Search Results (143)

We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove a Cauchy characterization: fuzzy statistical convergence implies fuzzy statistical Cauchyness, while the converse holds in fuzzy-complete spaces (and in the completion, otherwise). We further develop an inclusion theory linking fuzzy strong Cesàro summability—including weighted means—to fuzzy statistical convergence. Via the discrete Q-operator, all statements transfer verbatim between nabla-left and delta-right GL forms, clarifying the binomial GL↔discrete Riemann–Liouville correspondence. Beyond structure, we propose density-based residual diagnostics for GL discretizations of fractional initial-value problems: when GL residuals are fuzzy statistically negligible, trajectories exhibit Ulam–Hyers-type robustness in the fuzzy topology. We also formulate a fuzzy Korovkin-type approximation principle under GL smoothing: Cesàro control on the test set $\{1,x,x^2\}$ propagates to arbitrary targets, yielding fuzzy statistical convergence for positive-operator sequences. Worked examples and an engineering-style case study (thermal balance with memory and bursty disturbances) illustrate how the diagnostics certify robustness of GL numerical schemes under sparse spikes and imprecise data. Full article

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

There is voluminous literature concerning the scope of topological relations that span various embedding spaces from ${\mathbb{R}}^1$ to ${\mathbb{R}}^2$, ${\mathbb{Z}}^2$ , ${\mathbb{S}}^1$ and ${\mathbb{S}}^2$ , and ${\mathbb{T}}^2$. In the case of the ${*}^1$ spaces, those relations have been considered as conceptualizations of both spatial relations and temporal relations. Missing from that list are the set of digital relations that exist within ${\mathbb{Z}}^1$ , representing discretized time, discretized ordered line segments, or discretized linear features as embedding spaces. Discretized time plays an essential role in timeseries data, spatio-temporal information systems, and geo-foundation models where time is represented in layers of consecutive spatial rasters and/or spatial vector objects colloquially referred to as space–time cubes or spatio-temporal stacks. This paper explores the digital relations that exist in ${\mathbb{Z}}^1$ interpreted as a regular topological space under the digital Jordan curve model as well as a folded-over temporal interpretation of that space for use in spatio-temporal information systems and geo-foundation models. The digital Jordan curve model represents the maximum expressive power between discretized objects, making it the ideal paradigm for a decision support system model. It identifies 34 9-intersection relations in ${\mathbb{Z}}^1$ , 42 9-intersection + margin relations in ${\mathbb{Z}}^1$ , and 74 temporal relations in ${\mathbb{Z}}^1$ , utilizing the 9+-intersection, the commercial standard for spatial information systems for querying topological relations. This work creates opportunities for better spatio-temporal reasoning capacity within spatio-temporal stacks and a more direct interface with intuitive language concepts, instrumental for effective utilization of spatial tools. Three use cases are demonstrated in the discussion, representing each of the utilities of ${\mathbb{Z}}^1$ within the spatial data science community. Full article

The decline and revitalization of vitality in historic districts of small- and medium-sized cities undergoing rapid urbanization is a frontier issue in global heritage conservation and urban regeneration. Using the East Street Historic District in Mengzi, Yunnan, as a case study, this study proposes a “space–function–time” coupling framework. Topological accessibility is quantified through space syntax metrics—Integration Value (2021) and Integration Value (2025), as well as Choice Value (2021) and Choice Value (2025)—while functional aggregation is represented by POI kernel density analysis. A “Deviation Degree–Change in Deviation Degree” model is developed to track the dynamic evolution before and after the implementation of the conservation plan (2021–2025). The findings indicate that (1) the linear correlation between Integration Value and POI density decreases from a moderate level (r = 0.42) in 2021 to a weak correlation (r = 0.32) in 2025, revealing that the spatial–functional coordination mechanism in small- and medium-sized city historic districts is considerably more fragile than in large cities; (2) Identifying streets with abnormal deviations: The primary street, Renmin Middle Road, exhibits a deviation degree as high as 4.160 due to excessive commercial aggregation, resulting in a “high accessibility–high load” imbalance. The secondary street, Dashu Street, although demonstrating a relatively high Integration Value (0.663), shows a “high accessibility–low vitality” condition due to insufficient functional facilities; (3) the Deviation Degree–Change in Deviation Degree model accurately identifies High Deviation Streets, Medium Deviation Streets, and Low Deviation Streets, and provides quantitative thresholds for planning feedback. This study introduces the Deviation Degree–Change in Deviation Degree model for the first time into the evaluation of historic district renewal in small- and medium-sized cities, establishing a closed-loop “diagnosis–intervention–reassessment” tool. The proposed framework offers both a methodological and operational paradigm for precision-oriented urban regeneration in historic districts. Full article

