementation. A three-phase active front-end (AFE) rectifier topology is considered in the modeling and control system design for the active part of the DC off-board charger. The control system consists of a dual-loop voltage–current controller and is used to ensure AC to DC power conversion for charging and to achieve the targeted grid current total harmonic distortion (THD) and unity power factor (PF). Linear and nonlinear simulation models are developed in MATLAB/Simulink for optimum control design and to validate the voltage and current control performances. Four types of controllers (i.e., proportional–integral (PI), lead–lag, proportional–resonant (PR), and modified proportional–resonant (MPR)) are designed as current controllers, and a comparative analysis is conducted on the simulation model. In addition, the final design of the dual-loop controller is implemented on the RT–FPGA platform of dSpace MicroLabBox. It is then tested with the charger to validate the control performance with experimental data. The simulation and experimental results demonstrate the correct operation of the converter control performance by tracking the reference commands. Full article

With the emergence of various types of applications such as delay-sensitive applications, future communication networks are expected to be increasingly complex and dynamic. Network Function Virtualization (NFV) provides the necessary support towards efficient management of such complex networks, by virtualizing network functions and placing them on shared commodity servers. However, one of the critical issues in NFV is the resource allocation for the highly complex services; moreover, this problem is classified as an NP-Hard problem. To solve this problem, our work investigates the potential of Deep Reinforcement Learning (DRL) as a swift yet accurate approach (as compared to integer linear programming) for deploying Virtualized Network Functions (VNFs) under several Quality-of-Service (QoS) constraints such as latency, memory, CPU, and failure recovery requirements. More importantly, the failure recovery requirements are focused on the node-outage problem where outage can be either due to a disaster or unavailability of network topology information (e.g., due to proprietary and ownership issues). In DRL, we adopt a Deep Q-Learning (DQL) based algorithm where the primary network estimates the action-value function Q, as well as the predicted Q, highly causing divergence in Q-value’s updates. This divergence increases for the larger-scale action and state-space causing inconsistency in learning, resulting in an inaccurate output. Thus, to overcome this divergence, our work has adopted a well-known approach, i.e., introducing Target Neural Networks and Experience Replay algorithms in DQL. The constructed model is simulated for two real network topologies—Netrail Topology and BtEurope Topology—with various capacities of the nodes (e.g., CPU core, VNFs per Core), links (e.g., bandwidth and latency), several VNF Forwarding Graph (VNF-FG) complexities, and different degrees of the nodal outage from 0% to 50%. We can conclude from our work that, with the increase in network density or nodal capacity or VNF-FG’s complexity, the model took extremely high computation time to execute the desirable results. Moreover, with the rise in complexity of the VNF-FG, the resources decline much faster. In terms of the nodal outage, our model provided almost 70–90% Service Acceptance Rate (SAR) even with a 50% nodal outage for certain combinations of scenarios. Full article

The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function $F:X\to cc\left(Y\right)$, where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X. Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where $X={\mathbb{R}}^2$ and $Y={\mathbb{R}}^n$, $n\in \mathbb{N}$, and G is the unitary group $U\left(1\right)$. Full article