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29 pages, 2297 KB  
Article
From Job Postings to Vocational Education Standards: Mapping Competency Requirements for NEV Sales and Livestreaming Hosts
by Yang Zhou, Li Tao, Zhiyan Xue and Wanwen Dai
World Electr. Veh. J. 2026, 17(3), 162; https://doi.org/10.3390/wevj17030162 - 23 Mar 2026
Viewed by 182
Abstract
This study maps competency requirements for two representative frontline marketing roles in China’s new energy vehicle (NEV) sector, NEV sales consultants and livestreaming hosts, and examines their alignment with current vocational education standards. Using a market-oriented, data-driven design, recruitment texts were collected from [...] Read more.
This study maps competency requirements for two representative frontline marketing roles in China’s new energy vehicle (NEV) sector, NEV sales consultants and livestreaming hosts, and examines their alignment with current vocational education standards. Using a market-oriented, data-driven design, recruitment texts were collected from Zhaopin across more than 20 major Chinese cities. Latent Dirichlet Allocation (LDA) identified competency themes, which were then organized into work-process task domains and visualized as position–task–competency mappings. Mapping these demand-side requirements to national teaching standards reveals relatively strong alignment for sales in market insight and sales strategy, but also gaps in omni-channel lead operations, customer experience management, and operational coordination; livestreaming roles show systematic gaps across the entire work process, particularly in on-air control, customer conversion process design, and data-driven optimization. Building on the identified gaps, the study proposes a position–task–competency-to-curriculum translation pathway to support modular updates in NEV marketing talent development within vocational education and training. Full article
(This article belongs to the Section Marketing, Promotion and Socio Economics)
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49 pages, 8802 KB  
Article
An Efficient Solver for Fractional Diffusion on Unbounded Combs with Exact Absorbing Boundary Conditions
by Jingyi Mo, Guitian He, Yan Tian and Hui Cheng
Fractal Fract. 2026, 10(3), 208; https://doi.org/10.3390/fractalfract10030208 - 23 Mar 2026
Viewed by 111
Abstract
Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay [...] Read more.
Despite its importance in modeling subdiffusion in fractal and heterogeneous media, a rigorous and computational scheme for solving the fractional diffusion equation on generalized comb structures over unbounded domains has remained elusive, mainly due to the nonlocal memory effect and slow spatial decay of solutions. To the best of our knowledge, we address this long-standing gap by presenting a fully integrated framework that simultaneously resolves both challenges. We derive the governing equation from constitutive relations and establish exact absorbing boundary conditions (ABCs) for the multi-skeleton comb model, a result absent in prior work. A transparent Dirichlet-to-Neumann (DtN) map, constructed via Laplace analysis, rigorously handles skeletal Dirac delta singularities and eliminates spurious reflections without empirical parameters. Furthermore, we propose a novel structure-preserving finite difference scheme that applies the sum-of-exponentials (SOE) approximation not only to the interior Caputo derivative but also to the convolution kernels arising from the ABCs. This yields a dramatic reduction in computational complexity, from quadratic O(Nt2) to quasi-linear O(NtlogNt), while preserving the physics of anomalous transport. We prove the well-posedness, unconditional stability, and convergence of the method. Numerical results confirm theoretical error estimates and show excellent agreement between simulated particle distributions, mean square displacement profiles, and exact asymptotics, validating both accuracy and robustness. The speedup (CPU time ratio Direct/Fast) is about 1.00×1.23× for Nt=5000 in our tests. Our approach sets a new benchmark for simulating anomalous dynamics in fractal-inspired media. Full article
(This article belongs to the Section Numerical and Computational Methods)
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18 pages, 1251 KB  
Article
A Bayesian Framework with Dirichlet Priors and Spatial Smoothing for Protein Rotamer Prediction
by Kamal Al Nasr, Ahmad Jad Allah, Mohammad Alamri and Mohammad Al Sallal
Int. J. Mol. Sci. 2026, 27(6), 2869; https://doi.org/10.3390/ijms27062869 - 22 Mar 2026
Viewed by 157
Abstract
Accurate prediction of protein sidechain conformations is a fundamental challenge in structural biology, with diverse applications ranging from protein structure determination to computational drug design. The performance of backbone-dependent rotamer libraries is often limited by discrete binning artifacts and difficulties handling sparse conformational [...] Read more.
