Search Results (1,398)

Finite-difference methods are widely used to solve partial differential equations in diverse practical applications. Despite their prevalence, the computational efficiency of these methods encounters limitations due to the need to solve linear equation systems through matrix inversion or iterative solver, which is particularly challenging in scenarios involving high dimensions. The demand for numerical methods with high accuracy and fast computational speed is steadily increasing. To address this challenge, we present an efficient and accurate algorithm for high-dimensional numerical modeling. This approach combines a central finite-difference method with the discrete Sine transform (DST) scheme to solve the Poisson equation under Dirichlet boundary conditions (DBCs). To balance numerical accuracy and computation, the DST scheme is applied along one direction in the 2D case and two directions in the 3D case. This strategy effectively reduces problem complexity while maintaining low computational cost. The hybrid DST-accelerated finite-difference approach substantially lowers the computational cost associated with solving the Poisson equation on large grids. Comprehensive numerical experiments for 2D and 3D Poisson equations with DBCs have been conducted. The obtained numerical results demonstrate that the proposed hybrid method not only significantly reduces the computational expenses, but also maintains the central finite-difference accuracy. Full article

In this paper, we investigate $h_2$-optimal model reduction methods for discrete-time linear time-invariant systems. Similar to the continuous-time case, we will formulate this problem as an optimization problem over a Grassmann manifold. We consider constructing reduced systems by both one-sided and two-sided projections. For one-sided projection, by utilizing the principle of the Grassmann manifold, we propose a gradient flow method and a sequentially quadratic approximation approach to solve the optimization problem. For two-sided projection, we apply the strategies of alternating direction iteration and sequentially quadratic approximation to the minimization problem and develop a numerically efficient method. One main advantage of these methods, based on the formulation of optimization over a Grassmann manifold, is that stability can be preserved in the reduced system. Several numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper. Full article

This study introduces a promising authentication framework utilizing brain–computer interface (BCI) technology to enhance both security protocols and user experience. A key strength of this approach lies in its reliance on objective, physiological signals—specifically, brainwave patterns—which are inherently difficult to replicate or forge, thereby providing a robust foundation for secure authentication. The authentication system was developed and implemented in four sequential stages: signal acquisition, preprocessing, feature extraction, and classification. Objective feature extraction methods, including Fisher’s Linear Discriminant (FLD) and Discrete Wavelet Transform (DWT), were employed to isolate meaningful brainwave features. These features were then classified using advanced machine learning techniques, with Quadratic Discriminant Analysis (QDA) and Convolutional Neural Networks (CNN) achieving accuracy rates exceeding 99%. These results highlight the effectiveness of the proposed BCI-based system and underscore the value of objective, data-driven methodologies in developing secure and user-friendly authentication solutions. To further address usability and efficiency, the number of BCI channels was systematically reduced from 64 to 32, and then to 16, resulting in accuracy rates of 92.64% and 80.18%, respectively. This reduction streamlined the authentication process, demonstrating that objective methods can maintain high performance even with simplified hardware and pointing to future directions for practical, real-world implementation. Additionally, we developed a real-time application using our custom dataset, reaching 99.75% accuracy with a CNN model. Full article

As shallow mineral resources become increasingly depleted, the search for deep-seated orebodies has emerged as a crucial focus in modern gold exploration. This study investigates Vein 171 in the Linglong gold field, Jiaodong Peninsula, using 3D attribute modeling for deep mineralization prediction and precise orebody delineation. The research integrates surface and block models through Vulcan 2021.5 3D mining software to reconstruct the spatial morphology and internal attribute distribution of the orebody. Geostatistical methods were applied to identify and process high-grade anomalies, with grade interpolation conducted using the inverse distance weighting (IDW) method. The results reveal that Vein 171 is predominantly controlled by NE-trending extensional structures, and grade enrichment occurs in zones where fault dips transition from steep to gentle. The grade distribution of the 171₁ and 171_sub-1 orebodies demonstrates heterogeneity, with high-grade clusters exhibiting periodic and discrete distributions along the dip and plunge directions. Key enrichment zones were identified at elevations of –1800 m to –800 m near the bifurcation of the Zhaoping Fault, where stress concentration and rock fracturing have created complex fracture networks conducive to hydrothermal fluid migration and gold precipitation. Nine verification drillholes in key target areas revealed 21 new mineralized bodies, resulting in an estimated additional 2.308 t of gold resources and validating the predictive accuracy of the 3D model. This study not only provides a reliable framework for deep prospecting and mineral resource expansion in the Linglong Goldfield but also serves as a reference for exploration in similar structurally controlled gold deposits globally. 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

