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Mathematics, Volume 14, Issue 1 (January-1 2026) – 203 articles

Cover Story (view full-size image): The generalized circular cosine (c) represents the time t dependence of the displacement ζ(t) [electric current j(t)] of analogous (a) mechanical system [(b) electrical circuit], with mass M(t) [induction L(t)] and spring resilience K(t) [capacity C(t)], all functions of time, such that the natural frequency ω = √(K/M)  (ω = 1/√LC) is a power of time ω(t) ∼ tm with exponent m. View this paper
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21 pages, 3463 KB  
Article
A Practical CNN–Transformer Hybrid Network for Real-World Image Denoising
by Ahhyun Lee, Eunhyeok Hwang and Dongsun Kim
Mathematics 2026, 14(1), 203; https://doi.org/10.3390/math14010203 - 5 Jan 2026
Viewed by 405
Abstract
Real-world image denoising faces a critical trade-off: Convolutional Neural Network (CNN)-based methods are computationally efficient but limited in capturing long-range dependencies, while Transformer-based approaches achieve superior global modeling at prohibitive computational costs (>100 G Multiply–Accumulate Operations, MACs). This presents significant challenges for deployment [...] Read more.
Real-world image denoising faces a critical trade-off: Convolutional Neural Network (CNN)-based methods are computationally efficient but limited in capturing long-range dependencies, while Transformer-based approaches achieve superior global modeling at prohibitive computational costs (>100 G Multiply–Accumulate Operations, MACs). This presents significant challenges for deployment in resource-constrained environments. We present a practical CNN–Transformer hybrid network that systematically balances performance and efficiency under practical deployment constraints for real-world image denoising. By integrating key components from NAFNet (Nonlinear Activation Free Network) and Restormer, our method employs three design strategies: (1) strategic combination of CNN and Transformer blocks enabling performance–efficiency trade-offs; (2) elimination of nonlinear operations for hardware compatibility; and (3) architecture search under explicit resource constraints. Experimental results demonstrate competitive performance with significantly reduced computational cost: our models achieve 39.98–40.05 dB Peak Signal-to-Noise Ratio (PSNR) and 0.958–0.961 Structural Similarity Index Measure (SSIM) on the SIDD dataset, and 39.73–39.91 dB PSNR and 0.959–0.961 SSIM on the DND dataset, while requiring 7.18–16.02 M parameters and 20.44–44.49 G MACs. Cross-validation results show robust generalization without significant performance degradation across diverse scenes, demonstrating a favorable trade-off among performance, efficiency, and practicality. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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29 pages, 2736 KB  
Article
Quantitative Analysis of Manufacturing Flexibility and Inventory Management: Impact on Total Flow Time in Production System
by Pedro Palominos, German Moncada, Guillermo Fuertes and Luis Quezada
Mathematics 2026, 14(1), 202; https://doi.org/10.3390/math14010202 - 5 Jan 2026
Viewed by 251
Abstract
Improving responsiveness and efficiency in production systems requires an understanding of how manufacturing flexibility and inventory management interact under conditions of uncertainty. This study examines the combined effect of four types of flexibility, machine, labor, routing, and volume, together with the use of [...] Read more.
Improving responsiveness and efficiency in production systems requires an understanding of how manufacturing flexibility and inventory management interact under conditions of uncertainty. This study examines the combined effect of four types of flexibility, machine, labor, routing, and volume, together with the use of buffers, on the total flow time of production batches. A total of 84 experimental configurations were simulated, of which 35 were feasible and statistically valid, using a discrete-event simulation model developed in Arena and validated with industrial data. The results show that combining high machine and labor flexibility reduces total flow time from 5450 to 3050 min (a 44% decrease), whereas routing and volume flexibility exhibit minor effects. Moreover, the inclusion of buffers further improves performance, reducing times by approximately 1000 min in low-flexibility configurations. These findings provide robust quantitative evidence to guide the design of adaptive production systems by jointly evaluating the flexibility and inventory management dimensions that are typically studied in isolation. Full article
(This article belongs to the Special Issue Recent Advances in Optimization Algorithms for Scheduling and Operations Research)
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26 pages, 6557 KB  
Article
Research on Rolling Bearing Fault Diagnosis Based on IRBMO-CYCBD
by Dawei Guo, Jiaxun Chen, Xiaodong Liu and Jiyou Fei
Mathematics 2026, 14(1), 201; https://doi.org/10.3390/math14010201 - 5 Jan 2026
Viewed by 196
Abstract
This paper introduces an Improved Red-Billed Blue Magpie Optimizer (IRBMO) to enhance the Maximum Second-Order Cyclostationary Blind Deconvolution (CYCBD) method, which traditionally depends on manual, experience-based setting of its key parameters (filter length L and cyclic frequency α). By adopting an Improved [...] Read more.
This paper introduces an Improved Red-Billed Blue Magpie Optimizer (IRBMO) to enhance the Maximum Second-Order Cyclostationary Blind Deconvolution (CYCBD) method, which traditionally depends on manual, experience-based setting of its key parameters (filter length L and cyclic frequency α). By adopting an Improved Envelope Spectrum Entropy (EK) as the fitness function, the IRBMO autonomously optimizes these parameters, eliminating the need for prior knowledge and improving its applicability in industrial settings. The Improved Red-Billed Blue Magpie algorithm is employed to adaptively optimize the penalty parameter and kernel function parameter of the support vector machine, thereby obtaining an optimal support vector machine model. By introducing fuzzy entropy theory, the feature vectors of filtered signals—processed by the Cyclostationary Blind Deconvolution method with optimal parameters—are extracted and used as input for the optimally parameterized support vector machine, achieving multi-fault classification for bogie bearings. The results show that the IRBMO-CYCBD method significantly enhances the periodic weak fault impulse components and improves the signal-to-noise ratio of the processed signal. Envelope spectrum analysis of the filtered signal allows for clear observation of shaft frequency components, as evidenced by the accurate identification of the 110 Hz fundamental frequency and its harmonic components at 220 Hz, 330 Hz, and 440 Hz in the spectrum. Simulation tests verify the efficacy of the IRBMO-CYCBD method in processing rolling bearing vibration signals under strong noise interference. Under laboratory conditions, simulation experiments were conducted by collecting vibration acceleration signals from rolling bearings in various states. The aforementioned method was applied for fault diagnosis, achieving a maximum diagnostic accuracy of 100%. Through repeated experiments, it was verified that this method meets the fault diagnosis requirements for rolling bearings in metro train bogies. Full article
(This article belongs to the Special Issue Applied Computing and Artificial Intelligence, 2nd Edition)
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35 pages, 5897 KB  
Article
An Extrinsic Enriched Finite Element Method Based on RBFs for the Helmholtz Equation
by Qingliang Liu, Zhihong Zou, Yingbin Chai, Wei Li and Wei Chu
Mathematics 2026, 14(1), 200; https://doi.org/10.3390/math14010200 - 5 Jan 2026
Viewed by 312
Abstract
The traditional finite element method (FEM) usually exhibits significant numerical dispersion error for solving the Helmholtz equation in relatively high-frequency range, resulting in insufficiently accurate solutions. To address this problem, this paper proposes a novel enriched finite element method (EFEM) based on radial [...] Read more.