Accurate prediction of protein sidechain conformations is a fundamental challenge in structural biology, with diverse applications ranging from protein structure determination to computational drug design. The performance of backbone-dependent rotamer libraries is often limited by discrete binning artifacts and difficulties handling sparse conformational regions. In this work, we present a Bayesian framework for rotamer prediction that addresses these limitations through Dirichlet priors and spatial smoothing. Our approach models rotamer probabilities as continuous functions of backbone dihedral angles, using circular Gaussian convolution, to make the most of statistical strength from neighboring conformations while respecting the periodic nature of angular data. We constructed rotamer libraries through structural clustering of sidechain conformations rather than chi angle binning, ensuring that each rotamer represents a distinct three-dimensional geometry. We evaluated and compared our framework against the state-of-the-art libraries on two independent test sets. Our Dirichlet model achieved chi angle prediction accuracy of 59–60%. Notably, our method produced consistently lower angular errors, an approximate 13% reduction in mean deviation, suggesting that the continuous probability distributions better capture subtle conformational preferences. Further, we explored the incorporation of non-sequential context by including the identity of nearby non-neighboring residues as an example of extensibility of our framework. Full article
(This article belongs to the Section Molecular Biophysics)
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23 pages, 1511 KB  
Article
Estimator Statistics from Simulation-Free Dirichlet Block-Bootstrap Resampling
by Tillmann Rosenow
Stats 2026, 9(2), 32; https://doi.org/10.3390/stats9020032 - 20 Mar 2026
Viewed by 188
Abstract
Since the initiation of two variants of the bootstrap method by Efron and Rubin in the late 1970s, a variety of advancements has emerged in the literature. The subsampling of blocks enabled the estimation of the actual variance of the sample mean. The [...] Read more.
Since the initiation of two variants of the bootstrap method by Efron and Rubin in the late 1970s, a variety of advancements has emerged in the literature. The subsampling of blocks enabled the estimation of the actual variance of the sample mean. The equivalence of the data-level and the estimator-level resampling is easily established for the sample mean and estimators alike. For Rubin’s variant of the bootstrap we apply an algorithm by Diniz et al. which allows for the numerically stable computation of the sample-based cumulative distribution function of the estimator under investigation. No actual Monte-Carlo resampling is necessary in this setting and we demonstrate how we get access to the very small probabilities of the tails and moreover to confidence intervals. We do this at the example of a well-known test model that exhibits geometrically decaying spatial correlations. The analysis naturally applies to temporally correlated systems or to the correlations occurring in Markov chains, as well. Full article
(This article belongs to the Section Time Series Analysis)
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25 pages, 1131 KB  
Article
A Bayesian Approach for Clustering Constant-Wise Change-Point Data
by Ana Carolina da Cruz and Camila P. E. de Souza
Stats 2026, 9(2), 31; https://doi.org/10.3390/stats9020031 - 17 Mar 2026
Viewed by 259
Abstract
Change-point models deal with ordered data sequences. Their primary goal is to infer the locations where an aspect of the data sequence changes. In this paper, we propose and implement a nonparametric Bayesian model for clustering observations based on their constant-wise change-point profiles [...] Read more.
