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Keywords = two points approximation scheme

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21 pages, 1601 KB  
Article
NOMA-Enabled Cooperative Two-Way Communications for Both Primary and Secondary Systems
by Dong-Hua Chen and Kaiwei Ruan
Electronics 2026, 15(2), 389; https://doi.org/10.3390/electronics15020389 - 15 Jan 2026
Viewed by 137
Abstract
With the aid of non-orthogonal multiple access (NOMA), this paper investigates simultaneous two-way communications for cooperative cognitive radio networks, where a group of secondary access points (APs) scattered over a primary cell not only serve their own users but also help the primary [...] Read more.
With the aid of non-orthogonal multiple access (NOMA), this paper investigates simultaneous two-way communications for cooperative cognitive radio networks, where a group of secondary access points (APs) scattered over a primary cell not only serve their own users but also help the primary cell-edge users′ transmissions cooperatively. As a reward for the cooperation, these APs are granted full access to the primary frequency spectrum. To coordinate the two-way transmissions of the primary and secondary networks, we propose a spectrum-efficient cooperative scheme that only involves two transmission phases, and particularly, the two variable-length transmission phases endow the system with the capability of adapting to possible DL and UL traffic asymmetry. For the system design, we formulate a power minimization problem subject to the bidirectional transmission rate constraints of both networks. The formulated problem is shown to be nonlinear and nonconvex, and for the numerically efficient solution, we propose an iterative algorithm facilitated by the successive convex approximation technique. Simulation results show that the proposed design algorithm has fast convergence speed and is superior to the hybrid orthogonal multiple access and NOMA schemes. Full article
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24 pages, 3069 KB  
Review
Dispersion Compensation Scheme with a Simple Structure in Ultra-High-Speed Optical Fiber Transmission Systems
by Ying Wu, Ying Wang, Luhan Jiang and Jianjun Yu
Photonics 2026, 13(1), 39; https://doi.org/10.3390/photonics13010039 - 31 Dec 2025
Viewed by 336
Abstract
With the explosive growth of global data traffic, long-distance fiber optic transmission systems are continuously evolving towards higher capacity and longer distances. However, to overcome the high complexity of fiber dispersion compensation algorithms, various dispersion compensation techniques have emerged. This paper aims to [...] Read more.
With the explosive growth of global data traffic, long-distance fiber optic transmission systems are continuously evolving towards higher capacity and longer distances. However, to overcome the high complexity of fiber dispersion compensation algorithms, various dispersion compensation techniques have emerged. This paper aims to systematically review and summarize dispersion compensation algorithms in long-distance fiber optic transmission. First, we briefly introduce the physical mechanism of fiber dispersion. Then, this paper focuses on digital domain compensation algorithms, dividing them into two major categories: compensation algorithms without penalty and with penalty. For compensation algorithms without penalty, we elaborate on traditional block processing strategies such as Overlap-Save (OLS), and various enhanced strategies combining intelligent filter segmentation and optimized frequency domain workflows. For compensation algorithms with penalty, we focus on analyzing a scheme that redesigns chromatic dispersion compensation (CDC) algorithm into a hardware-friendly structure using geometric clustering of taps, and finite-impulse-response (FIR) filters based on frequency response approximating the ideal inverse chromatic dispersion (CD) transfer function. By numerical simulation, we analyze the core principles, computational complexity, and compensation performance of each type of algorithm. Finally, this paper summarizes the limitations and development trends of existing dispersion compensation algorithms, pointing out that low-complexity and small-scale deployment algorithm structures will be an important research direction in the future. Full article
(This article belongs to the Special Issue Machine Learning and Artificial Intelligence for Optical Networks)
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12 pages, 1183 KB  
Article
Load-Balanced Pickup Strategy for Multi-UAV Systems with Heterogeneous Capabilities
by Jun-Pyo Hong
Mathematics 2026, 14(1), 9; https://doi.org/10.3390/math14010009 - 19 Dec 2025
Viewed by 202
Abstract
This paper investigates a load-balanced pickup strategy for heterogeneous multi-UAV systems, where unmanned aerial vehicles (UAVs) with different flight speeds and payload capacities cooperatively collect spatially distributed parcels while avoiding no-fly zones. The goal is to minimize the maximum mission completion time among [...] Read more.
