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Search Results (738)

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Keywords = Hidden Markov Models

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25 pages, 1791 KB  
Article
Data-Driven State Estimation for Nonlinear Stochastic Systems Using Gaussian Process-Based Adaptive Interacting Multiple Model Particle Filtering
by Xueqi Yuan and Qing Sun
Automation 2026, 7(3), 97; https://doi.org/10.3390/automation7030097 (registering DOI) - 18 Jun 2026
Viewed by 82
Abstract
This paper focuses on state estimation for nonlinear stochastic systems with multiple switching models, especially under challenging conditions where the model dynamics are unknown and the transition probability matrix is uniformly distributed. Gaussian process regression is employed to learn the unknown system dynamics [...] Read more.
This paper focuses on state estimation for nonlinear stochastic systems with multiple switching models, especially under challenging conditions where the model dynamics are unknown and the transition probability matrix is uniformly distributed. Gaussian process regression is employed to learn the unknown system dynamics from an offline discrete dataset and is integrated into an interacting multiple model particle filtering framework. GPR enables data-driven learning of both state transition and observation functions. To cope with model uncertainty and uninformative prior transition knowledge, particularly under uniformly initialized TPM, a dual-layer adaptive TPM update strategy based on hidden Markov model inference is further incorporated. Finally, the proposed method is validated through simulations and compared with IMMPF under different assumptions on system dynamics and TPMs. The results show that, even without prior knowledge of the system dynamics or precise TPM information, the proposed GP-AIMMPF maintains robust and accurate state estimation performance. Full article
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17 pages, 7519 KB  
Article
Genome-Wide Identification of the MYB Family in Morus atropurpurea and Functional Characterization of MaDIV for Its Possible Involvement in Anthocyanin Biosynthesis
by Xuefei Chen, Yixin Liang, Xingxing Liu, Baozhong Zhu, Chengli Zhou, Wei Fan and Aichun Zhao
Genes 2026, 17(6), 702; https://doi.org/10.3390/genes17060702 - 17 Jun 2026
Viewed by 236
Abstract
Background: Anthocyanin biosynthesis is tightly controlled by MYB transcription factors, yet the role of repressors, particularly those in the DIVARICATA-like (DIV) subfamily, remains poorly characterized. Methods: A genome-wide identification of MYB family members was performed in the mulberry (Morus atropurpurea [...] Read more.
Background: Anthocyanin biosynthesis is tightly controlled by MYB transcription factors, yet the role of repressors, particularly those in the DIVARICATA-like (DIV) subfamily, remains poorly characterized. Methods: A genome-wide identification of MYB family members was performed in the mulberry (Morus atropurpurea) genome using a hidden Markov model and BLAST-based searches. Putative MYB genes were phylogenetically classified, and their expression profiles were analyzed across three fruit developmental stages. A DIV-like R2R3-MYB candidate, MaDIV, was functionally characterized via subcellular localization, quantitative real-time PCR, and heterologous overexpression in tobacco. Results: A total of 145 MaMYB genes were identified and classified into 31 distinct subfamilies. MaDIV expression showed a progressive decline during fruit ripening, which significantly correlated with increasing anthocyanin accumulation. Heterologous overexpression of MaDIV in tobacco led to a 42% reduction in floral anthocyanin content compared with wild-type plants. Concomitantly, the expression of the key anthocyanin biosynthetic gene NtDFR was strongly suppressed, whereas the flavonol synthase gene NtFLS1 was significantly upregulated. Conclusions: These findings point to a possible involvement of MaDIV in the regulation of anthocyanin biosynthesis and provide preliminary evidence for the functional diversification of the DIV-like MYB subfamily in plants. The results contribute to a better understanding of the transcriptional control of fruit pigmentation in mulberry and related species. Full article
(This article belongs to the Section Plant Genetics and Genomics)
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20 pages, 2882 KB  
Article
Coupling Divergence Under Regime Switching: A Methodology for Structural Systemic Risk in Heterogeneous Subsystems
by Marin Pamukov and Nikolay Hinov
Entropy 2026, 28(6), 689; https://doi.org/10.3390/e28060689 - 15 Jun 2026
Viewed by 195
Abstract
Background: Systemic risk in heterogeneous multi-subsystem settings has been addressed by composite stress indices, spectral entropy of correlation matrices, and regime-switching copula models; none directly measures structural divergence between regime-conditional coupling matrices under an explicit hidden-regime model. Methods: We embed whitened subsystem indicators [...] Read more.