Change-point models deal with ordered data sequences. Their primary goal is to infer the locations where an aspect of the data sequence changes. In this paper, we propose and implement a nonparametric Bayesian model for clustering observations based on their constant-wise change-point profiles via a Gibbs sampler. Our model incorporates a Dirichlet process on the constant-wise change-point structures to cluster observations while simultaneously performing multiple change-point estimation. Additionally, our approach controls the number of clusters in the model, not requiring specification of the number of clusters a priori. Satisfactory clustering and estimation results were obtained when evaluating our method under various simulated scenarios and on a real dataset from single-cell genomic sequencing. Our proposed methodology is implemented as an R package called BayesCPclust and is available from the Comprehensive R Archive Network. Full article
(This article belongs to the Section Bayesian Methods)
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28 pages, 2882 KB  
Article
Semantic Divergence in AI-Generated and Human Influencer Product Recommendations: A Computational Analysis of Dual-Agent Communication in Social Commerce
by Woo-Chul Lee, Jang-Suk Lee and Jungho Suh
Appl. Sci. 2026, 16(6), 2816; https://doi.org/10.3390/app16062816 - 15 Mar 2026
Viewed by 357
Abstract
The proliferation of generative artificial intelligence (AI) as an autonomous recommendation agent fundamentally challenges traditional paradigms of marketing communication. As AI systems increasingly mediate consumer–brand relationships, understanding how artificial agents construct persuasive discourse—distinct from human communicators—becomes critical for developing effective dual-channel marketing strategies. [...] Read more.
The proliferation of generative artificial intelligence (AI) as an autonomous recommendation agent fundamentally challenges traditional paradigms of marketing communication. As AI systems increasingly mediate consumer–brand relationships, understanding how artificial agents construct persuasive discourse—distinct from human communicators—becomes critical for developing effective dual-channel marketing strategies. Grounded in Source Credibility Theory and the Computers Are Social Actors (CASA) paradigm, this study investigates the semantic and structural divergence between AI-generated product recommendations and human influencer marketing messages in social commerce contexts. Employing a mixed-methods computational approach integrating term frequency analysis, TF-IDF weighting, Latent Dirichlet Allocation (LDA) topic modeling, and BERT-based contextualized semantic embedding analysis (KR-SBERT), we examined 330 Instagram influencer posts and 541 AI-generated responses concerning inner beauty enzyme products—a hybrid category combining functional health claims with hedonic beauty appeals—in the Korean social commerce market. AI-generated responses were collected through a systematically designed query protocol with empirically grounded prompts derived from actual consumer search behaviors, and analytical robustness was verified through sensitivity analyses across multiple parameter thresholds. Our findings reveal a fundamental divergence in persuasive architecture: human influencers construct experiential narratives exhibiting message characteristics typically associated with peripheral-route cues (sensory descriptions, emotional testimonials, social context), while AI recommendations employ systematic, evidence-based discourse exhibiting message characteristics typically associated with central-route argumentation (functional mechanisms, ingredient specifications, objective criteria). Topic modeling identified four distinct thematic clusters for each source type: human discourse centers on embodied experience and relational consumption, whereas AI discourse organizes around informational utility and rational decision support. Jensen–Shannon Divergence analysis (JSD = 0.213 bits) confirmed moderate distributional divergence, while chi-square testing (χ2 = 847.23, p < 0.001) and Cramér’s V (0.312, indicating a medium-to-large effect) demonstrated statistically significant and substantively meaningful differences. These findings extend CASA theory by demonstrating that AI recommendation agents develop a characteristic “AI communication signature” distinguishable from human persuasion patterns. We propose an integrated Dual-Agent Persuasion Proposition—synthesizing CASA, ELM, and Source Credibility perspectives—suggesting that AI and human recommenders serve complementary functions across different stages of the consumer decision journey—a proposition whose predictions regarding sequential persuasive effectiveness and consumer processing routes await experimental validation. These findings carry implications for AI content strategy optimization, platform design, and emerging regulatory frameworks for AI-generated content labeling. Full article
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24 pages, 2044 KB  
Article
Evaluating the Structural Quality of Agricultural S&T Commercialization Policies: An Integrated Approach Combining Latent Dirichlet Allocation and the PMC Index
by Pingkai Wang, Mingwei Song, Mixue Liu and Shibo Chen
Sustainability 2026, 18(6), 2822; https://doi.org/10.3390/su18062822 - 13 Mar 2026
Viewed by 206
Abstract
Promoting the commercialization of agricultural science and technology (S&T) achievements is a critical pathway toward achieving agricultural sustainability and a key governance challenge in advancing global food security and the Sustainable Development Goals (SDGs). However, China faces a structural paradox: despite sustained expansion [...] Read more.
