Mathematics

29 pages, 1792 KB

Open AccessArticle

Data-Driven Certified Mode Detection for Switched Discrete-Time Takagi–Sugeno Systems with Adaptive Observation Window

by Essia Ben Alaia, Slim Dhahri, Afrah Alanazi, Sahar Almenwer and Omar Naifar

Mathematics 2026, 14(9), 1532; https://doi.org/10.3390/math14091532 (registering DOI) - 30 Apr 2026

This paper addresses active-mode detection for switched discrete-time Takagi–Sugeno systems from noisy input–output data under candidate-dependent input correction and uncertainty in data-driven observability subspaces. A lifted input–output formulation is developed in which each candidate mode is associated with a mode-dependent forced-response correction and [...] Read more.

This paper addresses active-mode detection for switched discrete-time Takagi–Sugeno systems from noisy input–output data under candidate-dependent input correction and uncertainty in data-driven observability subspaces. A lifted input–output formulation is developed in which each candidate mode is associated with a mode-dependent forced-response correction and a nominal observability subspace identified offline from representative data. Based on this construction, a practical residual criterion is introduced together with an ideal residual criterion defined by the exact residual projector. An online verifiable sufficient condition is then derived to guarantee consistency between the practical and ideal residual orderings, yielding a conservative but theorem-consistent certification mechanism. To quantify the effect of measurement uncertainty, a component-wise noise-to-signal ratio (NSR) analysis is established, leading to explicit conservative NSR bounds when signal-floor conditions are available offline. These results motivate an adaptive observation-window strategy driven by an explicit online NSR estimate. In addition, an uncertainty-corrected discernibility index based on principal angles between estimated observability subspaces is introduced to assess offline mode separability. Simulations on a switched T–S benchmark show high practical detection accuracy, sound but conservative certification, informative NSR bounds, and stable adaptive-window regulation, including under reviewer-motivated switching stress tests and baseline comparison experiments. Full article

(This article belongs to the Special Issue Advances and Applications for Data-Driven/Model-Free Control)

21 pages, 289 KB

Open AccessArticle

The Structure of Primitive Leibniz Algebras via Maximal Subalgebras

by Zekiye Çiloğlu Şahin

Mathematics 2026, 14(9), 1531; https://doi.org/10.3390/math14091531 (registering DOI) - 30 Apr 2026

Abstract

In this paper, we investigate the structure of primitive Leibniz algebras via their maximal subalgebras and minimal ideals. Using a two-sided definition of the centraliser, we show that the centraliser of a minimal ideal is again an ideal. Unlike the Lie algebra case, [...] Read more.

In this paper, we investigate the structure of primitive Leibniz algebras via their maximal subalgebras and minimal ideals. Using a two-sided definition of the centraliser, we show that the centraliser of a minimal ideal is again an ideal. Unlike the Lie algebra case, the use of this two-sided centraliser is essential in the Leibniz setting and accommodates genuinely new structural phenomena. In particular, we prove that a primitive Leibniz algebra has at most two minimal ideals and classify such algebras into three distinct types according to the structure of the socle, extending the classical Lie-theoretic classification. In the solvable case, we obtain an alternative characterisation of primitive Leibniz algebras of type 1 in terms of split extensions by self-centralising minimal ideals. Full article

(This article belongs to the Section A: Algebra and Logic)

14 pages, 325 KB

Open AccessFeature PaperArticle

Positional Numeral Systems over Polyadic Rings

by Steven Duplij

Mathematics 2026, 14(9), 1530; https://doi.org/10.3390/math14091530 (registering DOI) - 30 Apr 2026

Abstract

We construct positional numeral systems that work natively over nonderived polyadic

(m, n)

-rings whose addition takes m arguments and multiplication takes n. In such rings, the length of an admissible additive word and a multiplicative tower are not arbitrary (as [...] Read more.

We construct positional numeral systems that work natively over nonderived polyadic

(m, n)

-rings whose addition takes m arguments and multiplication takes n. In such rings, the length of an admissible additive word and a multiplicative tower are not arbitrary (as in the binary case) but “quantized”. Our main contributions are the following. Existence: Every commutative

(m, n)

-ring admits a base-p place–value expansion that respects the word length constraint in terms of numbers of operation compositions

ℓ_{m u l t} = ℓ_{a d d} (m - 1) + 1

. Lower bound: The minimum number of digits is greater than or equal to the arity of addition m. Representability gap: For

m, n \geq 3

only a proper subset of ring elements possesses finite expansions, characterized by congruence-class arity shape invariants

