Mathematics doi: 10.3390/math14132285

Authors: Cong Wang Wei Xin Jun Li Xigui Zheng Yu Zhao Zhongguo He

Hydraulic supports in coal mining faces require continuous pressure monitoring to detect anomalies indicative of roof instability or equipment failure. Existing reconstruction-based methods rely on standard convolutional or recurrent encoders whose limited receptive fields or coarse temporal representations restrict detection accuracy; static per-window thresholding further discards temporal continuity during online deployment. This study proposes a temporal convolutional network autoencoder (TCN-AE) coupled with a Cumulative Sum (CUSUM) control chart for online anomaly detection in hydraulic support pressure data. The TCN encoder uses dilated convolutions with symmetric padding and residual connections, producing an exponentially expanding receptive field that captures temporal patterns at multiple scales. The CUSUM chart accumulates sustained positive deviations in the reconstruction error sequence, improving detection sensitivity while suppressing isolated false alarms. Component analysis experiments on synthetic anomalies show TCN-AE achieves an AUC of 0.811, outperforming CNN, LSTM, GRU, and fully connected autoencoder variants, along with Isolation Forest and One-Class SVM. On a manually curated real fault test set, where per-window reconstruction scores carry negligible discriminative information (AUC = 0.586, near chance), the CUSUM strategy exploits temporal continuity to improve F1 from 0.213 to 0.905 for TCN-AE. This +0.692 gain is driven entirely by temporal accumulation rather than model discriminability, demonstrating that the CUSUM framework is most valuable precisely when per-window signals are weakest.

Mathematics doi: 10.3390/math14132284

Authors: Borislav Penev

The proposed approach decomposes in a special way the original two-input linear time-optimal control problem into two single-input linear time-optimal problems whose optimal solutions are subsequently recombined. A lemma and a theorem establish conditions under which the recombined control vector is a candidate for the optimal solution and provide a simple criterion, based on the Pontryagin Maximum Principle, to determine whether the obtained control is truly optimal or only near optimal. The method is illustrated on a modified canonical double integrator system with two independent inputs. The resulting control system preserves the bang-bang structure and switching sequence of the true optimal solution, while providing a transition time that exceeds the optimal value by only 0.55%. The proposed method offers a basis for developing a technique regarding the multi-input linear time-optimal control problems.

Mathematics doi: 10.3390/math14132283

Authors: Daozheng Qu Yanfei Ma Jingke Yan Mykhailo Pyrozhenko

Dynamic community detection seeks to identify changing structural groups in temporal graphs; however, current neural methodologies are susceptible to misinterpreting transient edges, noisy temporal variations, or unusual spectral disturbances as authentic structural changes. This research introduces TriMeta-BFNet, a tri-meta stacked atypical-frequency Bayesian Fourier neural network designed for hallucination-resistant community discovery. The proposed system presents a three-dimensional meta-counterbalance mechanism that includes topological consistency, Fourier-domain atypical frequency modeling, and Bayesian posterior uncertainty estimation. Initially, temporal graph signals are converted into the Fourier domain to distinguish stable low-frequency community patterns from erratic high-frequency disturbances. Secondly, unusual frequency points are detected by spectral energy deviation and integrated into a stacked neural representation module, enabling the model to differentiate significant structural alterations from extraneous oscillations. Third, Bayesian inference is employed to assess posterior uncertainty regarding community assignments, therefore mitigating overconfident predictions in the presence of ambiguous or noisy graph evolution. The three components are simultaneously optimized via a cohesive objective function that integrates community detection loss, structural consistency regularization, atypical-frequency penalty, temporal stability management, and Bayesian calibration loss. The resultant structure offers both resilient community divisions and comprehensible hallucination-risk assessments. TriMeta-BFNet theoretically conceptualizes hallucination in dynamic community detection as an imbalance of structural, spectral, and uncertainty factors, and it develops a mathematically rigorous counterbalance mechanism to mitigate erroneous community evolution. The suggested model presents a novel approach to uncertainty-aware, frequency-sensitive, and interpretable dynamic graph learning.

Mathematics doi: 10.3390/math14132282

Authors: Victor D. Cruz-González Héctor Benítez-Pérez Rocío Aldeco-Pérez

In this paper, we propose a multilevel stochastic model for the energy consumption of public proof-of-work blockchains. The main novelty is the proposal of a closed form for the expected energy consumption in one proof of work mining round. In the case of homogeneous per-hash efficiency, this proposition shows that the expected spending is e0/p depending only on the protocol difficulty and not on the distribution of the hash power among the miners. The proposal connects three levels of analysis: a local model of mining at the node level, a semi-global model of competitive block discovery and propagation, and a global stochastic model of workload, computational capacity, network connectivity and power consumption. This leads to the above closed form energy result. The mining process is approximated locally by exponential waiting times of Bernoulli hash trials. This extends to the semi-global model where the competition among miners and the delay in the propagation lead to the wasted computation. The global layer is modeled as a set of stochastic differential equations which models the interaction between workload dynamics, capacity constraints and communication overheads. The core analysis does not need Bayesian or Markov decision components but these are recommended for modeling estimation and adaptive control. We start with preliminary simulations on the VIBES platform and find qualitative properties of the full model: the total energy cost scales roughly linearly with the size of the network, the average energy per node decreases with increasing network size, the propagation latency is the primary source of wasted computation due to stale blocks and nodes tend to operate in a capacity-depleted regime with the workload-induced degradation being substantially higher than the recovery rate. The results give a structural analysis of how the design of the protocol and the network conditions affect the energy consumption and emphasize the importance of quantitatively calibrating with empirical data from Bitcoin.

Mathematics doi: 10.3390/math14132281

Authors: Ignacio Alejandro Sepulveda Carrasco Bernardo A. Hernandez Vicente

In this paper we implement robust switching model predictive control to solve the dual control problem of simultaneous regulation and system identification, for linear time varying systems subject to bounded external disturbances and confined instances of variation. We leverage the piece-wise linear control law resulting from a fictitious switching architecture to generate closed-loop data that ensures strong system identifiability, while guaranteeing stability and constraint satisfaction under unknown—but bounded—disturbances and parameter variation. We pair the switching controller with a standard recursive estimation algorithm with forgetting factor, which yields unbiased estimates with variance associated to the external disturbance, showcasing the success of the switching at producing information in the closed-loop trajectories.

Mathematics doi: 10.3390/math14132280

Authors: Tao Yang Lirong Ma Run Yang Changyou Wang

Max-type fuzzy difference equations constitute an emerging research area arising from the integration of fuzzy mathematics and discrete dynamical systems. By characterizing uncertainty through fuzzy numbers, these equations provide rigorous mathematical modeling tools for practical problems involving both discreteness and uncertainty. This paper systematically investigates the dynamical properties of a class of max-type fuzzy difference equations. First, fuzzy set theory is used to transform the fuzzy difference equation into a corresponding system of parametric ordinary difference equations. Then, using the iterative method, inequality techniques, and mathematical induction, an expression for the periodic solutions of the max-type ordinary difference equation is derived, from which an expression for the periodic solutions of the max-type fuzzy difference equation is further obtained. In addition, the boundedness and persistence of the solutions to the fuzzy difference equation are proved. Finally, numerical simulations are conducted in MATLAB 2024, and the results illustrate the theoretical findings. This study not only enriches the theoretical framework of fuzzy difference equations but also provides new insights and methodological support for the modeling and analysis of uncertain discrete systems.

Mathematics doi: 10.3390/math14132276

Authors: Yang Cao Zilin Li

The Artificial Bee Colony (ABC) algorithm is widely used for continuous optimization, but the standard ABC still suffers from insufficient use of neighborhood information, limited adaptability of search behavior, and random restarts in the scout bee phase, which may lead to slow convergence and reduced solution quality on complex problems. To address these limitations, this paper proposes an artificial bee colony algorithm with dual groups and multiple strategies based on reinforcement learning, named RLDMS-ABC. In the employed bee phase, Q-learning is used to adaptively adjust the neighborhood size of each food source according to search feedback, and the best individual selected from the sampled neighborhood guides candidate solution generation. In the onlooker bee phase, selected food sources are divided into elite and ordinary groups according to relative quality, and different search strategies are assigned to balance exploration and exploitation. In the scout bee phase, a guided restart mechanism combining opposition-based learning and the current global best solution is designed to help stagnated individuals escape local optima. Experiments on the CEC 2014 benchmark set show that RLDMS-ABC outperforms several representative ABC variants on most functions in terms of solution quality, convergence speed, and robustness.

Mathematics doi: 10.3390/math14132279

Authors: Blanca Verónica Zuñiga-Núñez Erick Israel Guerra-Hernández Patricia Batres-Mendoza Itandehui Belem Gallegos-Velasco Marco Aurelio Sotelo-Figueroa

Grammatical Evolution is a technique for evolving structured solutions using a genotype-to-phenotype mapping based on formal grammar. Optimization is typically performed on the genotype values. However, the use of permutations to guide mapping has been shown to improve solution performance. Traditionally, the focus has been on single-level optimization of the genotype values or the order in which codons are consumed during mapping. This motivates the use of a bilevel approach that enables the simultaneous optimization of genotype values and their ordering. This paper proposes a bilevel Grammatical Evolution approach called BiGE, in which the upper level optimizes the genotype values, whereas the lower level optimizes the order in which these same values are used in the mapping process. The approach was implemented using both Depth-First (DF) and Breadth-First (BF) mapping processes, which are the canonical mapping strategies in Grammatical Evolution. The proposed approach was evaluated on the Symbolic Regression Problem and compared with state-of-the-art approaches under identical experimental conditions. Statistical tests were performed to determine whether significant differences existed among the compared approaches. The results revealed statistically significant differences, indicating that incorporating a bilevel optimization strategy into the mapping process can improve the quality of the generated solutions

Mathematics doi: 10.3390/math14132278

Authors: Jen Chieh Lo

In this paper, we establish new Milne–Mercer-type inequalities via Atangana–Baleanu conformable fractional integral operators for differentiable functions whose derivatives in absolute value are h-convex. First, we derive a novel identity involving the Atangana–Baleanu conformable fractional integral operators. Then, by employing the properties of h-convex functions and fractional integral operators, several new inequalities of the Milne–Mercer type are obtained. The results presented in this paper extend and generalize various previously known inequalities, including classical Milne inequalities, Riemann–Liouville fractional integral inequalities, and conformable fractional integral inequalities. Moreover, several special cases are discussed to demonstrate the generality and applicability of the obtained results. The findings provide new refinements in the theory of fractional integral inequalities and contribute to the development of convex analysis within fractional frameworks.

Mathematics doi: 10.3390/math14132277

Authors: Hanifah Al Affiani Muhamad Deni Johansyah Endang Rusyaman Sukono Nurfadhlina Binti Abdul Halim Alim Jaizul Wahid Moch Panji Agung Saputra Astrid Sulistya Azahra Aceng Sambas

Rainfall-index-based disaster insurance is an efficient approach to mitigating hydrometeorological losses. However, conventional premium pricing models generally assume memoryless stochastic dynamics that do not fully capture the long-range dependence inherent in rainfall data. This study develops a hydrometeorological disaster insurance model within a fractional Black–Scholes framework to incorporate long-memory effects. The model is formulated using fractional differential equations and solved semi-analytically by integrating the Daftardar–Jafari Method (DJM) with the Kashuri–Fundo (KF) transform, yielding a closed-form solution expressed in terms of the Mittag–Leffler function. The proposed contract is structured as parametric rainfall insurance with a multi-layer payout mechanism based on percentiles corresponding to minor, moderate, and severe housing damage. The results show that variations in the fractional-order parameter significantly affect premium estimation. In particular,  δ = 0.5 recovers the classical model and tends to generate higher premiums than the fractional model with δ = 0.23153, whereas the model with δ = 0.73153 yields lower premiums. These findings indicate that fractional-order parameterization can accommodate diverse risk characteristics and policyholders’ economic capacities, enabling more adaptive, risk-sensitive premium structures. In line with SDG 13 (Climate Action), the proposed framework offers a climate-responsive disaster-mitigation strategy through accessible, actuarially relevant insurance design.  recovers the classical model and tends to generate higher premiums than the fractional model with , whereas the model with  yields lower premiums. These findings indicate that fractional-order parameterization can accommodate diverse risk characteristics and policyholders’ economic capacities, enabling more adaptive, risk-sensitive premium structures. In line with SDG 13 (Climate Action), the proposed framework offers a climate-responsive disaster-mitigation strategy through accessible, actuarially relevant insurance design.

Mathematics doi: 10.3390/math14132275

Authors: Qian Zhang Hai Huang Zhiguo Tan Kaili Feng Yilin Wu

This study proposes an incremental neural network adaptive control algorithm based on composite learning for a two-degree-of-freedom (2-DOF) helicopter system characterised by dynamic event triggering and input saturation. Firstly, by integrating a composite learning strategy within the incremental neural network control framework, the study aims to overcome the challenges posed by system dynamic uncertainties. The proposed novel update algorithm effectively incorporates estimation error terms into the weight adaptation process, thereby improving the approximation capability for system dynamics while alleviating the dependence on the classical persistent excitation condition. In addition, to reduce the communication load between the controller and the actuator, we introduce an adaptive dynamic event-triggered mechanism. Furthermore, a saturation-resistant auxiliary system is constructed to address the input saturation phenomenon present in the system. Subsequently, the system is proven to be semi-globally consistent and bounded stable via Lyapunov functions. Finally, the effectiveness of the control strategy proposed in this study is verified through simulation.

Mathematics doi: 10.3390/math14132274

Authors: JangHo Seo Joonwoo Lee

Grid-based multi-agent path finding (MAPF) solvers scale to large teams, but their discrete schedules may not provide high-quality continuous finite-radius motions near the square-grid corner-passing threshold. We study endpoint-time-preserving geometric smoothing for disk agents at radius 0.35. We establish an embedded-graph corner-passing threshold for synchronized finite-radius local passes and derive the square-grid radius rc=2/4. Finite-radius realizations are formulated as Lipschitz trajectories, and we prove that standard four-neighbor schedules without vertex conflicts or head-on edge swaps are pairwise continuously feasible up to this threshold. The smoother replaces windows by shortcuts only when speed, obstacle-clearance, pairwise continuous-collision detection, and length checks pass. Accepted shortcuts preserve endpoint times, schedule-level makespan, discrete arrival records, and discrete sum-of-costs while enforcing geometric length non-increase; the strict-decrease subset yields the reported geometric sum-of-costs reductions. Across six MovingAI map settings, LaCAM solves 575 benchmark instances; 570 smoothed trajectories pass finite-radius validation, with median geometric sum-of-costs reductions of 9.9% on the main slice and 11.2% on the five-map extension. A targeted 100-agent radius sweep further supports the threshold interpretation by showing a clean feasibility transition around the predicted corner-passing radius. The results support time-preserving smoothing as a validated geometric-quality layer for scalable grid planners.

Mathematics doi: 10.3390/math14132273

Authors: Ömer Faruk Çaparoğlu Yeşim Ok Nadide Çağlayan Özaydın

The main motivation for this study is to develop a predictive framework that provides high accuracy at lower computational and experimental costs, resulting in better decision-making in the chosen application domain. Artificial neural networks (ANNs) are widely used for prediction, classification, and pattern recognition tasks. However, their performance is sensitive to the selection of architectural and learning parameters. Hence, an important research challenge is the effective selection of architectural and learning parameters. Several hybrid GA–PSO approaches have been proposed, but most of the existing studies simultaneously optimize network architecture and trainable parameters or focus on a single application domain. However, there is still a lack of systematic framework that optimizes these components separately and validates its performance on multiple heterogeneous datasets. To fill this gap, this study proposes a novel hybrid optimization algorithm, called GAPSO, which combines the genetic algorithm (GA) and particle swarm optimization (PSO) for efficient tuning of artificial neural network (ANN) parameters. The proposed framework is evaluated on five benchmark datasets, including AirPassengers, Sunspots, Death and Injury, Earthquake, and Insurance. In the proposed approach, PSO is used for determination of optimal network architecture (number of hidden neurons) and GA is used for optimization of connection weights and threshold values. The experimental results demonstrate that for four out of five datasets, the lowest MAPE values were achieved by GAPSO-ANN, and were competitive compared to ANN, GA-ANN, PSO-ANN, LSTM and XGBoost models. Additionally, the Wilcoxon signed-rank test showed statistically significant performance improvements (p = 0.03125).