Promoting the commercialization of agricultural science and technology (S&T) achievements is a critical pathway toward achieving agricultural sustainability and a key governance challenge in advancing global food security and the Sustainable Development Goals (SDGs). However, China faces a structural paradox: despite sustained expansion of policy supply, the performance gains in technology commercialization remain limited. To uncover the underlying causes, this study integrates Latent Dirichlet Allocation (LDA) topic modeling with the Policy Modeling Consistency (PMC) index to conduct a systematic analysis of 82 central-level policy documents issued between 2015 and 2025. The findings reveal that policy attention is heavily concentrated on upstream R&D support, while insufficient emphasis is placed on downstream “last-mile” enablers—such as diffusion services, risk-sharing mechanisms, and intermediary capacity building. Moreover, many policies exhibit structural deficiencies in temporal specificity and multi-actor coordination, which hinder the formation of closed-loop implementation chains. The results suggest that policy structural inconsistency may be a key mechanism constraining policy effectiveness. By adopting a dual analytical lens of “attention allocation–structural design,” this study provides empirical evidence for optimizing policy formulation and enhancing institutional efficacy in agricultural S&T commercialization. Full article
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17 pages, 5402 KB  
Article
Fourth-Order Compact Finite-Difference Scheme with Discrete Sine Transform for Solving 2D Heat Conduction Equation with DBCs
by Chunming Liu and Xiaozhong Tong
Mathematics 2026, 14(6), 949; https://doi.org/10.3390/math14060949 - 11 Mar 2026
Viewed by 246
Abstract
Finite-difference approaches are widely employed to solve partial differential equations in numerous practical applications. However, their computational efficiency is often limited by the need to solve linear systems through matrix inversion or iterative solvers, a challenge that is particularly acute in high-dimensional problems. [...] Read more.
Finite-difference approaches are widely employed to solve partial differential equations in numerous practical applications. However, their computational efficiency is often limited by the need to solve linear systems through matrix inversion or iterative solvers, a challenge that is particularly acute in high-dimensional problems. Consequently, there is a growing demand for methods that ensure both high accuracy and computational efficiency. To address the two-dimensional (2D) heat conduction problem, we propose a novel hybrid technique that integrates a fourth-order implicit compact finite-difference approach with the discrete sine transform (DST). The incorporation of the DST significantly reduces the computational burden associated with solving the heat conduction equation on large grids. Detailed numerical experiments were conducted to evaluate this solver for 2D heat conduction equations subject to homogeneous Dirichlet boundary conditions (DBCs). The results demonstrate that the proposed method not only achieves substantial reductions in computational cost but also maintains a high level of numerical accuracy. All numerical experiments were performed on a computer running MATLAB R2024b. Full article
(This article belongs to the Special Issue Numerical Methods for Scientific Computing)
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48 pages, 1081 KB  
Article
Survival Probabilities for Correlated Drifted Brownian Motions via Exit from Simplicial Cones
by Tristan Guillaume
AppliedMath 2026, 6(3), 45; https://doi.org/10.3390/appliedmath6030045 - 10 Mar 2026
Viewed by 271
Abstract
This paper investigates the finite-horizon survival probability for a system of correlated arithmetic Brownian motions with heterogeneous drifts and volatilities, focusing on the event in which one component remains strictly below all others. Using a whitening transformation of the covariance structure, we reduce [...] Read more.