I^{(m)}

and

J^{(n)}

. Mixed-base “polyadic clocks”: Allowing a different base at each position enlarges the design space quadratically in the digit count. Catalogs: Explicit tables for the integer rings

Z_{4, 3}

and

Z_{6, 5}

illustrate how ordinary integers lift to distinct polyadic variables. These results lay the groundwork for faster arity-aware arithmetic, exotic coding schemes, and hardware that exploits operations beyond the binary pair. Full article

19 pages, 2845 KB

Open AccessArticle

Efficient Calibration for Option Pricing via a Physics-Informed Chebyshev Kolmogorov–Arnold Network

by Sumei Zhang, Tianci Wu, Haiyang Xiao, Yi Gong and Weihong Xu

Mathematics 2026, 14(9), 1529; https://doi.org/10.3390/math14091529 (registering DOI) - 30 Apr 2026

Abstract

Efficient calibration is essential for the practical application of option pricing models. The Fractional Stochastic Volatility Jump Diffusion (FVSJ) model can reproduce several stylized features observed in option markets, including the volatility smile, volatility clustering, and long-memory effects. However, its multiple stochastic components [...] Read more.

Efficient calibration is essential for the practical application of option pricing models. The Fractional Stochastic Volatility Jump Diffusion (FVSJ) model can reproduce several stylized features observed in option markets, including the volatility smile, volatility clustering, and long-memory effects. However, its multiple stochastic components make conventional calibration computationally expensive. This paper proposes a two-step calibration framework that combines a neural network with a differential evolution (DE) algorithm. In the first step, we construct a Physics-Informed Kolmogorov–Arnold Network (PCKAN) to approximate the FVSJ pricing map. Specifically, we replace the B-spline basis in KAN with second-kind Chebyshev polynomials and incorporate a Black–Scholes PDE residual as an additional penalty term in the training objective, aiming to improve global approximation and enhance numerical stability and interpretability. In the second step, the trained PCKAN is used as a fast surrogate pricer within the DE algorithm to accelerate parameter estimation. Empirical results show that the proposed method achieves calibration accuracy comparable to direct pricing while substantially reducing computational time. Full article

(This article belongs to the Section E5: Financial Mathematics)

27 pages, 23053 KB

Open AccessFeature PaperArticle

CNN–Attention–LSTM with Bayesian Optimization for Multi-Level Sump Well Anomaly Early Warning

by Yining Lin and Changchun Cai

Mathematics 2026, 14(9), 1528; https://doi.org/10.3390/math14091528 (registering DOI) - 30 Apr 2026

Abstract

Reliable anomaly early warning for hydropower station sump wells remains challenging due to the strong nonlinearity of water level dynamics and the limited adaptability of conventional fixed-threshold alarms. Here, we present a hybrid deep learning framework—termed CNN–Attention–LSTM–BO—that fuses multi-scale local feature extraction, adaptive [...] Read more.

Reliable anomaly early warning for hydropower station sump wells remains challenging due to the strong nonlinearity of water level dynamics and the limited adaptability of conventional fixed-threshold alarms. Here, we present a hybrid deep learning framework—termed CNN–Attention–LSTM–BO—that fuses multi-scale local feature extraction, adaptive temporal weighting, and sequential dependency modeling within a unified architecture, with all critical hyperparameters tuned via Bayesian optimization. A four-dimensional input representation is first constructed from the raw water level signal and its first- and second-order differences together with the drainage pump operating state, capturing both trend and transient information. One-dimensional convolutions at multiple kernel scales encode short-range fluctuation patterns, a Bahdanau-style temporal attention layer selectively amplifies informative time steps, and a stacked LSTM propagates long-horizon risk dependencies. At the decision stage, a dual dynamic thresholding scheme couples an improved

3 σ

criterion with kernel density estimation (KDE) to partition the smoothed risk score into three graded alert levels (normal/warning/critical), replacing the binary alarm paradigm. Experiments on the SWaT benchmark yield an average area under the ROC curve (AUC) of 0.9246, an average Accuracy of 0.8812, and a best single-well false alarm rate (FAR) of 3.21% (Well-4), with an average FAR of 8.97% across three wells, outperforming both traditional limit-value alarms and ablated variants lacking CNN or attention modules. Full article

(This article belongs to the Special Issue Artificial Intelligence, Algorithms, and Databases: Innovations and Cross-Disciplinary Impact)

39 pages, 9751 KB

Open AccessArticle

Subject-Specific Comparative Performance Analysis of Deep Learning Architectures for Motor Imagery Classification

by Bandile Mdluli, Philani Khumalo and Rito Clifford Maswanganyi

Mathematics 2026, 14(9), 1527; https://doi.org/10.3390/math14091527 - 30 Apr 2026

Abstract

Motor Imagery (MI)-based brain–computer interfaces (BCIs) offer promising solutions for enhancing communication and motor functions in individuals with neurological impairments. However, decoding EEG signals accurately is difficult because of their poor signal-to-noise ratio and variability across subjects and sessions. In addition, EEG signals [...] Read more.

