Mathematics

24 pages, 2427 KB

Open AccessFeature PaperArticle

ReDyGait: Representation Disentanglement with Gated Attention for Invariant-Contextual Transfer in Stance Detection

by Yanzhou Ma, Yun Luo and Mingyang Peng

Mathematics 2026, 14(7), 1237; https://doi.org/10.3390/math14071237 - 7 Apr 2026

Viewed by 424

Cross-topic stance detection degrades when encoders entangle stance signals with topic-specific vocabulary, causing representations that fail to transfer to unseen targets. Existing methods commit to either topic-invariant or topic-aware representations and apply the same strategy uniformly to every input, sacrificing complementary information. We [...] Read more.

Cross-topic stance detection degrades when encoders entangle stance signals with topic-specific vocabulary, causing representations that fail to transfer to unseen targets. Existing methods commit to either topic-invariant or topic-aware representations and apply the same strategy uniformly to every input, sacrificing complementary information. We propose ReDyGait, a three-stage framework that disentangles these two types of signals through dedicated contrastive pre-training and recombines them adaptively at inference time. Stage 1 trains a topic-invariant encoder with supervised contrastive loss over cross-topic positives. Stage 2 trains a topic-contextual encoder with bidirectional pair contrastive loss over within-topic positives; both stages employ topic-aware hard negative mining to prevent shortcut learning. Stage 3 freezes the two contrastive encoders and learns a gating network that produces per-instance weights over invariant, contextual, and base-encoder pathways. On VAST, ReDyGait achieves a macro-averaged F1 of 0.782 in the zero-shot setting and 0.752 in the few-shot setting, improving over the strongest baseline by 1.1 points in both; on SEM16t6 in a leave-one-target-out setup, ReDyGait reaches an average F1 of 0.612. Analysis of the learned gate weights shows that the model shifts toward the invariant pathway for unfamiliar topics and toward the contextual pathway when topic-specific patterns are available, confirming that the disentanglement operates as intended. Full article

(This article belongs to the Special Issue Machine Learning and Graph Neural Networks)

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28 pages, 8022 KB

Open AccessArticle

Quantum-Inspired Variational Inference for Non-Convex Stochastic Optimization: A Unified Mathematical Framework with Convergence Guarantees and Applications to Machine Learning in Communication Networks

by Abrar S. Alhazmi

Mathematics 2026, 14(7), 1236; https://doi.org/10.3390/math14071236 - 7 Apr 2026

Viewed by 578

Abstract

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational [...] Read more.

Non-convex stochastic optimization presents fundamental mathematical challenges across machine learning, wireless networks, data center resource allocation, and optical wireless communication systems, where complex loss landscapes with multiple local minima and saddle points impede classical variational inference methods. This paper introduces the Quantum-Inspired Variational Inference (QIVI) framework, which systematically integrates quantum mechanical principles (superposition, entanglement, and measurement operators) into classical variational inference through rigorous mathematical formulations grounded in Hilbert space theory and operator algebras. We develop a unified optimization framework that encodes classical parameters as quantum-inspired states within finite-dimensional complex Hilbert spaces, employing unitary evolution operators and adaptive basis selection governed by gradient covariance eigendecomposition. The core mathematical contribution establishes that QIVI achieves a convergence rate of

O ({log}^{2} T / T^{1 / 2})

for

σ

-strongly non-convex functions, provably improving upon the classical

O (T^{- 1 / 4})

rate, yielding a theoretical speedup factor of

1.85

–

1.96 \times

. Comprehensive experiments across synthetic benchmarks, Bayesian neural networks, and real-world applications in network optimization and financial portfolio management demonstrate 23–

47 %

faster convergence, 15–

35 %

superior objective values, and 28–

46 %

improved uncertainty calibration. The principal contributions include: (i) a rigorous Hilbert space-based mathematical framework for quantum-inspired variational inference grounded in operator algebras, (ii) a novel hybrid quantum–classical algorithm (QIVI) with adaptive basis selection via gradient covariance eigendecomposition, (iii) formal convergence proofs establishing provable improvement over classical methods, (iv) comprehensive empirical validation across diverse problem domains relevant to machine learning and network optimization, and (v) demonstration of the framework’s applicability to optimization problems arising in wireless networks, data center resource allocation, and network system design. Statistical validation using the Friedman test (

χ^{2} = 847.3

,

p < 0.001

) and post hoc Wilcoxon signed-rank tests with Holm–Bonferroni correction confirm that QIVI’s improvements over all baseline methods are statistically significant at the

α = 0.05

level across all benchmark categories. The framework discovers

18.1

out of 20 true modes in multimodal distributions versus

9.1

for classical methods, demonstrating the potential of quantum-inspired optimization approaches for challenging stochastic problems arising in machine learning, wireless communication, and network optimization. Full article

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23 pages, 9838 KB

Open AccessArticle

Bimodal Image Fusion and Brightness Piecewise Linear Enhancement for Crack Segmentation

by Yong Li, Nian Ji, Fuzhe Zhao, Huaiwen Zhang, Zeqi Liu, Laxmisha Rai and Zhaopeng Deng

Mathematics 2026, 14(7), 1235; https://doi.org/10.3390/math14071235 - 7 Apr 2026

Viewed by 477

Abstract

Accurate segmentation of structural cracks is a core prerequisite for quantifying crack parameters, assessing damage severity, and providing early warning of structural safety. However, different types of structures exhibit significant individual variations in features such as color, texture, and brightness. Consequently, commonly used [...] Read more.

Accurate segmentation of structural cracks is a core prerequisite for quantifying crack parameters, assessing damage severity, and providing early warning of structural safety. However, different types of structures exhibit significant individual variations in features such as color, texture, and brightness. Consequently, commonly used image segmentation algorithms struggle to establish a universal mathematical model, making it challenging to robustly identify and precisely segment crack targets amidst multi-feature disparities. To address the issue, this paper proposes a crack-segmentation algorithm based on bimodal image fusion and brightness piecewise linear enhancement (CSA-BB), and further enables parameter extraction and crack monitoring. The algorithm utilizes the complementary properties of visible-light and pseudo-color images for bimodal image fusion, thereby enhancing the detailed features of cracks. Furthermore, a brightness piecewise linear function has been devised that automatically selects appropriate parameters for image enhancement of structural cracks across varying background brightness. Subsequently, the crack region is effectively segmented using the bottom-hat transform and the OTSU algorithm. Ultimately, the crack’s safety level is determined from the acquired crack parameters, thereby enabling effective monitoring and assessment of the crack development process. In this paper, the proposed method achieves the best segmentation performance with a Dice coefficient of 0.4511 and a Jaccard index of 0.2981. Compared to the second-best algorithm, it yields significant improvements of 26.9% and 34.5%, respectively, demonstrating higher consistency with the ground truth. Moreover, superior computational efficiency and robustness are achieved, fulfilling the operational demands of real-world engineering environments. Full article

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35 pages, 474 KB

Open AccessReview

Developments in Modular Space Fixed Point Theory

by Wojciech M. Kozlowski

Mathematics 2026, 14(7), 1234; https://doi.org/10.3390/math14071234 - 7 Apr 2026

Viewed by 588

Abstract

This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the [...] Read more.