This paper investigates a load-balanced pickup strategy for heterogeneous multi-UAV systems, where unmanned aerial vehicles (UAVs) with different flight speeds and payload capacities cooperatively collect spatially distributed parcels while avoiding no-fly zones. The goal is to minimize the maximum mission completion time among UAVs while ensuring balanced workload distribution according to their heterogeneous capabilities. The formulated problem is a mixed-integer nonlinear program that jointly optimizes pickup assignment, trajectory planning, and slot duration allocation under mobility, safety, and payload constraints. To address the nonconvexity of the optimization problem, the successive convex approximation and penalty convex–concave procedure are applied, leading to a two-stage iterative algorithm that efficiently derives practical UAV strategies for load-balanced parcel pickup. The first stage minimizes the maximum completion time, and the second stage further refines the trajectories to reduce the total travel distance. Simulation results demonstrate that the proposed scheme effectively adapts to UAV capability asymmetry and achieves superior time efficiency compared to benchmark schemes. The results also point to future research opportunities, such as incorporating energy models, communication constraints, or stochastic task dynamics to extend the applicability of the proposed framework. Full article
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29 pages, 8063 KB  
Article
Deformation Characteristics of Joints in Ultra-Shallow Precast Prefabricated Underground Tunnels Under Dynamic Loads
by Zhiyi Jin, Yongxu Jia, Tong Han and Ning Xu
Appl. Sci. 2025, 15(24), 13253; https://doi.org/10.3390/app152413253 - 18 Dec 2025
Viewed by 198
Abstract
Ultra-shallow prefabricated underpass tunnel technology has been widely adopted in urban transportation construction owing to its advantages of rapid construction and minimal environmental impact. However, the deformation behavior of tunnel joints under long-term vehicular dynamic loads remains unclear, which constrains the reliability and [...] Read more.
Ultra-shallow prefabricated underpass tunnel technology has been widely adopted in urban transportation construction owing to its advantages of rapid construction and minimal environmental impact. However, the deformation behavior of tunnel joints under long-term vehicular dynamic loads remains unclear, which constrains the reliability and durability of this technology. To address this, this study focuses on a large cross-section tunnel with five bidirectional lanes. A combined methodology of “refined numerical simulation + long-term cyclic loading model tests” was employed to systematically investigate the dynamic response and cumulative deformation patterns of tunnel joints under different burial depths (3 m, 5 m, and 8 m) and prestress levels (0–0.5 MPa). First, based on the analysis of structural bending moment distribution, various division principles such as zero-moment points and maximum-moment points were compared, leading to the determination of a joint layout scheme primarily adopting a two-segment division. On this basis, a refined numerical model integrating pavement excitation and vehicle dynamic coupling was established, supplemented by a model test with 2 million loading cycles, to reveal the deformation mechanism of joints under both moving vehicle loads and long-term loading. The results indicate the following: (1) burial depth is the decisive factor controlling overall joint deformation—increasing the depth from 3 m to 8 m can reduce the maximum joint opening and slip by approximately 60%; (2) prestress serves as a key measure for restraining joint opening and ensuring waterproofing performance, with its effect being particularly pronounced under shallow burial conditions; (3) based on the dynamic attenuation coefficient, the concept of “sensitive burial depth” (approximately 3.7 m) is proposed, providing a quantitative criterion for identifying tunnels susceptible to surface traffic loads; (4) the recommended two-segment structural division scheme effectively controls deformation while considering construction convenience and waterproofing reliability. The methodological framework of “numerical simulation + model testing” established in this study can provide theoretical support and engineering reference for the long-term performance design and assessment of ultra-shallow prefabricated tunnels. Full article
(This article belongs to the Special Issue Advances in Tunnel Excavation and Underground Construction)
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14 pages, 1413 KB  
Article
Impact of Concurrent Appointment of Recycled Aggregate Quality Managers on Post-Certification Quality Audit Results in Korea
by Soo-Min Jeon, Myun-Jung Kim and Sung-Hoon Kang
Appl. Sci. 2025, 15(24), 12878; https://doi.org/10.3390/app152412878 - 5 Dec 2025
Viewed by 564
Abstract
This study assessed whether permitting certified recycled aggregate companies to assign both quality and environmental management responsibilities to a single individual affects the effectiveness of post-certification quality management. Using data from 242 post-certification audits conducted in 2023, six regulatory audit items were quantified [...] Read more.