Motor Imagery (MI)-based brain–computer interfaces (BCIs) offer promising solutions for enhancing communication and motor functions in individuals with neurological impairments. However, decoding EEG signals accurately is difficult because of their poor signal-to-noise ratio and variability across subjects and sessions. In addition, EEG signals are sensitive to noise. Moreover, the low spatial resolution of EEG signals makes model generalization unreliable due to differences between signals across subjects. While several deep learning models have been developed, a fair comparison remains difficult due to differences in pre-processing, training procedures, and evaluation protocols. This study provides a systematic, controlled comparison of five deep learning approaches for subject-specific classification—EEGNet, EEG-TCNet, ShallowConvNet, DeepConvNet, and CTNet—using the BCI Competition IV datasets 2a and 2b. To enable an unbiased comparison, all models are trained using the same pipeline, with uniform pre-processing and training. Apart from classical accuracy scores, the effect of a constant set of hyper-parameters on the training dynamics, generalization capacity, and the susceptibility to overfitting is evaluated. The performance of the above-stated models is evaluated based on training dynamics, computational efficiency, accuracy, and the quality of the features learned by the models. Using the five-dimensional analysis framework consisting of quantitative performance metrics, training curves, confusion matrix analysis, ROC analysis, and t-SNE visualization techniques, the performance of the brain–computer interfaces is comprehensively analyzed. The experimental analysis confirms that CTNet outperforms other models, with accuracy values of 82.56% and 86.42% on the BCI competition IV datasets 2a and 2b, respectively. The EEGNet model is recognized as having the most potential in the field of real-time applications, owing to its light structure; meanwhile, the DeepConvNet model shows signs of overfitting, despite showing good accuracy. These findings highlight that model training characteristics and sensitivity to the hyper-parameters are important factors in evaluating deep learning models for MI-EEG classification problems. Full article

47 pages, 1265 KB

Open AccessArticle

Deterministic Q-Learning with Relational Game Theory: Polynomial-Time Convergence to Minimal Winning Coalitions in Symmetric Influence Networks and Extension

by Duc Nghia Vu and Janos Demetrovics

Mathematics 2026, 14(9), 1526; https://doi.org/10.3390/math14091526 - 30 Apr 2026

Abstract

This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties [...] Read more.

This paper presents a theoretically grounded integration of deterministic Q-learning with relational game theory (QLRG) for efficiently identifying minimal winning coalitions in Online Social Networks (OSNs). We address the fundamental challenge that coalition formation is NP-hard under traditional approaches by leveraging structural properties of relational dependencies and Armstrong’s axioms to transform the problem into one solvable in polynomial time. Our framework reduces the state space from exponential O(2ⁿ) to O(n²) through a sufficient statistic representation based on coalition size, follower reach, and terminal status, while achieving O(n⁴) time complexity under deterministic, static, and sufficiently symmetric influence structures. The QLRG framework introduces three critical innovations: (1) a principled agent selection mechanism derived directly from the Q-function that eliminates heuristic weight tuning; (2) a formal Boost action defined through temporal closure operators that captures influence spread dynamics; and (3) a constrained MDP formulation that enforces relational consistency through action elimination rather than penalty terms. We prove that the Bellman optimality operator forms a contraction mapping, guaranteeing deterministic convergence to optimal policies with established rates of O(1/√k) for decreasing learning rates or linear convergence up to bias for constant rates. To bridge the gap between this idealized model and the asymmetry inherent in real OSNs, we further develop a cluster-based sufficient statistics approach. By partitioning the network into communities with bounded internal variation, we relax the global symmetry requirement while preserving polynomial state space complexity, and obtaining a single within-community swap changes the optimal Q-value by at most ε_i/(1−γ), which is a local Lipschitz continuity result. The implications of this are both theoretical and practical, and they form the bedrock for relaxing the global symmetry assumption in the QLRG framework. Empirical validation on synthetic networks satisfying the symmetry assumption demonstrates that QLRG consistently identifies minimal winning coalitions matching the optimal solutions found by exhaustive search, while operating with polynomial-time complexity. Unlike conventional approaches, our framework simultaneously satisfies four critical properties: deterministic convergence, policy optimality, minimal coalition identification, and computational tractability. The work bridges computational social science and operations research, providing a mathematically rigorous foundation for strategic decision-making in influencer marketing and coalition formation. While the framework requires symmetry assumptions that may only hold approximately in real-world OSNs, it establishes an idealized baseline for future extensions addressing stochasticity, dynamics, and partial observability. This research represents a paradigm shift from empirical improvements to theoretically grounded convergence guarantees for coalition formation problems, demonstrating how structural mathematical insights can transform intractable problems into efficiently solvable ones without sacrificing solution quality. Full article