The traditional finite element method (FEM) usually exhibits significant numerical dispersion error for solving the Helmholtz equation in relatively high-frequency range, resulting in insufficiently accurate solutions. To address this problem, this paper proposes a novel enriched finite element method (EFEM) based on radial basis functions (RBFs) which are frequently used in meshless numerical techniques. In the proposed method, the partition of unity (PU) framework is retained, and nodal interpolation functions are formed using the RBFs. Furthermore, the linear dependence (LD) problem commonly encountered in many of the PU-based methods using polynomial basis functions (PBFs) is effectively avoided by using the present RBFs. To enrich the approximation space generated by the RBFs, the PBFs are introduced to construct the local enrichment functions. Several typical numerical experiments are conducted in this work. The results indicate that the proposed method can significantly reduce the dispersion error and yield accurate solutions even for relatively high-frequency Helmholtz problems. More importantly, the proposed method can be directly implemented with standard quadrilateral meshes as in FEM. Therefore, the proposed method represents a promising numerical scheme for solving relatively high-frequency Helmholtz problems. Full article
(This article belongs to the Special Issue Advances in Numerical Analysis of Partial Differential Equations)
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35 pages, 2339 KB  
Article
The Effect of Bundled Payment Schemes on Cost–Speed Tradeoff for Outpatient Service: A Queueing-Game Analysis
by Xiuzhang Li and Minghui Fu
Mathematics 2026, 14(1), 199; https://doi.org/10.3390/math14010199 - 5 Jan 2026
Viewed by 206
Abstract
In recent years, payment schemes in healthcare have garnered attention for their potential impact on service delivery and cost management. This paper explores the impact of the bundled payment scheme (BP) on hospital outpatient services, focusing on the cost–speed tradeoff. Specifically, a higher [...] Read more.
In recent years, payment schemes in healthcare have garnered attention for their potential impact on service delivery and cost management. This paper explores the impact of the bundled payment scheme (BP) on hospital outpatient services, focusing on the cost–speed tradeoff. Specifically, a higher service rate increases patient demand but also raises medical costs. We consider a queueing-game theoretical model to analyze servers’ service rate behaviors under different payment schemes (fee-for-service and BP) and the payer’s optimal payment scheme setting. Our study shows that achieving the first-best outcome under centralized decision making using the BP requires specific conditions. When the medical budget is sufficiently high, the payer can guide hospitals toward the first-best decision by setting an optimal price under the BP. However, when the budget is at an intermediate level, hospitals may set slower equilibrium service rates to control costs. To address this issue, the payer can implement service level regulation based on the BP scheme to achieve the first-best outcome. This scheme encourages hospitals to choose higher service rates by limiting expected waiting times. When the budget is too low, hospitals may be unwilling to provide service due to unprofitability. Moreover, as competition between hospitals intensifies, it becomes easier to maximize social welfare under the BP scheme. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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14 pages, 254 KB  
Article
Parastrophe of Some Inverse Properties in Quasigroups
by Yakub T. Oyebo, Abdulafeez O. Abdulkareem, Hasan AlMutairi and Temitope F. Oshodi
Mathematics 2026, 14(1), 198; https://doi.org/10.3390/math14010198 - 5 Jan 2026
Viewed by 225
Abstract
This work investigates the relationship between the parastrophes of some notion of inverses in quasigroups. Our findings reveal that, of the 5 parastrophes of LIP quasigroup, (23) parastrophe is a LIP quasigroup, (12) and (132) parastrophes are RIP quasigroups, while (13) and (132) [...] Read more.
This work investigates the relationship between the parastrophes of some notion of inverses in quasigroups. Our findings reveal that, of the 5 parastrophes of LIP quasigroup, (23) parastrophe is a LIP quasigroup, (12) and (132) parastrophes are RIP quasigroups, while (13) and (132) parastrophes are an anti-commutative quasigroup. Similarly, the (12) and (132) parastrophes of a RIP quasigroup are LIP quasigroups; the (13) parastrophe of a RIP quasigroup is a RIP quasigroup, while the (23) and (123) parastrophes are anti-commutative quasigroups. As for the CIP quasigroup, only the (12) parastrophe is a CIP quasigroup; other parastrophes are symmetric quasigroups of order two. Finally, the (12) parastrophe of the WIP quasigroup is an IP quasigroup, the (13), (23), and (132) parastrophes of the WIP quasigroup are CIP quasigroups, while the (123) parastrophe of the WIP quasigroup is a WIP quasigroup. Full article
(This article belongs to the Section A: Algebra and Logic)
18 pages, 1037 KB  
Article
Proper Strict Efficiency in Set Optimization with Partial Set Order Relation
by Wenyan Han and Guolin Yu
Mathematics 2026, 14(1), 197; https://doi.org/10.3390/math14010197 - 5 Jan 2026
Viewed by 200
Abstract
This paper is devoted to the investigation of the proper strict efficient solutions to a set optimization problem with a partial set order relation. Firstly, the notion of proper strict efficient solution defined by the Minkowski difference is introduced, and it is worth [...] Read more.
This paper is devoted to the investigation of the proper strict efficient solutions to a set optimization problem with a partial set order relation. Firstly, the notion of proper strict efficient solution defined by the Minkowski difference is introduced, and it is worth mentioning that the introduced strict efficiency is different from those in the existing literature. Secondly, a class of generalized contingent derivatives for set-valued maps is proposed, which are characterized in terms of a set criterion. Finally, the necessary and sufficient optimality conditions and a scalarization theorem for proper strict efficiency are established. Some concrete examples are given to illustrate the obtained results. Full article
(This article belongs to the Section E: Applied Mathematics)
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22 pages, 12979 KB  
Article
A High-Breakdown MCD-Based Robust Concordance Correlation Coefficient
by Hasan Bulut, Müjgan Zobu and Vedat Sağlam
Mathematics 2026, 14(1), 196; https://doi.org/10.3390/math14010196 - 4 Jan 2026
Viewed by 336
Abstract
The concordance correlation coefficient (CCC) is a popular measure of agreement between two continuous variables but is highly sensitive to outliers and data contamination. In this study, we propose a robust reformulation of the CCC by replacing classical moment estimators with Minimum Covariance [...] Read more.