This study assessed whether permitting certified recycled aggregate companies to assign both quality and environmental management responsibilities to a single individual affects the effectiveness of post-certification quality management. Using data from 242 post-certification audits conducted in 2023, six regulatory audit items were quantified using a binary scoring scheme to produce a six-point score for each company. Audit outcomes were compared between companies employing dedicated quality managers (n = 147) and those operating with concurrently appointed managers (n = 95). Before conducting hypothesis testing, skewness, kurtosis, and F-tests were used to verify approximate normality and homogeneity of variances. Two-sample t-tests assuming equal variances revealed no statistically significant differences between the two personnel structures, and the effect size (Cohen’s d = 0.072) indicated negligible practical differences. Additionally, 52 companies (22%) experienced changes in their quality management personnel during the audit period. A separate comparison between companies with and without such changes also showed no statistically significant differences, with a small effect size (d = 0.276). These results suggest that the 2022 regulatory revision authorizing concurrent appointments did not exert any discernible adverse influence on post-certification audit performance and that additional administrative requirements for managing personnel changes may be unnecessary. The findings also highlight recurring deficiencies—particularly in quality testing and equipment management—which warrant continued attention from policymakers, certification bodies, and certified companies seeking to enhance the effectiveness of the recycled aggregate quality certification system. Full article
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17 pages, 344 KB  
Article
Common Fixed Point Approximation for Asymptotically Nonexpansive Mapping in Hyperbolic Space with Application
by Tehreem Ishtiaq, Afshan Batool, Aftab Hussain and Hamed Alsulami
Axioms 2025, 14(12), 889; https://doi.org/10.3390/axioms14120889 - 30 Nov 2025
Viewed by 505
Abstract
This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to [...] Read more.
This study presents a common fixed-point iteration process that includes two asymptotically nonexpansive self-mappings in a hyperbolic space and their delta convergence. To support our results, we provide an example with a comparison table and sufficient conditions for a modified iteration scheme to have strong convergence to approximate the fixed point. Full article
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications, 2nd Edition)
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18 pages, 1005 KB  
Article
An Online Generalized Multiscale Method for Embedded Discrete Fracture Model
by Zhengkang He and Bangmin Wu
Axioms 2025, 14(11), 820; https://doi.org/10.3390/axioms14110820 - 5 Nov 2025
Viewed by 411
Abstract
This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic [...] Read more.
This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic system for the unknown pressure. Then, by the use of a suitable local snapshot space and a well-designed spectral decomposition, we compute offline basis functions to capture local heterogeneity information on account of the presence of various fractures in each coarse cell. After that, we compute residual-based online basis functions that contain global multiscale information to enrich the multiscale space and thus achieve higher accuracy of the multiscale solution. Meanwhile, theoretical analyses are conducted to show the convergence behavior, and a number of numerical tests with different fracture configurations are performed to investigate the performance of online enrichment. Full article
(This article belongs to the Section Mathematical Analysis)
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17 pages, 1943 KB  
Article
Hearing Aid Amplification Schemes Adjusted to Tinnitus Pitch: A Randomized Controlled Trial
by Jose L. Santacruz, Emile de Kleine and Pim van Dijk
Audiol. Res. 2025, 15(6), 143; https://doi.org/10.3390/audiolres15060143 - 22 Oct 2025
Viewed by 1711
Abstract
Background/Objectives: Hearing aids can be used as a treatment for tinnitus. There are indications that this treatment is most effective when the tinnitus pitch falls in the frequency range of amplification of the hearing aid. Then, the hearing aid provides masking of [...] Read more.
