Search Results (182)

The dimension-balanced cycle (DBC) problem is new in graph theory, with applications such as 3D stereogram reconstruction. In a graph whose edges are partitioned into k dimensions, a cycle is dimension-balanced if edge counts across dimensions differ by at most one. When such a cycle is Hamiltonian, it is called a dimension-balanced Hamiltonian cycle (DBH). Since DBHs do not always exist, a relaxed notion—the weakly dimension-balanced Hamiltonian (WDBH) cycle—was considered, allowing a difference of up to three. We prove that WDBH always exists in any 3-dimensional toroidal mesh graph T_m,n,r for all positive integers m, n, and r. Full article

This study aims to investigate the computation of the partition dimension of various anti-myocardial infarction drugs, a graph-theoretical invariant of molecular graphs representing these drugs, for understanding and computationally characterizing structural properties of molecular networks. To improve the computational modeling of this topological invariant, advanced neural network techniques, specifically graph neural networks (GNNs) and deep neural networks (DNNs), are adopted. The GNN captures topological and molecular connection features from the molecular graph structures, which are then input into the DNN model. The DNN further processes these features to estimate the partition dimension, evaluating training performance, performing regression analysis, and producing error histograms. The model’s predictions are validated against reference values. Moreover, by analyzing the role that symmetry plays in determining the calculation of partition dimension, studying how the GNN takes advantage of permutation invariance concept related to symmetry principles to provide the DNN with symmetry-invariant features, and relating the degree of molecular symmetry to the predictive model’s accuracy and performance, its structural interpretation rather than direct chemical behavior. This dual-model approach permits a comprehensive evaluation of the model’s effectiveness in apprehending the structural characteristics of molecular graphs derived from drug molecules. The results are explicated in detail, focused on prediction accuracy, error distributions, and regression results. Moreover, this graph-theoretical metric analysis of partition dimension supports structure-based drug analysis and computational modeling, rather than direct prediction of pharmacokinetic properties, by integrating artificial neural network applications into pharmaceutical research. Full article

The electronic band structure of two-dimensional lithium is calculated using the Dirac equation. Lithium is modeled as a two-dimensional square lattice in which the two strongly bound inner electrons and the fixed nucleus are treated as a positively charged ion (+e), while the outer electron is assumed to be uniformly distributed within the cell. The electronic potential is obtained by considering Coulomb-type interactions between the charges inside the unit cell and those in the surrounding cells. A numerical method that divides the unit cell into small pieces is employed to calculate the potential and then the Fourier coefficients are obtained. The Bloch method is used to determine the energy bands, leading to an eigenvalue matrix equation (in momentum space) of infinite dimension, which is truncated and solved using standard matrix diagonalization techniques. Convergence is analyzed with respect to the key parameters influencing the calculation: the lattice period, the dimension of the eigenvalue matrix, the unit-cell partition used to compute the potential’s Fourier coefficients, and the number of neighboring cells that contribute to the electronic interaction. Full article

We develop a topological-combinatorial framework applying classical Ramsey theory to systems of arcs connecting points on Jordan curves and their higher-dimensional analogues. A Jordan curve Λ partitions the plane into interior and exterior regions, enabling a canonical two-coloring of every arc connecting points on Λ according to whether its interior lies in Int(Λ) or Ext(Λ). Using this intrinsic coloring, we prove that any configuration of six points on Λ necessarily contains a monochromatic triangle, and that this property is invariant under all homeomorphisms of the plane. Extending the construction by including arcs lying on Λ itself yields a natural three-coloring, from which the classical value $R\left(3,3.3\right)=17$ guarantees the appearance of monochromatic triangles for sufficiently large point sets. For infinite point sets on Λ, the infinite Ramsey theorem ensures the existence of infinite monochromatic cliques, which we likewise show to be preserved under arbitrary topological deformations. The framework extends to Jordan surfaces and Jordan–Brouwer hypersurfaces in higher dimensions, where interior, exterior, and boundary regions again generate canonical colorings and Ramsey-type constraints. These results reveal a general principle: the separation properties of codimension-one topological boundaries induce universal combinatorial structures—such as monochromatic triangles and infinite monochromatic subsets—that are stable under continuous deformations. The approach offers new links between geometric topology, extremal combinatorics, and the analysis of constrained networks and interfaces. Full article