Background: Systemic risk in heterogeneous multi-subsystem settings has been addressed by composite stress indices, spectral entropy of correlation matrices, and regime-switching copula models; none directly measures structural divergence between regime-conditional coupling matrices under an explicit hidden-regime model. Methods: We embed whitened subsystem indicators in a two-regime Gaussian-copula hidden Markov process and define the coupling divergence as the matrix relative entropy between regime-conditional correlation matrices. We establish non-negativity, reduction to scalar Kullback–Leibler divergence between sorted eigenvalue distributions under commutativity, orthogonal invariance, and vanishing under the no-regime-switching null. Results: On stylized simulation, the framework separates regime-switching from single-regime null cases at an operating window T ∈ [250, 1000]; it isolates eigenbasis-rotation signals invisible to any sorted-eigenvalue method, with 99.9% of the divergence in the rotation regime residing in the non-commutative component; it tolerates Gaussian-copula misspecification under heavy-tailed processes with a quantifiable upward bias; and expectation–maximization convergence behavior serves as an auxiliary null-identification diagnostic. Conclusions: The framework composes existing primitives into a regime-to-regime structural divergence and isolates a compositional mode of regime change beyond scalar methods. Results are internal-validity claims on synthetic data; external validation on real multi-subsystem data is an open question. Full article
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21 pages, 2106 KB  
Article
A Bilevel Programming Framework for Demand Response Incentive Design with Non-Intrusive Load Monitoring-Based Flexibility Estimation
by Ye Ding, Kai Zhou, Xiuming He and Yuan Sun
Energies 2026, 19(12), 2818; https://doi.org/10.3390/en19122818 - 12 Jun 2026
Viewed by 145
Abstract
Demand response (DR) plays a key role in enhancing power system flexibility under increasing renewable penetration, yet most existing approaches rely on aggregate demand models that fail to capture appliance-level heterogeneity. A bilevel programming framework for DR incentive design incorporating non-intrusive load monitoring [...] Read more.
Demand response (DR) plays a key role in enhancing power system flexibility under increasing renewable penetration, yet most existing approaches rely on aggregate demand models that fail to capture appliance-level heterogeneity. A bilevel programming framework for DR incentive design incorporating non-intrusive load monitoring (NILM)-based flexibility estimation is proposed. A conditional factorial hidden Markov model (CFHMM) is used to disaggregate smart meter data and recover appliance-level consumption patterns, which are then mapped to willingness-to-accept (WTA) values to construct device-informed DR potential functions. These estimates are embedded in a bilevel optimization model, where a retailer determines optimal incentives while accounting for the endogenous impact of demand response on locational marginal prices through market clearing. The model is reformulated as a single-level mixed-integer linear program using Karush–Kuhn–Tucker (KKT) conditions. Case studies using real-world data and the IEEE test system show that the proposed framework produces more effective incentive strategies than aggregate DR modeling, leading to improved DR utilization and higher retailer profitability. Full article
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19 pages, 4341 KB  
Article
A Standardized Prism-Based TIRF Platform for Quantitative Single-Molecule Fluorescence Studies of Biomolecular Dynamics
by Arijit Patra, Lunden Melton, Lenwood S. Sawyer, Tate King and Sujay Ray
Biosensors 2026, 16(6), 331; https://doi.org/10.3390/bios16060331 - 10 Jun 2026
Viewed by 374
Abstract
Single-molecule Förster resonance energy transfer (smFRET) enables direct measurement of nanoscale conformational dynamics and heterogeneity in biomolecules, but quantitative interpretation of smFRET data critically depends on well-controlled excitation geometry, low background fluorescence, robust calibration, and reproducible data-analysis workflows. Prism-based total internal reflection fluorescence [...] Read more.