Mathematics doi: 10.3390/math14132272

Authors: Yohannes Lisanewerk Mulualem Yeabisra Wubishet Engda Tewodros Asfaw Gebretsadik Gang Gyoo Jin Yung Deug Son Jongkap Ahn

Maintaining precise liquid levels in interconnected tank systems is a critical requirement in many industrial processes; however, achieving reliable control remains challenging due to inherent nonlinearities and external disturbances. This paper presents a comparative analysis of three control strategies—sliding mode control (SMC), feedback linearization (FL), and proportional–integral–derivative (PID) control—applied to a nonlinear two-tank system. To address the practical limitation of unmeasured system states, a high-gain observer (HGO) is integrated into the control architecture to reconstruct unmeasured water levels. In addition, the controller and observer parameters are optimized using a hybrid genetic algorithm to balance tracking precision and control effort. Simulation results demonstrate that, although all three methods achieve acceptable setpoint tracking performance, the SMC-HGO configuration exhibits superior robustness. Specifically, it outperforms FL and PID in rejecting external disturbances and maintaining stability under significant parameter variations, such as changes in discharge coefficients.

Mathematics doi: 10.3390/math14132271

Authors: Pengcheng Xiao Ben Wood

We develop a two-age smoking-dynamics model for youth and adult groups that incorporates education acquisition, aging, cessation and relapse, disease progression, age-dependent social mixing, and a weak Allee effect in smoking initiation. Education is modeled as a protective status acquired through schooling and aging transitions, while initiation depends on both education status and prevalence-dependent social reinforcement. We establish the well-posedness of the system, derive the smoking-free equilibrium in closed form, and obtain the compact age-structured threshold R0age=ρdiag(gY,gA)C, where C is the age-mixing matrix and ga summarizes the within-age smoking-invasion potential. Using center-manifold analysis, we derive conditions under which Allee-type social reinforcement can generate a backward bifurcation, implying that reducing R0age below one may not always be sufficient for elimination when endemic prevalence is high. We also analyze the impact of cross-age mixing on the threshold and use a quasi-steady-state approximation to characterize the quitting–relapse loop while preserving the threshold structure. Numerical simulations illustrate baseline youth and adult prevalence trends, identify youth initiation, relapse, cessation, and education protection as dominant drivers of threshold sensitivity, and show that education-based interventions are most effective when they directly reduce the susceptibility of educated youths to smoking initiation.

Mathematics doi: 10.3390/math14132270

Authors: Nguyen Thi Mai Chi Jirachai Buddhakulsomsiri Pham Duc Tai

The selection of transportation service providers (TSPs) is a strategically critical decision in sustainable supply chain management. However, existing decision-making frameworks exhibit three recurring limitations: the absence of formally validated, sector-specific sustainability criteria; reliance on weighting methods that inadequately handle expert judgment uncertainty; and limited application to emerging market contexts, particularly export-oriented garment and textile industries facing growing environmental, social, and traceability pressures from global buyers. To address these gaps, this study develops and validates an integrated multi-criteria decision-making framework combining Content Validity Ratio CVR analysis, the Fuzzy Best–Worst Method (FBWM), and Fuzzy Additive Ratio Assessment (FARAS). CVR analysis was applied to an initial pool of 28 candidate criteria, retaining 22 validated criteria spanning economic, environmental, social, and operational dimensions. FBWM was subsequently used to derive criterion weights from nine decision-makers (DMs) representing garment manufacturers, transportation providers, and academia in Vietnam, while FARAS ranked five candidate TSPs. Results indicate that operational and economic criteria are the most influential dimensions, while cost for the service, financial performance, industry experience, environmental awareness, and environmental legal and policy framework emerge as the five highest-weighted sub-criteria. The final ranking order, TSP2 > TSP4 > TSP5 > TSP1 > TSP3, remained stable across benchmarking with FTOPSIS, FVIKOR, and FMOORA, as well as underweight perturbation and equal-weighting scenarios, confirming the robustness of the ranking results.

Mathematics doi: 10.3390/math14132269

Authors: Gabriel Marín Díaz

The cosmic microwave background (CMB) contains key information about the early Universe, particularly through its polarization structure. This work proposes a Fuzzy and Explainable Artificial Intelligence framework (FAS-XAI) for the regional analysis of CMB polarization using Planck SMICA data. From the Stokes components Q and U, the polarization amplitude P and the scalar polarization modes E and B are derived. Regional features are then extracted over a HEALPix grid, considering only polarization-valid regions defined by the Planck polarization mask. Fuzzy C-Means identifies four interpretable polarization regimes: high-polarization structured regions, E-dominated medium-polarization regions, B-enhanced medium-polarization regions, and low-polarization regions. An XGBoost-SHAP layer is used to explain the resulting fuzzy memberships. XGBoost accurately reproduces the memberships, with R2 > 0.98 for all clusters, while SHAP confirms the physical relevance of amplitude-related features and the log(B/E) balance. Finally, controlled perturbations in P and log(B/E) reveal a globally robust fuzzy structure with localized sensitivity. The proposed framework provides an interpretable methodology for studying regional CMB polarization patterns and their stability under controlled perturbations.

Mathematics doi: 10.3390/math14132268

Authors: Konstantinos Kalimeris Leonidas Mindrinos Athanasios Paraskevopoulos

In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under these assumptions, Richards’ equation reduces to Burgers’ equation, which we then linearize via the Hopf–Cole transformation. This turns the initial boundary value problem into a diffusion equation on a finite interval with mixed boundary conditions. To solve it, we use the Unified Transform Method (also known as the Fokas method). This approach gives an explicit integral representation of the solution, and when evaluated numerically, the results match classical Fourier series solutions exactly, but with better convergence and stability. Two examples from hydrological applications are examined.

Mathematics doi: 10.3390/math14132266

Authors: Hassan Ranjbar Afshin Babaei

In-depth analysis of epidemic models, particularly for cholera, is crucial because they serve as significant tools for disease transmission prediction, evaluation of control strategies, and optimization of healthcare resource management. The stochastic models provide increased realism by incorporating environmental uncertainty such as variability in water quality, disparities in access to sanitation, and population mobility. The present work generalizes a deterministic two-patch cholera model to a stochastic framework. We first prove the existence and uniqueness of global solutions, then establish the extinction condition R0*<1 for disease eradication in the long term. A key contribution lies in proving the existence of a unique ergodic stationary distribution when R0(1)>1 and R0(2)>1. Furthermore, we derive the stochastic threshold R0=max{R0(1),R0(2)}, which corresponds to the basic reproduction number R0=max{R0(1),R0(2)}. Lastly, numerical simulations are employed to confirm theoretical results.

Mathematics doi: 10.3390/math14132267

Authors: Laura Gambera Salvatore A. Marano

The existence of solutions that are positive, pointwise decaying at infinity, and weak to a fractional p-Laplacian problem in the whole space and exhibit a singular reaction is established. Truncation arguments, variational methods, as well as suitable a priori estimates are exploited.

Mathematics doi: 10.3390/math14132265

Authors: Di Wang Hui Ren Perry Gu Chongchong Song

Multibody dynamics (MBD) simulations involving hundreds to thousands of bodies give rise to large-scale, sparse, and structurally indefinite linear systems. Traditional direct solvers incur prohibitive memory and computational costs, while iterative methods suffer from slow convergence due to severe ill-conditioning. This paper proposes HPI-MBD, a hybrid preconditioned iterative framework. It combines an algebraic multigrid (AMG) for global error smoothing with a block Jacobi preconditioner tailored to the kinematic constraint graph. The framework exploits graph topology to construct a block-diagonal Schur complement approximation, incorporates Tikhonov regularisation for redundant constraints, and maintains O(n) work per iteration, where n is the number of degrees of freedom. A rigorous spectral analysis supports the problem-size independent convergence of the Minimal Residual (MINRES) solver. Evaluated on five benchmark systems with 104 to 106 degrees of freedom, the HPI-MBD achieves speedups up to 12.7× and memory reductions up to 68% against MA57, with comparable gains against PARDISO. All solutions maintain relative residuals below 10−6. Comparisons against ILU(0)-preconditioned Generalised Minimal Residual (GMRES), Finite Element Tearing and Interconnecting method (FETI-1), and a block-Jacobi-only variant confirm the essential role of AMG. The framework exhibits near-linear scalability and strong parallel efficiency on up to 32 processors, along with robust performance under redundant constraints and varying time step sizes. These results position HPI-MBD as a scalable, memory-efficient alternative for real-time simulation in virtual prototyping, robotics, and biomechanics.

Mathematics doi: 10.3390/math14132264

Authors: Hongguang Wu Chenyang Gao Jie Yang Yuelin Gao

This paper studies a vehicle routing problem with simultaneous pickup and delivery (VRPSPD), which has an important application in logistics and other areas. The problem is that the depot provides both forward supply service and reverse recovery service to customers, and determines the lowest-cost vehicle distribution routes that satisfy the needs of all customers on the basis of considering constraints. To solve this problem, we develop an improved ant colony optimization algorithm based on candidate strategy and grid search (ACO-CS). The candidate strategy of ACO-CS reduces the running cost and speeds up the convergence rate by limiting and reducing the number of unvisited nodes. At the same time, we propose to use the grid search method to tune the parameters to enhance the algorithm’s optimization capability and improve its performance. Three benchmark test problems are selected to verify the effectiveness of the proposed algorithm for solving different types and sizes of instances. The computational results show that the proposed algorithm is competitive in solving the Dethloff (2001) and Montane & Galveo (2006) test problems, and its solution quality, calculation time and algorithm stability are better than the variant algorithms in the literature. Finally, a practical case of logistics distribution is introduced to verify the reliability of the algorithm, and the results show that the ACO-CS can provide a more reasonable and economical solution.

Mathematics doi: 10.3390/math14132263

Authors: Jihong Zhang Xiaochun Sun

We construct Wick products by creation and annihilation operators on Guichardet–Fock spaces F and obtain commutation relations and s—adapted characters about the Wick products. Meanwhile, we introduce a concept of singular Bogoliubov transformation on Guichardet–Fock space, and prove that the Wick product under the singular Bogoliubov transformation still satisfies the commutative relationships.

Mathematics doi: 10.3390/math14132262

Authors: Ibraheem M. Alsulami

The aim of the present study is to propose a new mathematical model of compartment type for an epidemic problem using fractional order derivatives. This epidemic model takes into account vaccination, hospitalization, asymptomatic infection, and health awareness programs. Caputo fractional derivatives are used to model the temporal non-locality of epidemic phenomena in the proposed model. The qualitative analysis of the model includes the characterization of equilibrium points and their stability. The disease-free equilibrium (DFE) is shown to be locally asymptotically stable when the basic reproduction number R0<1, and unstable otherwise. Conversely, an endemic equilibrium emerges when R0>1, corresponding to the instability of the DFE. Periodic oscillation is observed for a higher rate of infection transmission. A fractional optimal control problem is formulated to minimize disease prevalence through vaccination, hospitalization, and treatment strategies, supported by sustained awareness campaigns. The results emphasize the role of vaccination, treatment and awareness campaign in controlling Mpox outbreaks, showing their success in minimizing the epidemic. In addition, a fractional optimal control model is proposed to reduce disease prevalence using preventive measures such as vaccinations and treatments coupled with awareness impacts. From these results, one can clearly understand that vaccinations and continuous public health awareness are essential in reducing Mpox cases, which help flatten epidemic trends.

Mathematics doi: 10.3390/math14132261

Authors: Yizhou Chu Guiyang Liu Qiuyu Yu Chunyan Yang

The financial early warning mechanism of listed companies has an important strategic value for maintaining the stability of the capital market and preventing systemic financial risks. This study proposes a hybrid model (EBWO-BP) based on the improved beluga optimisation algorithm (EBWO) and BP neural network for financial early warning research. Innovative T-SNE nonlinear dimensionality reduction technique is applied to the multidimensional evaluation system constructed by 23 financial and two non-financial indicators. The empirical evidence based on the data of A-share listed companies in 2022–2024 shows that the accuracy of the EBWO-BP test set reaches 86.51% (AUC = 0.83), which demonstrates a significant prediction advantage compared with the optimisation algorithm models such as GA-BP and PSO-BP, as well as the CNN and LSTM deep learning models; when the sample size is increased to 700 groups, the accuracy is improved to 89.05%, verifying the model robustness. The method achieves significant improvement of financial risk prediction through algorithm fusion innovation, and provides methodological innovation and practical reference for intelligent financial risk monitoring.

Mathematics doi: 10.3390/math14132260

Authors: Qianhao Sun Guo Li Jinxian Shen Rui Wu Weihua Zhang Mingyang Geng

Source-Seeking in unknown scalar fields is a fundamental problem in robotics with applications in environmental monitoring and disaster response. In this work, we present a source-seeking approach with non-reversing forward velocity regulation by fusing measurement data from multiple sensors within the Stochastic Extremum Seeking (SES) framework. Specifically, a device model with multiple sensors is first constructed, and then a velocity regulation scheme is designed by leveraging the boundedness of the hyperbolic tangent function and the non-negativity of the exponential function to guarantee strictly positive forward velocity. We then evaluate the algorithm both in simulation environments and on the real-world Two-Wheeled Differential Drive Robot platform. The experiments show that our approach not only ensures the forward velocity remains non-negative, aligning with the design expectation, but also accurately locates the source. This work provides new insights into the design of velocity regulation strategies within the SES framework.

Mathematics doi: 10.3390/math14132257

Authors: Sukono Gumgum Darmawan Muhamad Deni Johansyah Igif Gimin Prihanto Hadi Kardoyo Hendy Gunawan Syafrizal Maludin Astrid Sulistya Azahra Moch Panji Agung Saputra Norizan Mohamed

Temperature variability and weather-related fluctuations significantly affect the energy, agricultural, and industrial sectors that are highly sensitive to meteorological changes. These conditions may lead to financial losses caused by demand fluctuations and operational disruptions. This study aims to develop a fractional weather-derivative pricing model based on temperature dynamics by integrating the Ornstein–Uhlenbeck (OU) process, the classical Black–Scholes model (BSM), and the fractional Black–Scholes model (fBSM). Daily temperature data from 2016 to 2025 obtained from the Bandung Geophysical Station, West Java, Indonesia, were used as the basis of analysis. Temperature dynamics were modeled using an OU process, and parameter estimation was conducted using Ordinary Least Squares (OLS). The strike price was determined using Historical Burn Analysis (HBA), whereas weather-derivative pricing was performed using call and put option approaches under both the BSM and fBSM frameworks, incorporating the Hurst parameter to capture long-term memory effects. The results indicate that the fractional Black–Scholes model analytical solution is obtained using the Daftardar–Gejji Aboodh method. Furthermore, the OU process successfully captured daily temperature dynamics, yielding a Mean Absolute Percentage Error (MAPE) of 4.344% and a Root Mean Square Error (RMSE) of 1.396 C, indicating high predictive accuracy across both relative and absolute error measures. In addition, the fBSM consistently generated higher option values than the classical BSM, particularly under higher observed temperatures during the study period and at higher strike prices. These findings demonstrate that long-term memory significantly influences effective volatility and option valuation. This study is expected to contribute to the development of weather derivative models that more realistically represent temperature dynamics and to serve as a reference for weather derivative pricing, hedging, and decision-making, as well as for more measurable, systematic, and sustainable climate-related financial analysis using derivative pricing frameworks.