To address the challenges in unstructured orchard environments, including high geometric similarity between fruit trees (with the measured average Euclidean distance difference between point cloud descriptors of adjacent trees being less than 0.5 m), significant dynamic interference (e.g., interference from pedestrians or moving equipment can occur every 5 min), and uneven terrain, this paper proposes an improved mapping algorithm named OSC-LIO (Orchard Scan Context Lidar Inertial Odometry via Smoothing and Mapping). The algorithm designs a dynamic point filtering strategy based on Euclidean clustering and spatiotemporal consistency within a 5-frame sliding window to reduce the interference of dynamic objects in point cloud registration. By integrating local semantic features such as fruit tree trunk diameter and canopy height difference, a two-tier verification mechanism combining “global and local information” is constructed to enhance the distinctiveness and robustness of loop closure detection. Motion compensation is achieved by fusing data from an Inertial Measurement Unit (IMU) and a wheel odometer to correct point cloud distortion. A three-level hierarchical indexing structure—”path partitioning, time window, KD-Tree (K-Dimension Tree)”—is built to reduce the time required for loop closure retrieval and improve the system’s real-time performance. Experimental results show that the improved OSC-LIO system reduces the Absolute Trajectory Error (ATE) by approximately 23.5% compared to the original LIO-SAM (Tightly coupled Lidar Inertial Odometry via Smoothing and Mapping) in a simulated orchard environment, while enabling stable and reliable path planning and autonomous navigation. This study provides a high-precision, lightweight technical solution for autonomous navigation in orchard scenarios. Full article

Understanding how carnivores coexist is central to ecological theory and conservation. Coexistence among sympatric species arises through niche partitioning across spatial, temporal, and trophic dimensions, yet these mechanisms remain poorly explored in Central African forests where leopards (Panthera pardus) and African golden cats (Caracal aurata) act as dominant and subordinate carnivores. Using camera trap data and molecular scat analyses from two sites in northern Congo, we provided the first robust leopard density estimates for the region (i.e., semideciduous forests in Central Africa) and assessed coexistence mechanisms between the two felids across spatial, temporal, and trophic axes. Spatially explicit capture–recapture models revealed comparable leopard densities across sites (5–6 individuals/100 km²), exceeding the regional average for Central and East Africa. Spatiotemporal occupancy models indicated spatial and temporal overlap, with no evidence of predictive or reactive temporal avoidance, though fine-scale co-occurrence declined near linear forest features (i.e., main rivers and roads) where both species’ marginal occupancy was highest. Conversely, dietary analyses showed trophic segregation: leopards consumed medium- to large-sized ungulates (>20 kg), whereas golden cats relied on smaller prey (≤5 kg), identifying trophic partitioning as the main axis facilitating coexistence in this prey-rich system. Maintaining prey diversity and minimizing disturbance are key to sustaining both species and their coexistence mechanisms. Such multidimensional approaches are essential to understand intraguild interactions and anticipate community shifts under increasing pressure. Full article

Establishing a reduced-order model (ROM) of the wind turbine generator system (WTGS) preserving transient characteristics is a fundamental requirement for the transient stability analysis of power systems. This study introduces a novel dimension reduction framework based on trajectory eigenvalues, integrated with virtual inertia control (VIC). The framework facilitates multi-timescale state variable partitioning through a reversible mapping, which is derived from eigenvalue dominance and participation metrics. Based on this, dimension reduction is performed using singular perturbation theory (SPT). Taking a direct-drive wind turbine generator as an example, this paper establishes a ROM of the WTGS with VIC preserving transient characteristics, based on the proposed reduction method. Comprehensive time-domain simulations in MATLAB/Simulink validate the model’s accuracy and computational efficacy. Full article

