Advancing Open Science

In real life, almost all systems are nonlinear in nature. The electromagnetic levitation system (EMLS) is one such system that has a wide range of applications due to its frictionless, fast, and affordable technique. Optimal control and sliding mode control (SMC) techniques are often used controllers for EMLS. However, these techniques can achieve the required levitation but lag in having perfect set-point tracking and robustness against uncertainties. To get over these drawbacks, this article proposes the design of unconstrained mismatched uncertainties, constrained mismatched uncertainties, and integral sliding mode control with mismatched uncertainties for the current-controlled-type electromagnetic levitation system (CC-EMLS). The modeled equations of CC-EMLS are transfomed in terms of the mismatched uncertainties, and the required control action is obtained with and without constraints on the control input. The quadratic performance function is suggested for the unconstrained control scheme and is solved using the Hamilton–Jacobi–Bellman (HJB) equation. The non-quadratic cost function is designed for the constrained control method, and the HJB equation is utilized to obtain the solution. Both control schemes provide robustness to the system, but deviations in the set point are observed in tracking the position of the ball when the changes in the payload occur in the system. Therefore, integral sliding mode control with robust–optimal (IOSMC) gain is proposed for the CC-EMLS to overcome the steady-state error in the other two schemes. The stability is proven using the direct method of Lyapunov stability. The essential studies based on the simulation are carried out to showcase the performance of the proposed control schemes. The integral performance indicators are compared for all three proposed control schemes to highlight the efficacy, robustness, and efficiency of the designed controllers.

Patients with severe structural tooth wear present significant restorative challenges, including compromised oral function and the loss of essential anatomical landmarks such as marginal ridges, incisal edges, cusps, occlusal planes, and vertical dimension of occlusion (VDO). Successful management requires meticulous diagnosis, comprehensive treatment planning, and careful selection of restorative materials with appropriate biomechanical properties. Digital technologies have become integral to this process, particularly for enhancing diagnostic accuracy, material selection, and tooth preparation design within a fully digital workflow. This clinical case report illustrates a complete digital approach, beginning with an initial intraoral scan merged with a digital wax-up STL file featuring varying translucency dimensions to guide tooth preparation. This workflow enabled precise planning of tooth reduction, accurate assessment of available interocclusal space, and determination of material thickness requirements prior to irreversible procedures. Additionally, the integration of digital visualization improved patient communication, treatment predictability, and interdisciplinary collaboration. Overall, this case highlights the value of CAD/CAM technology in supporting complex oral rehabilitation for patients with advanced tooth wear, demonstrating its capacity to enhance efficiency, precision, and outcome quality in full-mouth zirconia ceramic restorations.

Pan evaporation (PE) is widely used as an indicator of atmospheric evaporative demand and is relevant to irrigation demand and climate-related hydrological changes. Using daily records from 759 meteorological stations across China during 2002–2018, this study investigated the temporal trends, spatial patterns, and climatic controls of PE across seven major climate zones. Multiple decomposition techniques revealed a dominant annual cycle and a pronounced peak in 2018, while a decreasing interannual trend was observed nationwide. Spatial analyses showed a clear north–south contrast, with the strongest declines occurring in northern China. A random forest (RF) model was employed to quantify the contributions of climatic variables, achieving high predictive performance. RF results indicated that the dominant drivers of PE varied substantially across climate zones: sunshine duration (as a proxy for solar radiation) and air temperature mainly controlled PE in humid regions, while wind speed and relative humidity (RH) exerted stronger influences in arid and semi-arid regions. The widespread decline in northern China is consistent with concurrent changes in wind speed and sunshine duration, together with humidity conditions, which modulate evaporative demand at monthly scales. These findings highlight substantial spatial heterogeneity in PE responses to climate forcing and provide insights for drought assessment and water resource management in a warming climate.

Background: Arthroscopic anterior cruciate ligament (ACL) reconstruction is widely recognised as the primary treatment for ACL injuries. However, with the increasing incidence of sports-related injuries and growing demand for rehabilitation services, conventional rehabilitation models—largely reliant on therapists’ experience and subjective assessment—are increasingly insufficient to meet the clinical need for precise and individualised rehabilitation programmes. This study aimed to evaluate the effectiveness of a rehabilitation protocol incorporating an artificial intelligence (AI)-based assessment and correction system on functional recovery following ACL reconstruction. Methods: Using convenience sampling, 80 patients undergoing ACL reconstruction between June to December 2024 were recruited for this randomised controlled trial. Participants were randomly assigned to either a control group (n = 40), which received conventional functional exercise training, or a trial group (n = 40), which received rehabilitation intervention guided by an AI-based assessment and correction system. Knee function scores (Lysholm score, IKDC score), Berg Balance Scale (BBS) scores, joint range of motion (ROM), and rehabilitation exercise compliance scores were collected and analysed 1, 2, 3, and 4 months postoperatively. Results: Compared with the control group, the trial group demonstrated significantly greater improvements in Lysholm score, IKDC score, BBS score, and active knee joint ROM (p < 0.05) at postoperative assessment points. Additionally, rehabilitation exercise adherence was significantly higher in the trial group compared to the control group (p < 0.05). Conclusions: Rehabilitation protocols integrating AI-based assessment and correction systems effectively enhance knee function recovery, joint mobility and balance ability following ACL reconstruction. Moreover, these protocols significantly improve rehabilitation exercise adherence, demonstrating superior efficacy compared to conventional rehabilitation approaches. This digital rehabilitation model represents an efficient and promising intervention for postoperative ACL rehabilitation.