Mathematics doi: 10.3390/math14132259

Authors: George A. Anastassiou Seda Karateke

We introduce and study a class of multi-composite sigmoid neural network operators for Banach space-valued approximation. The proposed operators are generated by density-type kernels induced by finite compositions of seven standard sigmoid-type activation functions. The approximation is considered for continuous functions on compact intervals of the real line and on the whole real line, with values in an arbitrary Banach space (X,∥·∥). We prove quantitative pointwise and uniform convergence results by means of Jackson-type inequalities expressed through the first modulus of continuity. Higher-order and fractional approximation results are also obtained in terms of Banach space-valued derivatives and Caputo–Bochner fractional derivatives. The associated feed-forward neural network representation has one hidden layer and uses the multi-composite sigmoid function as its activation. Numerical experiments are presented to validate the theoretical estimates and to illustrate the approximation behavior of the proposed operators. In particular, we compare classical tanh-based operators, normalized self-composed activation operators, and heterogeneous multi-composite activation operators. The results show that self-composition and heterogeneous composition may improve the uniform approximation error for certain activation families and parameter choices, while also indicating that the observed improvement is activation-dependent and influenced by the composition order, kernel localization, and the regularity of the target function.

Mathematics doi: 10.3390/math14132258

Authors: Adem Akdoğan Murat Kurt

Product tables in invoices are obtained autonomously via a deep learning model named ExTTNet. Text information is first extracted from invoice images using Optical Character Recognition (OCR) techniques; both the Tesseract OCR engine and PaddleOCR were evaluated to determine the most effective method. Based on comparative analysis, PaddleOCR was selected due to its superior runtime performance, particularly with GPU acceleration, and its deep learning-based feature extraction capabilities. Each OCR token is labelled as a table element or a non-table element, and a multilayer artificial neural network is trained on the enriched feature set. Training was carried out on an Nvidia RTX 3090 graphics card in 62 min. The trained model achieves a macro-averaged F1 score of 0.91 and a class-1 F1 score of 0.90 on a private German invoice dataset, and a macro-averaged F1 score of 0.997 on the public FATURA benchmark.

Mathematics doi: 10.3390/math14132256

Authors: Weifan Zhang Yizhong Wu

The Absolute Nodal Coordinate Formulation (ANCF) is extensively utilized in the field of flexible multibody dynamics because it offers a constant mass matrix and inherently eliminates Coriolis forces. However, ANCF requires the computation of complex nonlinear elastic internal forces and thermal deformation forces at each time step, which imposes a significant computational burden. To alleviate this burden, researchers have developed local linearization (LL) methods. The local linearization method constructs constant elastic and thermal stiffness matrices within a small range by means of Taylor expansion, effectively reducing the number of stiffness matrix updates. But the method suffers from error accumulation and relies on displacement-based update criteria that are inefficient for systems with large rigid-body motion. This paper proposes an improved local linearization (I-LL) method to address these issues. Two key enhancements are introduced: (1) the update criterion for the elastic and thermal stiffness matrices is modified from displacement-based to total strain-based, enabling more accurate and size-independent updates; (2) accurate elastic or thermal deformation force calculations are inserted within the local linearization iteration cycle to mitigate error accumulation. These two improvements reduce the number of calculations of the nonlinear internal forces and, at the same time, lessen the error accumulation in the simplified model. The accuracy and effectiveness of the I-LL algorithm are demonstrated through three numerical examples.

Mathematics doi: 10.3390/math14132255

Authors: Phuong-Nhung Nguyen Thu-Hien Nguyen Thu-Nga Nguyen Manh-Dong Tran Truong-Thang Nguyen Tuan-Linh Nguyen

We develop SAFIRE (Self-Attention Fuzzy-Inspired Rule Estimator), a differentiable fuzzy-inspired rule-scoring surrogate for binary medical tabular classification coupling multi-head self-attention, Gaussian membership functions, and Hard Concrete gates for continuous rule scoring. We position SAFIRE as a smooth surrogate of the discrete L0-regularised rule-selection problem and establish five mathematical results and one complexity remark: (1) the relaxed objective is differentiable almost everywhere under positive Gaussian widths (enforced by a Softplus reparameterisation) and fixed batch-normalisation statistics; (2) the deterministic-inference active threshold is strictly stricter than the expected-nonzero training threshold, identifying Hard Concrete gates as continuous rule-scoring devices rather than automatic pruning mechanisms; (3) per-sample forward complexity identifies attention and rule layers as the dominant terms; (4) the Softplus–BatchNorm–linear rule operator violates all four triangular-norm axioms—with necessary and sufficient conditions per axiom and a no-finite-parameterisation impossibility result—while a Softplus reparameterisation restores coordinate-wise monotonicity; (5) a margin-based upper bound characterises disagreement between the full classifier and a top-k rule-only surrogate; and (6) the Softplus-reparameterised constrained variant is provably coordinate-wise monotone with explicit asymptotic regimes. Evaluated on four University of California, Irvine (UCI), medical binary tabular benchmarks under repeated stratified cross-validation, SAFIRE-Prog is statistically competitive with strong interpretable, modern, and gradient-boosting baselines, with one Bonferroni-significant gain over RuleFit on the Diabetic Retinopathy Debrecen corpus. The 48-configuration Hard Concrete sweep, constrained-variant comparison, and a top-k fidelity analysis (per-fold range 0.73–0.95) provide quantitative companion measurements for the mathematical framework. A supplementary large-scale hospital electronic health record (EHR) benchmark (Diabetes 130-US Hospitals, n=101,766) shows the rule-scoring mechanism scales to ∼105 records and, under severe class imbalance, statistically matches gradient boosting on accuracy while significantly exceeding it on macro-F1. The results offer a mathematically auditable pathway towards interpretable, auditable rule scoring for medical tabular classification, with rule signatures defined in a projected latent space rather than over raw clinical variables.

Mathematics doi: 10.3390/math14132254

Authors: Zhenzhang Liu Yanping Feng Dachang Zhu

The design of intravascular ultrasound (IVUS) catheters involves inherently coupled acoustic, hemodynamic, and structural requirements. Existing design strategies, which often rely on empirical geometric refinement or single-physics optimization, are limited in their ability to simultaneously ensure acoustic transmission efficiency, flow compatibility, and mechanical reliability. A multiphysics topology optimization method for the integrated design of IVUS catheters under acoustic–fluid–structure interactions is proposed in this paper. A density-based design variable is introduced to characterize the material distribution within the design domain, and consistent interpolation schemes are employed to relate this variable to the effective acoustic properties in the Helmholtz equation, the Brinkman penalization coefficient in the incompressible Navier–Stokes equations, and the elastic stiffness tensor in the structural equilibrium equation. The optimization problem is formulated as a normalized multi-objective minimization of acoustic transmission loss, flow resistance, and structural compliance, subject to constraints on material volume, received acoustic energy, wall shear stress, and structural displacement. Density filtering and smooth Heaviside projection are incorporated to regularize the design field and promote well-defined material boundaries. An adjoint sensitivity formulation is further developed to enable efficient gradient evaluation for the coupled system. Compared with the initial design, the average acoustic transmission efficiency has increased by 59.01%, the shear stress has decreased by 53.87%, and the stiffness matching rate has reached 98.27%. The objective function converged after 35 iterations, demonstrating the numerical stability of the proposed acoustic–fluid–structure topology optimization framework.

Mathematics doi: 10.3390/math14132253

Authors: Chih-Ta Tsai Yung-Fu Huang Ming-Wei Weng

Centered on lean production, this study integrates operational technologies (OT), communication technologies (CT), and information technologies (IT) within an open-system software architecture. Under stochastic customer demand, reliance on static data and experience-based decision-making constrains firms’ responsiveness to market. The integration of lean management with a data-driven database enhances operational flexibility and decision quality, enabling small and medium-sized enterprises (SMEs) in the bicycle industry to develop responsive digital factory environments with real-time monitoring and improved operational transparency. The proposed platform is applicable to both manufacturing processes and operational management, improving overall equipment effectiveness (OEE), production efficiency, process optimization, and reducing quality losses, inventory levels, and workforce misallocation. This study investigates the application of the Analytic Hierarchy Process (AHP) and multi-criteria decision-making (MCDM) within a performance framework integrating ESG indicators and a balanced scorecard to identify key success factors for digital lean improvement in the bicycle industry. A case study of a bicycle manufacturer was conducted using questionnaire surveys and expert interviews with exporters. The results indicate that the five most critical success factors are: enhancing return on invested capital, strengthening digital capabilities, improving product quality, minimizing inventory waste, and reducing lead time. These findings provide practical guidance for decision-makers in designing more effective lean management strategies in highly competitive digital markets. Furthermore, by facilitating the adoption of appropriate digital technologies under a reasonable return on investment, this approach supports the systematic implementation of Industry 4.0 initiatives and transforms traditional lean practices into more efficient and sustainable digital lean operations.

Mathematics doi: 10.3390/math14132252

Authors: Ruipeng Chen Xiaqiu Cui

The existence of coexistence states of a non-cooperative nuclear reactor model is investigated in this paper. Differently from the existing literature, we allow the nonlinearities to not necessarily be linearizable at zero and infinity, and the boundary condition in the model implies that the nuclear reactor has heat exchange with the external environment, which much more closely reflects the situation in reality. Several novel existence theorems distinct from existing results in the literature are established by means of bifurcation theory. Our main findings will not only be helpful to enrich the related theories of nuclear reactor models but also have certain guiding significance for the safe operation of reactors.

Mathematics doi: 10.3390/math14132251

Authors: Mashael Bander Alshammari Norazrizal Aswad Abdul Rahman Abdullah Haif Alshammari

Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical spreading patterns that are not adequately represented by conventional integer-order diffusion models. In this study, a modeling and simulation framework is developed for anomalous heat transport in heterogeneous media using a two-dimensional time-fractional porous medium equation. The model combines a Caputo fractional time derivative, which represents thermal memory, with nonlinear degenerate porous-medium diffusion, spatially heterogeneous conductivity, localized volumetric heating, and Robin-type convective boundary exchange. A conservative fully discrete numerical scheme is constructed using flux-based finite differences for the heterogeneous nonlinear diffusion operator and an L1 approximation for the Caputo derivative. The nonlinear algebraic system at each time level is solved using an under-relaxed Picard frozen-coefficient iteration with non-negativity enforcement and sparse direct solution of the resulting linear systems. The numerical implementation is verified through a manufactured-solution convergence study, and additional analyses are performed to examine computational cost, Picard iteration behavior, coefficient-regularization sensitivity, strong-source effects, heterogeneous conductivity structures, and long-time thermal-footprint persistence. The results show that heterogeneous conductivity mainly redirects heat through preferential pathways and enlarges the spatial footprint while producing negligible changes in global heat content. Stronger fractional memory, represented by smaller fractional order, increases the persistence and spatial reach of moderate heating, whereas larger porous-medium exponents confine heat near the source and preserve higher local peaks. Source amplitude increases the thermal burden and footprint monotonically over the tested range, including strong forcing, without producing an abrupt localization-spreading transition. Boundary exchange remains secondary in the short-time interior-heating regime considered. These findings demonstrate that the proposed two-dimensional time-fractional porous medium framework provides a verified and physically interpretable model for non-Fourier heat transport in heterogeneous materials, where local intensity, global heat retention, and spatial thermal exposure must be assessed jointly.

Mathematics doi: 10.3390/math14132250

Authors: Bing Lv Jiayu Liu Lei Kou

With the deep integration of artificial intelligence and big data, intelligent optimization algorithms have become key tools for solving many complex problems. However, as problem scale and complexity grow rapidly, the performance of traditional algorithms often faces significant challenges. The Teaching Learning Based Optimization algorithm has attracted widespread attention for its simple structure, few parameters, and high solution efficiency, and has been successfully applied across various engineering and scientific fields. Nevertheless, when dealing with high-dimensional, multimodal global optimization problems and real-world applications, the standard Teaching Learning Based Optimization still exhibits certain limitations, such as reduced accuracy of the optimal solution due to insufficient initial population diversity, and difficulty in escaping local optima caused by premature convergence. To address these issues, this paper proposes an Improved Teaching Learning Based Optimization algorithm. The improved ITLBO upgrades original TLBO from three perspectives: first, a population interaction strategy combining chaotic disturbance and Gaussian mutation is designed to enrich initial population diversity; second, bipolar cooperative search utilizing dynamic weighting of optimal and worst individuals balances global exploration and local exploitation to avoid premature convergence; third, oscillatory random mapping learning with sinusoidal oscillation factor periodically perturbs individuals to continuously replenish population diversity in iterations. Numerical results show that the proposed method exhibits superior convergence performance and stability on classical global optimization benchmarks. Furthermore, the algorithm is applied to practical cloud resource scheduling problems, and experimental outcomes verify that ITLBO improves solution accuracy by approximately one order of magnitude over original TLBO and reduces small-scale cloud scheduling cost by 12% while achieving preferable robustness.

Mathematics doi: 10.3390/math14132249

Authors: Yang Li Yu Zheng Dong Sui

AI-generated images (AIGIs) often contain perceptual defects that differ from the distortions commonly studied in conventional no-reference image quality assessment (NR-IQA). This work investigates image-only AIGC image quality assessment, where no prompt text is used and the quality score must be inferred from visual evidence such as artifacts, structure, and semantic plausibility. We propose a dual-pathway wavelet-attention framework built on a Swin Transformer V2-Base backbone. The artifact pathway employs a Noise Perceptive Attention Module (NPAM) with fixed Haar wavelet decomposition to describe generation-related sub-band degradation cues, whereas the image-perception pathway models semantic, structural, and contextual quality evidence using multi-scale attention, global–local spatial-channel attention, and pyramid pooling. The two pathways are integrated through adaptive fusion and a spatially weighted regression head with an auxiliary global prediction. Experiments on AGIQA-1K, AGIQA-3K, and AIGCIQA2023 demonstrate competitive in-domain performance, including SRCC values of 0.8418 on AGIQA-3K and 0.8445 on the quality dimension of AIGCIQA2023. The evaluation further covers individual module ablations, score-fusion variants, seed stability, qualitative error analysis, and cross-database transfer, revealing both the contribution of the proposed components and the remaining difficulty of source-disjoint generalization.

Mathematics doi: 10.3390/math14132248

Authors: Maria Luminita Scutaru Pop Nicolae Sorin Vlase Ana Maria Mitu Tudor Sireteanu Violeta Mihaela Munteanu

The mechanical behavior of a composite is determined by the value of the engineering constants for the composite under consideration. If we study a homogeneous and isotropic composite, then two engineering elastic constants are needed to characterize the material; if we refer to a transversely isotropic composite, five elastic constants are needed. For more complex materials it can be necessary to determine more elastic constants in order to obtain the behavior of the composite in practical applications. In this paper, the authors present the main classic methods for calculating the engineering constants of a fiber composite material that are used in parallel with the finite element method (FEM) and highlight the advantages (and disadvantages) of using direct FEM to achieve this. The arrangement of identical fibers provides regularities that allow for easier calculations and, in some cases, the application of simple methods. The results that have already become classics, current results, and unusual examples are all critically presented in this study. All of these findings are discussed in relation to the use of the FEM, either as the primary calculation method or as a useful aid in the application of classical methods. The paper focuses on presenting research on the use of FEM for this purpose. For the different approaches discussed and for the area overall, future research directions are emphasized.