In this study, we examine the impact of government green subsidies on corporate ESG performance. We employ the method of double machine learning for causal inference. We use all A-share listed companies in China from 2013 to 2023 as the research sample. After excluding financial and insurance companies, those in ST/*ST/PT status, and those with missing key indicators, we ultimately obtain 2337 sample observations. Our baseline results based on double machine learning reveal government green subsidies significantly enhance corporate ESG performance. The findings suggest that this enhancement occurs notably through the mediating variables of digital technology innovation and technology conversion efficiency. We also introduce heterogeneous dimensions such as the level of digital inclusive finance, the intensity of environmental regulations, and the scale of enterprises. Meanwhile, we adopt multiple robustness test methods, including changing the dependent variable, excluding data from special years, controlling for exogenous policy shocks, using instrumental variable methods, and resetting the double machine learning model—adjusting the sample partition ratio from the original 1:4 to 1:9 and replacing the prediction algorithm from random forest to gradient boosting, lasso regression, and ensemble machine learning methods—to ensure the reliability and scientific nature of the research conclusions. Additional tests indicate that the regression coefficient remains positive and is significant, indicating the robustness of our conclusions. This research offers implications for further optimizing the design of government green subsidy policies, and to promote the improvement of enterprises’ ESG performance and economic green transformation. Full article

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We first present a detailed geometric and analytical foundation for intrinsic quantization on the unit sphere, including definitions of great and small circles, spherical triangles, geodesic distance, Slerp interpolation, the Fréchet mean, spherical Voronoi regions, centroid conditions, and quantization dimensions. Building upon this framework, we develop explicit continuous and discrete quantization models on spherical curves, namely great circles, small circles, and great circular arcs—supported by rigorous derivations and pedagogical exposition. For uniform continuous distributions, we compute optimal sets of n-means and the associated quantization errors on these curves; for discrete distributions, we analyze antipodal, equatorial, tetrahedral, and finite uniform configurations, illustrating convergence to the continuous model. The central conclusion is that for a uniform probability distribution supported on a one-dimensional geodesic subset of total length L, the optimal n-means form a uniform partition and the quantization error satisfies $V_n=L^2/\left(12n^2\right)$.The exposition emphasizes geometric intuition, detailed derivations, and clear step-by-step reasoning, making it accessible to beginning graduate students and researchers entering the study of quantization on manifolds. This article is intended as an expository and tutorial contribution, with the main emphasis on geometric reformulation and pedagogical clarity of intrinsic quantization on spherical curves, rather than on the development of new asymptotic quantization theory. Full article

As a multi-switching power electronic circuit with complex variable topology, the three-level active neutral point clamped (ANPC) converter is a complex system with strong coupling and low linearity. It has numerous high-speed switching devices, a large number of switch states, and a high matrix dimension. Modeling each switch will undoubtedly further increase the circuit size. While in real-time simulation, updating all states of the model to produce outputs within a single time step results in a significant computational load, causing an increasing consumption of FPGA hardware resources as the number of switches and circuit size grow. In order to solve this problem, the current common practice is to decompose the entire complex power electronic system into smaller serial subsystems for modeling. The overall modeling approach for small circuits can be achieved, but when the size of the circuit increases, the overall modeling complexity and difficulty are increased or even impossible to achieve. Decoupling power electronic circuits with this decomposition into subsystem modeling not only reduces the matrix dimension and simplifies the modeling process, but also improves the computational efficiency of the real-time simulator. However, this inevitably generates simulation delays between different subsystems, leading to numerical oscillations. In an effort to overcome this challenge, this paper adopts the method of parallel computation after subsystem partitioning. There is no one-beat delay between different subsystems, and there is no loss of accuracy, which can improve the numerical stability of the modeling and can effectively reduce the step length of real-time simulation and alleviate the problem of real-time simulation resource consumption. In addition, to address the problems of low accuracy due to the traditional forward Euler method as a solver and the possibility of significant errors at some moments, this paper uses a modified prediction correction method to solve the discrete mathematical model, which provides higher accuracy as well as higher stability. And, different from the traditional control method, this paper uses an improved FCS-MPC strategy to control the switching transients of the ANPC model, which achieves a very good control effect. Finally, a simulation step size of less than 60 ns is successfully realized by empirical demonstration on the Speedgoat test platform. Meanwhile, the accuracy of our model can be objectively evaluated by comparing it with the simulation results of the Matlab Simpower system. Full article