9 pages, 237 KB

Open AccessArticle

Calculating the Inverse Matrix After Some Elements in the Matrix Change

by Wei Zheng and Weiguo Li

Mathematics 2026, 14(9), 1525; https://doi.org/10.3390/math14091525 - 30 Apr 2026

Abstract

In the current paper two research issues are addressed. First, a new efficient computational formula is presented that can calculate the inverse of a matrix when two elements are perturbed. The formula extends the result of G. Zielke. Second, a fast algorithm for [...] Read more.

In the current paper two research issues are addressed. First, a new efficient computational formula is presented that can calculate the inverse of a matrix when two elements are perturbed. The formula extends the result of G. Zielke. Second, a fast algorithm for computing an element in an inverse matrix has been derived. This algorithm is very practical in real-world scenarios. Interesting numerical examples demonstrate the feasibility of these algorithms. Full article

(This article belongs to the Section E: Applied Mathematics)

23 pages, 1287 KB

Open AccessArticle

Reliability Analysis of a Hardware–Software Series Repairable System with Multiple Vacations of a Repairman

by Qi Tu and Xue Feng

Mathematics 2026, 14(9), 1524; https://doi.org/10.3390/math14091524 - 30 Apr 2026

Abstract

This paper develops a reliability analysis model for a class of computer systems composed of hardware and software in series, considering a repairman taking multiple vacations. The system follows a series failure rule: hardware can be repaired to be as good as new [...] Read more.

This paper develops a reliability analysis model for a class of computer systems composed of hardware and software in series, considering a repairman taking multiple vacations. The system follows a series failure rule: hardware can be repaired to be as good as new after failure; software undergoes minor repairs to maintain operability after the first

N - 1

failures with an increasing failure rate, and is overhauled to be as good as new with cycle reset after the N-th failure. Based on the principle of probability conservation and the supplementary variable method, the state probability evolution equations of the system are derived. A Banach space is constructed, and a linear operator is defined, whose denseness, dissipativity, and closedness are verified. It has been proven that the operator generates a positive contractive

C_{0}

-semigroup, thus rigorously establishing the well-posedness of the model and the existence of a unique positive dynamic solution. Further spectral analysis verifies that zero belongs to the continuous spectrum rather than the point spectrum of the system operator.This indicates that the investigated system admits no time-invariant constant steady-state probability distribution,and only presents slowly decaying quasi-stationary dynamic behavior. The results can provide theoretical support for the reliability design and maintenance strategy optimization of hardware–software series repairable systems. Full article

40 pages, 980 KB

Open AccessFeature PaperArticle

Optimal Consumption and Investment with Consumption Comfort Zones

by Geonwoo Kim and Junkee Jeon

Mathematics 2026, 14(9), 1523; https://doi.org/10.3390/math14091523 - 30 Apr 2026

Abstract

We study an infinite-horizon consumption–investment problem in which an investor endogenously manages a consumption comfort zone above a fixed subsistence benchmark. Consumption can move freely within the prevailing admissible interval, while upward expansions of the upper endpoint are irreversible and costly. This captures [...] Read more.

We study an infinite-horizon consumption–investment problem in which an investor endogenously manages a consumption comfort zone above a fixed subsistence benchmark. Consumption can move freely within the prevailing admissible interval, while upward expansions of the upper endpoint are irreversible and costly. This captures downward rigidity not through a single ratcheting reference level but through the endogenous management of a sustainable expenditure range. Using the dual martingale method together with singular stochastic control, we reduce the problem to a one-sided singular control problem for the comfort-zone width process. The associated dual Hamilton–Jacobi–Bellman equation becomes a gradient-constrained free-boundary problem, which admits a one-dimensional reduction under CRRA utility. We characterize the optimal comfort-zone expansion rule, consumption policy, risky portfolio rule, and value function. Economically, the model implies infrequent upward revisions of the sustainable consumption ceiling, smoother consumption than in the frictionless Merton benchmark, and state-dependent portfolio behavior. A key implication of the additive specification is that proportional consumption flexibility shrinks as the upper endpoint rises, so higher consumption states become endogenously tighter and require a larger wealth buffer to sustain. The infinite-horizon formulation is interpreted as a stationary benchmark that isolates the economics of costly lifestyle upgrading. Full article