Mathematics doi: 10.3390/math14132247

Authors: Neda Godarzi Farzad Hejazi

Recent advancements in structural engineering have driven the development of sophisticated damping mechanisms aimed at reducing the detrimental effects of structural vibrations. As a result, accurate numerical modeling and analytical evaluation have become essential for assessing structural stability and enhancing seismic resilience. This study introduces a model-updating framework to develop analytical constitutive models for structural damping systems. The proposed approach employs a genetic algorithm (GA) to calibrate model parameters by minimizing the discrepancy between analytical predictions and experimental responses. Experimental force–displacement hysteresis data and displacement time-history records are used at both the element and system levels for model calibration. The methodology is applied to a rubber isolator, a 10-story structure equipped with Pall friction dampers, and a 6-story structure with friction dampers to evaluate its performance under different dynamic characteristics and damping mechanisms. The results indicate that the proposed approach achieves very high accuracy, with prediction errors reduced to negligible levels for both force and displacement responses in all cases. Consistent performance is observed using both global and local displacement measures in friction-damped systems, indicating the robustness of the proposed method. Overall, the findings indicate that the GA-based model-updating framework provides an efficient and reliable tool for improving the predictive capability of analytical models of structures with nonlinear damping devices and is suitable for practical structural engineering applications.

Mathematics doi: 10.3390/math14132240

Authors: Michel Planat

We investigate the onset of hyperbolicity in Jensen polynomials Jd,n associated with the Riemann Ξ-function and identify a robust parity-driven bifurcation with a natural geometric interpretation. Numerical analysis for degrees 5≤d≤16 reveals two distinct regimes. For even d, the roots form a compact complex cluster whose imaginary extent decreases smoothly, and the transition to hyperbolicity is governed by a single complex-conjugate pair, consistent with a low-dimensional (tame) geometric structure. For odd d, a hierarchy of more intricate onset mechanisms emerges, including single-event transitions (d=11) and intermittent regimes (d≥13) with decoupled geometric invariants, suggestive of dynamics on decorated (wild) character varieties. We interpret this dichotomy through a connection with the PIII(D6) tau-function arising in the Painlevé confluence diagram. Defining τ(t)=Ξ(12+−t)/Ξ(12), we construct a generating function B(w)=∑j≥0bjwj from the cumulants of logΞ(12+z) using high-precision Cauchy/DFT methods (280–400-digit arithmetic), without explicit use of the zero expansion. Two independent numerical diagnostics indicate that B exhibits Stieltjes-type behavior: (i) positivity of Hankel determinants up to order N=30 and (ii) Padé approximants whose poles converge to γk2 (squares of Riemann-zero ordinates) with stabilizing residues. These results provide strong evidence that the parity bifurcation observed in Jensen polynomial onset reflects a finite-dimensional manifestation of an underlying moment-based positivity structure. Motivated by this correspondence, we formulate a conjecture relating the Stieltjes nature of B(w) to the eventual hyperbolicity of Jensen polynomials. This conjecture suggests a bridge between finite-dimensional root geometry and an infinite-dimensional kernel-based positivity framework, while leaving open the problem of establishing such positivity independently of the zero expansion.

Mathematics doi: 10.3390/math14132246

Authors: Shu Wu Lina Zhang Rende Li

Raw sentiment extracted from Chinese financial news is noisy and difficult to use directly for market prediction. This study proposes a mathematical filtering framework that converts noisy Chinese financial news sentiment into reliable quantitative signals for financial market prediction. Three daily sentiment measures were constructed from Chinese financial news: sentiment mean, sentiment dispersion, and polarity imbalance. Seven filtering methods were applied to each measure, including exponential smoothing, autoregressive filtering, ARIMA filtering, moving average smoothing, discrete wavelet transform, Savitzky–Golay filtering, and Kalman filtering. The seven filtered outputs were averaged to produce an ensemble-smoothed sentiment signal. Support vector machines and neural networks were then used to compare the predictive performance of raw and filtered signals for stock index log returns and realized volatility. Filtering reduced the standard deviation of sentiment mean by 48%, sentiment dispersion by 55%, and polarity imbalance by 50%, while mean levels remained stable. Filtered sentiment consistently outperformed raw sentiment across all model configurations. The improvement was larger for realized volatility than for returns: the best support vector machine reduced volatility prediction error by 16.9% and return prediction error by 5.8%. A moderate neural network with 20 hidden neurons achieved optimal performance for both outcomes. Mathematical filtering extracts stable and informative sentiment signals from Chinese financial news. Filtered sentiment is more useful than raw sentiment for predicting market volatility, and the improvement holds across multiple machine learning models.

Mathematics doi: 10.3390/math14132245

Authors: Tianbao Nie Yu Yang Xiang Li

Fatigue health monitoring of engineering structures requires continuous degradation assessment, yet ground-truth health labels are unavailable during run-to-failure tests. Existing self-supervised approaches rely on monotonic degradation assumptions that are violated by the structured non-monotonic behaviour of acoustic emission signals during fatigue. A self-supervised framework called Cross-Modal Degradation Rivalry (CMDR) is proposed, which introduces the Modal Rivalry Index (MRI) as a directional measure of cross-modal predictability between heterogeneous sensor modalities. CMDR comprises a label-free representation-learning stage trained via the Cross-Modal Prediction Asymmetry (CMPA) pretext task, followed by a lightweight supervised stage that maps MRI features to scalar health indicators (HIs) using normalised lifecycle labels. The MRI is conceptually related, under the stated assumptions only loosely met in practice, to the Transfer Entropy difference between sensor latent channels. Experiments on a structural fatigue dataset with seven specimens under two loading conditions demonstrate that CMDR achieves competitive trendability and prognosability, as well as the lowest remaining useful life (RUL) error in three of four scenarios. RUL evaluations are additionally repeated under a fully online estimator that uses only training specimens. A strictly inductive ablation that re-pre-trains the self-supervised stage within each leave-one-specimen-out fold confirms a bounded transductive-vs-inductive gap, and CMDR remains the best against three further self-supervised baselines on the within-condition and mixed-condition scenarios. Ablation studies confirm the necessity of directional asymmetry, bottleneck architecture, and momentum-updated target encoders.

Mathematics doi: 10.3390/math14132243

Authors: Zhanyu Zhong Chang Yang Cong Chen Fukang Zhao Kaixing Tang

Multi-criteria group decision making (MCGDM) under linguistic uncertainty remains a fundamental challenge in applied mathematics, where decision makers seldom assign crisp numerical evaluations and frequently exhibit heterogeneous risk attitudes shaped by behavioural factors. An integrated mathematical framework, hereafter PLR-3WBC (Probabilistic Linguistic Regret-driven Three-Way Bayesian Consensus), is developed to systematically integrate four methodological components that have each been individually validated in the MCGDM literature: representation of decision information with explicit probability mass on linguistic terms; quantification of decision-maker regret and rejoice psychology under linguistic uncertainty; classification of alternatives into three actionable decision regions rather than a single-valued ranking; and group consensus reaching with credal weight aggregation. Each component has demonstrated its effectiveness in its respective domain; the present framework capitalises on their complementary strengths by embedding them within a single pipeline equipped with formal guarantees, an integration that has not been previously reported. The framework integrates five methodological components: probabilistic linguistic term sets (PLTS) for information representation; the Bayesian best–worst method (BBWM) for credal criterion weighting; a regret–rejoice value function adapted to the linguistic domain for behavioural evaluation; three-way decision (3WD) thresholds derived from a loss-function model for actionable classification; and a distance-based consensus reaching process with feedback mechanism for group convergence. A case study on age-friendliness evaluation of twelve aging urban residential communities under an indicator system of five dimensions and eighteen criteria, with four expert decision makers, demonstrates that PLR-3WBC delivers an actionable three-way classification, recovers a transparent group consensus, and produces rankings broadly consistent with classical TOPSIS, VIKOR, PROMETHEE-II, and BWM-TOPSIS (Spearman rank correlation exceeding 0.97), thereby confirming that the integrated framework preserves the ordinal reliability of these established methods, while additionally delivering three outputs that arise from the methodological integration: an actionable three-way classification enabling discrete budget-aligned decisions, credal weight intervals quantifying the depth of expert agreement on criterion importance, and a behavioural reordering of borderline non-dominated alternatives that reflects the loss-averse psychology of the decision panel and would remain hidden under single-method deployment. Sensitivity analyses with respect to the regret aversion coefficient, the loss function parameters, and the consensus threshold confirm that the qualitative classification is stable across a wide parameter envelope, supporting the practical deployment of PLR-3WBC in age-friendly community renewal programmes.

Mathematics doi: 10.3390/math14132244

Authors: Chun-Yao Lee Kuan-Yu Huang Truong-An Le Guang-Lin Zhuo Mu-Ze Li Chung-Hao Huang

Diagnosing bearing faults remains a crucial challenge, particularly in effectively extracting fault information and achieving high diagnostic accuracy. To address this issue, this study presents a model for diagnosing bearing faults, which comprises three primary stages: feature extraction, feature selection, and classification. In the feature extraction stage, features are extracted from raw motor signals using empirical mode decomposition (EMD) and fast Fourier transform (FFT). In the feature selection stage, an effective method based on binary grey wolf optimization (BGWO) and the equilibrium optimizer (EO) is developed to remove redundant and irrelevant features. Finally, k-nearest neighbours (KNNs) and support vector machine (SVM) classifiers are used to identify bearing fault conditions. The proposed model is evaluated using four datasets: the University of California, Irvine (UCI) benchmark datasets, a motor bearing fault current-signal dataset, the Case Western Reserve University (CWRU) benchmark dataset, and the Machinery Failure Prevention Technology (MFPT) benchmark dataset. The experimental results show that the proposed method improves bearing fault diagnosis accuracy and demonstrates strong robustness compared with conventional methods.

Mathematics doi: 10.3390/math14132238

Authors: Usman Younas Reem Abdullah Aljethi Fengping Yao Jan Muhammad

A novel modified generalized Riccati equation mapping neural network-based approach is the basic theme of this study by exploring the nonlinear dynamical characteristics of the the strain wave model’s soliton solutions, which govern wave propagation in micro structured solids. Strain waves are particularly intriguing, since they preserve their form and speed throughout transmission. The nonlinear dynamical behaviors of strain waves may be modeled by partial differential equations in micro structured materials. In the realm of micro structured solids, there exists a class of phenomena that are referred to as micro strain waves. These waves arise in solids possessing intricate internal architectures, including periodic lattices, precisely engineered metamaterials Understanding these waves is key to designing more complex materials and new acoustic technologies. The activation function and the weight function of the neural network are assigned to each input layer, hidden layer and output layer and the neural network itself is a multi-layer computational network. Using the structure of the neural network, every neuron in the first hidden layer is given solutions to the Riccati equation, and the new highly expressive trial functions are generated in a systematic way. In this way, a large variety of exact soliton solutions are obtained, such as bright, dark, kink, and combined solitons as well as periodic and hyperbolic wave profiles. The influence of the essential physical and mathematical parameters is explored systematically using three-dimensional, two-dimensional and contour visualizations, which illustrate how parameter variations lead to changes in the amplitude, shape and stability of the wave structures. The solutions presented reveal the dynamic properties of micro strain solitons which leads to new avenues of investigation in the study of related nonlinear phenomena in micro structured solids. In a broader context, our results highlight the great potential of analytical techniques using neural networks as a powerful and versatile toolset to study complex nonlinear wave models within the applied sciences from acoustics to photonics to smart materials engineering.

Mathematics doi: 10.3390/math14132242

Authors: Mingyu Wang Yu Xiao Zhengxun Guo Mengjia Xu Xiaoshun Zhang

As power systems continue to expand and grow in complexity, power flow calculation remains a fundamental task in power system analysis and operation. Conventional methods rely on iterative solvers and detailed grid models, yet are often hindered by non-convergence and unreliable modeling assumptions. To address these limitations, this paper introduces a deep learning-based approach that integrates graph neural networks (GNNs) and recurrent neural networks (RNNs) for power flow calculation. The proposed model captures spatial dependencies through graph convolutional layers and temporal dynamics through recurrent layers, enabling accurate prediction of node voltage magnitudes, phase angles, and branch power flows. To enhance transparency, SHAP (Shapley Additive exPlanations)-based feature attribution and multi-modal visualizations are employed to interpret the model’s predictions. Experimental results on the IEEE 9-bus, 39-bus, and 118-bus systems demonstrate prediction errors within 4% and a computational speedup of approximately 40-fold over traditional Newton–Raphson methods. Beyond technical performance, these results suggest that the proposed method can support more efficient and reliable grid operation, thereby contributing to the integration of renewable energy, enhancement of grid resilience, and advancement of sustainable energy systems.

Mathematics doi: 10.3390/math14132241

Authors: Jen-Chieh Lo

This paper introduces a multiplicative Atangana–Baleanu–conformable fractional integral operator in the setting of multiplicative calculus. The proposed operator is formulated by applying the Atangana–Baleanu–conformable fractional integral structure to the logarithmic representation of positive functions, thereby combining multiplicative behavior, nonsingular memory effects, and conformable scaling in a single framework. Appropriate function-space assumptions are imposed to ensure that the operator is well defined. Based on this operator, we establish a new auxiliary identity and derive several multiplicative Milne–Mercer-type inequalities for multiplicatively convex functions. The obtained results include multiplicative Riemann–Liouville-type, multiplicative Atangana–Baleanu-type, and conformable-type inequalities as special cases under suitable choices of the parameters. To clarify the role of the fractional parameters, numerical examples are provided together with logarithmic gap values, relative-error comparisons, heatmaps, contour plots, and parameter-sensitivity analyses. These computations illustrate the validity of the derived inequalities and compare the proposed bounds with their reduced special cases.

Mathematics doi: 10.3390/math14132239

Authors: Ahmed Alqurashi Abdullah Alharthi

Objective diagnosis in psychiatry remains challenging due to the lack of reliable biological markers and the presence of confounding variables in observational data. While EEG-based machine learning models have shown promising classification performance, their validity remains unclear when confounding factors such as age are not explicitly controlled. In this work, we propose a confound-aware mathematical framework for supervised learning, where classification is formulated as a mapping f:RE×C×T→Y under the presence of a confounding variable A. Within this formulation, model performance is interpreted as a function of both predictive structure and confound dependence. The proposed framework integrates classification, regression, and feature selection into a unified evaluation pipeline. A central contribution is the Cross-Task Explanation Concordance (CTEC) index, a rank-based metric that quantifies the stability of feature importance across models and predictive tasks. Experimental results on a large-scale EEG dataset (N = 670) demonstrate that deep learning models outperform handcrafted approaches under standard evaluation. However, under confound-controlled settings, handcrafted models show a dual response to confound control: age residualization improves classification by removing feature-level noise (+20.3%), while age-matching collapses performance to chance (balanced accuracy, BA = 0.238) by eliminating demographic separability. Deep learning models retain partial robustness under both conditions. These findings highlight that conventional performance metrics may overestimate model validity in the presence of structured bias. The proposed framework provides a general mathematical approach for evaluating supervised learning models under confounding effects and is applicable to a wide range of data-driven systems beyond EEG.

Mathematics doi: 10.3390/math14132237

Authors: Mohamed Elgharib Gomah Guichen Li Naseer Muhammad Khan Changlun Sun Jiahui Xu Ahmed A. Omar B. G. Mousa Marzouk Mohamed Aly Abdelhamid M. M. Zaki

The journal retracts the article titled “Prediction of Strength Parameters of Thermally Treated Egyptian Granodiorite Using Multivariate Statistics and Machine Learning Techniques” [...]