Quantum error correction (QEC) is crucial for achieving reliable quantum computation. Among topological QEC codes, color codes can correct bit-flip and phase-flip errors simultaneously, enabling efficient resource utilization. However, existing decoders such as the Union–Find (UF) algorithm exhibit limited accuracy under high noise levels. We propose a hybrid decoding framework that augments a modified UF algorithm—enhanced with a secondary growth strategy—with a lightweight recurrent neural network (RNN). The RNN refines the error chains identified by UF, improving resolution without significantly increasing computational overhead. The simulation results show that our method achieves notable accuracy gains over baseline UF decoding, particularly in high-error regimes, while preserving the near-linear runtime scaling and low memory footprint of UF. At higher physical error rates, RNN-based path optimization improves UF decoding accuracy by approximately 4.7%. The decoding threshold of the color code reaches 0.1365, representing an increase of about 2% compared to UF without RNN optimization. With its simple data structure and low space complexity, the proposed method is well suited for low-latency, resource-constrained quantum computing environments. Full article

In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of fuzzy linear logical functions. We call such a space a logifold. In applications, the charts are constructed by machine learning with neural network models. We implement the logifold formulation to find fuzzy domains of a dataset and to improve accuracy in data classification problems. Full article

Gear whine noise is governed not only by intentional microgeometry modifications but also by unavoidable pitch (indexing) deviation. This study presents a workflow that couples a tooth-resolved surface scan with a calibrated pitch-deviation table, both imported into a multibody dynamics (MBD) model built in MSC Adams View. Three operating scenarios were evaluated—ideal geometry, measured microgeometry without pitch error, and measured microgeometry with pitch error—at a nominal speed of 1000 r min⁻¹. Time domain analysis shows that integrating the pitch table increases the mean transmission error (TE) by almost an order of magnitude and introduces a distinct 16.66 Hz shaft order tone. When the measured tooth topologies are added, peak-to-peak TE nearly doubles, revealing a non-linear interaction between spacing deviation and local flank shape. Frequency domain results reproduce the expected mesh-frequency side bands, validating the mapping of the pitch table into the solver. The combined method therefore provides a more faithful digital twin for predicting tonal noise and demonstrates why indexing tolerances must be considered alongside profile relief during gear design optimization. Full article

A graph’s minimum cycle basis is defined as the smallest collection of cycles that exhibit linear independence in the cycle space, serving as fundamental building blocks for constructing any cyclic structure within the graph. These bases are useful in various contexts, including the intricate analysis of electrical networks, structural engineering endeavors, chemical processes, and surface reconstruction techniques, etc. This study investigates the urban road networks of six Chinese cities to analyze their topological features, node centrality, and robustness (resilience to traffic disruptions) using motif analysis and minimum cycle bases methodologies. Some interesting conclusions are obtained: the frequency of motifs containing cycles exceeds that of random networks with equivalent degree sequences; the frequency distribution of minimum cycle lengths and surface areas obeys the power-law distribution. The cycle contribution rate is introduced to investigate the centrality of nodes within road networks, and has a significant impact on the total number of cycles in the robustness analysis. Finally, we construct two types of cycle-based dual networks for urban road networks by representing cycles as nodes and establishing edges between two cycles sharing a common node and edge, respectively. The results show that cycle-based dual networks exhibit small-world and scale-free properties. The research facilitates a comprehensive understanding of the cycle structure characteristics in urban road networks, thereby providing a theoretical foundation for both subsequent modeling endeavors of transportation networks and optimization strategies for existing road infrastructure. Full article

We present a study of relic gravitational waves based on a foliated gauge field theory defined over a spacetime endowed with a noncommutative algebraic–geometric structure. As an ontological extension of general relativity—concerning manifolds, metrics, and fiber bundles—the conventional space and time coordinates, typically treated as classical numbers, are replaced by complementary quantum dual fields. Within this framework, consistent with the Bekenstein criterion and the Hawking–Hertog multiverse conception, singularities merge into a helix-like cosmic scale factor that encodes the topological transition between the contraction and expansion phases of the universe analytically continued into the complex plane. This scale factor captures the essence of an intricate topological quantum-leap transition between two phases of the branching universe: a contraction phase preceding the now-surpassed conventional concept of a primordial singularity and a subsequent expansion phase, whose transition region is characterized by a Riemannian topological foliated structure. The present linearized formulation, based on a slight gravitational field perturbation, also reveals a high sensitivity of relic gravitational wave amplitudes to the primordial matter and energy content during the universe’s phase transition. It further predicts stochastic homogeneous distributions of gravitational wave intensities arising from the interplay of short- and long-spacetime effects within the non-commutative algebraic framework. These results align with the anticipated future observations of relic gravitational waves, expected to pervade the universe as a stochastic, homogeneous background. 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