The concordance correlation coefficient (CCC) is a popular measure of agreement between two continuous variables but is highly sensitive to outliers and data contamination. In this study, we propose a robust reformulation of the CCC by replacing classical moment estimators with Minimum Covariance Determinant (MCD) estimators. The proposed robust CCC preserves the interpretability of the classical coefficient while providing substantially improved robustness. Comprehensive Monte Carlo simulations under normal and non-normal distributions, varying sample sizes, correlation levels, and contamination schemes compare the proposed coefficient with the classical CCC and existing robust alternatives. The results show that the proposed robust CCC achieves superior stability and accuracy in contaminated settings while remaining competitive under clean data. Theoretical properties of the estimator are discussed, and its practical usefulness is demonstrated using real glucose measurement and blood pressure data sets. The proposed method is implemented in the MVTests R package, enabling straightforward application to real-world data. Full article
(This article belongs to the Special Issue Advances in Statistical Approaches with Applications for Multivariate Data Analysis)
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25 pages, 1675 KB  
Article
Solving the Shared Capacity Vehicle Routing Problem with Simultaneous Pick-Up and Delivery in Omni-Channel Retailing Using a Modified Differential Evolution Algorithm
by Vincent F. Yu, Sy Hoang Do, Xin-Ying He, Kuan-Fu Chen and Shih-Wei Lin
Mathematics 2026, 14(1), 195; https://doi.org/10.3390/math14010195 - 4 Jan 2026
Viewed by 290
Abstract
This study examines the logistical challenges arising in omni-channel retailing, where the interaction between traditional stores and online channels requires flexible and efficient transportation planning. In particular, the growth of Buy-Online-and-Pick-up-in-Store (BOPS) services has intensified the need to manage both forward deliveries and [...] Read more.
This study examines the logistical challenges arising in omni-channel retailing, where the interaction between traditional stores and online channels requires flexible and efficient transportation planning. In particular, the growth of Buy-Online-and-Pick-up-in-Store (BOPS) services has intensified the need to manage both forward deliveries and customer returns, the latter being a costly component of reverse logistics. To address these challenges, this study introduces the Shared Capacity Vehicle Routing Problem with Simultaneous Pickup and Delivery (SCVRP-SPD), which minimizes total operational cost by considering both transportation costs and the additional transfer costs incurred when reallocating store visits to more efficient delivery paths. In the SCVRP-SPD, stores are designed to serve a dual role as both pickup and return points, and a shared-capacity mechanism is incorporated to utilize leftover capacity in pre-planned trips, improving efficiency while reducing overall logistics cost. A mixed-integer programming model is developed for the problem, and solutions are obtained using GUROBI (version 11.0) and a newly designed Modified Differential Evolution (MDE) algorithm. Numerical experiments are conducted to evaluate the performance of the proposed MDE algorithm and to generate managerial insights, showing that the SCVRP-SPD is a promising strategy for omni-channel retailers seeking to reduce transportation costs, streamline reverse logistics, and better utilize resources. Full article
(This article belongs to the Section D: Statistics and Operational Research)
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23 pages, 1864 KB  
Article
Novel Hybrid Unequal-Sized WENO Scheme Employing Trigonometric Polynomials for Solving Hyperbolic Conservation Laws on Structured Grids
by Yanmeng Wang, Liang Li and Jun Zhu
Mathematics 2026, 14(1), 194; https://doi.org/10.3390/math14010194 - 4 Jan 2026
Viewed by 226
Abstract
This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address hyperbolic conservation laws on structured grids. Firstly, we propose three [...] Read more.
This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address hyperbolic conservation laws on structured grids. Firstly, we propose three unequal-degree reconstruction polynomials in the new trigonometric polynomial space to devise a novel fifth-order US-TWENO scheme. Then, we devise a novel troubled cell indicator capable of accurately identifying troubled cells containing strong discontinuities: the existence of extreme points of the trigonometric polynomials within the smallest interval (the target cell itself) is determined by whether the estimated minimum and maximum values of their derivative trigonometric polynomials have opposite signs. To the best of our knowledge, this is the first troubled cell indicator devised specifically within the target cell interval. The HUS-TWENO scheme is improved, offering greater efficiency, lower dissipation, and higher resolution. Numerical experiments demonstrate the effectiveness of the HUS-TWENO scheme. Full article
(This article belongs to the Special Issue Recent Developments in Partial Differential Equations and Their Applications)
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16 pages, 332 KB  
Article
Pair of Associated η-Ricci–Bourguignon Almost Solitons with Vertical Torse-Forming Potential on Almost Contact Complex Riemannian Manifolds
by Mancho Manev
Mathematics 2026, 14(1), 193; https://doi.org/10.3390/math14010193 - 4 Jan 2026
Viewed by 167
Abstract
Each of the studied manifolds has a pair of B-metrics, interrelated by an almost contact structure. The case where each of these metrics gives rise to an η-Ricci–Bourguignon almost soliton, where η is the contact form, is studied. In addition, the geometry-rich [...] Read more.
Each of the studied manifolds has a pair of B-metrics, interrelated by an almost contact structure. The case where each of these metrics gives rise to an η-Ricci–Bourguignon almost soliton, where η is the contact form, is studied. In addition, the geometry-rich case where the soliton potential is torse-forming and is pointwise collinear on the Reeb vector field with respect to each of the two metrics is considered. Ricci tensors and scalar curvatures are expressed as functions of the parameters of the pair of almost solitons. Particular attention is paid to the special case when the manifold belongs to the only possible basic class of the corresponding classification. A necessary and sufficient condition has been found for these almost solitons to be η-Einstein for both metrics. Full article
(This article belongs to the Special Issue Analysis on Differentiable Manifolds)
43 pages, 1507 KB  
Article
Customized Product Design and Cybersecurity Under a Nash Game-Enabled Dual-Channel Supply Chain Network
by Parthasarathi Mandal, Rekha Guchhait, Bikash Koli Dey, Mitali Sarkar, Sarla Pareek and Anirban Ganguly
Mathematics 2026, 14(1), 192; https://doi.org/10.3390/math14010192 - 4 Jan 2026
Viewed by 300
Abstract
Dual-channel retailing empowers the manufacturer to benefit from market opportunities by producing customized items that fulfill client requirements. The manufacturer and retailer sell customized products, which allow customers to express their chosen style to increase both the likelihood of customers making a purchase [...] Read more.