Mathematics doi: 10.3390/math14122236

Authors: You Zhou Mao Wang Shaowu Zhou

This paper investigates the problem of multi-target search by an Autonomous Underwater Vehicle (AUV) swarm in unknown three-dimensional (3D) underwater environments with obstacles under limited communication conditions. To address this problem, a distributed cooperative search framework is proposed. Within this framework, an adaptive dual-state search mechanism driven by a target response function is designed. This mechanism enables the swarm to transition between independent large-scale roaming search and precise cooperative search. On this basis, a multi-target search method is developed by integrating a virtual force model, motion-constrained 3D Particle Swarm Optimization (PSO), and a sectional 3D tangent-plane obstacle-avoidance method. Simulation results demonstrate the effectiveness and engineering feasibility of the proposed framework. Under the conditions of unknown terrains and communication limits, the AUV swarm can adaptively execute state transitions, safely avoid 3D obstacles, and complete multi-target search tasks. Specifically, as the swarm size increases from 30 to 60 AUVs, the mean number of iterations drops from 432.97 to 269.73, while the total energy consumption expectedly rises from 11.79 × 104 to 15.51 × 104, reflecting a well-balanced trade-off between efficiency and cost. This study provides a practical distributed control reference for AUV swarms in complex communication-constrained underwater scenarios.

Mathematics doi: 10.3390/math14122235

Authors: Khalid Alluhydan M. N. Abd EL-Salam

A Negative Derivative Feedback (NDF) controller is designed for vibrations suppression of an atomic force microscope (AFM) model. The controlled system is modeled as a two-degree-of-freedom (2-DOF) closed-loop dynamic system. The average method was used to derive approximate analytical solutions. All possible resonance conditions were identified, with particular attention given to the simultaneous resonance case Ω=ω1, Ω1=2ω1, ω2=ω1, identified as the most critical. For validation and proper insights, the system was also solved numerically using the fourth-order Rung–Kutta method. The time response of the AFM system in contact mode was analyzed before and after applying the NDF controller under the worst-case resonance conditions. A comprehensive parametric study was conducted to evaluate the controller’s robustness and effectiveness. The results demonstrate a high degree of agreement between the numerical simulations and the analytical approximations, confirming the reliability of the approach.

Mathematics doi: 10.3390/math14122234

Authors: Fatimah A. Almulhim A. T. A. Hammad Fathy H. Riad M. A. El-Qurashi

One of the most widely used regression models for count data is the Conway–Maxwell–Poisson regression model (CMPRM), which often provides a better fit for over- and underdispersed count data than traditional models, such as Poisson regression and negative binomial regression. Parameter estimation in the CMPRM is typically performed using the maximum likelihood estimation (MLE) method. However, when explanatory variables are highly correlated, a phenomenon known as multicollinearity arises, posing a significant challenge to the analysis. Multicollinearity makes it difficult to identify the individual effects of explanatory variables, leading to inflated variances and larger standard errors of the MLEs. To address the issue of multicollinearity, this paper introduces a new class of Liu-type estimators within the CMPRM. The proposed estimators aim to improve the estimation accuracy and reliability of the CMPRM compared with existing biased estimation methods. The efficiency of the proposed estimator is evaluated through theoretical comparisons and Monte Carlo simulation experiments conducted under various conditions. Furthermore, two real-data applications are presented to demonstrate the practical usefulness of the proposed estimation method. The results from the theoretical analysis, simulation study, and empirical applications indicate that the proposed estimators outperform existing methods in terms of achieving more accurate and reliable estimates.

Mathematics doi: 10.3390/math14122233

Authors: Qiang Zhang Chaobang Gao

Classical tools for time series dependence analysis are primarily designed for linear dependence and may fail to detect serial structure when a series is uncorrelated but not independent. To address this problem, we propose the auto ball covariance function and the corresponding auto ball correlation function for measuring lag-specific nonlinear dependence in strictly stationary time series taking values in a separable Banach space. The proposed diagnostic uses metric-ball probabilities to measure fixed-lag distributional dependence without moment requirements, making it suitable for vector-, function-, and norm-induced object-valued time series. Under suitable conditions, we show that the proposed measure is zero if and only if the lagged components are independent. We further develop sample versions of the proposed statistics and establish their large-sample properties, including strong consistency under absolute regularity and a fixed-lag null asymptotic law under a finite-range dependence condition on the lagged-pair process. Simulation studies demonstrate that the proposed method performs well in a variety of settings, especially for nonlinear, heavy-tailed time series. A real-data analysis of annual sunspot numbers further illustrates how the proposed diagnostic can reveal nonlinear residual dependence that is not visible from ordinary autocorrelation diagnostics.

Mathematics doi: 10.3390/math14122232

Authors: Çiğdem Seçkin Gürel Berker Yalçın

In this study, a novel aperiodic photonic crystal (PC) structure is designed using the golden ratio-based Lucas sequence, and its infrared (IR) transmission characteristics are investigated. Transmission behavior demonstrates a strong dependence on the number of unit cells and parity (even or odd) of the defect layer repetitions, enabling the formation of a predetermined number of resonant modes around the operating wavelength and broad photonic stopbands at longer wavelengths with sharp defect modes. With its high spectral tunability, the proposed new Lucas sequence-based structure represents a viable candidate for the design of high-performance optical filters and components. These findings indicate that novel Lucas sequence-based PC designs will provide new opportunities for manipulating light–matter interactions in future studies.

Mathematics doi: 10.3390/math14122231

Authors: Khaled Aldwoah Faez A. Alqarni Osman Osman L. M. Abdalgadir Amel Touati Waleed Adel

This study develops and analyzes a four-state nonlinear policy–feedback dynamical system that couples a system stressor, an accumulated burden, a signed mitigation–response variable, and a signed policy-pressure variable. The proposed model represents governance response through a smooth threshold-centered feedback mechanism, in which the policy-pressure dynamics depend continuously on the deviation of the stressor from a prescribed reference threshold. Unlike reduced-order formulations with purely exogenous interventions, the present framework generates endogenous interactions among stress accumulation, burden evolution, mitigation response, and policy adjustment. The qualitative analysis establishes local well-posedness in the admissible phase domain, conditional nonnegativity of the accumulated burden, and boundedness of trajectories on admissible intervals. An autonomous effective system is then derived to characterize quasi-stationary mean behavior of the periodically forced dynamics. For this effective system, local stability is investigated using Gershgorin estimates and Routh–Hurwitz criteria, leading to explicit analytical conditions for local asymptotic stability and a critical policy-responsiveness threshold associated with possible Hopf-type oscillatory transitions. The analysis highlights the stabilizing role of mitigation damping and cubic saturation in regulating the feedback loop. To approximate the nonlinear system, a Physics-Informed Neural Network (PINN) surrogate is constructed by embedding the governing equations into a differentiable residual loss while enforcing the initial conditions analytically. The accumulated burden is represented through an admissible neural-network ansatz to preserve the well-definedness of the logarithmic coupling term, while the mitigation–response and policy-pressure variables remain signed in accordance with the model formulation. Numerical validation against reference ode45 solutions across two governance regimes shows maximum absolute errors of order 10−3, indicating that the PINN provides a reliable differentiable surrogate for the coupled policy–feedback dynamics. The resulting framework offers a foundation for future inverse modeling, parameter estimation, and data-assimilation studies involving policy responsiveness, intervention thresholds, and burden- suppression effects.

Mathematics doi: 10.3390/math14122230

Authors: Shin-ichi Inage

This paper studies the continuation problem for the three-dimensional compressible Navier–Stokes–Fourier system inside an admissible thermo-acoustic regime under periodic boundary conditions. The analysis considers strong solutions in the Sobolev class HsΩ, s> 5/2, with positive density and temperature and strict subsonic evolution. Using dyadic Fourier–triadic decomposition together with localized Littlewood–Paley analysis, the nonlinear transfer structure is decomposed into perturbative interaction classes and coherent same-scale High–High interactions. Within the present framework, coherent same-scale High–High persistence is identified as the only currently identified potentially nonperturbative concentration mechanism. A transport–acoustic alternative structure is then derived connecting persistent transport concentration with nonvanishing pressure response. The resulting pressure response is decomposed into thermodynamic and acoustic branches. The transonic acoustic branch is shown to be incompatible with the strict subsonic admissible class. The remaining interaction structure is controlled through entropy-driven thermodynamic dissipation and localized thermo-acoustic regularization. The exclusion of dynamically sustained critical thermo-acoustic concentration yields a localized ε-regularity framework combining thermodynamic dissipation, Campanato decay, and interior parabolic regularization. The resulting estimates provide localized Lipschitz control sufficient for the continuation of admissible strong solutions within the same thermo-acoustic class. The framework further remains compatible with weak–strong stability and irreversible long-time thermodynamic relaxation through the relative entropy structure and free-energy dissipation.

Mathematics doi: 10.3390/math14122229

Authors: Jianli Cao Bingchen Han Zirui Xiang Yongyi Fang Kejie Zou Hangxing Ding Xinyu Liu

Underground mine production scheduling under uncertainty is a complex and multi-field coupling system project. In this study, underground mine production scheduling seeks to determine the optimal start time of extraction-related projects, with the objectives of maximizing net present value, minimizing makespan, and maximizing resource utilization rate. The Copula function is adopted to formulate the correlation between uncertain project duration and cost and generate a set of stochastic scenarios. Then, the K-means algorithm classifies the scenarios into multiple scenario families, and the SBR algorithm is adopted to perform scenario reduction. Moreover, a rank choice function-based hyper-heuristic algorithm is extended to solve the multi-objective optimization model, which makes an excellent balance among the three objective functions. For determining the optimal scheduling plan, the cross-efficiency DEA algorithm is used to evaluate the archive set, sort the optimal solution, and guide the next iteration. The computational case verifies the effectiveness and efficiency of the multi-objective underground mine scheduling model, stochastic scenario and technical and hyper-heuristic algorithm.

Mathematics doi: 10.3390/math14122228

Authors: Alexey Kirpikov Vladislav Oboskalov Murodbek Safaraliev Ismoil Odinaev Mihail Senyuk Svetlana Beryozkina

This paper addresses probabilistic and statistical methods for calculating technical energy losses in direct current (DC) networks. A DC network model is adopted as the basis for the analysis, and several approaches are compared in terms of qualitative features and computational efficiency. The load profile is described using probabilistic indicators, emphasizing the importance of accounting for correlation moments (CMs) between node powers and CMs between voltages to reduce calculation errors. A correction procedure for the mathematical expectation of node voltages is proposed, which significantly improves the accuracy of loss estimation. Simulation studies on representative four-node DC test networks show that the proposed method reduces the root mean square error in loss estimation by up to 15–20% compared with traditional approaches based solely on mean load values. The results confirm that the correction of node voltage expectations provides a good balance between accuracy and computational cost and can be recommended as an independent procedure within existing probabilistic frameworks for loss assessment.

Mathematics doi: 10.3390/math14122227

Authors: Aristea Kontogianni Konstantina Chrysafiadi Maria Virvou Efthimios Alepis

Wikidata provides extensive coverage of tourism-related Points of Interest (POIs), yet its heterogeneous type system and uneven metadata limit its direct use in smart tourism applications. This paper presents an end-to-end pipeline that transforms Wikidata POIs into a compact and interpretable tourism-oriented representation supporting multi-category assignments. We collect POIs from six countries—Greece, Italy, Spain, Norway, Sweden, and Denmark—and construct a dataset that integrates core identifiers with textual descriptions, type information, heritage indicators, geographic coordinates, and Wikipedia sitelinks. We introduce an eight-category tourism taxonomy capturing key themes, including cultural venues, archaeological and historic sites, monuments, fortifications, religious sites, protected areas, natural features, and coastal or water locations. As a reproducible baseline, category likelihoods are estimated using sentence embeddings and similarity to category anchor descriptions, producing a probability vector for each POI. Building on this baseline, we propose a fuzzy inference layer that integrates embedding-based probabilities with structured Wikidata signals to generate interpretable membership degrees across categories and enable principled multi-category classification. This fusion is particularly valuable for smart tourism applications, as it supports robust faceted exploration and personalized recommendations (e.g., “historic + coastal”), while providing evidence-based explanations that enhance user trust and facilitate curator oversight when POI metadata is sparse or ambiguous. The resulting pipeline produces ranked POI catalogs by country and category, country-level tourism profiles, and diagnostic views for examining uncertain cases. The approach is fully reproducible and readily adaptable to other geographic regions or domain taxonomies.

Mathematics doi: 10.3390/math14122223

Authors: Laszlo Csirmaz

Let N be a finite set of cardinality n, and let a∈N. A submodular function f on N with f(a)=1 is defined to be a-reduced if, for any decomposition f=g+h into submodular functions, where h does not depend on a, it follows that h is identically zero. The maximal possible value of f on the remaining singletons defines a quantity λ that characterizes the degree to which one variable can constrain the value of another; geometrically, it also limits the possible elongation of the associated submodular base polytope. The parameter has concrete relevance: it caps the share-size lower bounds provable for secret-sharing schemes via the basic Shannon inequalities, and it controls the geometry of the base polytopes on which greedy submodular-optimization algorithms operate. We construct an example demonstrating that λ can be as large as Ω(n/logn). Furthermore, we establish a doubly exponential upper bound on λ. The problem of narrowing the gap between these bounds remains open.

Mathematics doi: 10.3390/math14122225

Authors: Yanghui Liu Bowen Zhou Liaoyi Ning Juan Yan

Data centers have become essential infrastructure for digital services, while their rapidly growing electricity demand makes coordinated workload and power management an important optimization problem. This paper studies the multi-data-center operation problem under time-of-use electricity pricing and formulates it as a multi-data-center mixed-integer nonlinear programming model (MDC-MINLP). The model jointly represents binary task scheduling decisions, including temporal workload shifting and spatial task migration, and continuous power-side variables, including device-level utilization, IT and auxiliary power consumption, energy storage dynamics, grid power procurement, and quality-of-service constraints. The objective is to minimize the total operating cost by integrating electricity purchasing cost, IT operation loss, storage degradation cost, and migration cost. To solve the resulting large-scale discrete–continuous coupled problem, an Adaptive Large Neighborhood Search algorithm with Hierarchical Collaboration (HC-ALNS) is proposed. HC-ALNS reconstructs feasible task action sets, employs a surrogate objective for fast candidate screening, performs accurate power-layer evaluation for selected solutions, and adaptively adjusts search intensity according to convergence behavior. Numerical results show that HC-ALNS reduces the total operating cost by 3.67% and achieves better convergence and solution quality than NSGA-II and PSO. These findings demonstrate that the proposed MDC-MINLP and HC-ALNS provide an effective mathematical optimization framework for coordinated computation–power scheduling.

Mathematics doi: 10.3390/math14122226

Authors: Sami H. Saif Shayea Aldossari

Asymmetric quantum codes are useful for quantum channels in which phase and bit errors occur with different probabilities, since the two distances, dz and dx, can be controlled separately. We develop a permutation-paired matrix-product construction for such codes over Fq. The main task is to build classical code pairs C,D⊆Fq2kn satisfying the Hermitian inclusion D⊥H⊆C, while keeping explicit dimension and distance bounds. Let A∈Fq2k×k be a non-singular-by-columns (NSC) matrix with AA†=DPτ, where D is an invertible diagonal and Pτ corresponds to an involution τ. For C=[C1,…,Ck]A and D=[D1,…,Dk]A, we prove D⊥H=[Dτ(1)⊥H,…,Dτ(k)⊥H]A. Thus, the global inclusion D⊥H⊆C is equivalent to the shorter paired inclusions Dτ(i)⊥H⊆Ci. This yields asymmetric quantum codes with parameters [[kn,∑i=1k(ri+si)−kn,dz/dx]]q, where the bounds for dz and dx follow from NSC matrix-product distance estimates. For nested maximum distance separable (MDS) constituents, the paired conditions reduce to ri+sτ(i)≥n, giving explicit infinite families. Concrete τ-OD matrices and numerical examples show that nontrivial permutations can increase the quantum dimension while preserving prescribed lower bounds for dz and dx.