This survey article offers a snapshot view of the present state of fixed point theory within modular spaces, highlighting fundamental principles and their applications. The discussion primarily revolves around operators and their semigroups that satisfy pointwise asymptotic nonexpansive and contractive conditions in the modular sense, and the results can also be applied directly to Banach spaces. Utilizing the framework of regular and super-regular modular spaces, our research generalizes several established results concerning fixed points of nonlinear operators, applicable to both Banach spaces and modular function spaces. The study seeks to identify and discuss current challenges, knowledge gaps, and unresolved questions, providing insights into the potential of future research opportunities. Full article

(This article belongs to the Special Issue Advances in Nonlinear Analysis and Applications)

21 pages, 586 KB

Open AccessArticle

Analysing Digital Government Performance Indicators Using a Clustering Technique-Embedded Fuzzy Decision-Making Framework

by Mehmet Erdem, Akın Özdemir, Hatice Yalman Kosunalp and Bozhana Stoycheva

Mathematics 2026, 14(7), 1233; https://doi.org/10.3390/math14071233 - 7 Apr 2026

Viewed by 619

Abstract

Digital transformation is reshaping societies by promoting the adoption of advanced technologies. Moreover, the digitization of public services has become an important focus for governments. In this paper, digital government performance indicators are analyzed to improve the efficiency of digitizing public services. Based [...] Read more.

Digital transformation is reshaping societies by promoting the adoption of advanced technologies. Moreover, the digitization of public services has become an important focus for governments. In this paper, digital government performance indicators are analyzed to improve the efficiency of digitizing public services. Based on this awareness, the seven main criteria and twenty-one sub-criteria are determined. Then, a fuzzy decision-making framework is proposed to evaluate digital government performance across 165 countries as alternatives. To the best of our knowledge, limited studies have investigated an integrated clustering-based fuzzy decision-making framework for evaluating digital government performance. The intuitionistic trapezoidal fuzzy number-based analytical hierarchy process (ITFNAHP), a part of the introduced framework, is developed to find the weights of the main criteria and sub-criteria. Digital technologies, innovation, and the economy are the most significant criteria for digital government operations. The k-means clustering method is then employed to group the alternatives. The four clusters are obtained from the clustering technique. Next, the technique of order preference similarity to ideal solution (TOPSIS) is introduced to rank the digital governments of each cluster. Switzerland, Rwanda, North Macedonia, and Eswatini are the top choices among others in each cluster, respectively. Additionally, a sensitivity analysis is conducted considering the ten different situations. In addition, the managerial and policy implications are discussed, including the achievement of Sustainable Development Goals (SDGs). Full article

(This article belongs to the Special Issue Advances in Multiple-Criteria Decision Making: New Trends and Applications)

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27 pages, 3039 KB

Open AccessArticle

Dynamic Fee Markets at Sub-Second Timescales: Adapting EIP-1559 for High-Throughput Blockchains

by Petar Zhivkov and Eric Chen

Mathematics 2026, 14(7), 1232; https://doi.org/10.3390/math14071232 - 7 Apr 2026

Viewed by 1097

Abstract

Dynamic fee market mechanisms, exemplified by EIP-1559, have been extensively studied for Ethereum’s 12 s block environment but remain uncharacterized at sub-second timescales. We present an agent-based simulation study of an EIP-1559 adaptation for Injective, a Layer 1 blockchain combining native EVM compatibility [...] Read more.

Dynamic fee market mechanisms, exemplified by EIP-1559, have been extensively studied for Ethereum’s 12 s block environment but remain uncharacterized at sub-second timescales. We present an agent-based simulation study of an EIP-1559 adaptation for Injective, a Layer 1 blockchain combining native EVM compatibility with CometBFT consensus, operating at 600 ms block times. Across twelve simulation runs (four parameter configurations × three demand scenarios), our analysis yields three findings: (1) temporal smoothing mechanisms (MA-25, 25-block trailing average) produce mixed effects in sub-second environments with up to 47% basefee overshoot during spam attacks and slight smoothing elsewhere, making per-block mechanisms preferable for consistent performance; (2) transitioning from 150M (66.66% target) to 300M (50% target) configuration reduces peak fees by 31% during variable demand; during spam attacks, the 300M configuration peaks 32% higher but recovers faster with block capacity as the primary driver for spam throughput; and (3) per-block mechanisms establish initial spam barriers within 17–32 s versus Ethereum’s 4–6 min, economically justifying lower minimum fees. We provide the first systematic sub-second EIP-1559 analysis and a parameter optimization framework for high-throughput chains. With proper tuning, dynamic fee mechanisms are compatible with high-throughput architectures. Full article

(This article belongs to the Special Issue Mathematical Foundations of Blockchain Technology)

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67 pages, 7738 KB

Open AccessReview

An Overview of Complex Time Series Analysis

by Alejandro Ramírez-Rojas, Leonardo Di G. Sigalotti, Luciano Telesca and Fidel Cruz

Mathematics 2026, 14(7), 1231; https://doi.org/10.3390/math14071231 - 7 Apr 2026

Viewed by 880

Abstract

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including [...] Read more.

Different methodologies have been developed for the analysis and study of dynamical systems, including both theoretical models and natural systems. Examples span a wide range of applications, such as astronomy, financial and economic time series, biophysical systems, physiological phenomena, and Earth sciences, including seismicity and climatic processes. The study of these complex systems is commonly based on the analysis of the signals they generate, using mathematical tools to extract relevant information. A broad spectrum of mathematical disciplines converges in this context, including stochastic, probability and statistical theory, entropic and informational measures, fractal and multifractal analysis, natural time analysis, modeling of non-linearity and recurrence methods, generalized entropies, non-extensive systems, machine learning, and high-dimensional and multivariate complexity. Research in this area is largely focused on the characterization of complex systems, providing indicators of determinism or stochasticity, distinguishing between regularity, chaos, and noise, and identifying topological as well as disorder-regularity features. In addition, short- and long-term forecasting, together with the identification of short- and long-range correlations, play a central role in such characterization. To address these objectives, numerous mathematical tools have been developed for the analysis of time series and point processes, each designed to capture specific signal properties. In this work, many of the most important tools used in time series analysis are compiled and reviewed, highlighting their main characteristics and the different types of complex systems to which they have been applied. Full article

(This article belongs to the Special Issue Recent Advances in Time Series Analysis, 2nd Edition)

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21 pages, 3856 KB

Open AccessArticle

Metal Artifact Reduction in CT Based on a Nonlinear Weighted Anisotropic TV Regularization

by Shuangyang Liu, Haiyang Wang and Yizhuang Song

Mathematics 2026, 14(7), 1230; https://doi.org/10.3390/math14071230 - 7 Apr 2026

Viewed by 449

Abstract

Metal artifact reduction (MAR) remains a long-standing challenge in computed tomography (CT) reconstruction. Metallic implants introduce inconsistencies between the acquired projection data and the ideal Radon transform, resulting in severe streaking artifacts in images reconstructed using the conventional filtered back projection (FBP) algorithm. [...] Read more.