Background/Objectives: Hearing aids can be used as a treatment for tinnitus. There are indications that this treatment is most effective when the tinnitus pitch falls in the frequency range of amplification of the hearing aid. Then, the hearing aid provides masking of the tinnitus. Alternatively, it has been suggested that a gap in the amplification around the tinnitus pitch would engage lateral inhibition and thereby reduce the tinnitus. Methods: To test these ideas, we conducted a randomized controlled trial. Patients were fitted with hearing aids using three different amplification schemes: (1) standard amplification according to the NAL-NL2 prescription procedure, (2) boosted amplification at the tinnitus frequency to enhance tinnitus masking, and (3) notch-filtered amplification at the tinnitus frequency to engage lateral inhibition and suppress tinnitus. The goal was to compare the boosted and notched amplification schemes to standard amplification. The primary outcome measure was tinnitus handicap as measured by the Tinnitus Functional Index (TFI). The trial was designed as a double-blind Latin square balanced crossover study. Eighteen tinnitus patients with moderate hearing loss were included. All of them were experienced hearing aid users. After two weeks of initial adaptation to the new hearing aids with standard settings, each setting was tried for four weeks. Results: There was an average reduction of 6.9 points on the TFI score after the adaptation phase, possibly due to a placebo effect. The TFI score did not differ significantly from the standard setting after using the notched or the boosted settings. Although notched amplification performed better than boosted amplification, this difference did not reach the clinical significance level. Regardless of the TFI outcomes, most participants had an individual preference for a particular setting. This preference was approximately uniformly distributed across the three amplification schemes. Conclusions: Notch-filtered and boosted amplification did not provide better tinnitus suppression than standard amplification. The individual preferences highlighted the importance of tailor-made approaches to hearing aid amplification in clinical practice. Further studies should explore the differences among patient’s tinnitus and their preference for a hearing aid setting. Full article
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24 pages, 6573 KB  
Article
Heat Pump Optimization—Comparative Study of Different Optimization Algorithms and Heat Exchanger Area Approximations
by Eivind Brodal
Energies 2025, 18(19), 5270; https://doi.org/10.3390/en18195270 - 3 Oct 2025
Cited by 1 | Viewed by 888
Abstract
More energy efficient heat pumps can be designed if the industry is able to identify reliable optimization schemes able to predict how a fixed amount of money is best spent on the different individual components. For example, how to optimally design and size [...] Read more.
More energy efficient heat pumps can be designed if the industry is able to identify reliable optimization schemes able to predict how a fixed amount of money is best spent on the different individual components. For example, how to optimally design and size the different heat exchangers (HEs) in a heat pump with respect to cost and performance. In this work, different optimization algorithms and HE area integral approximations are compared for heat pumps with two and three HEs, with or without ejectors. Since the main goal is to identify optimal numerical schemes, not optimal designs, heat transfer is simplified, assuming a constant U-value for all HEs, which reduces the computational work significantly. Results show that high-order HE area approximations are 10400 times faster than conventional trapezoidal and adaptive integral methods. High-order schemes with 45 grid points (N) obtained 80100% optimization success rates. For subcritical processes, the LMTD method produced accurate results with N5, but such schemes are unreliable and difficult to extend to real HE models with non-constant U. Results also show that constrained gradient-based optimizations are 10 times faster than particle swarm, and that conventional GA optimizations are extremely inefficient. This study therefore recommends applying high-order HE area approximations and gradient-based optimizations methods developing accurate optimization schemes for the industry, which include realistic heat transfer coefficients. Full article
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29 pages, 3223 KB  
Article
Optimization of Prefabricated Building Component Distribution Under Dynamic Charging Strategy for Electric Heavy-Duty Trucks
by Xinran Qi, Weichen Zheng, Heping Wang and Fuyu Wang
World Electr. Veh. J. 2025, 16(9), 509; https://doi.org/10.3390/wevj16090509 - 10 Sep 2025
Viewed by 807
Abstract
To align with the adoption of electric vehicles in the transportation sector, this paper proposes the use of electric heavy-duty trucks for the logistics and distribution of large prefabricated building components. This approach aims to address the problems of high total costs and [...] Read more.