This paper investigates the finite-horizon survival probability for a system of correlated arithmetic Brownian motions with heterogeneous drifts and volatilities, focusing on the event in which one component remains strictly below all others. Using a whitening transformation of the covariance structure, we reduce the problem to the survival of a standard Brownian motion in a simplicial cone, characterized by its spherical cross-section. While explicit solutions are available in low dimensions, we address the computationally challenging tetrahedral angular case. We derive a semi-analytic formula for the survival probability via an eigenfunction expansion of the Dirichlet Laplace–Beltrami operator on this curved domain. For efficient implementation, we construct a diffeomorphism from the spherical tetrahedron to a fixed Euclidean tetrahedron, enabling the computation of angular eigenpairs through a stable finite-element scheme. For higher-dimensional regimes, we also introduce a covariance-based difficulty index and geometric bounds based on an inscribed spherical cap to assess spectral convergence and estimate long-time decay rates. Numerical experiments show that this offline–online approach achieves high accuracy and substantial speedups relative to Monte Carlo benchmarks. Full article
(This article belongs to the Section Probabilistic & Statistical Mathematics)
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34 pages, 7889 KB  
Article
Examining Topics and Trends in Cyber Aggression and Abuse: A Latent Dirichlet Allocation Analysis
by Amir Alipour Yengejeh and Larry Tang
Mathematics 2026, 14(6), 932; https://doi.org/10.3390/math14060932 - 10 Mar 2026
Viewed by 286
Abstract
Cyber aggression and abuse (CAA) has become a major interdisciplinary research area spanning psychology, communication, public health, and computer science. Existing reviews have largely focused on detection methods and model performance, offering limited insight into how CAA research themes have evolved over time [...] Read more.
Cyber aggression and abuse (CAA) has become a major interdisciplinary research area spanning psychology, communication, public health, and computer science. Existing reviews have largely focused on detection methods and model performance, offering limited insight into how CAA research themes have evolved over time at the field level. This study addresses this gap by, to the best of our knowledge, applying Latent Dirichlet Allocation (LDA) to 2309 Web of Science–indexed publications with English-language abstracts published between 2000 and 2024, providing a large-scale, longitudinal, and multi-level analysis of the literature. The model identifies 29 latent topics, which are organized using the User–Activity–Content (UAC) framework to link psychosocial research, platform-mediated behaviors, and computational detection approaches. Temporal analysis reveals a clear methodological transition: early dominance of survey-based and psychosocial themes gradually declines in relative prominence, while computational topics related to machine learning, deep learning, and pre-trained language models exhibit sustained growth, particularly after 2010. A Hot–Cold topic classification further distinguishes emerging, stable, and declining research directions. Journal-level, disciplinary, and geographic analyses reveal systematic differentiation across venues and regions, with complementary emphases on psychosocial and computational approaches. These findings provide a structured, field-level perspective on the evolution of CAA research and offer practical value for researchers, funding agencies, journal editors, and publishers by identifying dominant, emerging, and declining themes that can inform research prioritization, editorial planning, and strategic investment. Full article
(This article belongs to the Special Issue Statistics and Data Science)
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38 pages, 2678 KB  
Systematic Review
Integration of Artificial Intelligence into Human Resource Management in Manufacturing Enterprises: A Systematic Literature Review of Challenges, Approaches, and Evolution (2000–2025)
by Qunwei Wu, Xudong Gao and Anastassiya Lipovka
Sustainability 2026, 18(5), 2618; https://doi.org/10.3390/su18052618 - 7 Mar 2026
Viewed by 511
Abstract
With the advancement of digital technology and Industry 4.0, artificial intelligence (AI) is gradually embedded in human resource management and has become an important digital foundation to support the sustainable transformation of enterprises. However, the research in the manufacturing context, particularly through the [...] Read more.