Dual-channel retailing empowers the manufacturer to benefit from market opportunities by producing customized items that fulfill client requirements. The manufacturer and retailer sell customized products, which allow customers to express their chosen style to increase both the likelihood of customers making a purchase and their level of satisfaction with the product. This trend is demonstrated by the current study, in which customized consumer items are considered through online and offline channels. On the other hand, cybersecurity has become a crucial aspect of the digital era, ensuring the protection of sensitive data, networks, and systems from cyberattacks and unauthorized access. This study develops with a modern cybersecurity framework to protect against cyberattacks and increase customer trust. This model is based on customized product design, cybersecurity investment, advertisement investment, and increasing the green level of customized products. The model is solved using both centralized policy and vertical Nash policy. Numerical results indicate that centralized profit is 2.37% more than the decentralized profit. Without investing in customized products and cybersecurity, the profit of the supply chain decreases by 2.33% and 1.99% for the centralized method, 1.28% and 1.15% for the vertical Nash method for the retailer, and 1.85% and 1.38% for the vertical Nash method for the manufacturer. Full article
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40 pages, 1118 KB  
Article
FORCE: Fast Outlier-Robust Correlation Estimation via Streaming Quantile Approximation for High-Dimensional Data Streams
by Sooyoung Jang and Changbeom Choi
Mathematics 2026, 14(1), 191; https://doi.org/10.3390/math14010191 - 4 Jan 2026
Viewed by 365
Abstract
The estimation of correlation matrices in high-dimensional data streams presents a fundamental conflict between computational efficiency and statistical robustness. Moment-based estimators, such as Pearson’s correlation, offer linear O(N) complexity but lack robustness. In contrast, high-breakdown methods like the minimum covariance [...] Read more.
The estimation of correlation matrices in high-dimensional data streams presents a fundamental conflict between computational efficiency and statistical robustness. Moment-based estimators, such as Pearson’s correlation, offer linear O(N) complexity but lack robustness. In contrast, high-breakdown methods like the minimum covariance determinant (MCD) are computationally prohibitive (O(Np2+p3)) for real-time applications. This paper introduces Fast Outlier-Robust Correlation Estimation (FORCE), a streaming algorithm that performs adaptive coordinate-wise trimming using the P2 algorithm for streaming quantile approximation, requiring only O(p) memory independent of stream length. We evaluate FORCE against six baseline algorithms—including exact trimmed methods (TP-Exact, TP-TER) that use O(NlogN) sorting with O(Np) storage—across five benchmark datasets spanning synthetic, financial, medical, and genomic domains. FORCE achieves speedups of approximately 470× over FastMCD and 3.9× over Spearman’s rank correlation. On S&P 500 financial data, coordinate-wise trimmed methods substantially outperform FastMCD: TP-Exact achieves the best RMSE (0.0902), followed by TP-TER (0.0909) and FORCE (0.1186), compared to FastMCD’s 0.1606. This result demonstrates that coordinate-wise trimming better accommodates volatility clustering in financial time series than multivariate outlier exclusion. FORCE achieves 76% of TP-Exact’s accuracy while requiring 104× less memory, enabling robust estimation in true streaming environments where data cannot be retained for batch processing. We validate the 25% breakdown point shared by all IQR-based trimmed methods using the ODDS-satellite benchmark (31.7% contamination), confirming identical degradation for FORCE, TP-Exact, and TP-TER. For memory-constrained streaming applications with contamination below 25%, FORCE provides the only viable path to robust correlation estimation with bounded memory. Full article
(This article belongs to the Special Issue Modeling and Simulation for Optimizing Complex Dynamical Systems)
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21 pages, 6915 KB  
Article
Spatiotemporal Pattern Selection in a Modified Leslie–Gower Predator–Prey System with Fear Effect and Self-Diffusion
by Xintian Jia, Lingling Zhao, Lijuan Zhang and Kunlun Huang
Mathematics 2026, 14(1), 190; https://doi.org/10.3390/math14010190 - 4 Jan 2026
Viewed by 213
Abstract
Indirect fear effects profoundly influence predator–prey dynamics by reducing prey reproduction. Whereas previous studies have investigated fear effects or self-diffusion separately in Leslie–Gower models, the novelty of this work lies in their simultaneous incorporation into a modified Leslie–Gower predator–prey system with Allee effect, [...] Read more.
Indirect fear effects profoundly influence predator–prey dynamics by reducing prey reproduction. Whereas previous studies have investigated fear effects or self-diffusion separately in Leslie–Gower models, the novelty of this work lies in their simultaneous incorporation into a modified Leslie–Gower predator–prey system with Allee effect, leading to previously unreported bifurcations and spatiotemporal pattern selection. The temporal system exhibits up to six equilibria and undergoes a codimension-2 Bogdanov–Takens bifurcation. In the spatial extension, Turing instability is triggered when the predator diffusion coefficient exceeds a critical threshold. Using weak nonlinear multiple-scale analysis, amplitude equations are derived, and their stability analysis classifies stationary patterns into spots, stripes, and spot–stripe mixtures depending on the distance from the Turing onset. Numerical simulations confirm that low, moderate, and high predator diffusivity, respectively, favour spotted, mixed, and striped prey distributions. These results emphasise the critical role of fear-mediated indirect interactions and diffusion in driving spatial heterogeneity and ecosystem stability. Full article
(This article belongs to the Special Issue Advanced Applications of Partial Differential Equations in Mathematical Biology)
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18 pages, 878 KB  
Article
Code Redteaming: Probing Ethical Sensitivity of LLMs Through Natural Language Embedded in Code
by Chanjun Park, Jeongho Yoon and Heuiseok Lim
Mathematics 2026, 14(1), 189; https://doi.org/10.3390/math14010189 - 4 Jan 2026
Viewed by 319
Abstract
Large language models are increasingly used in code generation and developer tools, yet their robustness to ethically problematic natural language embedded in source code is underexplored. In this work, we study content-safety vulnerabilities arising from ethically inappropriate language placed in non-functional code regions [...] Read more.