Metal artifact reduction (MAR) remains a long-standing challenge in computed tomography (CT) reconstruction. Metallic implants introduce inconsistencies between the acquired projection data and the ideal Radon transform, resulting in severe streaking artifacts in images reconstructed using the conventional filtered back projection (FBP) algorithm. In this work, we propose a nonlinear weighted anisotropic total variation (NWATV) regularization method to mitigate metal artifacts and improve CT image quality. The effectiveness of the NWATV method is evaluated through three experiments, and the results demonstrate that it achieves superior reconstruction performance compared to the conventional linear interpolation method, the normalized metal artifact reduction method and the anisotropic total variation (TV) regularization method. Full article

(This article belongs to the Special Issue Inverse Problems in Science and Engineering)

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27 pages, 3109 KB

Open AccessArticle

Early Detection of Virtual Machine Failures in Cloud Computing Using Quantum-Enhanced Support Vector Machine

by Bhargavi Krishnamurthy, Saikat Das and Sajjan G. Shiva

Mathematics 2026, 14(7), 1229; https://doi.org/10.3390/math14071229 - 7 Apr 2026

Viewed by 466

Abstract

Cloud computing is one of the essential computing platforms for modern enterprises. A total of 84 percent of large businesses use cloud computing services in 2025 to enable remote working and higher flexibility of operation with reduction in the cost of operation. Cloud [...] Read more.

Cloud computing is one of the essential computing platforms for modern enterprises. A total of 84 percent of large businesses use cloud computing services in 2025 to enable remote working and higher flexibility of operation with reduction in the cost of operation. Cloud environments are dynamic and multitenant, often demanding high computational resources for real-time processing. However, the cloud system’s behavior is subjected to various kinds of anomalies in which patterns of data deviate from the normal traffic. The varieties of anomalies that exist are performance anomalies, security anomalies, resource anomalies, and network anomalies. These anomalies disrupt the normal operation of cloud systems by increasing the latency, reducing throughput, frequently violating service level agreements (SLAs), and experiencing the failure of virtual machines. Among all anomalies, virtual machine failures are one of the potential anomalies in which the normal operation of the virtual machine is interrupted, resulting in the degradation of services. Virtual machine failure happens because of resource exhaustion, malware access, packet loss, Distributed Denial of Service attacks, etc. Hence, there is a need to detect the chances of virtual machine failures and prevent it through proactive measures. Traditional machine learning techniques often struggle with high-dimensional data and nonlinear correlations, ending up with poor real-time adaptation. Hence, quantum machine learning is found to be a promising solution which effectively deals with combinatorially complex and high-dimensional data. In this paper, a novel quantum-enhanced support vector machine (QSVM) is designed as an optimized binary classifier which combines the principles of both quantum computing and support vector machine. It encodes the classical data into quantum states. Feature mapping is performed to transform the data into the high-dimensional form of Hilbert space. Quantum kernel evaluation is performed to evaluate similarities. Through effective optimization, optimal hyperplanes are designed to detect the anomalous behavior of virtual machines. This results in the exponential speed-up of operation and prevents the local minima through entanglement and superposition operation. The performance of the proposed QSVM is analyzed using the QuCloudSim 1.0 simulator and further validated using expected value analysis methodology. Full article

(This article belongs to the Special Issue Emerging Applications of Artificial Intelligence Algorithms in Computer and Network Security)

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34 pages, 1260 KB

Open AccessArticle

Conformally Compactified Minkowski Space: A Re-Examination with Emphasis on the Double Cover and Conformal Infinity

by Arkadiusz Jadczyk

Mathematics 2026, 14(7), 1228; https://doi.org/10.3390/math14071228 - 7 Apr 2026

Viewed by 488

Abstract

This paper presents a detailed re-examination of the conformalcompactification

\bar{M}

of Minkowski space

M

, constructed as the projective null cone of the six-dimensional space

R^{4, 2}

. We provide an explicit and basis-independent formulation, emphasizing geometric clarity. A central [...] Read more.

This paper presents a detailed re-examination of the conformalcompactification

\bar{M}

of Minkowski space

M

, constructed as the projective null cone of the six-dimensional space

R^{4, 2}

. We provide an explicit and basis-independent formulation, emphasizing geometric clarity. A central result is the explicit identification of

\bar{M}

with the unitary group

U (2)

via a diffeomorphism, offering a clear matrix representation for points in the compactified space. We then systematically construct and analyze the action of the full conformal group

O (4, 2)

and its connected component

{SO}_{0} (4, 2)

on this manifold. A key contribution is the detailed study of the double cover,

\tilde{M}

, which is shown to be diffeomorphic to

S^{3} \times S^{1}

. This construction resolves the non-effectiveness of the

SO (4, 2)

action on

\bar{M}

, yielding an effective group action on the covering space. A significant portion of our analysis is devoted to a precise and novel geometric characterization of the conformal infinity. Moving beyond the often-misrepresented “double cone” description, we demonstrate that the infinity of the double cover,

{\tilde{M}}_{\infty}

, is a squeezed torus (specifically, a horn cyclide), while the simple infinity,

{\bar{M}}_{\infty}

, is a needle cyclide. We provide explicit parametrizations and graphical representations of these structures. Finally, we explore the embedding of five-dimensional constant-curvature spaces, whose boundary is the compactified Minkowski space. The paper aims to clarify long-standing misconceptions in the literature and provides a robust, coordinate-free geometric foundation for conformal compactification, with potential implications for cosmology and conformal field theory. Full article

(This article belongs to the Section E4: Mathematical Physics)

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24 pages, 671 KB

Open AccessArticle

Statistical Indistinguishability in Multi-User Covert Communications Without Secret Information

by Jinyoung Lee, Junguk Park and Sangseok Yun

Mathematics 2026, 14(7), 1227; https://doi.org/10.3390/math14071227 - 7 Apr 2026

Viewed by 524

Abstract

This paper proposes a novel covert communication paradigm in which covertness emerges from network-induced structural uncertainty, eliminating the traditional reliance on pre-shared secret pilots in multi-user cooperative networks. Unlike conventional schemes that create information asymmetry through secret training sequences, we show that structural [...] Read more.