With the advancement of digital technology and Industry 4.0, artificial intelligence (AI) is gradually embedded in human resource management and has become an important digital foundation to support the sustainable transformation of enterprises. However, the research in the manufacturing context, particularly through the challenge perspective at different levels, remains fragmented. This work represents a systematic review of 347 articles from Scopus and Web of Science from 2000 to 2025 and employs a dual-method analysis strategy embracing metrics and in-depth coding on 100 core publications. Excel, Bibliometrix, CiteSpace, Latent Dirichlet Allocation (LDA), and VOSviewer were utilized for quantitative analysis, while open–axial–selective coding of the Grounded theory approach was applied to generate qualitative results. The findings revealed six key challenges in integrating AI-HRM within manufacturing and six approaches to solve the identified issues. The Challenge–Approach Matching Matrix was constructed, illustrating the suitability of different pathways for addressing specific challenges. Analysis of thematic evolution in AI-HRM research resulted in the identification of three distinctive phases and demonstrated a consistent shift from technology-centric approaches towards human–machine collaboration. The primary contribution of this research lies in proposing a Multi-Level Embedded Framework providing a complex view of AI-HRM in a manufacturing sector at micro, meso, and macro levels. The absence of sustainable HR transformation through AI integration was identified as the critical challenge at the macro level. This research provides theoretical and practical implications for designing the sustainable HRM system based on ESG principles and favors the United Nations Sustainable Development Goals 9 and 12. Full article
(This article belongs to the Special Issue Achieving Sustainability Goals Through Artificial Intelligence)
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37 pages, 2784 KB  
Article
FedSMOTE-DP: Privacy-Aware Federated Ensemble Learning for Intrusion Detection in IoMT Networks
by Theyab Alsolami and Mohammad Ilyas
Sensors 2026, 26(5), 1592; https://doi.org/10.3390/s26051592 - 3 Mar 2026
Viewed by 291
Abstract
The Internet of Medical Things (IoMT) transforms healthcare through interconnected medical devices but faces significant cybersecurity threats, particularly intrusion and exfiltration attacks. Centralized intrusion detection systems (IDSs) require data aggregation, presenting privacy and scalability risks. This paper proposes FedEnsemble-DP, a privacy-aware Federated Learning [...] Read more.
The Internet of Medical Things (IoMT) transforms healthcare through interconnected medical devices but faces significant cybersecurity threats, particularly intrusion and exfiltration attacks. Centralized intrusion detection systems (IDSs) require data aggregation, presenting privacy and scalability risks. This paper proposes FedEnsemble-DP, a privacy-aware Federated Learning (FL) framework for decentralized intrusion detection in IoMT networks. The framework integrates three data balancing scenarios (Raw Imbalanced, Local SMOTE, Centralized SMOTE) with Differential Privacy (DP) and Secure Aggregation mechanisms. Extensive experiments on WUSTL-EHMS-2020 and CIC-IoMT-2024 datasets under non-IID settings (Dirichlet α = 0.3) demonstrate that models with strong privacy guarantees (ε = 3.0) frequently match or exceed non-private baselines. Key findings show Local SMOTE with ε = 3.0 achieved 94.60% accuracy and 0.9598 AUC, while Raw Imbalanced with ε = 3.0 attained 94.50% accuracy and 0.9494 AUC. Even with strict privacy (ε = 3.0), these results surpassed the non-private baseline (93.20% accuracy) in the raw scenario. Centralized SMOTE showed effectiveness but introduced training instability. These results indicate that local data balancing combined with calibrated DP noise can yield high detection performance while preserving privacy, effectively bridging security-performance and data confidentiality requirements in distributed healthcare networks. Full article
(This article belongs to the Special Issue Blockchain Technology for Internet of Things)
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17 pages, 484 KB  
Article
A Federated Learning-Based Network Intrusion Detection System for 5G and IoT Using Mixture of Experts
by Loukas Ilias, George Doukas, Vangelis Lamprou, Spiros Mouzakitis, Christos Ntanos and Dimitris Askounis
Electronics 2026, 15(5), 1057; https://doi.org/10.3390/electronics15051057 - 3 Mar 2026
Viewed by 399
Abstract
Fifth generation (5G) networks have significantly enhanced connectivity, speed, and reliability, transforming industries with faster and more efficient communication. The Internet of Things (IoT) has introduced unprecedented convenience and automation, revolutionizing sectors such as healthcare, finance, and smart infrastructure. However, both 5G networks [...] Read more.