Rural areas are currently facing a deepening “social-ecological divide,” where the fragmentation of natural, economic, and cultural data—often trapped in “data silos”—hinders effective systemic governance. To bridge this gap, in this study, the Rural Landscape Information Model (RLIM), an integrative framework designed to reconfigure rural connections through data fusion, process coordination, and performance feedback, is proposed. We validate the framework’s effectiveness through a comparative analysis of two distinct rural archetypes in China: the innovation-driven Yu Village and the heritage-conservation-oriented Hani Terraces. Our results reveal that digital technologies drive distinct empowerment pathways moderated by regional contexts: (1) In the data domain, heterogeneous resources were successfully integrated into the framework in both cases (achieving a Monitoring Coverage > 80%), yet served divergent strategic ends—comprehensive territorial management in Yu Village versus precision heritage monitoring in the Hani Terraces. (2) In the process domain, digital platforms restructured social interactions differently. Yu Village achieved high individual participation (Participation Rate ≈ 0.85) via mobile governance apps, whereas the Hani Terraces relied on cooperative-mediated engagement to bridge the digital divide for elderly farmers. (3) In the performance domain, the interventions yielded contrasting but positive economic-ecological outcomes. Yu Village realized a 25% growth in tourism revenue through “industrial transformation” (Ecology+), while the Hani Terraces achieved a 12% value enhancement by stabilizing traditional agricultural ecosystems (Culture+). This study contributes a verifiable theoretical model and a set of operational tools, demonstrating that digital technologies are not merely instrumental add-ons but catalysts for fostering resilient, collaborative, and context-specific rural socio-ecological systems, ultimately offering scalable governance strategies for sustainable rural revitalization in the digital era.

Type 2 diabetes is increasingly prevalent among children and adolescents with overweight or obesity, and although lifestyle interventions remain first-line preventive strategies, long-term adherence and effectiveness are often limited. Metformin has demonstrated efficacy in delaying type 2 diabetes onset in adults at high risk, but its preventive role in pediatric populations remains unclear. This systematic review and meta-analysis aims to evaluate the effectiveness of metformin, alone or in combination with lifestyle interventions, in preventing or delaying type 2 diabetes among children and adolescents with overweight or obesity. The protocol is registered in PROSPERO (CRD42024615622), MEDLINE (PubMed), Embase, Cochrane Library, Scopus, and Web of Science and will be searched from inception to June 2025. Eligible studies include randomized controlled trials, quasi-experimental studies, and prospective cohort studies involving individuals under 18 years of age. The primary outcome is incidence of type 2 diabetes, with secondary outcomes including fasting plasma glucose, HbA1c, insulin resistance, BMI z-score, adherence, and adverse events. Where appropriate, random-effects meta-analyses will be conducted. This review will synthesize current evidence on metformin for pediatric type 2 diabetes prevention and inform future preventive strategies and clinical decision-making.

While Neural Architecture Search (NAS) has revolutionized the automation of deep learning model design, gradient-based approaches like DARTS often suffer from high computational overheads, the collapse of skip-connections, and optimization instability. To address these limitations, we propose Efficient and Lightweight Differentiable Architecture Search (EL-DARTS). EL-DARTS constructs a compact and redundancy-reduced search space, integrates a partial channel strategy to lower memory usage, employs a Dynamic Coefficient Scheduling Strategy to balance edge importance, and introduces entropy regularization to sharpen operator selection. Experiments on CIFAR-10 and ImageNet demonstrate that EL-DARTS substantially improves both search efficiency and accuracy. Remarkably, it attains a 2.47% error rate on CIFAR-10, requiring merely 0.075 GPU-days for the search. On ImageNet, the discovered architecture achieves a 26.2% top-1 error while strictly adhering to the mobile setting (<600 M MACs). These findings confirm that EL-DARTS effectively stabilizes the search process and pushes the efficiency frontier of differentiable NAS.

The first aim of this study is to point out new aspects of approximation theory applied to a few classes of holomorphic functions via Vitali’s theorem. The approximation is made with the aid of the complex moments of the involved functions, which are defined similarly to the moments of a real-valued continuous function. By applying uniform approximation of continuous functions on compact intervals via Korovkin’s theorem, the hard part concerning uniform approximation on compact subsets of the complex plane follows according to Vitali’s theorem. The theorem on the set of zeros of a holomorphic function is also applied. In the end, the existence and uniqueness of the solution for a multidimensional moment problem are characterized in terms of limits of sums of quadratic expressions. This is the application appearing at the end of the title. Consequences resulting from the first part of the paper are pointed out with the aid of functional calculus for self-adjoint operators.