We analyzed the accuracy of digitized adiabatic quantum computing to form the entangled three-qubit Greenberger–Horne–Zeilinger (GHZ) state on two IBM quantum computers and four quantum simulators by comparison with direct calculations using a Python code (version 3.12). We initialized three-qubit systems in the ground state of the Hamiltonian for noninteracting spins in an applied magnetic field in the x direction. We then gradually varied the Hamiltonian to an Ising model form with nearest-neighbor zz spin coupling with an eight-step discretization. The von Neumann entropy provides an indicator of the accuracy of the discretized adiabatic evolution. The von Neumann entropy of the density matrix from the Python code remains very close to zero, while the von Neumann entropy of the density matrices on the quantum computers increases almost linearly with the step number in the process. The GHZ witness operator indicates that the quantum simulators incorporate a GHZ component in part. The states on the two quantum computers acquire partial GHZ character, even though the trace of the product of the GHZ witness operator with the density matrix not only remains positive but also rises monotonically from Step 5 to Step 8. Each of the qubits becomes entangled during the adiabatic evolution in all of the calculations, as shown by the single-qubit reduced density matrices. Full article

Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To overcome these deficiencies, this paper proposes a fuzzy integral direct discrete recurrent neural network (FITDRNN) model. The FITDRNN model incorporates an integral term to counteract noise interference and employs a fuzzy logic system for dynamic adjustment of the integral parameter magnitude, thereby further enhancing its noise resistance. Theoretical analysis, combined with numerical experiments and robotic arm trajectory tracking experiments, verifies the convergence and noise resistance of the proposed FITDRNN model. Full article

Background/Objectives: Physical training and Pulmonary Rehabilitation in Patients with Cystic Fibrosis: A Systematic Review and Meta-Analysis of Clinical Trials. Pulmonary rehabilitation and physical training are essential components of the comprehensive management of patients with cystic fibrosis. Despite documented benefits for some clinical outcomes, uncertainty exists regarding their overall effects. Therefore, the objective of the present meta-analysis is to determine the effectiveness of physical training and pulmonary rehabilitation in patients with CF. Methods: This systematic review and meta-analysis of randomized controlled trials published between 1990 and 2025 was conducted using the PubMed, Cochrane Clinical Trial, SCOPUS, Science Direct, Web of Science, Scielo, and LILAC databases. The risk of bias was evaluated using the RoB 2 tool, the quality of the evidence with the Jadad scale, and the certainty of the evidence for each outcome was assessed according to GRADE guidelines. This meta-analysis was developed using the statistical packages RevMan 5.4^® and Jamovi 2.3.28^®. Results: Twenty-three studies with a total of 800 patients with CF were included. This meta-analysis showed that pulmonary rehabilitation and physical training did not affect pulmonary function, as observed in FEV1 (SMD: 0.05; 95% CI: −0.09 to 0.20; p = 0.46) and FVC (SMD: 0.11; 95% CI: −0.04 to 0.27; p = 0.14). However, it has a discrete impact on exercise capacity, producing an increase in VO₂ max (MD: 2.74; 95% CI: 0.43 to 5.04; p = 0.02). Subgroup analyses did not yield relevant findings, and sensitivity analyses did not produce modifications in the direction or magnitude of the effect. Conclusions: The intervention evaluated in this meta-analysis does not have effects on pulmonary function but may influence exercise capacity, particularly VO₂ max. It is recommended to interpret the findings with caution due to the limited certainty of the available evidence. Full article