This paper proposes a novel covert communication paradigm in which covertness emerges from network-induced structural uncertainty, eliminating the traditional reliance on pre-shared secret pilots in multi-user cooperative networks. Unlike conventional schemes that create information asymmetry through secret training sequences, we show that structural uncertainty naturally arises from user selection in spatially dispersed networks. Specifically, we consider a public pilot aided system under a worst-case adversarial assumption where Willie possesses full knowledge of all individual channel state information (CSI) but remains uncertain about the active subset of cooperative users. We prove that this selection-induced structural uncertainty renders different transmission states statistically indistinguishable from Willie’s perspective, thereby forcing the optimal detector to reduce to an energy-based test. The proposed framework demonstrates that robust covertness can be achieved without secrecy-based coordination, providing a scalable and practically viable alternative to secret pilot management in future wireless networks. Full article

(This article belongs to the Special Issue Computational Methods in Wireless Communications with Applications)

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22 pages, 4848 KB

Open AccessArticle

A Lightweight Improved RT-DETR for Stereo-Vision-Based Excavator Posture Recognition

by Yunlong Hou, Ke Wu, Yuhan Zhang, Mengying Zhou, Jiasheng Lu and Zhao Zhang

Mathematics 2026, 14(7), 1226; https://doi.org/10.3390/math14071226 - 7 Apr 2026

Cited by 1 | Viewed by 575

Abstract

In intelligent excavator applications, traditional excavator posture recognition methods face two major challenges: limited recognition accuracy and insufficient computing resources on edge devices. To address these issues, this study proposes an excavator posture recognition method based on an improved Real-Time Detection Transformer (RT-DETR). [...] Read more.

In intelligent excavator applications, traditional excavator posture recognition methods face two major challenges: limited recognition accuracy and insufficient computing resources on edge devices. To address these issues, this study proposes an excavator posture recognition method based on an improved Real-Time Detection Transformer (RT-DETR). First, a new backbone network is designed based on the Reparameterized Vision Transformer to improve feature utilization efficiency while reducing computational demands. Next, the overall architecture is optimized by introducing lightweight Dynamic Upsamplers, which reduce information loss during upsampling and enhance multi-scale feature fusion. In addition, a Cross-Attention Fusion Module is adopted to strengthen local feature extraction while retaining the global modeling capability of the Transformer, thereby improving the discrimination between foreground and background. Finally, a Multi-Scale Fusion Network is introduced to further enhance the multi-scale feature representation ability of RT-DETR. Experimental results show that the proposed method achieves a mean average precision (mAP) of 94.29% for small object detection, which is 7.96% higher than that of the baseline RT-DETR, while reducing the number of model parameters by 34.95%. Compared with YOLO-series models, the proposed method improves mAP by 8.62% to 12.75%. These results indicate that the proposed method outperforms existing methods in both detection accuracy and computational efficiency and provides an efficient and feasible solution for real-time excavator posture recognition. Full article

(This article belongs to the Topic AI and Data-Driven Advancements in Industry 4.0, 2nd Edition)

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23 pages, 375 KB

Open AccessArticle

Quantum Gravity Applications: Free Scalar Particle Motion in Expanding Universe Metrics and Age Estimation

by John R. Fanchi

Mathematics 2026, 14(7), 1225; https://doi.org/10.3390/math14071225 - 6 Apr 2026

Viewed by 702

Abstract

Applications of Parametrized Relativistic Quantum Theory (PRQT) in curved spacetime are considered here. PRQT in curved spacetime is applied to the motion of free scalar particles in expanding universe metrics, including a generalized expanding universe (EU) metric and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. Governing [...] Read more.

Applications of Parametrized Relativistic Quantum Theory (PRQT) in curved spacetime are considered here. PRQT in curved spacetime is applied to the motion of free scalar particles in expanding universe metrics, including a generalized expanding universe (EU) metric and the Friedmann–Lemaître–Robertson–Walker (FLRW) metric. Governing equations are derived and solved through separation of variables. In addition, modern observational parameters and a rescaled Friedmann equation are used to estimate the age of the universe. Implications for cosmological models are discussed. Full article

(This article belongs to the Special Issue Advanced Approaches to Mathematical Physics Problems in High-Energy Physics)

41 pages, 699 KB

Open AccessArticle

Mathematical Framework for Characterizing Emotional Individuality in Large Language Models: Temperature Control, Fuzzy Entropy, and Persona-Based Diversity Analysis

by Naruki Shirahama, Yuma Yoshimoto, Naofumi Nakaya and Satoshi Watanabe

Mathematics 2026, 14(7), 1224; https://doi.org/10.3390/math14071224 - 6 Apr 2026

Viewed by 585

Abstract

Evaluating emotional understanding in Large Language Models (LLMs) is challenging because assessments are subjective, ambiguous, multidimensional, and sensitive to controllable generation parameters. We developed a unified mathematical framework for characterizing LLM “emotional individuality” that integrates softmax sampling–temperature control (the decoding-time temperature parameter exposed [...] Read more.

Evaluating emotional understanding in Large Language Models (LLMs) is challenging because assessments are subjective, ambiguous, multidimensional, and sensitive to controllable generation parameters. We developed a unified mathematical framework for characterizing LLM “emotional individuality” that integrates softmax sampling–temperature control (the decoding-time temperature parameter exposed by the API and typically used to modulate output randomness during token generation), fuzzy set theory with Shannon-type fuzzy entropy, and persona-based cognitive diversity analysis. We evaluated 36 API-accessible LLMs from seven major vendors on Japanese literary texts, using four personas each assigned a sampling temperature (

T \in {0.1, 0.4, 0.7, 0.9}

), yielding 4227/4320 trial responses (97.8% coverage), of which 4067/4227 contained valid numeric emotion scores (96.2%). Temperature controllability varied approximately 25-fold (

κ_{M} \in [0.039, 0.982]

) with both positive and negative temperature–variance relationships across models. Because each sampling temperature is deterministically assigned to a persona in our design,

κ_{M}

should be interpreted as an operational temperature–variance association across persona conditions rather than an isolated causal temperature effect. The model-level mean fuzzy entropy ranged from approximately 0.40 to 0.66, and the numerical stability consistency scores ranged from approximately 0.548 to 0.780. We also observed text-dependent structure, including genre-specific variation in the Interest–Sadness relationship. For practitioners, the framework is most directly useful as a benchmark-design and model-screening template for structured emotion-scoring tasks; its empirical conclusions remain limited to the present Japanese literary, text-only setting. Full article

(This article belongs to the Special Issue IIHMSP: Intelligent Information Hiding and Multimedia Signal Processing)

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20 pages, 11231 KB

Open AccessArticle

YOLO-Based Shading Artifact Reduction for CBCT-to-MDCT Translation Using Two-Stage Learning

by Yangheon Lee and Hyun-Cheol Park

Mathematics 2026, 14(7), 1223; https://doi.org/10.3390/math14071223 - 6 Apr 2026

Viewed by 565

Abstract

Cone-beam computed tomography (CBCT) offers advantages of low radiation dose and rapid acquisition but suffers from scatter-induced shading artifacts that limit diagnostic value compared to multi-detector CT (MDCT). While CycleGAN enables unpaired image translation, its uniform loss application struggles with localized artifact removal. [...] Read more.