Mathematics doi: 10.3390/math14122224

Authors: Abdullah Alsaiari Turki Turki Y-h. Taguchi

Ovarian cancer is a gynecological cancer, which, if metastasized and not detected early, can cause death among women. Therefore, accurate prediction of drug responses to ovarian cancer is needed. A gynecological pathologist inspects abnormality in tissues and provides a report for patients; however, this diagnostic process (1) is difficult to undertake; (2) requires experience; and (3) is time-consuming. Moreover, existing tools are imperfect. Hence, we present a computational pipeline to improve predictions of drug response pertaining to ovarian cancer. First, we downloaded digital pathology images pertaining to ovarian responses to bevacizumab from the Cancer Imaging Archive Repository. We employed a histogram of oriented gradients for images, constructed feature vectors, and used Fisher’s linear discriminant analysis to alter data representations through dimensionality reduction. This reduced-dimensionality data was used for regression analysis, employing support vector regression coupled with various kernels and calculating the area under the ROC curve (AUC). Experimental results were validated using transformer-based models (ViT and Swin) and other deep learning (DL) models (VGG16, ResNet50, InceptionV3, MobileNetV2, and EfficientNetB6). Our approach using a radial kernel (named SVRD + R) improved AUC performance by 17% compared to the best-performing transformer-based model (ViT). Likewise, AUC performance improved by 14.9% when compared against the best DL-based model (MobileNetV2). These results demonstrate feasibility, showing that induced models via the presented AI-based pipeline can lead to superior performance when investigating prediction problems pertaining to gynecologic cancer studies.

Mathematics doi: 10.3390/math14122222

Authors: Dmytro Babets Amirbek Yerkinbekov Serik Moldabayev Samal Assylkhanova Volodymyr Hnatushenko Olena Sdvyzhkova

This study presents an intelligent framework for the analysis of multidimensional geomechanical states in underground mining systems based on numerical simulation and machine learning methods. A three-dimensional geomechanical model of the Zholymbet deposit was developed in the RS3 environment using the generalized Hoek–Brown failure criterion. Numerical simulations were performed for representative mining scenarios characterized by complex excavation interaction and stress redistribution. The modelling results were transformed into a multidimensional geomechanical dataset containing stress, deformation, displacement, and yielding parameters. Principal component analysis (PCA) was applied to investigate the internal structure of the geomechanical state space and identify dominant patterns controlling the rock mass behavior. Clustering analysis revealed several geomechanical regimes corresponding to stable, transitional, and instability-prone conditions. Isolation Forest anomaly detection demonstrated that atypical geomechanical states are not randomly distributed but spatially localized near excavation systems and mining horizons. The obtained results indicate that hazardous geomechanical conditions are governed by complex interactions between stress concentration, deformation intensity, yielding processes, and excavation geometry. The proposed approach provides a basis for intelligent interpretation of large-scale numerical modelling results and may support geomechanical risk assessment in underground mining operations.

Mathematics doi: 10.3390/math14122220

Authors: Nícolas Samuel Assis Socorro Rangel Helio Yochihiro Fuchigami

Permutation flow shop scheduling is an important production planning problem handled in different contexts. Just-in-time measures have been significant in the optimization of real problems and one is specifically addressed here: the total earliness and tardiness of jobs. The most used approach in the literature to mathematically express this measure is to sum them up using unit weights thus obtainning a mono-objective function. In this paper it is shown that this is a simplification of a problem that is inherently multi-objective, highlighting how a more comprehensive approach can better support decision-making. A bi-objective mathematical optimization model and tools capable of analyzing the mono-objective solution within the multi-objective perspective are proposed. A computational study to analyze the benefits and difficulties of the solution using the bi-objective approach is presented. The results show that for large-scale instances in which the tardiness factor is small, the conflict between the objectives of minimizing the total earliness and minimizing the total tardiness of jobs increases significantly. Specifically, the mono-objective solution is unbalanced in 50.00% of the analyzed instance structures. However, in 48.12% of the instances, alternative Pareto-optimal trade-offs can be achieved with zero increase to the mono-objective optimal value. Therefore, the multi-objective approach has a greater potential to support decision-makers. Furthermore, we show that the choice of the solution method must be carefully considered, since the Pareto frontier associated with most instances has many non-supported points, representing up to 66.71% of the non-dominated set.

Mathematics doi: 10.3390/math14122221

Authors: G. Sudhaamsh Mohan Reddy Lateef Ahmad Wani Mudasir Younis Saiful R. Mondal

In this article, we construct a framework for analyzing the equilibrium and stability of networked multi-sector economic systems via fixed-point analysis. We represent directional intersectoral dependencies, nonlinear feedback effects, and heterogeneous adjustment dynamics in the model by the coupled and tripled fixed-point theory in the graphically extended suprametric spaces. The graphical structure encodes supply-chain and influence networks, whereas asymmetric and nonuniform interaction strengths are encoded in the suprametric setting. Furthermore, we prove the existence, uniqueness, and convergence of equilibrium solutions under new generalized contraction conditions. We apply the theoretical findings in nonlinear state systems in which prices in interdependent markets are adjusted using integral equations. The results of numerical simulations show consistent convergence, and the sensitivity parameter of the network structure significantly influences the determination of economic stability and speed of adjustment.

Mathematics doi: 10.3390/math14122219

Authors: Vanusa Rocha Miguel Felgueiras Vera Afreixo

Rosenthal’s fail-safe number is widely used to assess the robustness of meta-analysis results against publication bias; however, its statistical properties remain insufficiently understood. This paper re-evaluates the coverage performance of confidence intervals for the Rosenthal’s fail-safe number using an updated simulation framework that incorporates zero truncation, an epsilon correction to the expected value, and a restriction to statistically significant meta-analyses. In addition to the standard normal bootstrap approximation, bias-corrected and accelerated bootstrap confidence intervals are considered. Simulation results show that standard bootstrap intervals tend to be conservative under symmetric settings and exhibit substantial deviations under asymmetric distributions. The bias-corrected and accelerated bootstrap method improves coverage accuracy, particularly under asymmetry and moderate sample sizes, although both methods exhibit conservative behavior in several scenarios. Overall, reliable inference for the fail-safe number depends on both appropriate parameter specification and bootstrap procedures that account for bias and asymmetry.

Mathematics doi: 10.3390/math14122218

Authors: Ernesto Estrada

We introduce a geometric framework for continuous-time quantum walks on graphs by embedding each vertex into a Euclidean space through its time-dependent quantum probability distribution. This construction induces a rich geometry in which quantum transport is characterized by distances, radii, angles, and simplex volumes, allowing interference, localization, and spreading to be analyzed within a unified metric-angular formalism. We prove that, in contrast to classical diffusion, which collapses to a spherical geometry, quantum dynamics generate a generically non-spherical affine geometry with persistent anisotropy. Applying this theory to real-world networks—including transportation systems, semantic graphs, and neuronal connectomes—we show that quantum geometry reveals dynamically meaningful backbones, interference-based “communities”, and vulnerability structures that are invisible to classical random-walk and spectral methods. In particular, angular and radial quantum descriptors isolate functional hubs, control cores, and coherence classes without any topological or dimensionality assumptions. Together, these results demonstrate that quantum-walk-induced geometry provides a powerful new lens for understanding structure and function in complex networks.

Mathematics doi: 10.3390/math14122216

Authors: Qiu Yu Xin Zhang Zhiyang Jia Chen Peng

Large-amplitude and long-term vibration deformation under external environmental loads often occurs on tensile membrane structures. Proper sensor placement plays a vital role in effectively achieving the objectives of a structural health monitoring system. In order to optimize the sensor placement to identify the modal vibration parameters for tensile membrane structures, this paper proposes an optimal sensor placement method based on the Fisher information matrix (FIM) and improved random strategy discrete particle swarm optimization algorithm (IRSDPSO). Firstly, the structural modal order is selected by using the two-norm difference and trace change rate of FIM, and the number of sensors is determined based on the QR decomposition and MAC criterion. Secondly, an improved particle swarm optimization algorithm named IRSDPSO, which has the discrete characteristic, is proposed to arrange the placement of sensors. Finally, the convergence, stability and sensitivity are used to evaluate the effectiveness of optimal sensor placement results using a numerical modal test example of the plane bidirectional tensile membrane structure. The results show that the first nineteen modal frequencies can be accurately identified. This indicates that the proposed optimal sensor placement method can determine the number of sensors and arrange the placement of the sensors. The work is reasonable and feasible in the optimal sensor placement for the tensile membrane structure.

Mathematics doi: 10.3390/math14122217

Authors: Vinicius Minatogawa Mitsuyoshi Fukushi Jose Garcia Jorge Rojas Jose Gornall Alfredo Angulo Jefferson Pinto

Small and medium enterprises routinely face a paradox in financial monitoring: their accounting documents exist, but the cost of converting heterogeneous PDFs into timely financial signals is prohibitive without dedicated analytical staff or specialized software. This paper presents a two-layer artifact, designed under Design Science Research, that bridges this gap using only public-web large language models (LLMs) and a parsimonious multi-criteria decision routine. Layer 1 implements a structured LLM-driven workflow that extracts account–value pairs from annual tax balance sheets without code, APIs, or fine-tuning. Layer 2 reconstructs auditable accounting aggregates and ranks yearly financial condition through TOPSIS with min–max normalization—a deliberate replacement for classical vector normalization, which fails when profitability indicators are negative, as routinely occurs in distress years. To avoid size effects and algebraic redundancy, the decision matrix uses only three criteria spanning liquidity, profitability, and solvency. The artifact is demonstrated in a four-year case study of an anonymized construction SME (2021–2024), with accountant-verified document-level match rates of 0.810, 0.998, 0.950, and 0.909. Equal weighting is the only weighting configuration used; a supplementary entropy-based dispersion diagnostic yields the same ordinal ranking—2024 > 2023 > 2021 > 2022—and 10,000 Monte Carlo replications, with uncertainty injected at the reconstructed-aggregate level, confirm that the extreme ranks are invariant across all runs. The contribution is methodological and practical: a transparent, low-infrastructure pipeline that brings first-pass financial screening within reach of SMEs operating under severe data and budget constraints.

Mathematics doi: 10.3390/math14122215

Authors: Xuefeng Mao Biyan Zhu

Let A be a connected cochain differential graded algebra and P a finitely generated differential graded A-module. We show that P is semi-free if it is semi-projective and it is categorically free if it is categorically projective. It can be considered as a generalization of the well-known Quillen–Suslin Theorem in differential graded context. As an application, we show that the ghost length and the cone length of a compact differential graded module coincide.

Mathematics doi: 10.3390/math14122214

Authors: Ru Xiao Jiyang Xu Jiabo Li

Accurate remaining useful life (RUL) prediction is critical for the reliable operation of lithium-ion batteries. Traditional data-driven methods often suffer from parameter redundancy and error accumulation in state prediction. This paper proposes a hybrid data-driven RUL prediction framework based on Gaussian process regression (GPR) optimized by the lightning search algorithm (LSA). First, both local and global indirect health features (HFs) are extracted from the external characteristic parameter curves and the incremental capacity curves during battery charging/discharging. Second, the Pearson correlation coefficient is applied to select highly relevant features, forming a compact feature set. Third, a GPR model is developed, and the LSA is introduced to optimize its hyperparameters, overcoming the tendency of the conjugate gradient method to fall into local optima or fail to converge. Experimental results under identical conditions show that the proposed LSA–GPR model achieves a prediction error of 3% or less.

Mathematics doi: 10.3390/math14122213

Authors: Elisa Munich Jérémie Schutz Christophe Sauvey Yves Gillet

This paper presents and validates a unified spreadsheet-based framework for engineering mechanics education and preliminary design. Three modules are integrated within a single openly available workbook: multi-point resultant force and moment computation; axial normal stress with stress concentration effects for three geometric configurations (plate with hole, shoulder plate, stepped shaft); and beam deflection for simply supported and cantilever configurations under point loads. All governing equations are implemented as explicit closed-form expressions validated against analytical reference solutions for six independent cases; relative errors fall below 10−10 in all cases. Three worked exercises demonstrate the practical scope of the framework. A biomechanical multi-point force system yields joint moments of −6880, −33,421, and −58,241 N·mm at the wrist, elbow, and shoulder, respectively. A tensile shoulder plate with Kt≈1.85 produces σmax=232 MPa against σy=200 MPa, identifying a design failure; a parametric redesign with fillet radius r=10 mm reduces Kt to approximately 1.59 and σmax to approximately 198.7 MPa, restoring structural safety. A cantilever beam subjected to a 20,000 N tip load yields a maximum deflection of 13,133 μm. The framework constitutes a validated intermediate layer between manual analytical derivations and high-fidelity numerical simulations, applicable to preliminary design, parametric sensitivity studies, and engineering education at the linear elastic level.

Mathematics doi: 10.3390/math14122211

Authors: Bader Albader

Gaussian networks are degree-four symmetric interconnection networks defined over residue classes of Gaussian integers. Earlier work showed that, when the generator α=a+bi satisfies gcd(a,b)=1, the real and imaginary dimensions directly form two edge-disjoint Hamiltonian cycles. A later construction extended the result to the non-coprime case gcd(a,b)=d>1, but its proof relied on long node-sequence tables and separate odd/even cases for d. This paper presents a unified closed-form construction that covers both d=1 and d>1, and both odd and even d, without separate case tables. In the rectangular representation with d rows and r=(a2+b2)/d columns, the construction uses a constant-time local switch rule, meaning constant time per individual switch, for each q=1,2,…,d−1 at column aq=q−1. Each switch removes two horizontal edges and inserts two vertical edges. The switched horizontal structure forms the first Hamiltonian cycle, while its edge-complement in the Gaussian network forms the second Hamiltonian cycle. Thus, the full edge set is partitioned into two edge-disjoint Hamiltonian cycles. The construction requires O(d) switch-generation time and O(N) time to list the two cycles, where N=a2+b2. Exhaustive validation for all 1≤a≤b≤100, excluding only the degenerate N=2 network, and large-scale validation up to N=3,250,000 confirm implementation correctness and demonstrate practical scalability.

Mathematics doi: 10.3390/math14122212

Authors: Feras Yousef Tariq Al-Hawary Ibtisam Aldawish

The interplay between special functions and geometric function theory continues to inspire significant advances in the study of analytic and multivalent functions. In this work, we introduce and investigate several new subfamilies of multivalent functions associated with the generalized Mittag-Leffler-type Poisson distribution in the open unit disk. We establish necessary and sufficient conditions characterizing membership in these classes and derive meaningful inclusion relationships among them. Furthermore, we define a novel integral operator linked to the generalized Mittag-Leffler-type Poisson distribution and examine its mapping properties and structural connections with the proposed function classes. The results presented herein not only unify and extend a variety of earlier contributions but also demonstrate the effectiveness of distribution-theoretic methods in the analysis of multivalent functions.

Mathematics doi: 10.3390/math14122210

Authors: Wenjie Li Yongming Xie Yinglong Dai

Sequential data prediction is a crucial area in healthcare. Healthcare data have the characteristics of non-stationarity, long-range dependence (LRD), and irregular sampling. Modeling these complex temporal features is highly challenging. Recurrent Neural Networks (RNNs) and their variants are limited in learning long-range dependencies (LRDs) due to the inherent issues of vanishing and exploding gradients. Transformers alleviate this limitation by using the self-attention mechanism. Its quadratic computational complexity and memory bottleneck limit its scalability in long-range healthcare data. In this context, Structured State Space Models (SSMs) have emerged as a promising alternative. Compared with conventional RNNs, they can alleviate the difficulty of modeling LRDs more efficiently, and many modern SSM variants achieve linear time sequence modeling while reducing the computational burden associated with Transformers. In this review, we provide a formal definition of Healthcare Process Modeling, compare the core theoretical frameworks of RNNs, Transformers, and SSMs, trace the architectural evolution of SSM architectures, and provide a comprehensive review of healthcare applications and open challenges, including LSSL, S4, S5, Mamba, and their related variants. Existing studies suggest that structured SSMs are promising for selected long-sequence healthcare prediction tasks, particularly when computational efficiency and long-context retention are important. With these advantages, they may help alleviate the computational burden in certain healthcare tasks and provide a basis for further exploring the practical application of data-driven healthcare systems in clinical practice.