This paper considers the multi-term subdiffusion equation with weakly singular solutions. In order to use sparser meshes near the initial time, a novel scheme (which we call the corrected L1 scheme) on graded meshes is constructed to estimate the multi-term Caputo fractional derivative by investigating a corrected term for the nonuniform L1 scheme. Combining this nonuniform corrected L1 scheme in the temporal direction and the finite element method (FEM) in the spatial direction, a fully discrete scheme for solving the multi-term subdiffusion equation is developed. The stability result of the developed scheme is given. Furthermore, the optimal pointwise-in-time error estimate of the developed scheme is derived. Finally, several numerical experiments are conducted to verify our theoretical findings. Full article

The dynamic fracture of rocks under impact loads has many engineering applications such as rock blasting. This study reviews the recent achievements of investigating rock dynamic fracturing and its application in rock blasting using computational mechanics methods and highlights the prospects of modelling them with a hybrid finite-discrete element method (HFDEM) originally developed by the authors. The review first summarizes the peculiarities of rock dynamic fracturing compared with static fracturing, which are that the physical-mechanical properties of rocks, including stress wave propagation, strength, fracture toughness, energy partition and cracking mechanism, depend on loading rate. Then the modelling of these peculiarities and their applications in rock blasting using fast developing computational mechanics methods are reviewed with a focus on the advantages and disadvantages of prevalent finite element method (FEM) as representative continuum method, discrete element method (DEM) as representative discontinuum method and combined finite-discrete element (FDEM) as representative hybrid method, which highlights FDEM is the most promising method for modelling rock dynamic fracture and blasting application as well as points out the research gaps in the field of modelling the dynamic fracture of rocks under impact loads. After that, the progress of shortening some of these gaps by developing and applying HFDEM, i.e., the authors’ version of FDEM, for modelling rock dynamic fracture and applications in rock blasting are reviewed, which include the features of modelling the effects of loading rate; stress wave propagation, reflection and absorbing as well as stress wave-induced fracture; explosive-rock interaction including detonation-induced gas expansion and flow through fracturing rock; coupled multiaxial static and dynamic loads; heterogeneous rock and rock mass with pre-existing discrete fracture network; and dynamic fracturing-induced fragment size distribution. Finally, the future directions of modelling the dynamic fracture of rocks under impact loads are highlighted and a systematic numerical approach is proposed for modelling rock blasting. Full article

Structural safety is of utmost importance for polar icebreakers under both navigation and icebreaking conditions. In this research, the Palmgren–Miner linear cumulative damage theory is employed to evaluate the structural fatigue lifespan of polar icebreakers. A spectral analysis, incorporating the time distribution coefficients for three load conditions, is executed to assess the fatigue damage at typical hot spots during navigation. For icebreaking activities, the ship–ice interaction loads with time history are simulated using the discrete ice element method, taking into account five sub-operating conditions. This simulation is coupled with rainflow counting to evaluate the fatigue damage. The results show that the cumulative fatigue damage during navigation is much less than that during icebreaking. Additionally, shoulder areas suffer more serious fatigue damage during icebreaking as a result of the direct impact of broken ice. Consequently, both navigation and icebreaking conditions should be considered in the design of hull structures and the assessment of fatigue strength for polar icebreakers. Full article

Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement learning with metaheuristic optimization through a three-stage hierarchical architecture. The framework employs Q-learning to generate a global guidance path in a discretized 2D grid environment using an eight-directional symmetric action space that embodies rotational symmetry at π/4 intervals, ensuring uniform exploration capabilities and unbiased path planning. A crucial intermediate stage transforms the discrete 2D path into a 3D initial trajectory, bridging the gap between discrete learning and continuous optimization domains. The MOPSO algorithm then performs fine-grained refinement in continuous 3D space, guided by a novel Q-learning path deviation objective that ensures continuous knowledge transfer throughout the optimization process. Experimental results demonstrate that the symmetric action space design yields 20.6% shorter paths compared to asymmetric alternatives, while the complete QL-MOPSO framework achieves 5% path length reduction and significantly faster convergence compared to standard MOPSO. The proposed method successfully generates Pareto-optimal solutions that balance multiple objectives while leveraging the symmetry-aware guidance mechanism to avoid local optima and accelerate convergence, offering a robust solution for complex multi-objective UAV path planning problems. Full article