Cone-beam computed tomography (CBCT) offers advantages of low radiation dose and rapid acquisition but suffers from scatter-induced shading artifacts that limit diagnostic value compared to multi-detector CT (MDCT). While CycleGAN enables unpaired image translation, its uniform loss application struggles with localized artifact removal. We propose a two-stage learning framework with YOLO-based region correction loss. Stage 1 trains a standard CycleGAN to establish stable CBCT-MDCT domain mapping. Stage 2 fine-tunes the model by applying gradient magnitude minimization loss selectively to artifact regions detected by a pretrained YOLO detector, enabling focused correction while preserving anatomical structures. Using 11,000 2D CBCT slices from 17 patients (14 training, 3 testing) and 23,500 2D MDCT slices from 50 patients, our method achieves a 14.0% reduction in artifact score compared to baseline CycleGAN while maintaining high structural similarity (SSIM > 0.96). Independent evaluation using integral nonuniformity (INU) and shading index (SI) confirms consistent improvement across physics-based metrics. The self-regulating mechanism, where YOLO detection confidence naturally decreases as artifacts diminish, provides automatic adjustment without manual intervention. This work demonstrates that combining staged learning with object detection offers an effective solution for localized artifact removal in medical image translation, potentially improving diagnostic accuracy while preserving the low-dose benefits of CBCT. Full article

(This article belongs to the Special Issue Application of Machine Learning and Mathematical Methods in Image Analysis and Computer Vision)

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18 pages, 2109 KB

Open AccessArticle

PAGF: Short-Horizon Forecasting of 3D Facial Landmarks

by Mingzhu Yan, Ye Yuan, Jian Liu and Fangyan Yang

Mathematics 2026, 14(7), 1222; https://doi.org/10.3390/math14071222 - 6 Apr 2026

Viewed by 517

Abstract

Short-term facial landmark forecasting is important for anticipatory facial behavior in human–robot interaction, yet models trained with pointwise reconstruction losses often suffer from mean reversion, producing low-error predictions with weakened motion dynamics. To address this issue, we propose a peak-aware gated recurrent unit [...] Read more.

Short-term facial landmark forecasting is important for anticipatory facial behavior in human–robot interaction, yet models trained with pointwise reconstruction losses often suffer from mean reversion, producing low-error predictions with weakened motion dynamics. To address this issue, we propose a peak-aware gated recurrent unit (GRU) framework that separates forecasting into peak planning and peak-conditioned trajectory generation. The planning stage estimates the timing and intensity of a salient motion peak within the forecast horizon together with a global motion direction, and the generation stage produces short-horizon landmark displacements through temporal gating and structured motion composition. The model is trained with reconstruction loss, peak supervision, peak-integrity regularization, and correlation-based temporal-shape regularization. Experiments on the MEAD dataset using 3D facial landmarks under a subject-independent protocol show a clear distortion–dynamics trade-off. Compared with static and sequence-to-sequence baselines, the proposed method better preserves peak-related facial dynamics while maintaining competitive 24-step prediction accuracy. Full article

(This article belongs to the Special Issue Advanced Control of Complex Dynamical Systems and Robotics with Applications)

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18 pages, 6999 KB

Open AccessArticle

A Simplified Approach to Investigating the Oscillatory Behavior of Nonlinear Even-Order Neutral Differential Equations

by Amany Nabih and Mohamed F. Abouelenein

Mathematics 2026, 14(7), 1221; https://doi.org/10.3390/math14071221 - 6 Apr 2026

Viewed by 567

Abstract

This article explores the oscillation properties of solutions for higher-order nonlinear neutral functional differential equations. This study sought to establish applicable oscillation conditions for nonlinear NDDEs when

α \neq β

. Our analysis focused on identifying the key asymptotic characteristics of positive solutions [...] Read more.

This article explores the oscillation properties of solutions for higher-order nonlinear neutral functional differential equations. This study sought to establish applicable oscillation conditions for nonlinear NDDEs when

α \neq β

. Our analysis focused on identifying the key asymptotic characteristics of positive solutions in the noncanonical case. Based on these properties, we developed a multi-conditional criterion that guarantees oscillation, thereby extending previously established results for second-order equations. Unlike previous results, which involved arbitrary constants and were thus difficult to apply, the criteria derived in this work do not contain such constants, making them directly applicable. Moreover, to overcome the complexity introduced by the multiple constraints of this criterion, we propose a new and previously unreported simplified oscillation condition. The effectiveness of this simplified criterion is demonstrated through an illustrative example. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)

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29 pages, 423 KB

Open AccessArticle

Reliability-Aware Multilingual Sentiment Analytics for Agricultural Market Intelligence

by Jantima Polpinij, Christopher S. G. Khoo, Wei-Ning Cheng, Thananchai Khamket, Chumsak Sibunruang and Manasawee Kaenampornpan

Mathematics 2026, 14(7), 1220; https://doi.org/10.3390/math14071220 - 5 Apr 2026

Viewed by 655

Abstract

Public opinion on online platforms now plays an important role in agricultural markets, which have always been unpredictable. Although sentiment analysis has been widely applied to agricultural texts, most existing studies typically focus only on classification accuracy without connecting results to actual market [...] Read more.

Public opinion on online platforms now plays an important role in agricultural markets, which have always been unpredictable. Although sentiment analysis has been widely applied to agricultural texts, most existing studies typically focus only on classification accuracy without connecting results to actual market intelligence systems, especially in multilingual contexts. This paper introduces a reliability-aware transformer-based framework for analyzing sentiment in agricultural market intelligence across multiple languages. The framework leverages weakly supervised multilingual transformers to extract sentiment signals from large-scale unlabeled Thai and English texts about major agricultural commodities found online. To enhance robustness under weak supervision, the framework incorporates reliability-aware mechanisms, including confidence-based pseudo-label filtering, cross-source consistency refinement, and expert-guided calibration to reduce noise and account for bias between different data sources. Sentiment predictions are further aligned with market intelligence objectives through reliability-weighted aggregation, yielding interpretable sentiment indices that enable cross-lingual and cross-source comparability. We tested the framework extensively using a multilingual agricultural corpus derived from social media and news coverage of agriculture. The results show consistent improvements over both classical machine learning approaches and standard multilingual transformer baselines. Additional ablation studies and sensitivity analyses confirmed that reliability-aware mechanisms, particularly confidence thresholding, play a crucial role in getting the right balance between label quality and data coverage. Overall, the results indicate that reliability-aware multilingual sentiment analytics provide robust and actionable insights for agricultural market monitoring and policy analysis. Full article

(This article belongs to the Special Issue Application of Machine Learning and Data Mining, 2nd Edition)

33 pages, 947 KB

Open AccessArticle

Global Dynamics for a Distributed Delay SVEIR Model for Measles Transmission with Imperfect Vaccination: A Threshold Analysis

by Mohammed H. Alharbi and Ali Rashash Alzahrani

Mathematics 2026, 14(7), 1219; https://doi.org/10.3390/math14071219 - 5 Apr 2026

Cited by 1 | Viewed by 492

Abstract

Measles remains a significant public health threat despite widespread vaccination, with recent resurgences driven by vaccine hesitancy and coverage gaps. Existing mathematical models often fail to capture the substantial temporal heterogeneity in incubation periods, vaccine-induced protection, and recovery processes that characterize measles transmission. [...] Read more.