(This article belongs to the Special Issue Recent Advances in Stochastic Processes and Their Applications)

48 pages, 2547 KB

Open AccessReview

Security and Privacy in Generative Semantic Communication Systems: A Comprehensive Survey

by Mehwish Ali Naqvi and Insoo Sohn

Mathematics 2026, 14(9), 1522; https://doi.org/10.3390/math14091522 - 30 Apr 2026

Abstract

semantic communication (SemCom) has emerged as a task-oriented communication paradigm that prioritizes meaning delivery over exact bit recovery. The integration of generative artificial intelligence (GenAI) into SemCom further enables knowledge-guided inference, multimodal reconstruction, and semantic compression through architectures such as large language models, [...] Read more.

semantic communication (SemCom) has emerged as a task-oriented communication paradigm that prioritizes meaning delivery over exact bit recovery. The integration of generative artificial intelligence (GenAI) into SemCom further enables knowledge-guided inference, multimodal reconstruction, and semantic compression through architectures such as large language models, variational autoencoders, generative adversarial networks, and diffusion models. At the same time, this integration introduces new security and privacy risks, including semantic eavesdropping, model inversion, semantic jamming, covert backdoors, prompt manipulation, and knowledge-base leakage, which are not adequately captured by conventional communication security models. In this survey, we provide a security-centric review of GenAI-assisted semantic communication systems by organizing the literature according to threat models, attack surfaces, defence strategies, and semantic modalities across text, image, and multimodal settings. The survey was conducted using IEEE Xplore, ACM Digital Library, SpringerLink, arXiv, and Google Scholar. Approximately 180 papers were initially screened, and 53 representative studies published between 2021 and 2026 were selected for detailed review. Based on this analysis, we classify the major threats into adversarial perturbation, jamming, poisoning and backdoor attacks, privacy leakage and semantic eavesdropping, and generative-model-specific vulnerabilities involving diffusion, large language models, and multimodal foundation models. We further map the corresponding defences, including adversarial training, model ensembling, semantic-aware encryption, diffusion-guided denoising, privacy-preserving representation learning, and secure resource allocation. The survey also identifies persistent open challenges, including the lack of standardized semantic security metrics, unified benchmarks, cross-layer evaluation frameworks, and robust defences for GenAI-native and multimodal semantic communication systems. Overall, this work provides a structured reference for the design of secure, trustworthy, and attack-resilient generative semantic communication systems for future intelligent networks. Full article

(This article belongs to the Special Issue Advances in Blockchain and Intelligent Computing)

21 pages, 1353 KB

Open AccessArticle

Causal-Patched Attention Network: Mitigating Contextual Bias and False Associations in Multi-Label Image Classification

by Baiqing Liu, Weiyuan He, Yingchang Jiang, Qing Yu and Fei Chen

Mathematics 2026, 14(9), 1521; https://doi.org/10.3390/math14091521 - 30 Apr 2026

Abstract

Multi-label image classification (MLIC) is vulnerable to contextual bias, where models may exploit spurious label–context associations rather than object evidence, leading to degraded generalization under distribution shifts. To address this issue, we propose CPAN, a causal-inspired framework that integrates label-specific feature decoupling, prototype-based [...] Read more.

Multi-label image classification (MLIC) is vulnerable to contextual bias, where models may exploit spurious label–context associations rather than object evidence, leading to degraded generalization under distribution shifts. To address this issue, we propose CPAN, a causal-inspired framework that integrates label-specific feature decoupling, prototype-based mediator modeling, patch-level evidence aggregation, and adaptive fusion. Specifically, CPAN uses a Transformer decoder to extract label-specific representations from the whole image and local patches. We introduce a prototype dictionary as a surrogate mediator space to encourage the model to rely on object-relevant intermediate patterns rather than context-sensitive shortcuts. We further aggregate patch-level predictions to enhance direct object evidence and fuse them with whole-image predictions through a learnable gate. Experiments on two benchmark datasets show that CPAN consistently improves both recognition accuracy and robustness. On MS-COCO, CPAN achieves 85.26 mAP, 80.67 CF1, and 82.52 OF1; on NUS-WIDE, it reaches 66.11 mAP, 64.42 CF1, and 75.95 OF1. Under context-shifted evaluation on MS-COCO, CPAN further obtains 80.93 mAP, 75.84 CF1, and 77.87 OF1, indicating stronger robustness to contextual bias. These results show that CPAN learns more object-centered representations and reduces reliance on spurious contextual correlations. Full article