Ecological theory suggests that interspecific interactions and environmental heterogeneity promote temporal niche partitioning, whereby species segregate their activity along diel and seasonal axes. For ectotherms, temperature is a critical niche dimension because heat availability regulates activity and phenology. Here, we used data from a hyperdiverse rainforest in the Ecuadorian Amazon to compare community dynamics across two temporal scales and to test their relationship with temperature fluctuations. Butterflies were periodically sampled using Pollard walks in a permanent plot over eight field campaigns spanning two years. We compared environmental temperature fluctuations, diversity metrics, and niche-overlap estimates of community assemblages at both diel and seasonal scales. We recorded 1003 individuals representing 222 species. Temperature differences among seasons were comparable to those observed across times of day. Consistently, our analyses revealed distinct community assemblages across both diel and seasonal scales. Furthermore, butterfly activity tended to increase during warmer hours and in warmer seasons, yet overlap in activity within these timeframes was low at both the species and subfamily levels. These results highlight the contribution of both abiotic drivers and biotic interactions in structuring butterfly temporal abundance. More broadly, our study underscores the importance of explicitly considering temporal dimensions when examining tropical biodiversity. Full article

Phase optimization, aimed to enhance phase signal-to-noise ratio, is a critical component of the distributed scatterer interferometric synthetic aperture radar technique and directly determines the fineness and reliability of deformation monitoring. As a state-of-the-art method that balances computational efficiency and optimization performance in high-dimensional data environments, sequential phase optimization has been widely studied. However, the improper matrix partitioning and discontinuous sequence compensation in current sequential methods severely restrict their optimization performance. To address these limitations, an adaptive sequential phase optimization method (AdSeq) based on coherence stability detection and adjustment correction is proposed. A submatrix dimension adaptive estimation model driven by coherence stability detection is first established based on persistent exceedance detection analysis. Then, a covariance matrix adaptive sequential partitioning strategy is developed by introducing the submatrix overlap criterion. Finally, a phase reference correction model based on weighted least squares adjustment is proposed to improve phase continuity and overall optimization performance. Experiments with simulated and real datasets are performed to comprehensively evaluate the optimization performance. Experimental results demonstrate that, compared with traditional phase optimization methods, the monitoring point density obtained by AdSeq increased by over 21.07%, and the deformation monitoring accuracy reached 16.49 mm, representing an improvement exceeding 10.09%. These results confirm that the proposed AdSeq method achieves superior noise robustness and phase optimization performance, and provides a higher deformation monitoring accuracy. Full article