Large language models are increasingly used in code generation and developer tools, yet their robustness to ethically problematic natural language embedded in source code is underexplored. In this work, we study content-safety vulnerabilities arising from ethically inappropriate language placed in non-functional code regions (e.g., comments or identifiers), rather than traditional functional security vulnerabilities such as exploitable program logic. In real-world and educational settings, programmers may include inappropriate expressions in identifiers, comments, or print statements that are operationally inert but ethically concerning. We present Code Redteaming, an adversarial evaluation framework that probes models’ sensitivity to such linguistic content. Our benchmark spans Python and C and applies sentence-level and token-level perturbations across natural-language-bearing surfaces, evaluating 18 models from 1B to 70B parameters. Experiments reveal inconsistent scaling trends and substantial variance across injection types and surfaces, highlighting blind spots in current safety filters. These findings motivate input-sensitive safety evaluations and stronger defenses for code-focused LLM applications. Full article
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26 pages, 3857 KB  
Article
Analysis of Discretization Errors in the Signal Model of the Integrate-And-Dump Filter in Satellite Navigation Receivers
by Junbo Tie, Changqing Xun, Yan Guo, Li Luo, Menglong Lu, Yongwen Wang and Li Zhou
Mathematics 2026, 14(1), 188; https://doi.org/10.3390/math14010188 - 4 Jan 2026
Viewed by 201
Abstract
The integrate-and-dump filter is a core component of satellite navigation receivers, enabling the tracking of navigation satellite signals and significantly influencing receiver performance. Currently, satellite navigation receivers, particularly onboard unmanned aerial vehicles (UAVs), are vulnerable to spoofing. Whether counterfeit signals can successfully hijack [...] Read more.
The integrate-and-dump filter is a core component of satellite navigation receivers, enabling the tracking of navigation satellite signals and significantly influencing receiver performance. Currently, satellite navigation receivers, particularly onboard unmanned aerial vehicles (UAVs), are vulnerable to spoofing. Whether counterfeit signals can successfully hijack a receiver depends critically on how these signals alter the integrate-and-dump filter output. Existing research on satellite navigation spoofing often uses an output signal model for the integrate-and-dump filter derived from continuous-time integration. However, this model deviates from practical implementation because most modern navigation receivers are built on digital circuits that approximate continuous-time integration through discrete-time accumulation. Consequently, the discrete-time nature of actual hardware introduces errors that are not captured by the conventional continuous-time model. In this study, a mathematical model for the output signal of an integrate-and-dump filter was implemented via discrete-time accumulation. The accuracy of the proposed model was verified through simulations, and a comparative analysis with the traditional continuous-time integration model was conducted to highlight the impact of discretization errors. Full article
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21 pages, 3379 KB  
Article
KORIE: A Multi-Task Benchmark for Detection, OCR, and Information Extraction on Korean Retail Receipts
by Mahmoud SalahEldin Kasem, Mohamed Mahmoud, Mostafa Farouk Senussi, Mahmoud Abdalla and Hyun Soo Kang
Mathematics 2026, 14(1), 187; https://doi.org/10.3390/math14010187 - 4 Jan 2026
Viewed by 883
Abstract
We introduce KORIE, a curated benchmark of 748 Korean retail receipts designed to evaluate scene text detection, Optical Character Recognition (OCR), and Information Extraction (IE) under challenging digitization conditions. Unlike existing large-scale repositories, KORIE consists exclusively of receipts digitized via flatbed scanning (HP [...] Read more.
We introduce KORIE, a curated benchmark of 748 Korean retail receipts designed to evaluate scene text detection, Optical Character Recognition (OCR), and Information Extraction (IE) under challenging digitization conditions. Unlike existing large-scale repositories, KORIE consists exclusively of receipts digitized via flatbed scanning (HP LaserJet MFP), specifically selected to preserve complex thermal printing artifacts such as ink fading, banding, and mechanical creases. We establish rigorous baselines across three tasks: (1) Detection, comparing Weakly Supervised Object Localization (WSOL) against state-of-the-art fully supervised models (YOLOv9, YOLOv10, YOLOv11, and DINO-DETR); (2) OCR, benchmarking Tesseract, EasyOCR, PaddleOCR, and a custom Attention-based BiGRU; and (3) Information Extraction, evaluating the zero-shot capabilities of Large Language Models (Llama-3, Qwen-2.5) on structured field parsing. Our results identify YOLOv11 as the optimal detector for dense receipt layouts and demonstrate that while PaddleOCR achieves the lowest Character Error Rate (15.84%), standard LLMs struggle in zero-shot settings due to domain mismatch with noisy Korean receipt text, particularly for price-related fields (F1 scores ≈ 25%). We release the dataset, splits, and evaluation code to facilitate reproducible research on degraded Hangul document understanding. Full article
(This article belongs to the Special Issue Advanced Methods and Applications with Deep Learning in Object Recognition)
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22 pages, 1096 KB  
Article
Modeling DECT-2020 as a Tandem Queueing System and Its Application to the Peak Age of Information Analysis
by Dmitry Nikolaev, Anna Zhivtsova, Sergey Matyushenko, Yuliya Gaidamaka and Yevgeni Koucheryavy
Mathematics 2026, 14(1), 186; https://doi.org/10.3390/math14010186 - 4 Jan 2026
Viewed by 252
Abstract
The Peak Age of Information (PAoI) quantifies the freshness of updates used in cyber-physical systems (CPSs), realized within the Internet of Things (IoT) paradigm, encompassing devices, networks, and control algorithms. Consequently, PAoI is a critical metric for real-time applications enabled by Ultra-Reliable Low [...] Read more.
The Peak Age of Information (PAoI) quantifies the freshness of updates used in cyber-physical systems (CPSs), realized within the Internet of Things (IoT) paradigm, encompassing devices, networks, and control algorithms. Consequently, PAoI is a critical metric for real-time applications enabled by Ultra-Reliable Low Latency Communication (URLLC). While highly useful for system evaluation, the direct analysis of this metric is complicated by the correlation between the random variables constituting the PAoI. Thus, it is often evaluated using only the mean value rather than the full distribution. Furthermore, since CPS communication technologies like Wi-Fi or DECT-2020 involve multiple processing stages, modeling them as tandem queueing systems is essential for accurate PAoI analysis. In this paper, we develop an analytical model for a DECT-2020 network segment represented as a two-phase tandem queueing system, enabling detailed PAoI analysis via Laplace–Stieltjes transforms (LST). We circumvent the dependence between generation and sojourn times by classifying updates into four mutually exclusive groups. This approach allows us to derive the LST of the PAoI and determine the exact Probability Density Function (PDF) for M|M|1→M|M|1 system. We also calculate the mean and variance of the PAoIs and validate our results through numerical experiments. Additionally, we evaluate the impact of different service time distributions on PAoI variability. These findings contribute to the theoretical understanding of PAoI in tandem queueing systems and provide practical insights for optimizing DECT-2020-based communication systems. Full article
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35 pages, 6797 KB  
Systematic Review
Optimization Techniques for Improving Economic Profitability Through Supply Chain Processes: A Systematic Literature Review
by Ricardo Jarquin-Segovia and José Antonio Marmolejo-Saucedo
Mathematics 2026, 14(1), 185; https://doi.org/10.3390/math14010185 - 4 Jan 2026
Viewed by 393
Abstract
In today’s dynamic and global business landscape, economic profitability is essential for creating and sustaining competitive advantage. Nevertheless, a critical gap persists in the literature regarding the application of advanced optimization techniques that systematically link operational improvements in the supply chain with strategic [...] Read more.