Voltage source converter-based high-voltage direct current (VSC-HVDC) systems integrated into weak AC grids may exhibit oscillation-induced instability, posing significant threats to power system security. With increasing structural complexity and diverse control strategies, the stability characteristics of VSC-HVDC system require further investigation. This paper focuses on the stability of a receiving-end VSC-HVDC system consisting of a DC voltage-controlled VSC parallel-connected to a power-controlled VSC, under various operating conditions. First, small-signal models of each subsystem were developed and a linearized full-system model was constructed based on port relationships. Then, eigenvalue and participation factor analyses were utilized to evaluate the influence of control strategy, asymmetrical grid strength, power flow direction, and tie line on the system’s small-signal stability. A feasible short-circuit ratio (SCR) region was established based on joint power–topology joint, forming a stable operating space for the system. Finally, the correctness of the theoretical analysis was validated via MATLAB/Simulink time-domain simulations. Results indicate that, in comparison to the power control strategy, the DC voltage control strategy was more sensitive to variations in the AC system and demands a strong grid, and this disparity was predominantly caused by the DC voltage control. Furthermore, the feasible region of the short-circuit ratio (SCR) diminished with the increase in the length of the tie-line and alterations in power flow direction under the mutual-support power mode, leading to a gradual reduction in the system’s stability margin. 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

Thestability of a control system is essential for its effective operation. Stability implies that small changes in input, initial conditions, or parameters do not lead to significant fluctuations in output. Various stability properties, such as inner stability, asymptotic stability, and BIBO (Bounded Input, Bounded Output) stability, are well understood for classical linear control systems in Euclidean spaces. This paper aims to thoroughly address the stability problem for a class of linear control systems defined on matrix Lie groups. This approach generalizes classical models corresponding to the latter when the group is Abelian and non-compact. It is important to note that this generalization leads to a very difficult control system, due to the complexity of the state space and the special dynamics resulting from the drift and control vectors. Several mathematical concepts help us understand and characterize stability in the classical case. We first show how to extend these algebraic, topological, and dynamical concepts from Euclidean space to a connected Lie group of matrices. Building on classical results, we identify a pathway that enables us to formulate conjectures about stability in this broader context. This problem is closely linked to the controllability and observability properties of the system. Fortunately, these properties are well established for both classes of linear systems, whether in Euclidean spaces or on Lie groups. We are confident that these conjectures can be proved in future work, initially for the class of nilpotent and solvable groups, and later for semi-simple groups. This will provide valuable insights that will facilitate, through Jouan’s Equivalence Theorem, the analysis of an important class of nonlinear control systems on manifolds beyond Lie groups. We provide an example involving a three-dimensional solvable Lie group of rigid motions in a plane to illustrate these conjectures. Full article

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed to develop new CubeSat missions. It is approved for a Phase B study. In this work we describe some design solutions adopted for the most important design drivers of the payload. In particular, we report on the payload preliminary multi-physical design, including an orbital thermal environment preliminary assessment and a implementation of the static/dynamic finite element analysis. Moreover, a method for topology optimization of relevant components is discussed. Full article

The coupled-adaptive underactuated finger offers two motion modes: pre-grasping and self-adaptive grasping. It can execute anthropomorphic pre-grasp motions before the proximal phalanx contacts an object and transitions to adaptive enveloping once contact occurs. The key to designing a coupled-adaptive finger lies in its configuration and parameter, which are crucial for achieving a more human-like design for the prosthetic hand. Thus, this paper proposes a configuration topology and parameter optimization design method for a three-joint coupled-adaptive underactuated finger. The finger mechanism utilizes a combination of prismatic pairs and a compression spring to facilitate the transition between coupled motion and adaptive motion. This enables the underactuated finger to perform coupled movements in free space and adaptive grasping motions once it makes contact with an object. Furthermore, this paper introduces a finger linkage parameter optimization method that takes the joint motion angles and overall dimensions as constraints, aiming to linearize the joint coupling motion ratios as the primary optimization objective. The design method proposed in this paper not only presents a novel linkage mechanism but also outlines and compares its isomorphic types. Furthermore, the optimization results provide an accurate maximum motion value for the finger. Full article