Measles remains a significant public health threat despite widespread vaccination, with recent resurgences driven by vaccine hesitancy and coverage gaps. Existing mathematical models often fail to capture the substantial temporal heterogeneity in incubation periods, vaccine-induced protection, and recovery processes that characterize measles transmission. We develop and analyze an SVEIR epidemic model incorporating four independent distributed time delays with exponential survival factors, capturing the realistic variability in these epidemiological processes. The model features compartment-specific mortality rates, disease-induced mortality, and imperfect vaccination with failure probability

θ

. Using next-generation matrix methods adapted for delay kernels, we derive the delay-dependent reproduction number

R_{0}^{d}

and prove, via systematic construction of Volterra-type Lyapunov functionals, that it constitutes a sharp threshold: the disease-free equilibrium is globally asymptotically stable when

R_{0}^{d} \leq 1

, while a unique endemic equilibrium emerges and is globally stable when

R_{0}^{d} > 1

. Normalized forward sensitivity analysis reveals that the transmission rate

β

and recruitment rate

Λ

exhibit maximal positive elasticity, while the vaccination rate p, vaccine failure probability

θ

, and incubation delay

τ_{3}

possess the largest negative elasticities. Critically,

τ_{3}

exerts exponential influence via

e^{- n_{3} τ_{3}}

, making interventions that delay infectiousness—such as post-exposure prophylaxis—unusually potent. We derive an explicit expression for the critical delay

τ_{3}^{cr}

at which

R_{0}^{d} = 1

, demonstrating that prolonging the effective incubation period sufficiently can shift the system from endemic persistence to extinction. Numerical simulations using Dirac delta kernels confirm all theoretical predictions. These findings provide three actionable insights for public health: (1) maintaining high vaccination coverage among new birth cohorts remains paramount; (2) improving vaccine quality (reducing

θ

) yields substantial returns; and (3) the incubation delay represents a quantifiable, measurable target for evaluating the population-level impact of time-sensitive interventions. The framework is broadly applicable to infectious diseases characterized by significant temporal heterogeneity. Full article

(This article belongs to the Special Issue Advances in Epidemiological and Biological Systems Modeling)

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20 pages, 414 KB

Open AccessArticle

F(

R, T

)-Gravity with Anisotropic Fluid Admitting Hyperbolic Ricci Solitons with Torse-Forming Vector Field

by Mohd Danish Siddiqi and Fatemah Mofarreh

Mathematics 2026, 14(7), 1218; https://doi.org/10.3390/math14071218 - 4 Apr 2026

Viewed by 411

Abstract

This study is dedicated to a separable

F (R, T)

-gravity related to the anisotropic matter to extract the equation of state for

F (R, T)

-gravity. In this research, we offer insight into calculating the density [...] Read more.

This study is dedicated to a separable

F (R, T)

-gravity related to the anisotropic matter to extract the equation of state for

F (R, T)

-gravity. In this research, we offer insight into calculating the density and pressure in the phantom barrier, stiff fluid, and matter-dominated eras, respectively. As demonstrated, a spacetime in

F (R, T)

-gravity full of anisotropic matter is a generalized quasi-Einstein spacetime. In addition, we gain the equation of state of Codazzi type, Ricci semi-symmetric and Ricci-pseudo symmetric anisotropic fluid spacetime in

F (R, T)

-gravity. We prove an anisotropic spacetime in

F (R, T)

-gravity endowed with Codazzi-type Ricci tensor is a Yang Pure spacetime and Robertson–Walker spacetime. Furthermore, we try to give out the energy constraints of Penrose’s singularity theorem for black holes in an anisotropic fluid spacetime in

F (R, T)

-gravity. Lastly, we study hyperbolic Ricci solitons on anisotropic fluid spacetime in

F (R, T)

-gravity endowed with a torse-forming vector field, and for steady hyperbolic Ricci soliton, we deduced the equation of state of anisotropic fluid spacetime in

F (R, T)

-gravity. Full article

(This article belongs to the Special Issue Geometry Meets PDE: Analysis and Applications)

34 pages, 453 KB

Open AccessArticle

Parametric Estimation of a Merton Model Using SOS Flows and Riemannian Optimization

by Luca Di Persio and Paul Bastin

Mathematics 2026, 14(7), 1217; https://doi.org/10.3390/math14071217 - 4 Apr 2026

Viewed by 770

Abstract

We consider the problem of Bayesian parameter inference in the Merton structural credit risk model, where the posterior is induced by a jump-diffusion likelihood and the marginal evidence is not available in closed form. To approximate this posterior, we construct a variational family [...] Read more.

We consider the problem of Bayesian parameter inference in the Merton structural credit risk model, where the posterior is induced by a jump-diffusion likelihood and the marginal evidence is not available in closed form. To approximate this posterior, we construct a variational family based on triangular sum-of-squares (SOS) polynomial flows, in which each component map is monotone by construction: its diagonal derivative is a positive definite quadratic form on a monomial basis, yielding a closed-form log-Jacobian and explicit gradients with respect to all flow parameters. The symmetric positive definite matrices parametrizing the flow are optimized by intrinsic Riemannian gradient ascent on the positive definite cone equipped with the affine-invariant metric, which preserves feasibility at every iterate without projection. We show that the rank-one Jacobian gradients produced by the SOS structure have unit norm in the affine-invariant metric, establishing a direct algebraic coupling between the transport family and the optimization geometry and implying a universal 1-Lipschitz bound for the log-Jacobian along geodesics. On the likelihood side, we derive exact score identities for all five structural parameters of the Merton model—drift, volatility, jump intensity, jump mean, and jump volatility—through both the Poisson log-normal mixture and the Fourier inversion representations. Strictly positive parameters are handled via exponential reparametrization, and the resulting gradients propagate end-to-end through the flow. We establish uniform truncation bounds on compact parameter sets for the infinite mixture and its associated score series, providing rigorous control over the finite approximations used in practice. The base distribution is chosen to be uniform on

{[0, 1]}^{5}

, whose bounded support ensures uniform control of the monomial basis and stabilizes the polynomial calculus. These ingredients are assembled into a fully explicit modified ELBO with implementable gradients, combining Euclidean updates for vector parameters and intrinsic manifold updates for matrix parameters. Full article

(This article belongs to the Special Issue Applications of Time Series Analysis)

28 pages, 902 KB

Open AccessFeature PaperArticle

A Mixed-Integer Linear Programming Framework for Optimal Scheduling of Maritime Mobile Energy Storage

by Yunxiang Shu, Yu Guo, Yuquan Du and Shuaian Wang

Mathematics 2026, 14(7), 1216; https://doi.org/10.3390/math14071216 - 4 Apr 2026

Viewed by 502

Abstract

The offshore wind energy sector requires efficient logistics to retrieve generated electricity using maritime mobile energy storage systems. This study addresses the maritime mobile energy storage scheduling problem to maximise the total net energy delivered to the onshore grid. The proposed approach utilises [...] Read more.