Active inference offers a unified framework in which agents can exhibit both goal-directed and epistemic behaviors. However, implementing policy search in high-dimensional continuous action spaces presents challenges in terms of scalability and stability. Our previously proposed model, T-GLean, addressed this issue by enabling efficient goal-directed planning through low-dimensional latent space search, further reduced by conditioning on prior habituated behavior. However, the lack of an epistemic term in minimizing expected free energy limited the agent’s ability to engage in information-seeking behavior that can be critical for attaining preferred outcomes. In this study, we present EFE-GLean, an extended version of T-GLean that overcomes this limitation by integrating epistemic value into the planning process. EFE-GLean generates goal-directed policies by inferring low-dimensional future posterior trajectories while maximizing expected information gain. Simulation experiments using an extended T-maze task—implemented in both discrete and continuous domains—demonstrate that the agent can successfully achieve its goals by exploiting hidden environmental information. Furthermore, we show that the agent is capable of adapting to abrupt environmental changes by dynamically revising plans through simultaneous minimization of past variational free energy and future expected free energy. Finally, analytical evaluations detail the underlying mechanisms and computational properties of the model. Full article

To address compacted soils with high power consumption and waterlogging risks in rice–rapeseed rotation areas of the Yangtze River, this study designed a ditching machine combining a stepped cutter head and trapezoidal cleaning blade, where the mechanical synergy between components minimizes energy loss during soil-cutting and -throwing processes. We mathematically modeled soil cutting–throwing dynamics and blade traction forces, integrating soil rheological properties to refine parameter interactions. Discrete Element Method (DEM) simulations and single-factor experiments analyzed impacts of the inner/outer blade widths, blade group distance, and blade opening on power consumption. Results indicated that increasing the inner/outer blade widths (200–300 mm) by expanding the direct cutting area significantly reduced the cutter torque by 32% and traction resistance by 48.6% from reduced soil-blockage drag; larger blade group distance (0–300 mm) initially decreased but later increased power consumption due to soil backflow interference, with peak efficiency at 200 mm spacing; the optimal blade opening (586 mm) minimized the soil accumulation-induced power loss, validated by DEM trajectory analysis showing continuous soil flow. Box–Behnken experiments and genetic algorithm optimization determined the optimal parameters: inner blade width: 200 mm; outer blade width: 300 mm; blade group distance: 200 mm; and blade opening: 586 mm, yielding a simulated power consumption of 27.07 kW. Field tests under typical 18.7% soil moisture conditions confirmed a <10% error between simulated and actual power consumption (28.73 kW), with a 17.3 ± 0.5% reduction versus controls. Stability coefficients for the ditch depth, top/bottom widths exceeded 90%, and the backfill rate was 4.5 ± 0.3%, ensuring effective drainage for rapeseed cultivation. This provides practical theoretical and technical support for efficient ditching equipment in rice–rapeseed rotations, enabling resource-saving design for clay loam soils. Full article

This study evaluates the 2022 rollout of the Clean School Bus Rebate Program (CSBRP) to understand how eligibility rules and data practices shape funding distribution across communities with varying needs. We ask whether more accurate maps can improve environmental funding outcomes or whether challenges stem from how agencies define and apply eligibility criteria. Using logistic regression and dasymetric mapping, we find that prioritization criteria helped direct funds to underserved areas, but reliance on school district boundaries introduced inconsistencies that affected program reach. Including charter schools as independent applicants increased competition and sometimes diverted funds from larger public systems serving more. Our geospatial analysis shows that while refined mapping approaches improve resource targeting and reduce goal-outcome mismatches, agency discretion and administrative rules remain key factors in ensuring equitable outcomes. Full article