Fifth generation (5G) networks have significantly enhanced connectivity, speed, and reliability, transforming industries with faster and more efficient communication. The Internet of Things (IoT) has introduced unprecedented convenience and automation, revolutionizing sectors such as healthcare, finance, and smart infrastructure. However, both 5G networks and IoT environments are experiencing a high frequency of attacks. Intrusion detection systems (IDSs) built on federated learning (FL) are being proposed to boost data privacy and security. However, these IDSs are related with the inherent drawbacks of FL, namely the existence of non-independently and identically (non-IID) distributed features and the machine learning model complexity. To address these limitations, we present a study that integrates a Mixture of Experts (MoE) into an FL setting in the task of intrusion detection. Specifically, to mitigate the issues of model complexity within the FL setting, we use a sparsely gated MoE layer consisting of a router/gating network and a set of experts. Only a subset of experts is selected via applying noisy top-k gating. To alleviate the issue of non-IID data, we adopt the Label-based Dirichlet Partition method, utilizing Dirichlet sampling with a hyperparameter α to simulate a label-based non-IID data distribution. Four FL strategies are employed. We perform our experiments on the 5G-NIDD and BoT-IoT datasets. Findings show that the proposed approach achieves competitive performance across both datasets under heterogeneous federated settings. Full article
(This article belongs to the Special Issue Advances in 5G and Beyond Mobile Communication)
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22 pages, 397 KB  
Article
A Boundary Control Problem for the Stationary Darcy–Brinkman–Jeffreys System
by Evgenii S. Baranovskii, Mikhail A. Artemov, Sergey V. Ershkov and Alexander V. Yudin
Mathematics 2026, 14(5), 843; https://doi.org/10.3390/math14050843 - 1 Mar 2026
Viewed by 345
Abstract
This paper deals with a boundary control problem for the Darcy–Brinkman–Jeffreys system describing 3D (or 2D) steady-state flows of an incompressible viscoelastic fluid through a porous medium. Applying the elliptic regularization method and arguments from the topological degree theory, we prove a theorem [...] Read more.
This paper deals with a boundary control problem for the Darcy–Brinkman–Jeffreys system describing 3D (or 2D) steady-state flows of an incompressible viscoelastic fluid through a porous medium. Applying the elliptic regularization method and arguments from the topological degree theory, we prove a theorem about the weak solvability of the corresponding boundary value problem under an inhomogeneous Dirichlet boundary condition. Using this theorem, we obtain sufficient conditions for the existence of optimal weak solutions minimizing a given cost function. Moreover, it is shown that the set of all optimal weak solutions is bounded and sequentially weakly closed in an appropriate function space. Full article
(This article belongs to the Special Issue Mathematical Dynamic Flow Models, 2nd Edition)
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20 pages, 9148 KB  
Article
DDR-PINN: A Dynamic Domain–Gradient Reweighting Physics-Informed Neural Network
by Shangpeng Lei, Balakayeva Gulnar, Chenghan Yang, Nadezhda Kunicina, Roberts Grants and Uldis Grunde
Appl. Sci. 2026, 16(5), 2366; https://doi.org/10.3390/app16052366 - 28 Feb 2026
Viewed by 292
Abstract
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by embedding physical conditions as soft penalties into the loss function. However, the coexistence of multiple loss components often leads to gradient conflicts, degrading convergence and solution accuracy. To address this issue, we propose [...] Read more.
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by embedding physical conditions as soft penalties into the loss function. However, the coexistence of multiple loss components often leads to gradient conflicts, degrading convergence and solution accuracy. To address this issue, we propose a dynamic domain–gradient loss reweighting PINN (DDR-PINN). The proposed method introduces a dual-residual reweighting mechanism based on gradient variations, where adaptive weights are derived from the L2 norm of the dot product between loss gradients and residuals. These weights are further normalized through a nonlinear hyperbolic tangent transformation, enabling dynamic and balanced reweighting of interior, initial, and boundary domain losses throughout training. Extensive numerical experiments on PDEs with both Dirichlet and Neumann boundary conditions demonstrate that the DDR-PINN consistently outperforms the standard PINN, APINN, and VI-PINN with the fewest trainable parameters. Full article
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