To align with the adoption of electric vehicles in the transportation sector, this paper proposes the use of electric heavy-duty trucks for the logistics and distribution of large prefabricated building components. This approach aims to address the problems of high total costs and significant energy waste in prefabricated component transportation. Focusing on the multi-to-multi distribution mode, a two-level optimization model is constructed. The upper-level model is responsible for the reasonable allocation of demand points. The lower-level model optimizes the selection of road network nodes and charging stations along the delivery routes. It also dynamically adjusts charging timing and volume according to the real-time power situation. To enhance solution performance, a two-level multi-objective evolutionary algorithm based on Pareto theory is designed. This algorithm simultaneously optimizes distribution costs while coordinating path planning and charging strategies. Comparative experiments across different cases show that, compared with traditional single-level and multi-stage models, the proposed algorithm improves both solution accuracy and quality. Additionally, when compared with the scheduling scheme based on the full-charge capacity strategy, the dynamic charging strategy proposed in this paper reduces the total distribution cost by approximately 15.83%. These findings demonstrate that the constructed model and algorithm can effectively optimize the logistics and distribution of prefabricated components. They also provide a feasible solution for the practical application of electric vehicles in engineering logistics. Full article
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27 pages, 1630 KB  
Article
NNG-Based Secure Approximate k-Nearest Neighbor Query for Large Language Models
by Heng Zhou, Yuchao Wang, Yi Qiao and Jin Huang
Mathematics 2025, 13(13), 2199; https://doi.org/10.3390/math13132199 - 5 Jul 2025
Viewed by 968
Abstract
Large language models (LLMs) have driven transformative progress in artificial intelligence, yet critical challenges persist in data management and privacy protection during model deployment and training. The approximate nearest neighbor (ANN) search, a core operation in LLMs, faces inherent trade-offs between efficiency and [...] Read more.
Large language models (LLMs) have driven transformative progress in artificial intelligence, yet critical challenges persist in data management and privacy protection during model deployment and training. The approximate nearest neighbor (ANN) search, a core operation in LLMs, faces inherent trade-offs between efficiency and security when implemented through conventional locality-sensitive hashing (LSH)-based secure ANN (SANN) methods, which often compromise either query accuracy due to false positives. To address these limitations, this paper proposes a novel secure ANN scheme based on nearest neighbor graph (NNG-SANN), which is designed to ensure the security of approximate k-nearest neighbor queries for vector data commonly used in LLMs. Specifically, a secure indexing structure and subset partitioning method are proposed based on LSH and NNG. The approach utilizes neighborhood information stored in the NNG to supplement subset data, significantly reducing the impact of false positive points generated by LSH on query results, thereby effectively improving query accuracy. To ensure data privacy, we incorporate a symmetric encryption algorithm that encrypts the data subsets obtained through greedy partitioning before storing them on the server, providing robust security guarantees. Furthermore, we construct a secure index table that enables complete candidate set retrieval through a single query, ensuring our solution completes the search process in one interaction while minimizing communication costs. Comprehensive experiments conducted on two datasets of different scales demonstrate that our proposed method outperforms existing state-of-the-art algorithms in terms of both query accuracy and security, effectively meeting the precision and security requirements for nearest neighbor queries in LLMs. Full article
(This article belongs to the Special Issue Privacy-Preserving Machine Learning in Large Language Models (LLMs))
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21 pages, 472 KB  
Article
Energy Balancing and Lifetime Extension: A Random Quorum-Based Sink Location Service Scheme for Wireless Sensor Networks
by Yongje Shin, Jeongcheol Lee and Euisin Lee
Sensors 2025, 25(13), 4078; https://doi.org/10.3390/s25134078 - 30 Jun 2025
Cited by 1 | Viewed by 823
Abstract
Geographic routing is an appealing method for wireless sensor networks, as it routes data packets solely based on nodes’ location information rather than global network topology. A fundamental requirement for geographic routing is that source nodes must know the locations of sink nodes [...] Read more.