(This article belongs to the Special Issue Advances in Artificial Intelligence, Machine Learning and Optimization, 2nd Edition)

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67 pages, 3190 KB

Open AccessReview

Comparative Performance Analysis of Machine Learning Computational Pipelines and Deep Learning Architectures in EEG Motor Imagery BCIs

by Nerita Ramsoonder, Rito Clifford Maswanganyi and Philani Khumalo

Mathematics 2026, 14(9), 1520; https://doi.org/10.3390/math14091520 - 30 Apr 2026

Abstract

The deployment of Motor Imagery Brain–Computer Interfaces (MI-BCI) is constrained by the inherent physiological variabilities of Electroencephalography (EEG) and parametric opacity. This paper presents a targeted technical audit of ten high-density MI-BCI computational pipelines, evaluating how existing literature addresses low Signal-to-Noise Ratio (SNR), [...] Read more.

The deployment of Motor Imagery Brain–Computer Interfaces (MI-BCI) is constrained by the inherent physiological variabilities of Electroencephalography (EEG) and parametric opacity. This paper presents a targeted technical audit of ten high-density MI-BCI computational pipelines, evaluating how existing literature addresses low Signal-to-Noise Ratio (SNR), intra-subject variability, and session-to-session instability. The investigation focuses on the contamination of data by ocular and muscular artifacts that overlap with the spectral components of Mu and Beta rhythms, often leading to algorithmic overfitting. Furthermore, the paper evaluates the impact of manifold drift where fluctuations in user state necessitate frequent recalibration as a primary hurdle for BCI portability. By applying a forensic evaluation framework to standardize the analysis across the ten selected studies, this paper identifies a high-performance landscape within standardized benchmarks, with classification accuracies reaching peak values of 95.42%. The audit specifically identifies a performance-reporting gap; while hybrid architectures demonstrate superior noise-rejection, they are frequently characterized by undocumented computational overhead. Additionally, while Neighborhood Component Analysis (NCA) emerges as a stable feature selection algorithm across the sampled literature, the systemic absence of reported execution times prevents a verified assessment of its low-latency viability. A critical technical finding is the widespread issue of Parametric Opacity, particularly regarding the omission of essential deterministic variables such as filter orders, windowing constants, and the final dimensionality of feature vectors. The audit reveals that the frequent failure to report the exact number of features utilized for classification masks potential overfitting and prevents an accurate assessment of the system’s generalization capabilities. Furthermore, only a specialized subset of the reviewed literature validates performance through formal statistical testing, such as Friedman ANOVA or Wilcoxon Signed-Rank tests, with most studies relying on peak accuracy metrics that may disguise filtered artifact residuals. This lack of granular documentation disguises the computational complexity of proposed methods and complicates their feasibility for hardware-in-the-loop validation. The findings establish that standardizing the reporting of preprocessing variables and feature-space dimensions is a prerequisite for overcoming current performance plateaus in universal BCI architectures. Full article

30 pages, 6553 KB

Open AccessFeature PaperArticle

Self-Dual Symmetric Polynomials and Effective Isotropic Conductivity of Two-Dimensional Composites

by Leonid G. Fel

Mathematics 2026, 14(9), 1519; https://doi.org/10.3390/math14091519 - 30 Apr 2026

Abstract

We applied an algebraic approach, developed within the framework of the theory of a commutative monoid of self-dual symmetric polynomials, to the problem of effective isotropic conductivity

σ_{e} (σ_{1}, \dots, σ_{n})

in two-dimensional n-phase symmetric [...] Read more.

We applied an algebraic approach, developed within the framework of the theory of a commutative monoid of self-dual symmetric polynomials, to the problem of effective isotropic conductivity

σ_{e} (σ_{1}, \dots, σ_{n})

in two-dimensional n-phase symmetric composites with partial isotropic conductivities

σ_{j}

. The upper

Ω (σ_{1}, \dots, σ_{n})

and lower

ω (σ_{1}, \dots, σ_{n})

bounds for

σ_{e} (σ_{1}, \dots, σ_{n})

, found by the algebraic approach for

n = 3, 4

, are universal (independent of the composite microstructure) and possess all algebraic properties of

σ_{e} (σ_{1}, \dots, σ_{n})

that follow from physics: first-order homogeneity, full permutation invariance, Keller’s self-duality, positivity, and monotony. The bounds are compatible with the trivial solution

σ_{e} (σ, \dots, σ) = σ

and satisfy Dykhne’s ansatz. Their comparison with previously known numerical calculations, asymptotic analysis, and exact results for the effective isotropic conductivity