In today’s dynamic and global business landscape, economic profitability is essential for creating and sustaining competitive advantage. Nevertheless, a critical gap persists in the literature regarding the application of advanced optimization techniques that systematically link operational improvements in the supply chain with strategic financial indicators. Accordingly, this study aims to identify and synthesize the optimization techniques applied to supply chain processes and their impact on economic profitability. To achieve this objective, the PRISMA methodology was employed. A systematic literature review covering the last ten years (2015–2025) was conducted using the Web of Science database. After applying inclusion and exclusion criteria, 35 studies were selected, revealing a growing methodological diversity. Nature-Inspired Algorithms (NIAs) and hybrid approaches (such as MILP combined with Simulation) demonstrate greater capacity to address complex and multi-objective scenarios. Notably, hybrid techniques have been successfully applied to the maximization of Economic Value Added (EVA), a key strategic value indicator. Despite the sophistication of these optimization techniques, the predominant objective remains total cost minimization, often sidelining the direct optimization of strategic indicators such as EVA or the Cash Conversion Cycle (CCC). Additionally, a key research gap was identified in the development of adaptive and resilient models that integrate technologies such as Digital Twins, Blockchain, and Artificial Intelligence to dynamically manage physical and financial disruptions in supply chains. The study concludes by emphasizing the need for a theoretical shift toward models that go beyond cost minimization and focus on real value metrics, as well as the exploration of more accessible solutions for SMEs. This review contributes a reference framework for academics and practitioners to align the most suitable optimization techniques with strategic financial objectives in supply chain management. Full article
(This article belongs to the Special Issue Emerging Trends in Real-Time Optimization to Digitize Processes and Operations)
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15 pages, 1182 KB  
Article
Enhanced Recommender System with Sentiment Analysis of Review Text and SBERT Embeddings of Item Descriptions
by Doyeon Lim and Taemin Lee
Mathematics 2026, 14(1), 184; https://doi.org/10.3390/math14010184 - 3 Jan 2026
Viewed by 344
Abstract
As a transition from offline to online shopping is taking place in many societies, many studies have been conducted to align products with user preferences. However, the existing collaborative filtering technology has a small number of user–item interactions, resulting in data sparsity and [...] Read more.
As a transition from offline to online shopping is taking place in many societies, many studies have been conducted to align products with user preferences. However, the existing collaborative filtering technology has a small number of user–item interactions, resulting in data sparsity and cold start problems. This study proposes a recommendation system that combines customer preference for an item with quantitative indicators. To this end, the Amazon dataset is used to quantify an item’s attribute information through Sentence-BERT, and emotion analysis of the review data is performed. The model proposed in this study simultaneously utilizes the attribute information and review data of an item, proving that it provides higher performance than when using review text alone. Finally, we verified that our approach significantly outperforms traditional baseline models and rating predictions and effectively improves top K recommendation indicators. In addition, ablation studies found that integrating item attributes and review emotions performs better than using them individually. This means that the complementary synthesis of objective item meanings and subjective user emotions can model user preferences more accurately, enabling personalized recommendations. Full article
(This article belongs to the Special Issue Mathematical Foundations and Advances in Machine Learning and Data Mining)
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21 pages, 3447 KB  
Article
Vehicle Sideslip Angle Redundant Estimation Based on Multi-Source Sensor Information Fusion
by Danhua Chen, Jie Hu, Guoqing Sun, Feiyue Rong, Pei Zhang, Yuanyi Huang and Ze Cao
Mathematics 2026, 14(1), 183; https://doi.org/10.3390/math14010183 - 3 Jan 2026
Viewed by 329
Abstract
The sideslip angle is a key state for evaluating the lateral stability of a vehicle. Its accurate estimation is crucial for active safety and intelligent driving assistance systems. To improve the estimation accuracy and robustness of the sideslip angle for distributed drive electric [...] Read more.
The sideslip angle is a key state for evaluating the lateral stability of a vehicle. Its accurate estimation is crucial for active safety and intelligent driving assistance systems. To improve the estimation accuracy and robustness of the sideslip angle for distributed drive electric vehicles (DDEV) under extreme maneuvering conditions, this paper proposes a redundant estimation scheme based on multi-source sensor information fusion. Firstly, a dynamic model of the DDEV is established, including the vehicle body dynamics model, wheel rotation dynamics model, tire model, and hub motor model. Subsequently, robust unscented particle filtering (RUPF) and backpropagation (BP) neural network algorithms are developed to estimate the sideslip angle from both the vehicle dynamics and data-driven perspectives. Based on this, a redundant estimation scheme for the sideslip angle is developed. Finally, the effectiveness of the redundant estimation scheme is validated through the Matlab/Simulink-CarSim co-simulation platform using MATLAB R2022b and CarSim 2020.0. Full article
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21 pages, 328 KB  
Article
Analytic Study on Φ-Hilfer Fractional Neutral-Type Functional Integro-Differential Equations with Terminal Conditions
by Ravichandran Vivek, Abdulah A. Alghamdi, Mohamed M. El-Dessoky, Dhandapani Maheswari and Natarajan Bharath
Mathematics 2026, 14(1), 182; https://doi.org/10.3390/math14010182 - 3 Jan 2026
Viewed by 247
Abstract
The current manuscript is concerned with the uniqueness and existence of a solution for a new class of Φ-Hilfer fractional neutral functional integro-differential equations (Φ-HFNFIDEs) with terminal conditions. Firstly, employing Babenko’s approach, we convert the aforesaid equation under consideration into [...] Read more.
The current manuscript is concerned with the uniqueness and existence of a solution for a new class of Φ-Hilfer fractional neutral functional integro-differential equations (Φ-HFNFIDEs) with terminal conditions. Firstly, employing Babenko’s approach, we convert the aforesaid equation under consideration into an analogous integral equation. More precisely, using the multivariate Mittag-Leffler function, Banach contraction principle, and Krasnoselskii’s fixed-point theorem, we derive some conditions that guarantee the uniqueness and the existence of the solutions. For an illustration of our results in this manuscript, two examples are provided as well. Full article
37 pages, 3749 KB  
Article
Quantum-Enhanced Residual Convolutional Attention Architecture for Renewable Forecasting in Off-Grid Cloud Microgrids
by Ibrahim Alzamil
Mathematics 2026, 14(1), 181; https://doi.org/10.3390/math14010181 - 3 Jan 2026
Viewed by 235
Abstract
Multimodal forecasting is increasingly needed to maintain energy levels, storage capacity, and compute efficiency in off-grid, renewable-powered cloud environments. Variable sensor quality, uncertain interactions with renewable energy, and rapidly changing weather patterns make real-time forecasting difficult. Current transformer, GNN, and CNN systems suffer [...] Read more.