The offshore wind energy sector requires efficient logistics to retrieve generated electricity using maritime mobile energy storage systems. This study addresses the maritime mobile energy storage scheduling problem to maximise the total net energy delivered to the onshore grid. The proposed approach utilises a mixed-integer linear programming framework. The mathematical formulation integrates a replicated port node mechanism to plan multi-trip operations over a continuous planning horizon. Additionally, the model accounts for energy transfer loss coefficients and incorporates a speed discretisation strategy to balance propulsion consumption against retrieved electricity. Numerical experiments based on simulated operational scenarios demonstrate the effectiveness of this method. The results indicate that expanding vessel storage capacity from 500 to 600 megawatt-hours eliminates the necessity for multi-stop trips, thereby reducing propulsion energy consumption from 270.79 to 73.65 megawatt-hours. Furthermore, increasing the fleet size from five to six vessels enables the full retrieval of available offshore electricity while decreasing fleet propulsion consumption to 91.08 megawatt-hours. The solver consistently achieves optimal solutions within an average of 0.88 s. Consequently, this framework provides operators with precise decision support for determining fleet capacity and configuring offshore energy retrieval networks. Full article

(This article belongs to the Section E2: Control Theory and Mechanics)

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28 pages, 2341 KB

Open AccessArticle

Exploring Marshall–Olkin Models Through Bibliometric and Topic Modeling Approaches Using Latent Dirichlet Allocation (1981–2025): A Study Based on Scopus Data

by Humberto Llinás, Brian Llinás, Carlos López and Daniela Nuñez

Mathematics 2026, 14(7), 1215; https://doi.org/10.3390/math14071215 - 4 Apr 2026

Cited by 1 | Viewed by 557

Abstract

The Marshall–Olkin family of distributions has gained increasing attention in fields such as reliability engineering, survival analysis, financial risk modeling, and actuarial science because of its flexibility in modeling dependence among events and its wide range of extensions. Despite its growing relevance, a [...] Read more.

The Marshall–Olkin family of distributions has gained increasing attention in fields such as reliability engineering, survival analysis, financial risk modeling, and actuarial science because of its flexibility in modeling dependence among events and its wide range of extensions. Despite its growing relevance, a systematic understanding of how research on Marshall–Olkin models has evolved over time is still limited. This study addresses this gap by combining bibliometric techniques with topic modeling to analyze the structure and evolution of the scientific literature on Marshall–Olkin models. The analysis includes all 266 peer-reviewed publications on Marshall–Olkin models indexed in Scopus between 1981 and 2025. Bibliometric techniques (including heatmaps, clustering analyses, and temporal visualizations) are used to characterize publication patterns, source relationships, and thematic evolution. In addition, Latent Dirichlet Allocation (LDA) uncovered 27 topics and examined their prevalence across journals and time periods. The results reveal five main clusters of publication sources and three temporal groupings derived from hierarchical clustering of topic distributions, reflecting the thematic progression of the field. Overall, the findings highlight both the persistence of core research themes and the emergence of new applications, particularly in areas such as Bayesian competing risks, censoring models, and parameter estimation in Weibull-based frameworks. This study provides a systematic and data-driven perspective on the intellectual evolution of Marshall–Olkin research, helping scholars identify emerging trends and potential directions for future work. Full article

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15 pages, 289 KB

Open AccessArticle

A New Family of Szász–Mirakyan-Type Operators Preserving Two Exponential Functions

by Gülsüm Ulusoy Ada and Ali Aral

Mathematics 2026, 14(7), 1214; https://doi.org/10.3390/math14071214 - 4 Apr 2026

Cited by 1 | Viewed by 456

Abstract

This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exponential behaviors through a parameter sequence. Basic properties of the operators are [...] Read more.

This paper introduces a new family of Szász–Mirakyan-type operators defined by a convex combination of two Poisson-type constructions. The operators preserve the constant function and provide a continuous transition between different exponential behaviors through a parameter sequence. Basic properties of the operators are studied, including the preservation of exponential test functions and the behavior of the first and second central moments. Voronovskaja-type asymptotic results are obtained, describing the effect of the parameter on the asymptotic structure. Moreover, a necessary condition for faster-than

1 / n

approximation is derived. The behavior of the operators is examined through computational evidence, which also confirms the theoretical findings. Full article

(This article belongs to the Special Issue New Advances in Functional Analysis and PDEs)

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37 pages, 9096 KB

Open AccessFeature PaperArticle

A Numerical Study of Tunable Multifunctional Metastructures via Solid–Liquid Phase Transition for Simultaneous Control of Sound and Vibration

by Hyeonjun Jeong and Jaeyub Hyun

Mathematics 2026, 14(7), 1213; https://doi.org/10.3390/math14071213 - 4 Apr 2026

Viewed by 483

Abstract

Metastructures, waveguides composed of multiple unit cells (meta-atoms), have gained significant attention for controlling wave propagation in engineering applications, especially in the context of elastic and acoustic waves. However, existing metastructures often lack sufficient tunable functionality to dynamically control both elastic vibration and [...] Read more.

Metastructures, waveguides composed of multiple unit cells (meta-atoms), have gained significant attention for controlling wave propagation in engineering applications, especially in the context of elastic and acoustic waves. However, existing metastructures often lack sufficient tunable functionality to dynamically control both elastic vibration and acoustic wave transmission using a single external parameter. This study introduces a phase-change material (PCM)-embedded meta-atom, where a core mass is connected to an outer shell by Archimedean spiral bridges. The solid–liquid phase transition of PCM induces a notable change in the effective shear modulus, enabling dynamic wave control. The mechanism for bandgap formation transitions from Bragg scattering in the solid PCM state to local resonance in the liquid state. Core rotation, driven by the phase transition, is key to generating flat bands and low-frequency locally resonant bandgaps at high temperatures. Temperature-dependent, mode-selective transmission behavior is observed, with transverse vibrations and acoustic waves exhibiting opposite blocking and transmission characteristics at the same frequency. This design provides a promising approach for decoupling sound and vibration management, using temperature control driven by the PCM phase transition. The work contributes to multifunctional metastructures with applications in adaptive noise control, structural health monitoring, and tunable vibration isolation systems. Full article

(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)

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23 pages, 355 KB

Open AccessArticle

A Study of the Generalized Gabor Transform with Applications to Reproducing Kernel Theory

by Saifallah Ghobber and Hatem Mejjaoli

Mathematics 2026, 14(7), 1212; https://doi.org/10.3390/math14071212 - 3 Apr 2026

Viewed by 472

Abstract

The aim of this paper is to establish an inversion and Calderón formulas for the generalized Gabor transform associated with a class of Sturm–Liouville operators. We also investigate several problems related to reproducing kernel theory for this transform. In particular, we study the [...] Read more.