σ_{e} (σ_{1}, \dots, σ_{n})

of two-dimensional three- and four-phase composites showed complete agreement. The bounds

Ω (σ_{1}, \dots, σ_{n})

and

ω (σ_{1}, \dots, σ_{n})

in both cases

n = 3, 4

are stronger than the currently known variational bounds. Full article

21 pages, 1419 KB

Open AccessArticle

Sim-Exact Methods for Stochastic Optimization: A Complementary Approach to Simheuristics

by Angel A. Juan, Antonio R. Uguina, Marc Escoto and Veronica Medina

Mathematics 2026, 14(9), 1518; https://doi.org/10.3390/math14091518 - 30 Apr 2026

Abstract

This paper introduces a sim-exact methodology for stochastic combinatorial optimization problems. The approach combines exact optimization models with Monte Carlo or discrete-event simulation to evaluate candidate solutions under uncertainty. The method iteratively adjusts a control parameter based on simulation feedback and solves a [...] Read more.

This paper introduces a sim-exact methodology for stochastic combinatorial optimization problems. The approach combines exact optimization models with Monte Carlo or discrete-event simulation to evaluate candidate solutions under uncertainty. The method iteratively adjusts a control parameter based on simulation feedback and solves a sequence of deterministic optimization problems. Unlike scenario-based stochastic programming, the approach does not rely on explicit scenario enumeration, and unlike simheuristics, it preserves optimality with respect to each deterministic subproblem. The methodology is tested on the vehicle routing problem with stochastic demands under different levels of demand variability. Results are compared with a simheuristic approach and a sample average approximation (SAA) method. The results show that sim-exact performance is comparable to simheuristics, with no statistically significant differences in most cases, while SAA shows weaker performance under medium and high variability. Full article

(This article belongs to the Special Issue Intelligent Algorithms Hybridizing Optimization, Machine Learning, and Simulation: Methods and Applications)

37 pages, 918 KB

Open AccessArticle

One-Dimensional Solitary-Wave Solutions in Scalar–Tensor Gravity Coupled to Aharonov–Bohm Electrodynamics

by Rosario Pullano, Fernando Minotti and Giovanni Modanese

Mathematics 2026, 14(9), 1517; https://doi.org/10.3390/math14091517 - 30 Apr 2026

Abstract

A recently proposed tensor–scalar extension of gravity coupled to extended Aharonov–Bohm electrodynamics admits one-variable traveling reductions in which a longitudinal electromagnetic scalar mode

S = \partial_{μ} A^{μ}

couples nonlinearly to gravitational scalars. In the weak-field regime outside sources, a one-dimensional traveling [...] Read more.

A recently proposed tensor–scalar extension of gravity coupled to extended Aharonov–Bohm electrodynamics admits one-variable traveling reductions in which a longitudinal electromagnetic scalar mode

S = \partial_{μ} A^{μ}

couples nonlinearly to gravitational scalars. In the weak-field regime outside sources, a one-dimensional traveling ansatz depending on

ξ = x - v t

reduces the field equations to a coupled autonomous ODE system. The mathematical core of the reduction is a singular Newton-type equation whose classical mechanics counterpart is known; the novelty here lies in its derivation from the scalar–tensor/Aharonov–Bohm field system, in the physically motivated normalization of the traveling-wave families, and in the resulting phase–space interpretation for source-generated pulse selection. We provide a systematic classification of all admissible initial data and of the corresponding maximal solutions, distinguishing repulsive/attractive regimes and subcritical/critical/supercritical behaviors through a normalized parameter map. In particular, attractive branches may reach the singularity in finite time with a universal collision exponent

2 / 3

, while escaping branches exhibit asymptotically uniform motion with a computable logarithmic correction. Finally, we construct a numerical atlas of representative trajectories and validate the computations by cross-checking direct time integration against numerical inversion of the implicit quadrature, together with energy-defect diagnostics. Full article

(This article belongs to the Special Issue Numerical Solution of Differential Equations and Their Applications)

27 pages, 1853 KB

Open AccessArticle

Evidence Fusion Method for Fault Diagnosis Based on Optimal Coordination and Iteration Correction

by Xiaoyang Liu, Shulin Liu and Sha Wei

Mathematics 2026, 14(9), 1516; https://doi.org/10.3390/math14091516 - 30 Apr 2026

Abstract

In fault diagnosis, multi-source information fusion (MSIF) is usually more reliable than single-source information, and Dempster–Shafer (D-S) evidence theory provides a universal and popular decision-level fusion framework for MSIF. However, existing evidence fusion methods still have two limitations: (1) the overweighting effect of [...] Read more.