Multimodal forecasting is increasingly needed to maintain energy levels, storage capacity, and compute efficiency in off-grid, renewable-powered cloud environments. Variable sensor quality, uncertain interactions with renewable energy, and rapidly changing weather patterns make real-time forecasting difficult. Current transformer, GNN, and CNN systems suffer from sensor noise instability, multimodal temporal–spectral correlation issues, and challenges in the interpretability of operational decision-making. In this research, Q-RCANeX, a quantum-guided residual convolutional attention network for off-grid cloud infrastructures, estimates battery state of charge, renewable energy sources, and microgrid efficiency to overcome these restrictions. The system uses a Hybrid Quantum–Bayesian Evolutionary Optimizer, quantum feature embedding, temporal–spectral attention, residual convolutional encoding, and signal decomposition preprocessing. These parameters reinforce features, reduce noise, and align forecasting behavior with microgrid dynamics. Q-RCANeX obtains 98.6% accuracy, 0.992 AUC, and 0.986 R3 values for REAF, WGF, SOC-F, and EEIF forecasting tasks, according to a statistical study. Additionally, it determines inference latency to 4.9 ms and model size to 18.5 MB. Even with 20% of sensor data missing or noisy, the model outperforms 12 state-of-the-art baselines and maintains 96.8% accuracy using ANOVA, Wilcoxon, Nemenyi, and Holm tests. The findings indicate that the forecasting framework has high accuracy, clarity, and resilience to failures. This makes it useful for real-time, off-grid management of renewable cloud microgrids. Full article
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13 pages, 912 KB  
Article
Artificial Intelligence for Studying Interactions of Solitons and Peakons
by Angela Slavova and Ventsislav Ignatov
Mathematics 2026, 14(1), 180; https://doi.org/10.3390/math14010180 - 3 Jan 2026
Viewed by 315
Abstract
In this paper, Artificial Intelligence (AI) is developed for studying the Boussinesq Paradigm equation and so called b-equation based on Physics-Informed Cellular Neural Networks (PICNNs). The models studied here come from fluid dynamics. Machine learning through Physics-Informed Neural Networks (PINNs) is a powerful [...] Read more.
In this paper, Artificial Intelligence (AI) is developed for studying the Boussinesq Paradigm equation and so called b-equation based on Physics-Informed Cellular Neural Networks (PICNNs). The models studied here come from fluid dynamics. Machine learning through Physics-Informed Neural Networks (PINNs) is a powerful tool for solving complex problems arising in physical laws. By optimization and automatic differentiation, the solutions of the model under consideration can be approximated precisely and can be obtained in real time. In this paper, we shall apply a new algorithm based on Physics-Informed Cellular Neural Networks (PICNNs) for obtaining the interactions between solitons and peakons. The algorithm has many advantages, but the main ones are that it provides the fastest programming and solutions in real time. It is known that Cellular Neural Networks (CNNs) have the ability to approximate, in a very accurate way, nonlinear partial differential equations (PDEs) and to present their solutions in real time. By incorporating the physical laws into the learning process through PICNN we can solve various problems from fluid dynamics, material science, and quantum mechanics. Full article
(This article belongs to the Special Issue Applications of Differential Equations in Sciences)
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42 pages, 1106 KB  
Article
Nonlinear Transport of Tracer Particles Immersed in a Strongly Sheared Dilute Gas with Inelastic Collisions
by David González Méndez and Vicente Garzó
Mathematics 2026, 14(1), 179; https://doi.org/10.3390/math14010179 - 3 Jan 2026
Viewed by 197
Abstract
Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic [...] Read more.
Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic Boltzmann collision operator but consider inelastic Maxwell models (IMMs) instead of the realistic model of inelastic hard spheres (IHS). Using IMMs enables us to compute the collisional moments of the inelastic Boltzmann operator for mixtures without explicitly knowing the velocity distribution functions of the mixture. Second, we consider a kinetic model of the Boltzmann equation for IHS. This kinetic model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of IHS. We solve the Boltzmann–Lorentz kinetic equation for tracer particles using a generalized Chapman–Enskog-like expansion around the shear flow distribution. This reference distribution retains all hydrodynamic orders in the shear rate. The mass flux is obtained to first order in the deviations of the concentration, pressure, and temperature from their values in the reference state. Due to the anisotropy induced in the velocity space by shear flow, the mass flux is expressed in terms of tensorial quantities rather than conventional scalar diffusion coefficients. Unlike the previous results obtained for IHS using different approximations, the results derived in this paper are exact. Generally, the comparison between the IHS results and those found here shows reasonable quantitative agreement, especially for IMM results. This good agreement shows again evidence of the reliability of IMMs for studying rapid granular flows. Finally, we analyze segregation by thermal diffusion as an application of the theory. Phase diagrams illustrating segregation are presented and compared with previous IHS results, demonstrating qualitative agreement. Full article
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19 pages, 3550 KB  
Article
CAG-Net: A Novel Change Attention Guided Network for Substation Defect Detection
by Dao Xiang, Xiaofei Du and Zhaoyang Liu
Mathematics 2026, 14(1), 178; https://doi.org/10.3390/math14010178 - 2 Jan 2026
Viewed by 312
Abstract
Timely detection and handling of substation defects plays a foundational role in ensuring the stable operation of power systems. Existing substation defect detection methods fail to make full use of the temporal information contained in substation inspection samples, resulting in problems such as [...] Read more.
Timely detection and handling of substation defects plays a foundational role in ensuring the stable operation of power systems. Existing substation defect detection methods fail to make full use of the temporal information contained in substation inspection samples, resulting in problems such as weak generalization ability and susceptibility to background interference. To address these issues, a change attention guided substation defect detection algorithm (CAG-Net) based on a dual-temporal encoder–decoder framework is proposed. The encoder module employs a Siamese backbone network composed of efficient local-global context aggregation modules to extract multi-scale features, balancing local details and global semantics, and designs a change attention guidance module that takes feature differences as attention weights to dynamically enhance the saliency of defect regions and suppress background interference. The decoder module adopts an improved FPN structure to fuse high-level and low-level features, supplement defect details, and improve the model’s ability to detect small targets and multi-scale defects. Experimental results on the self-built substation multi-phase defect dataset (SMDD) show that the proposed method achieves 81.76% in terms of mAP, which is 3.79% higher than that of Faster R-CNN and outperforms mainstream detection models such as GoldYOLO and YOLOv10. Ablation experiments and visualization analysis demonstrate that the method can effectively focus on defect regions in complex environments, improving the positioning accuracy of multi-scale targets. Full article
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31 pages, 5845 KB  
Article
Gait Dynamics Classification with Criticality Analysis and Support Vector Machines
by Shadi Eltanani, Tjeerd V. olde Scheper, Johnny Collett, Helen Dawes and Patrick Esser
Mathematics 2026, 14(1), 177; https://doi.org/10.3390/math14010177 - 2 Jan 2026
Viewed by 293
Abstract
Classifying demographic groups of humans from gait patterns is desirable from several long-standing diagnostic and monitoring perspectives. IMU recorded gait patterns are mapped into a nonlinear dynamic representation space using criticality analysis and subsequently classified using standard Support Vector Machines. Inertial-only gait recordings [...] Read more.