Mathematics doi: 10.3390/math14122209

Authors: Ahad Hamoud Alotaibi Muhammad Saeed Ahmad Muhammad Waseem Asghar Mujahid Abbas

Machine learning practice often reduces a complex training or inference problem to a one-dimensional response curve, such as a validation-loss curve, calibration curve, robustness-budget profile, or checkpoint-interpolation path. This paper presents a functional-analytic formulation of proposed (v,w)–s–convex response-curve certification. The response curve is treated as an element of the Banach space of continuous functions under the supremum norm, while derivative-based certificates are handled in a Lipschitz and Sobolev-type norm when required. Generalized convexity is represented through a bounded structural operator, whose order condition defines a closed convex acceptance set. The violation score is measured by the positive part of the operator residual, and the Hermite–Hadamard, Fejér, and Ostrowski quantities are interpreted as bounded certificate functionals. The auxiliary profiles are constructed from validation-curve residuals through a split-calibrated procedure and then tested on held-out triples. The framework certifies only scalar response-curve summaries under explicit structural and empirical assumptions; it does not certify a full learning system, guarantee generalization, or replace dense sampling when the structural gate fails.

Mathematics doi: 10.3390/math14122208

Authors: Mostafa E. A. Ibrahim Alaa E. S. Ahmed Yassine Daadaa

Combinatorial optimization is a key component in critical decision problems such as routing, scheduling, network design, and graph optimization. Although combinatorial optimization methods, including exact algorithms, approximation methods, constraint programming, mixed integer programming, and metaheuristics, are widely available, they often face obstacles, such as limited scalability and adaptability in various applications. In this study, a systematic critical review of machine learning for combinatorial optimization is provided to characterize the usage and evaluation of learning-based approaches. A detailed analysis is used to infer and determine findings and limitations. The paper emphasizes how machine learning for computational optimization has changed over time, moving from end-to-end neural solvers to hybrid systems. Learning components are essential for directing, speeding up, or enhancing traditional solver backbones such as constraint programming and metaheuristics in hybrid systems. The review also critically examines current limits that impact performance in general, including scalability, deployment readiness, generalization, and benchmark consistency. Even though using large language models for problem formulation and heuristic synthesis has potential, more work needs to be done to ensure reliable validation. As a conclusion, this article examines recent studies’ findings, emphasizes the growing trend toward hybrid learning-driven optimization frameworks, and underlines important methodological limits and unresolved issues.

Mathematics doi: 10.3390/math14122207

Authors: Jianyue Su Ziying He

The sign of the maximal almost sure Lyapunov exponent determines the stability of stochastic systems, while its numerical computation for three-dimensional linear Stratonovich stochastic differential equations remains challenging due to the failure of classical two-dimensional strategies. The spherical angular motion of 3D systems produces a Fokker–Planck equation with intractable mixed partial derivatives, preventing conventional analytical solutions. This paper develops a unified computational framework for three-dimensional linear Stratonovich stochastic systems using analytical derivation for degenerate cases and physics-informed neural network (PINN) approximation for general non-degenerate scenarios. For degenerate systems, we reduce the coefficient matrix to a lower triangular form via orthogonal transformation and establish tight upper bounds based on the logarithmic growth property of the Wiener process, yielding closed-form expressions for the maximal almost sure Lyapunov exponent under all parameter sign configurations. For non-degenerate systems, we reformulate the Fokker–Planck equation in spherical coordinates and construct a customized PINN with trigonometric encoding to enforce periodic boundary conditions. The network is trained by joint loss functions of equation residuals, boundary constraints and normalization consistency, and the converged stationary density is substituted into the Furstenberg–Khasminskii formula to calculate the exponent via Gauss–Legendre quadrature. Monte Carlo simulations confirm the accuracy and robustness of the proposed method, which reliably identifies the sign of the maximal almost sure Lyapunov exponent even in near-critical regimes. Numerical experiments on a 3D stochastic Hopf bifurcation model show that noise negatively shifts the bifurcation point, with the offset linearly proportional to the squared noise intensity. This work extends Lyapunov stability analysis from two-dimensional to three-dimensional linear Stratonovich stochastic systems, offering an effective tool for stability evaluation of general three-dimensional stochastic dynamical models.

Mathematics doi: 10.3390/math14122206

Authors: Mario J. Seni Molina David Peidro Payá

In engineer-to-order (ETO) manufacturing environments, the high variability of final product configurations makes it difficult to consistently estimate material consumption and, consequently, to define appropriate inventory control policies. This paper proposes a data-driven framework based on unsupervised learning to identify product typologies from historical manufacturing orders in a real industrial context. The approach employs a fuzzy k-prototypes algorithm to cluster mixed-type data, allowing the simultaneous treatment of numerical and categorical variables. In the case study, the proposed crisp-BOM-based scenario achieved a 28.67% reduction in line-side WIP and a 10.79% reduction in linear storage space, corresponding to the release of approximately two to three assembly stations. From the resulting fuzzy memberships, probabilistic bill of materials (BOM) structures are constructed, capturing the inherent variability of material consumption across different product configurations. A defuzzification procedure is then applied to obtain a crisp BOM representation suitable for operational decision-making. Additionally, a material versatility indicator based on entropy is introduced to quantify the dispersion of each material across product typologies. This indicator, together with the estimated consumption per cluster, is used as input for an analytical inventory model that supports the classification of materials into kanban or kitting policies. The methodology is validated using real data from a high- and medium-voltage switchgear manufacturing plant, comprising over 60,000 order–material observations. The results show that the proposed framework enables a more structured characterization of material behavior, reducing reliance on planner experience and improving the consistency of inventory policy decisions. From an industrial perspective, the approach provides a practical and scalable tool for aligning inventory strategies with the actual consumption patterns of ETO systems.

Mathematics doi: 10.3390/math14122205

Authors: Dimitrios Georgiou Sotiris Kotsiantis Fotini Sereti

Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and machine learning (ML), TDA provides multiscale descriptions through persistent homology, Mapper (a graph-based method that summarizes the shape of high-dimensional data), and related topological signatures that are often inaccessible to standard linear and metric methods. In recent years, and especially during 2024–2025, TDA has expanded rapidly across science, engineering, biomedical research, and socio-economic studies, while also being integrated with modern learning paradigms such as deep learning (DL) and graph learning. This survey summarizes recent developments in TDA using a carefully selected set of articles, with emphasis on 2024–2025. We first present the mathematical and computational foundations of TDA, covering simplicial complexes, filtrations, persistent homology, the Mapper algorithm, and computational advances such as data simplification, stability, and efficiency. We then review applications in time series and dynamical systems, biomedical imaging and precision medicine, engineering and physical sciences, finance and risk analysis, DL and interpretability, and security and critical infrastructure systems. Throughout, we highlight how TDA can extract informative features, function as a model component, and provide a conceptual lens for studying complex systems. However, the survey also emphasizes recurrent failure patterns: TDA performance is highly sensitive to filtration, embedding, and vectorization choices; aggressive simplification can dilute or remove informative topological signals; and integration into standard ML workflows still lacks uniform validation and reporting protocols. We conclude by outlining key challenges—including scalability, statistical foundations, interpretability, and compatibility with rapidly evolving artificial intelligence (AI) paradigms—and by identifying directions for future research. The survey also provides a unifying design perspective for TDA systems, highlighting methodological trade-offs and emerging research directions for integrating topology with modern ML.

Mathematics doi: 10.3390/math14122204

Authors: Athanassios S. Fokas Jonatan Lenells

Several important functions, including the gamma function, as well as several infinite sums, admit integral representations involving the Hankel contour. In addition, the large t asymptotic analysis of several recently derived identities satisfied by the Riemann zeta function requires the computation of the asymptotic form of certain integrals which also involve the Hankel contour; these integrals depend on a real parameter, α. A rigorous asymptotic technique is presented here for computing such integrals to all orders. For certain values of α, the relevant formula, in addition to an asymptotic series of explicit terms, also contains a specific integral. It is shown that, remarkably, the leading behavior of this integral can be written in the form of the leading order of the Bleistein integral. The latter integral arises in the implementation of the classical steepest descent method in the case that the stationary point coincides with one of the boundary points of the integral under consideration.

Mathematics doi: 10.3390/math14122203

Authors: Dostonjon Numonjonovich Barotov

In this paper, we consider a system of 10 equations from the standpoint of the number of its natural solutions, containing a non-negative integer parameter n and describing the magic state of the corresponding special table of numbers. As a result of the study, it is constructively proven that, for each natural number m, there exist natural numbers nm and sm such that, for a non-negative integer parameter n equal to nm, this system has at least 2m solutions, and all ten coordinates of each of these solutions are sm-digit natural numbers, with the first, ninth, and tenth coordinates in decimal notation being represented only by the digits 0, 8, and 9, and the d-th coordinate, d∈{2,3,…,8}, being represented only by a single digit, equal to (d−1). This result, which constructively confirms the unboundedness of the number of solutions of this system depending on a non-negative integer parameter n, strengthens some recently published results.

Mathematics doi: 10.3390/math14122202

Authors: Hairong Zheng Xiaozheng Zeng Guoyu Hu Tingting Zhang

Stock index price series are composed of superimposed multi-frequency components, including long-term trends, cyclical fluctuations, and stochastic noise. Effectively decoupling these heterogeneous components and modeling them separately is key to improving forecasting accuracy. Existing methods under the “decomposition–prediction” paradigm mostly employ fixed-scale decomposition, and the forecasting models are not specifically adapted to the non-stationary and high-noise characteristics of financial data, resulting in limitations in adaptivity and local dynamic capture. This paper proposes a frequency-aware adaptive multi-scale decomposition Transformer hybrid model (FAMS-Transformer). At the decomposition level, the fast Fourier transform is used to dynamically identify dominant cycles, thereby adaptively decoupling trends and fluctuations, overcoming the limitations of fixed-scale decomposition. At the forecasting level, a lightweight depthwise separable convolution is embedded between the self-attention and feedforward network of the Transformer encoder, enhancing the model’s ability to capture local temporal dynamics and achieving collaborative modeling of global dependencies and local information. Comparative experiments with 15 baseline models including LSTM, Transformer, TimesNet, and FreTS on three representative Chinese market indices—Shanghai Composite Index, Shenzhen Component Index, and Small and Medium Enterprises 100 Index—across four prediction horizons from one step to 15 steps demonstrate that FAMS-Transformer achieves the best forecasting accuracy in all scenarios. The coefficient of determination for 15-step prediction remains stably between 0.730 and 0.928. Moreover, the model still performs well on the S & P 500 dataset. Ablation studies and significance tests further validate the effectiveness of each core module and the statistical significance of the performance improvements.

Mathematics doi: 10.3390/math14122201

Authors: G. Archana Alias Gurulakshmi Aliakbar Montazer Haghighi G. Ayyappan N. Arulmozhi Natarajan Aishwarya

This paper analyzes a single-server queueing system with infinite capacity, where arrivals follow a Markovian arrival process and service and repair times are modeled by phase-type distributions. The service mechanism is two-tier: every customer undergoes a mandatory primary service, after which an optional secondary service is available upon request. When the system is empty, the server initiates a closedown process before taking successive multiple vacations; upon return, the server goes through a setup process before beginning service again. Service can be interrupted by random breakdowns in either mode, triggering a phase-type repair. Matrix-analytic methods are used for the steady-state analysis, yielding the stability condition, stationary probability vectors, busy period analysis and key performance measures. A cost analysis framework is also developed. Numerical experiments validate the analytical results and illustrate the practical applicability of the model.

Mathematics doi: 10.3390/math14122200

Authors: Shuo Zhang Senxiang Lu Yichen Liu Liuqing He

Matching of multi-run magnetic flux leakage (MFL) in-line inspection data for oil and gas pipelines provides an essential basis for defect evolution analysis, corrosion growth assessment, and integrity management. However, in practical engineering applications, inconsistencies in total measured mileage, differences in the number of key points, and cumulative mileage errors across different inspection runs significantly increase the difficulty of data matching. To address these issues, this study proposes a report-level matching framework for multi-run MFL in-line inspection data that combines key-point alignment with defect matching. The proposed method improves the adaptability of defect matching under complex defect-size and spatial-distribution conditions through a dynamic-threshold mechanism and mitigates the influence of cumulative mileage errors on the matching results in later pipeline sections when large total mileage discrepancies exist between inspection runs through an adaptive anchor-based segmentation mechanism. Experiments based on multi-run MFL in-line inspection data from two actual pipelines demonstrate that the proposed method can achieve stable key-point and defect correspondence in scenarios with both small and large total mileage differences, thereby providing a basis for subsequent defect growth analysis.

Mathematics doi: 10.3390/math14122199

Authors: Tingwei Liang Feng Yu Jie Yan

The circadian clock is closely linked to glucose regulation, but the dynamical consequences of specific metabolic feedback pathways on core clock regulation remain incompletely understood. In this study, we developed a theoretical metabolic-circadian model incorporating a REV-ERBα-glucagon-glucose feedback pathway. The model extends a previously established mammalian circadian clock framework by introducing glucagon-mediated regulation of blood glucose and glucose-dependent modulation of Rev-erbα transcription. Using this model, we examined how the feedback pathway affects circadian oscillations, the sensitivity of period and amplitude to parameter perturbations, and phase-related responses under light stimulation and light–dark cycles. Simulations of the feedback-related parameters showed that the glucose-to-clock feedback strength had a marked effect on oscillation period and amplitude, motivating a further assessment of whether regular circadian dynamics were preserved under parameter perturbations. We therefore analyzed both one-parameter perturbations and simultaneous perturbations of all model parameters. For one-parameter scans, we quantified not only the oscillatory boundaries but also the period variation and the amplitude variation of Per and Rev-erbα within the oscillatory ranges. For simultaneous all-parameter perturbations, Latin hypercube sampling was used to compare coupled and uncoupled models under bounded perturbation ranges. The coupled model showed a higher fraction of regular circadian oscillations under local perturbations, mainly by reducing the probability of rhythm loss. We further examined phase responses and light–dark entrainment to assess how the feedback affects dynamical properties beyond period and amplitude. In the phase-response analysis, the feedback reduced excessive phase shifts in the model, suggesting a possible phase-response robustness effect in this theoretical framework. These theoretical results suggest that the REV-ERBα-glucagon-glucose feedback pathway may be relevant to circadian regulation under fasting-associated metabolic conditions.

Mathematics doi: 10.3390/math14122198

Authors: Shengchao Li Shixin Liu

This paper addresses a human resource allocation problem with spatial-temporal constraints (HRAP-SC) in the parallel assembly of complex products, such as satellites and aircraft. It involves coordinating a limited pool of multi-skilled workers across geographically distributed workstations, subject to rigorous constraints including team collaboration requirements, operation priorities, technological tail times (e.g., curing), and strict 8 h workdays. Existing exact approaches typically fail to converge due to the combinatorial explosion arising from the strong coupling of shared resources across workstations, while meta-heuristic methods often suffer from performance instability caused by hyper-parameter sensitivity. To overcome these limitations, we propose a pattern-based decomposition algorithm (PDA), a novel parameter-free exact solution framework. By exploiting the inherent symmetry of identical jobs and parallel workstations, PDA defines a set of canonical patterns to drastically reduce the search space. It employs an efficient traversal mechanism reinforced by rigorous mathematical bounds and pruning rules to eliminate unpromising solutions. Computational experiments demonstrate that PDA significantly outperforms state-of-the-art Mixed-Integer Programming (MIP) and Constraint Programming (CP) solvers. Unlike standard solvers, which frequently time out (3600 s), PDA strictly evaluates only a single pattern when proving optimality, and robustly scales to large industrial instances (e.g., six jobs comprising 78 operations) to provide high-quality schedules. By successfully solving complex scheduling problems that remain intractable for monolithic solvers, PDA provides a robust and automated decision-support tool for production management in complex manufacturing systems.