In fault diagnosis, multi-source information fusion (MSIF) is usually more reliable than single-source information, and Dempster–Shafer (D-S) evidence theory provides a universal and popular decision-level fusion framework for MSIF. However, existing evidence fusion methods still have two limitations: (1) the overweighting effect of high information volume on unreliable evidence is ignored, and (2) the fusion accuracy cannot be further improved, as only one-time evidence correction is considered. To overcome these limitations, an evidence fusion method based on optimal coordination and iterative correction is proposed for fault diagnosis. Firstly, the credibility and information volume of each piece of evidence are quantified by the Jousselme distance and Deng entropy, respectively. Then, using game theory combination weighting (GTCW), credibility and information volume are optimally coordinated to correct all pieces of evidence, which are then initially fused with Dempster’s rule. Ultimately, taking the initial fusion result as the reference, the credibility is iteratively recalculated to correct and fuse all pieces of evidence until the fusion result converges. The optimal coordination suppresses the overweighting effect caused by high information volume, and the iterative correction breaks the limitation of one-time fusion. Experimental results demonstrate that the proposed method outperforms existing methods and can significantly improve the fusion results in fault diagnosis. Full article

(This article belongs to the Special Issue Nonlinear Dynamics and Control of Vibrations)

19 pages, 327 KB

Open AccessArticle

Spectral Analysis and Topological Indices of Cozero-Divisor Graphs over Commutative Rings

by Amal S. Alali, Muzibur Rahman Mozumder, Asif Imtiyaz Ahmad Khan and Nawal H. Siddig

Mathematics 2026, 14(9), 1515; https://doi.org/10.3390/math14091515 - 30 Apr 2026

Abstract

Let

1 \neq 0

be the identity of the commutative ring R. The cozero-divisor graph of a ring R is an undirected simple graph, represented by

Γ^{'} (R)

, where two different vertices g and h are adjacent if [...] Read more.

Let

1 \neq 0

be the identity of the commutative ring R. The cozero-divisor graph of a ring R is an undirected simple graph, represented by

Γ^{'} (R)

, where two different vertices g and h are adjacent if and only if

g \notin R h

and

h \notin R g

. The vertices of this graph are given by the set of all non-zero and non-unit elements of R. The definition of a graph G’s

A_{α}

matrix is

A_{α} (G) = α D (G) + (1 - α) A (G)

, where

α \in [0, 1], D (G) = d i a g (d e g (c_{1}), d e g (c_{2}), \dots, d e g (c_{n}))

is the diagonal matrix and

A (G)

is the adjacency matrix of graph G. In this article, we calculate the sum-connectivity F-index, product-connectivity F-index of

Γ^{'} (Z_{n})

, when

n = ζ_{1} ζ_{2}, ζ_{1}^{2} ζ_{2}, ζ_{1} ζ_{2} ζ_{3}

, and the

A_{α}

eigenvalues of

Γ^{'} (Z_{n})

for

n = {ζ_{1}}^{u_{1}} ζ_{2} ζ_{3}

, where

ζ_{1}, ζ_{2}

,

ζ_{3}

are distinct primes. Full article

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24 pages, 5157 KB

Open AccessArticle

Model-Free H_∞ Control for Markov Jump Stochastic Systems with Mean-Field Terms Using On-Policy and Off-Policy Algorithms

by Xinyu Wang and Yaning Lin

Mathematics 2026, 14(9), 1514; https://doi.org/10.3390/math14091514 - 30 Apr 2026

Abstract

This paper presents on-policy and off-policy algorithms for the

H_{\infty}

control of continuous-time mean-field stochastic Markov jump systems. Using online state and input data, these algorithms can learn control and disturbance strategies without the need for prior knowledge of system matrices. Under [...] Read more.

This paper presents on-policy and off-policy algorithms for the

H_{\infty}

control of continuous-time mean-field stochastic Markov jump systems. Using online state and input data, these algorithms can learn control and disturbance strategies without the need for prior knowledge of system matrices. Under the standard assumptions that the system is mean-square stabilizable and detectable, we rigorously prove the monotonicity, boundedness, and convergence of the proposed iterative algorithms to obtain the unique stabilizing solution of cross-coupled generalized algebraic Riccati equations. Moreover, the off-policy algorithm features high data efficiency because the collected data can be utilized again after each iteration. Numerical simulations demonstrate the effectiveness of two algorithms and explicitly show that the off-policy algorithm achieves a faster convergence rate compared to its on-policy counterpart. Full article

(This article belongs to the Special Issue Stochastic System Analysis and Control)

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