Classifying demographic groups of humans from gait patterns is desirable from several long-standing diagnostic and monitoring perspectives. IMU recorded gait patterns are mapped into a nonlinear dynamic representation space using criticality analysis and subsequently classified using standard Support Vector Machines. Inertial-only gait recordings were found to readily classify in the CA representations. Accuracies across age categories for female versus male were 72.77%, 78.95%, and 80.11% for σ=0.1, 1, and 10, respectively; within the female group, accuracies were 73.36%, 76.70%, and 78.90%; and within the male group, 77.65%, 81.48%, and 81.05%. These results show that dynamic biological data are easily classifiable when projected into the nonlinear space, while classifying the data without this is not nearly as effective. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
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34 pages, 2671 KB  
Article
A Tuning-Free Constrained Team-Oriented Swarm Optimizer (CTOSO) for Engineering Problems
by Adel BenAbdennour and Abdulmajeed M. Alenezi
Mathematics 2026, 14(1), 176; https://doi.org/10.3390/math14010176 - 2 Jan 2026
Viewed by 295
Abstract
Constrained optimization problems (COPs) are frequent in engineering design yet remain challenging due to complex search spaces and strict feasibility requirements. Existing swarm-based optimizers often rely on penalty functions or algorithm-specific control parameters, whose performance is sensitive to problem-dependent tuning and may lead [...] Read more.
Constrained optimization problems (COPs) are frequent in engineering design yet remain challenging due to complex search spaces and strict feasibility requirements. Existing swarm-based optimizers often rely on penalty functions or algorithm-specific control parameters, whose performance is sensitive to problem-dependent tuning and may lead to premature convergence or infeasible solutions when feasible regions are narrow. This paper introduces the Constrained Team-Oriented Swarm Optimizer (CTOSO), a tuning-free metaheuristic that adapts the ETOSO framework by replacing linear exploiter movement with spiral search and integrating Deb’s feasibility rule. The population divides into Explorers, promoting diversity through neighbor-guided navigation, and Exploiters, performing intensified local search around the global best solution. Extensive evaluation on twelve constrained engineering benchmark problems shows that CTOSO achieves a 100% feasibility rate and attains the highest overall composite performance score among the compared algorithms under limited function-evaluation budgets. On the CEC 2017 constrained benchmark suite, CTOSO attains an average feasibility rate of 79.78%, generating feasible solutions on 14 out of 15 problems. Statistical analysis using Wilcoxon signed-rank tests and Friedman ranking with Nemenyi post hoc comparison indicates that CTOSO performs significantly better than several baseline optimizers, while exhibiting no statistically significant differences with leading evolutionary methods under the same experimental conditions. The algorithm’s design, requiring no tuning of algorithm-specific control parameters, makes it suitable for real-world engineering applications where tuning effort must be minimized. Full article
(This article belongs to the Special Issue Intelligent and Nature-Inspired Heuristics for Optimization and Decision-Making Problems)
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40 pages, 5732 KB  
Review
From Context to Human: A Review of VLM Contextualization in the Recognition of Human States in Visual Data
by Corneliu Florea, Constantin-Bogdan Popescu, Andrei Racovițeanu, Andreea Nițu and Laura Florea
Mathematics 2026, 14(1), 175; https://doi.org/10.3390/math14010175 - 2 Jan 2026
Viewed by 413
Abstract
This paper presents a narrative review of the contextualization and contribution offered by vision–language models (VLMs) for human-centric understanding in images. Starting from the correlation between humans and their context (background) and by incorporating VLM-generated embeddings into recognition architectures, recent solutions have advanced [...] Read more.
This paper presents a narrative review of the contextualization and contribution offered by vision–language models (VLMs) for human-centric understanding in images. Starting from the correlation between humans and their context (background) and by incorporating VLM-generated embeddings into recognition architectures, recent solutions have advanced the recognition of human actions, the detection and classification of violent behavior, and inference of human emotions from body posture and facial expression. While powerful and general, VLMs may also introduce biases that can be reflected in the overall performance. Unlike prior reviews that focus on a single task or generic image captioning, this review jointly examines multiple human-centric problems in VLM-based approaches. The study begins by describing the key elements of VLMs (including architectural foundations, pre-training techniques, and cross-modal fusion strategies) and explains why they are suitable for contextualization. In addition to highlighting the improvements brought by VLMs, it critically discusses their limitations (including human-related biases) and presents a mathematical perspective and strategies for mitigating them. This review aims to consolidate the technical landscape of VLM-based contextualization for human state recognition and detection. It aims to serve as a foundational reference for researchers seeking to control the power of language-guided VLMs in recognizing human states correlated with contextual cues. Full article
(This article belongs to the Special Issue Advance in Neural Networks and Visual Learning)
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13 pages, 290 KB  
Article
New Properties and Determinantal Representations of Leonardo Finite Operator Polynomials
by Emrah Polatlı, Can Kızılateş and Wei-Shih Du
Mathematics 2026, 14(1), 174; https://doi.org/10.3390/math14010174 - 2 Jan 2026
Viewed by 205
Abstract
The aim of this paper is to introduce Leonardo finite operator polynomials and obtain some of their new properties. We first present the recurrence relation provided by Leonardo finite operator polynomials. Then, we give a Binet-like formula, generating function, exponential generating function, and [...] Read more.
The aim of this paper is to introduce Leonardo finite operator polynomials and obtain some of their new properties. We first present the recurrence relation provided by Leonardo finite operator polynomials. Then, we give a Binet-like formula, generating function, exponential generating function, and a finite sum formula for Leonardo finite operator polynomials. We present a determinant representation for the nth term of Leonardo finite operator polynomials. Ultimately, by utilizing the generating function of the proposed polynomials, we establish generating relations for specific bilinear and bilateral polynomial families. This approach thus broadens the applicability of the finite operator framework to encompass a wider range of special functions. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
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