Mathematics doi: 10.3390/math14122197

Authors: Mahmoud Abdalla Mahmoud SalahEldin Kasem Mohamed Mahmoud Mostafa Farouk Senussi Abdelrahman Abdallah Hyun Soo Kang

Reasoning-intensive multimodal retrieval suffers from a counter-intuitive bottleneck: on MM-BRIGHT multimodal-to-text (Query+Image → Documents), the strongest dense multimodal encoder reaches only 27.6 nDCG@10 and the rest of the dense vision–language retrievers cluster between 10.0 and 23.0. The visual signal, encoded as a dense vector, adds noise rather than evidence; even augmenting strong text retrievers with raw image captions degrades performance by up to 12.0 points. We propose VISA, a Visual Symbolic Agent that re-casts multimodal-to-text as text retrieval over three parallel streams. A Vision LLM is dispatched in three roles via separate prompts: a zero-shot router that classifies the query image into up to three parser types from a fixed taxonomy of nine (chart, circuit, equation, screenshot, code, figure, diagram, map, photograph); typed parsers that extract structured text per type; and a holistic captioner. The agent constructs three text streams (raw query, query ⊕ symbolic, query ⊕ caption), scores each with a single frozen 4B-parameter retrieval LLM, and fuses the per-document scores via Reciprocal Rank Fusion or a confidence-weighted linear combination. The whole agent contains no trainable parameters. The key novelty is a change of substrate: rather than projecting the query image into a dense multimodal vector that competes with text, VISA is, to our knowledge, the first retrieval system to convert the image into typed symbolic text and keep retrieval entirely text-side, so that a frozen text retriever can match the literal tokens (axis values, variable names, function signatures) that answering documents actually contain. Across all 29 MM-BRIGHT multimodal-to-text domains, VISA achieves 32.4 nDCG@10, an absolute improvement of +4.8 over the strongest dense multimodal encoder and substantially larger margins over the remaining six dense vision–language baselines. Per-domain analysis shows VISA maintains its margin across STEM and software domains where image content is structure-heavy. In practical terms, VISA is training-free and model-agnostic: it requires no fine-tuning, reuses any off-the-shelf vision LLM and text retriever, caches all per-image parsing so re-runs cost only three query encodes, and can therefore be dropped into an existing text-retrieval stack to add reasoning-intensive multimodal capability without building or training a multimodal encoder.

Mathematics doi: 10.3390/math14122196

Authors: Abdulmajeed A. R. Alharbi

Nonparametric inference for residual-life functionals is a fundamental problem in mathematical statistics, reliability theory, and survival analysis, particularly in studies with limited sample sizes where empirical plug-in estimators may exhibit substantial sampling variability. In comparative lifetime analysis, additional qualitative information is often available regarding the relative behavior of two populations; however, such information is frequently too weak to justify classical stochastic dominance assumptions. Stochastic precedence provides a natural and interpretable framework for representing this partial ordering through a pairwise probabilistic constraint. This paper develops a constraint-adjusted nonparametric inference framework for estimating the mean residual life (MRL) and quantile residual life (QRL) functions under stochastic precedence information. The proposed approach replaces the ordinary empirical distribution function in standard residual-life plug-in estimators with a constraint-adjusted empirical distribution function that enforces the stochastic precedence relation at the sample level. The adjustment is governed by a data-driven scaling factor and is asymptotically negligible, thereby preserving the large-sample behavior of the ordinary empirical estimators while incorporating meaningful structural information in finite samples. Strong consistency of the proposed MRL and QRL estimators was established under mild regularity conditions. A Monte Carlo study based on Weibull and gamma lifetime models demonstrates that in the simulation settings considered, the proposed estimators provide improved finite-sample stability and generally achieve smaller mean squared errors than their ordinary empirical counterparts, especially for small and moderate sample sizes. The methodology is further illustrated using survival data from patients with squamous cell carcinoma of the oropharynx, highlighting its practical relevance in biomedical survival analysis. The proposed method offers a flexible, interpretable, and computationally simple framework for nonparametric inference with structured lifetime data under weak stochastic ordering information.

Mathematics doi: 10.3390/math14122194

Authors: Hai Shen Yu Li Jianbo Zhao Anqi Fan Xiaogang Zhao

As a cornerstone of global technological advancement, the semiconductor industry depends critically on supply chain stability, which directly influences the global economy and technological innovation. To address uncertainty in semiconductor supply chains, this study develops a Stackelberg game model incorporating Nash bargaining fairness concern to examine pricing strategies, ESG effort decisions, and their implications for supply chain stability under different fairness concern scenarios. A cost-sharing contract-based coordination mechanism is proposed, and numerical simulations verify the effects of fairness concern and ESG effort on stability, as well as the coordinating role of the cost-sharing contract under market uncertainty. The results show the following: (1) Manufacturer fairness concern boosts its profit and ESG effort, but excessive price hikes erode retailer profit and undermine stability. (2) Retailer fairness concern prompts the manufacturer to rebalance profit allocation via lower wholesale prices and reduced ESG effort, weakening supply chain competitiveness. (3) Cost-sharing contracts effectively mitigate the adverse effects of fairness concern and enhance semiconductor supply chain stability. This study provides a verifiable framework for semiconductor firms to improve cooperative stability and sustainable development.

Mathematics doi: 10.3390/math14122195

Authors: Aslı Durmuşoğlu

The vertical landing of quadrotor unmanned aerial vehicles (UAVs) involves highly transient impact dynamics that generate significant vibrations on the UAV body, particularly under uncertain touchdown conditions such as uneven terrain, asymmetric ground contact, and high-impact landing. In this study, a robust semi-active vibration control framework is proposed for a quadrotor UAV equipped with a four-point soft landing gear system. The UAV is modeled as a three-degree-of-freedom rigid body including heave, pitch, and roll motions, while each landing gear leg is represented by an equivalent spring-damper mechanism with adaptively controllable damping characteristics. To evaluate the effectiveness of the proposed framework, PID (Proportional–Integral–Derivative), GA-PID (Genetic Algorithm-Based Proportional–Integral–Derivative), Fuzzy–PID (Fuzzy Logic-Based Proportional–Integral–Derivative), and ANFIS-PID (Adaptive Neuro-Fuzzy Inference System-Based Proportional–Integral–Derivative) controllers are comparatively investigated under five different landing scenarios. The nonlinear touchdown dynamics are implemented in the MATLAB/Simulink environment using a state-space-based simulation model. The results demonstrate that intelligent adaptive control methods significantly improve landing stability and vibration attenuation compared to the conventional PID controller. Among all methods, the ANFIS-PID controller achieved the best overall performance. Under the most severe landing condition, the peak vertical displacement was reduced from 0.114 m to 0.025 m, while the maximum pitch and roll angles decreased from approximately 11° to nearly 2°. Additionally, the settling time was reduced from nearly 10 s to below 3 s.

Mathematics doi: 10.3390/math14122193

Authors: Müjgan Zobu Hasan Bulut Murat Sağır Vedat Sağlam

Hotelling’s T-squared statistic provides an interpretable framework for multivariate fault detection; however, its rolling implementation is highly sensitive to transient casewise outliers in the reference window. Such abnormal observations may inflate the sample covariance matrix, enlarge the monitoring boundary, and consequently mask subsequent moderate fault signals. This study proposes a robust rolling Hotelling fault detection method, denoted as RRH-FD, to reduce this masking effect. The proposed method estimates the rolling reference center and scatter matrix using reweighted minimum covariance determinant (RMCD) estimators, while each newly arriving observation is evaluated directly as a potential fault signal. The monitoring threshold is obtained using a robust Hotelling approximation rather than the classical Hotelling distribution. A simulation study was conducted under both clean and contaminated rolling reference scenarios. Under clean reference windows, the proposed robust procedures remained competitive with the classical rolling Hotelling detector, showing only a modest efficiency loss. Under contaminated reference windows, RRH-FD substantially improved detection performance. The adaptive RRH-FD method reduced the average detection delay by approximately 37.6% relative to the classical rolling detector, while the fixed MCD fraction 0.85 version achieved an approximate reduction of 42.4%. The proposed methods also improved early detection rates within the first 25 and 50 post-fault monitoring points. Boundary inflation was quantified using the log-determinant ratio between the classical sample covariance matrix and the RMCD scatter estimate. This analysis further confirmed that the advantage of RRH-FD becomes more pronounced as the classical covariance boundary is more strongly inflated by transient outliers. An R package, RRHFD, was developed to facilitate implementation and reproducibility.

Mathematics doi: 10.3390/math14122192

Authors: Kazuhisa Takemura Hajime Murakami Keita Kawasugi Zhengyue Gao Haoran Zuo

This paper proposes a mathematical model of price change perception in economic environments. The model introduces the Kullback–Leibler (KL) divergence between the expected price and the observed price as an index of attentional salience and integrates Takemura’s (1998, 2021) Mental Ruler Theory with the attention framework based on KL information proposed by Itti and Baldi (2009). We refer to this model as the SKL (Sum of the Kullback–Leibler Divergence) model, which explains the psychological mechanism underlying price judgment processes. Within this framework, the evaluation function for price change judgments is formulated as the integral of attentional salience, where attention is represented by the KL divergence associated with price changes. The proposed model is evaluated using 18 years of quarterly data (2008–2026) from the Bank of Japan’s Opinion Survey on General Public’s Views and Behavior, together with corresponding Consumer Price Index (CPI) data. Its explanatory power is assessed by comparison with conventional linear models, traditional psychophysical function models, and models based solely on KL information. The results indicate that the proposed model provides relatively superior explanatory performance, particularly in capturing periods of substantial changes in perceived inflation.

Mathematics doi: 10.3390/math14122190

Authors: Aleksandr N. Tynda Denis N. Sidorov Nikolai A. Sidorov Aliona I. Dreglea

The paper addresses an inverse problem for a nonlinear Volterra integral equation of the first kind with a piecewise continuous kernel whose discontinuity curves are the unknown functions. Such models arise in the theory of developing systems, power systems with energy storage, and related applications. We develop an iterative scheme based on the Newton–Kantorovich linearisation of the nonlinear integral operator and obtain explicit recurrent formulas for the discontinuity curve. Both the full Newton-like and a modified (simplified) iterative process are constructed, and their local convergence is proved under natural smoothness and smallness conditions. The performance and accuracy of the method are illustrated by several model problems with known and unknown exact solutions. The algorithm demonstrates rapid convergence and is robust with respect to the choice of the initial approximation.

Mathematics doi: 10.3390/math14122191

Authors: Zhenguo Yan Bo Yang Longcheng Zhang Yuxin Huang Chongwu Chen Jianing Ruan

Ventilation network feature graphs (Q-H graphs) are a key visualisation tool for mine ventilation systems, and their automated generation reduces to a combinatorial optimisation problem over independent-path permutations. Existing methods, however, exhibit three limitations: a single-dimensional evaluation criterion, inadequate nodal pressure-energy assignment, and unstable convergence in factorial-scale search spaces. This paper proposes an adaptive NSGA-II (A-NSGA-II) framework with coordinated enhancements at the evaluation, modelling, and algorithmic levels. A three-objective system that minimises split-block count, topological-spatial discrepancy, and layout fragmentation is established, together with an aggregate evaluation score (AES) for engineering decision-making; nodal pressure energies are reconstructed via the longest path on a directed acyclic graph; and topology-aware initialisation, Lagrange three-point interpolated adaptive operators, and periodic memetic local search are integrated within NSGA-II. Experiments on two mine ventilation networks (75 and 112 branches) over 30 independent trials show that A-NSGA-II consistently outperforms four benchmarks (NSGA-II, MOEA/D, SPEA2, and MOSA) in terms of split-block count, AES, and hypervolume; statistical tests confirm significant, large-effect HV advantages on the 112-branch network, while the 75-branch network shows a 56.6–71.5% reduction in HV standard deviation.

Mathematics doi: 10.3390/math14122189

Authors: Igor Podlubny

The notion of negative probability is almost one hundred years old, and so far, some results have been obtained in the direction of the theoretical development of the notion of extended probability. However, there is still a strong need for computational methods and tools, and the presented article is aimed at filling this gap. Several examples, including Feynman’s problem, of the numerical simulation of signed probability distributions are provided for the first time, along with the results of the simulation using the developed software toolbox. The presented methods and results might open wide possibilities for using signed probabilities in the fields of quantum computing, decision making, finance, insurance, large language models and artificial intelligence, and other fields where the use of signed probability distributions can extend the current level of mathematical modeling.

Mathematics doi: 10.3390/math14122188

Authors: Ayman A. Amin Shuhrah A. Alghamdi

Autoregressive models with exogenous variables (ARX) constitute a fundamental class of dynamic regression models used extensively for time series analysis across a wide range of applications. A pervasive limitation of the existing Bayesian analyses of ARX models is their near-exclusive reliance on the Gaussian error assumption, which is routinely violated in empirical applications exhibiting heavy-tailed innovations, distributional outliers, or excess kurtosis. To address this deficiency, we develop a rigorous Bayesian estimation framework for these models whose errors are drawn from the scale-mixtures of normal (SMN) family, which is a rich, symmetric, heavy-tailed class of distributions. Exploiting the hierarchical stochastic representation of the SMN family through observation-specific latent scale-mixing variables, the ARX model is embedded in an augmented data structure that restores Gaussian conditional structure. Under three distinct prior formulations—namely, normal-gamma, Zellner’s g-prior, and Jeffreys’ prior—we derive closed-form full conditional posterior distributions for the ARX coefficient vector and the error scale parameter, which follow multivariate normal and inverse-gamma distributions, respectively. In addition, for the SMN-specific shape parameters, we derive the full conditional posteriors for each distribution in the family, and some of them are non-standard distributions handled by embedding Metropolis-Hastings steps within the Gibbs sampler. The resulting hybrid MCMC algorithm is validated through a comprehensive simulation study spanning three ARX model configurations and all three SMN special cases. A real macroeconomic application to US consumer price inflation demonstrates the practical utility of the framework, confirming heavy-tailed residuals and yielding precise, well-calibrated posterior estimates.

Mathematics doi: 10.3390/math14122186

Authors: Igor Zeidis Klaus Zimmermann

Different approaches to describing the kinematics and dynamics of a mobile robot equipped with four Mecanum wheels are compared. Due to the no-slip rolling condition, the kinematic constraints imposed on the system are nonholonomic; therefore, the equations of nonholonomic mechanics must be used to model such a system. The necessary and sufficient conditions under which the dynamics of this system can be described using Lagrange equations of the second kind are derived. The solvability of the kinematic constraint equations using the pseudoinverse matrix is also analyzed.

Mathematics doi: 10.3390/math14122187

Authors: Abdelkadir Fellague Latifa Dekhici Khaled Guerraiche David A. Pelta José Luis Verdegay

The efficient management of power systems requires balancing electricity generation costs with associated environmental emissions under dynamically varying demand. This paper proposes a two-stage approach that combines machine learning (ML) with a metaheuristic optimization algorithm to address the dynamic economic–environmental load dispatch (DEELD) challenge. In the first stage, electricity consumption data are enriched with temporal features to capture demand patterns and enable accurate forecasting. In the second stage, the daily scheduling horizon is divided into multiple periods, and dispatch solutions are generated sequentially while enforcing ramp-rate constraints. To enhance operational realism, a priority-based generator scheduling mechanism is explicitly introduced, enforcing hierarchical unit commitment and reflecting practical dispatch policies. Rather than focusing on a single optimal solution, the proposed framework generates multiple feasible dispatch solutions and evaluates them using economic, environmental, and operational performance indicators. These solutions are then ranked according to predefined decision profiles, enabling system operators to select dispatch strategies that align with specific priorities. This transforms the dispatch process into a flexible decision-support tool capable of addressing diverse real-world requirements.