Hakka traditional vernacular dwellings embody regionally specific climatic adaptation strategies. This study takes the Meizhou Guangludi enclosed house as a case study to evaluate its climate adaptability with longevity and passive survivability factors of the Hakka three-hall enclosed house under subtropical climatic conditions. A mixed research method is employed, integrating visualized parametric modeling analysis and on-site measurement comparisons to quantify wind, temperature, solar radiation/illuminance, and humidity, along with human comfort zone limits and building environment. The results reveal that nature erosion in the Guangludi enclosed house is the most pronounced during winter and spring, particularly on exterior walls below 2.8 m. Key issues include bulging, spalling, molding, and fractured purlins caused by wind-driven rain, exacerbated by low wind speeds and limited solar exposure, especially at test spots like the E8–E10 and N1–N16 southeast and southern walls below 1.5 m. Fungal growth and plant intrusion are severe where surrounding trees and fengshui forests restrict wind flow and lighting. In terms of passive survivability, the Guangludi enclosed house has strong thermal insulation and buffering, aided by the Huatai mound; however, humidity and day illuminance deficiencies persist in the interstitial spaces between lateral rooms and the central hall. To address these issues, this study proposes strategies such as adding ventilation shafts and flexible partitions, optimizing patio dimensions and window-to-wall ratios, retaining the spatial layout and Fengshui pond to enhance wind airflow, and reinforcing the identified easily eroded spots with waterproofing, antimicrobial coatings, and extended eaves. Through parametric simulation and empirical validation, this study presents a climate-responsive retrofit framework that supports the sustainability and conservation of the subtropical Hakka enclosed house. Full article

As a new generation 3D video coding standard, 3D-HEVC offers highly efficient compression. However, its recursive quadtree partitioning mechanism and frequent rate-distortion optimization (RDO) computations lead to a significant increase in coding complexity. Particularly, intra-frame coding in depth maps, which incorporates tools like depth modeling modes (DMMs), substantially prolongs the decision-making process for coding unit (CU) partitioning, becoming a critical bottleneck in compression encoding time. To address this issue, this paper proposes a fast CU partitioning framework based on hierarchical feature fusion convolutional neural networks (HFF-CNNs). It aims to significantly accelerate the overall encoding process while ensuring excellent encoding quality by optimizing depth map CU partitioning decisions. This framework synergistically captures CU’s global structure and local details through multi-scale feature extraction and channel attention mechanisms (SE module). It introduces the wavelet energy ratio designed for quantifying the texture complexity of depth map CU and the quantization parameter (QP) that reflects the encoding quality as external features, enhancing the dynamic perception ability of the model from different dimensions. Ultimately, it outputs depth-corresponding partitioning predictions through three fully connected layers, strictly adhering to HEVC’s quad-tree recursive segmentation mechanism. Experimental results demonstrate that, across eight standard test sequences, the proposed method achieves an average encoding time reduction of 48.43%, significantly lowering intra-frame encoding complexity with a BDBR increment of only 0.35%. The model exhibits outstanding lightweight characteristics with minimal inference time overhead. Compared with the representative methods under comparison, this method achieves a better balance between cross-resolution adaptability and computational efficiency, providing a feasible optimization path for real-time 3D-HEVC applications. Full article

This paper presents an in-depth review of cybersecurity challenges and advanced solutions in modern power-generation systems, with particular emphasis on smart grids. It examines vulnerabilities in devices such as smart meters (SMs), Phasor Measurement Units (PMUs), and Remote Terminal Units (RTUs) to cyberattacks, including False Data Injection Attacks (FDIAs), Denial of Service (DoS), and Replay Attacks (RAs). The study evaluates cutting-edge detection and mitigation techniques, such as Cluster Partition, Fuzzy Broad Learning System (CP-BLS), multimodal deep learning, and autoencoder models, achieving detection accuracies of (up to 99.99%) for FDIA identification. It explores critical aspects of power generation, including resource assessment, environmental and climatic factors, policy and regulatory frameworks, grid and storage integration, and geopolitical and social dimensions. The paper also addresses the transmission and distribution (T&D) system, emphasizing the role of smart-grid technologies and advanced energy-routing strategies that leverage Artificial Neural Networks (ANNs), Generative Adversarial Networks (GANs), and game-theoretic approaches to optimize energy flows and enhance grid stability. Future research directions include high-resolution forecasting, adaptive optimization, and the integration of quantum–AI methods to improve scalability, reliability, and resilience. Full article