The aim of this paper is to establish an inversion and Calderón formulas for the generalized Gabor transform associated with a class of Sturm–Liouville operators. We also investigate several problems related to reproducing kernel theory for this transform. In particular, we study the concept of Tikhonov regularization and the extremal functions associated with the new generalized Gabor transform. Full article

(This article belongs to the Special Issue Recent Developments in Harmonic Analysis: Theory and Applications)

43 pages, 1881 KB

Open AccessArticle

Cognitive ZTNA: A Neuro-Symbolic AI Approach for Adaptive and Explainable Zero Trust Access Control

by Ahmed Alzahrani

Mathematics 2026, 14(7), 1211; https://doi.org/10.3390/math14071211 - 3 Apr 2026

Viewed by 734

Abstract

Zero Trust Network Access (ZTNA) has emerged as a fundamental paradigm for securing cloud-native and distributed computing environments. However, existing ZTNA implementations remain largely limited by static policy enforcement and opaque machine-learning-based anomaly detection mechanisms, which often lack contextual adaptability, policy awareness, and [...] Read more.

Zero Trust Network Access (ZTNA) has emerged as a fundamental paradigm for securing cloud-native and distributed computing environments. However, existing ZTNA implementations remain largely limited by static policy enforcement and opaque machine-learning-based anomaly detection mechanisms, which often lack contextual adaptability, policy awareness, and interpretable decision-making capabilities. These limitations create significant challenges in dynamic multi-cloud environments where access behavior continuously evolves and security decisions must be both accurate and explainable. To address these challenges, this study proposes Cognitive ZTNA framework, a unified neuro-symbolic trust enforcement framework that integrates transformer-based behavioral trust modeling with ontology-guided symbolic reasoning. The proposed architecture enables continuous trust evaluation by combining behavioral access patterns with explicit policy semantics through a hybrid trust fusion mechanism. This design allows the system to capture long-range behavioral dependencies while maintaining policy-compliant and interpretable access control decisions. The framework is evaluated using the CloudZT-Bench-2025 dataset, comprising 4.2 million cross-platform access events derived from enterprise security telemetry, AWS CloudTrail logs, and simulated adversarial scenarios. Experimental results demonstrate that Cognitive ZTNA achieves Precision = 0.96, Recall = 0.93, and F1-score = 0.95, significantly outperforming rule-based and machine-learning baselines while reducing the false positive rate to 0.03. In addition, the system maintains real-time feasibility with an average decision latency of 24 ms and explanation latency below 5 ms, while achieving 92% analyst-rated explanation sufficiency. These findings demonstrate that integrating behavioral intelligence with symbolic policy reasoning enables adaptive, interpretable, and policy-aware Zero Trust enforcement. The proposed framework therefore provides a practical foundation for next-generation ZTNA systems capable of supporting secure, transparent, and context-aware access control in modern cloud environments. Full article

(This article belongs to the Special Issue New Advances in Network Security and Data Privacy)

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26 pages, 429 KB

Open AccessFeature PaperArticle

Modified Asymptotic Solutions and Application to Asymptotic Expansions of Indicator Functions in Mixed-Type Media

by Mishio Kawashita and Wakako Kawashita

Mathematics 2026, 14(7), 1210; https://doi.org/10.3390/math14071210 - 3 Apr 2026

Viewed by 367

Abstract

Asymptotic solutions that can describe the incidence and reflection of waves have been used in various situations. They can also be applied to inverse problems and provide useful information in situations where a precise evaluation is required. However, the construction of standard asymptotic [...] Read more.

Asymptotic solutions that can describe the incidence and reflection of waves have been used in various situations. They can also be applied to inverse problems and provide useful information in situations where a precise evaluation is required. However, the construction of standard asymptotic solutions requires higher regularity with respect to the boundaries of the observation target. This article proposes a “modified asymptotic solution” to overcome this weakness. To demonstrate its usefulness, it is applied to the analysis of the indicator function in the enclosure method for the inverse problem of the wave equation in a mixed-type medium. Full article

(This article belongs to the Section C: Mathematical Analysis)

17 pages, 1903 KB

Open AccessArticle

An Improved LASSO Screening and Sparse Bayesian Learning Algorithm for GWAS

by Jieru Wang, Jiaqi Li, Guo Lin, Fengfei Ban, Yinan Wu, Siyu Su, Jin Zhang and Juncong Chen

Mathematics 2026, 14(7), 1209; https://doi.org/10.3390/math14071209 - 3 Apr 2026

Viewed by 429

Abstract

Genome-wide association studies (GWASs) are powerful and flexible tools for identifying single nucleotide polymorphisms (SNPs) associated with quantitative traits (yield, stress resistance) in plants. Variable selection and machine learning are two effective approaches in GWAS. However, both face limitations in complex, noisy data [...] Read more.

Genome-wide association studies (GWASs) are powerful and flexible tools for identifying single nucleotide polymorphisms (SNPs) associated with quantitative traits (yield, stress resistance) in plants. Variable selection and machine learning are two effective approaches in GWAS. However, both face limitations in complex, noisy data analysis in the big-data era. In this study, we integrated variable selection and machine learning under the mixed linear model framework, proposing a novel method, the improved LASSO screening and sparse Bayesian learning algorithm (ILSBL). The ILSBL first corrects the polygenic and environmental noise, then reduces genotypic dimensionality by LASSO-based variable selection, and finally performs parameter estimation using sparse Bayesian learning. Two simulation experiments and association analyses of three flowering-time-related traits in Arabidopsis thaliana were conducted to validate the new algorithm. The results showed that, compared to established methods, the ILSBL exhibited flexibility in simulation studies and maintained robust performance under complex genetic backgrounds, achieving a favorable balance among statistical power, parameter estimation accuracy, runtime efficiency, and false-positive rate. The analysis of the real Arabidopsis datasets further confirmed the advantages of ILSBL for GWASs, with 30 candidate genes adjacent to significant quantitative trait nucleotides (QTNs) associated with flowering-related traits. These results provide valuable insights for a better understanding of the genetic basis underlying flowering-related traits in Arabidopsis. Full article

(This article belongs to the Section E3: Mathematical Biology)

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20 pages, 1596 KB

Open AccessArticle

Modular Suprametric Spaces and Fixed-Point Principles with Applications in Fractional Burn-Healing Dynamics

by Marija Paunović, Abdurrahman Büyükkaya and Mahpeyker Öztürk

Mathematics 2026, 14(7), 1208; https://doi.org/10.3390/math14071208 - 3 Apr 2026

Cited by 1 | Viewed by 427

Abstract

We introduce a new nonlinear distance structure, a modular suprametric space, that integrates modular metrics with perturbations characteristic of suprametrics. Within this framework, we develop a contraction principle tailored to its nonlinear geometry and demonstrate the existence of fixed points under a generalized [...] Read more.

We introduce a new nonlinear distance structure, a modular suprametric space, that integrates modular metrics with perturbations characteristic of suprametrics. Within this framework, we develop a contraction principle tailored to its nonlinear geometry and demonstrate the existence of fixed points under a generalized iterative control. In order to showcase the practical application of this proposed structure, we analyze a burn-healing model driven by nonlinear recovery dynamics. The derived fixed-point conditions ensure both the existence and stability of the healing equilibrium. Our findings indicate that modular suprametric spaces serve as a versatile analytical tool for dynamical systems whose evolution exhibits nonstandard sensitivity, saturation effects, or exponential response behavior. Full article

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