Geographic routing is an appealing method for wireless sensor networks, as it routes data packets solely based on nodes’ location information rather than global network topology. A fundamental requirement for geographic routing is that source nodes must know the locations of sink nodes to deliver their data. To efficiently provide sink location information, quorum-based sink location service schemes have been introduced, using crossing points between sink location announcement (SLA) and sink location query (SLQ) quorums. However, existing quorum-based schemes typically construct quorums along fixed paths, causing rapid energy depletion of particular sensor nodes and resulting in shorter network lifetimes, especially in irregular sensor fields. To overcome this limitation, we propose an energy-efficient quorum-based sink location service scheme that extends network lifetime by reducing and balancing sensor nodes’ energy consumption. Specifically, our scheme constructs a quadrilateral-shaped SLA quorum using four randomly selected points, and a line-shaped SLQ quorum defined by two randomly chosen points located inside and outside the SLA quorum, respectively. We also address key issues of the proposed scheme, including network holes, irregular boundaries, multiple sources and sinks, and Base Zone sizing, and present methods to handle them. Simulation results demonstrate that the proposed scheme outperforms existing approaches, achieving approximately 29% lower total energy consumption and 27% higher energy balancing across sensor nodes on average. Full article
(This article belongs to the Special Issue Wireless Sensor Networks: Signal Processing and Communications)
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20 pages, 625 KB  
Article
Adaptive Fixed-Time NN-Based Tracking Control for a Type of Stochastic Nonlinear Systems Subject to Input Saturation
by Daohong Zhu, Zhenzhen Long and Liandi Fang
Mathematics 2025, 13(12), 2018; https://doi.org/10.3390/math13122018 - 18 Jun 2025
Viewed by 639
Abstract
This paper considers the adaptive fixed-time tracking control problem for stochastic systems subject to input saturation. Firstly, a smooth function approximation method is utilized to eliminate the effect of input saturation. Then, by combining the neural networks (NNs) approximation method with the backstepping-like [...] Read more.
This paper considers the adaptive fixed-time tracking control problem for stochastic systems subject to input saturation. Firstly, a smooth function approximation method is utilized to eliminate the effect of input saturation. Then, by combining the neural networks (NNs) approximation method with the backstepping-like technique, an adaptive fixed-time tracking control scheme is explicitly developed. The proposed scheme can ensure that the state variables are bounded in probability and the tracking error converges to a small region of the equilibrium point in a fixed time. Eventually, two numerical examples are given to indicate the performance and effectiveness of the presented strategy. Full article
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28 pages, 13036 KB  
Article
Statistical Analysis of a Generalized Variant of the Weibull Model Under Unified Hybrid Censoring with Applications to Cancer Data
by Mazen Nassar, Refah Alotaibi and Ahmed Elshahhat
Axioms 2025, 14(6), 442; https://doi.org/10.3390/axioms14060442 - 5 Jun 2025
Viewed by 1020
Abstract
This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility [...] Read more.
This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility for modeling diverse lifetime data patterns and hazard rate behaviors. Notably, its hazard rate function can exhibit five distinct shapes, including upside-down bathtub and bathtub shapes. The study focuses on classical and Bayesian estimation frameworks for the model parameters and associated reliability metrics under a unified hybrid censoring scheme. Methodologies include both point estimation (maximum likelihood and posterior mean estimators) and interval estimation (approximate confidence intervals and Bayesian credible intervals). To evaluate the performance of these estimators, a comprehensive simulation study is conducted under varied experimental conditions. Furthermore, two empirical applications on real-world cancer datasets underscore the efficacy of the proposed estimation methods and the practical viability and flexibility of the explored model compared to eleven other existing lifespan models. Full article
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16 pages, 649 KB  
Article
Adapted B-Spline Quasi-Interpolation for Approximating Piecewise Smooth Functions
by David Levin and Nira Gruberger
Algorithms 2025, 18(6), 335; https://doi.org/10.3390/a18060335 - 3 Jun 2025
Cited by 1 | Viewed by 975
Abstract
We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain Ω in Rd, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. This [...] Read more.
We address the challenge of efficiently approximating piecewise smooth functions, particularly those with jump discontinuities. Given function values on a uniform grid over a domain Ω in Rd, we present a novel B-spline-based approximation framework, using new adaptable quasi-interpolation operators. This approach integrates discontinuity detection techniques, allowing the quasi-interpolation operator to selectively use points from only one side of a discontinuity in both one- and two-dimensional cases. Among a range of candidate operators, the most suitable quasi-interpolation scheme is chosen to ensure high approximation accuracy and efficiency, while effectively suppressing spurious oscillations in the vicinity of discontinuities. Full article
(This article belongs to the Special Issue Nonsmooth Optimization and Its Applications)
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