Single-molecule Förster resonance energy transfer (smFRET) enables direct measurement of nanoscale conformational dynamics and heterogeneity in biomolecules, but quantitative interpretation of smFRET data critically depends on well-controlled excitation geometry, low background fluorescence, robust calibration, and reproducible data-analysis workflows. Prism-based total internal reflection fluorescence (pTIRF) microscopy provides important advantages for such measurements by physically separating excitation and emission paths and generating a highly confined evanescent field, yet practical guidance for implementing reproducible, quantitative pTIRF systems remains fragmented. Here we present a comprehensive, standardized framework for the design, alignment, calibration, validation, and operation of a prism-based TIRF microscope optimized for single-molecule fluorescence measurements. We describe the complete optical architecture for dual-color excitation and detection, establish alignment invariants that ensure reproducible evanescent excitation and stable donor–acceptor channel registration, and detail surface preparation, flow control, and photostabilization strategies required for reliable long-term imaging. Quantitative benchmarking protocols are introduced to evaluate signal-to-noise ratio, photobleaching kinetics, and spectral crosstalk, providing objective criteria for defining optimal operating conditions and instrument performance limits. Finally, we integrate these experimental procedures with an end-to-end single-molecule data-analysis workflow encompassing channel registration, automated and manual trajectory selection, FRET calculation, and kinetic analysis using hidden Markov modeling. The utility of the platform is demonstrated through smFRET measurements of conformational dynamics in a model nucleic acid system. Together, this work provides a reproducible and accessible methodology for implementing prism-based TIRF microscopy as a robust quantitative platform for single-molecule fluorescence studies across a wide range of biomolecular systems. Full article
(This article belongs to the Special Issue Single-Molecule Biosensors: Recent Advances and Future Challenges)
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16 pages, 2259 KB  
Article
Variational Bayesian DOA Estimation Based on Hidden Markov Models
by Yan Lu, Yaxin Liu, Xiaopeng Wang and Mai Lu
Electronics 2026, 15(12), 2508; https://doi.org/10.3390/electronics15122508 - 7 Jun 2026
Viewed by 156
Abstract
Aiming at the direction-of-arrival (DOA) estimation problem in pulse-disturbed and wireless transmission environments, this paper presents a variational Bayesian DOA estimation approach utilizing a Hidden Markov Model (HMM). First, a method for joint sparsity of signals and noise is used to build a [...] Read more.
Aiming at the direction-of-arrival (DOA) estimation problem in pulse-disturbed and wireless transmission environments, this paper presents a variational Bayesian DOA estimation approach utilizing a Hidden Markov Model (HMM). First, a method for joint sparsity of signals and noise is used to build a hierarchical Bayesian structure and, by means of mixed-noise modeling, to simulate practical scenarios. Next, a Forward-Backward algorithm for Hidden Markov Models is used to model the changes in noise state over time and thus capture the temporal correlation of impulse disturbances. Finally, it computes the posterior probability via variational inference and iteratively adjusts the arrival angle for higher accuracy. Simulation results show that, in the presence of mixed-noise conditions, this scheme has achieved relatively accurate direction-of-arrival (DOA) estimation with lower computational costs compared to other Bayesian learning methods. Full article
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36 pages, 1083 KB  
Article
Horizon- and Regime-Dependent Performance of GARCH-Type Models: Evidence from Volatility Forecasting in a Frontier Market
by Abraham Kisembe Wawire, Christine Nanjala Simiyu, Munene Laiboni and Rogers Ochenge
Int. J. Financial Stud. 2026, 14(6), 148; https://doi.org/10.3390/ijfs14060148 - 4 Jun 2026
Viewed by 467
Abstract
In frontier markets, financial volatility exhibits long-memory properties and regime-dependent asymmetries that standard linear models do not capture. This leads to inaccuracies in forecasting risk when a single model is applied across regimes. This study investigates the horizon- and regime-dependent performance of volatility [...] Read more.
In frontier markets, financial volatility exhibits long-memory properties and regime-dependent asymmetries that standard linear models do not capture. This leads to inaccuracies in forecasting risk when a single model is applied across regimes. This study investigates the horizon- and regime-dependent performance of volatility models within a horizon- and regime-sensitive evaluation framework that applies single-regime Generalized Autoregressive Conditional Heteroscedasticity (GARCH) variants alongside a Hidden Markov Model (HMM). We evaluate the predictive accuracy of GARCH, Exponential GARCH (EGARCH), Glosten-Jagannathan-Runkle GARCH (GJR-GARCH), Asymmetric Power ARCH (APARCH), Fractionally Integrated GARCH (FIGARCH), and an HMM. Diebold–Mariano test statistics reveal that predictive superiority is sensitive to the chosen benchmark. When EGARCH is the benchmark, results highlight the importance of leverage effects, whereas a FIGARCH benchmark demonstrates that short-memory models are rejected as horizons increase. While short-memory models capture immediate clustering, FIGARCH maintains stable performance via hyperbolic decay. HMM provides a superior in-sample fit by capturing transitions between calm and turbulent regimes. Economic validation through Value-at-Risk (VaR) and Expected Shortfall (ES) backtesting indicates that FIGARCH and APARCH offer more reliable coverage for early warning systems during market stress. The findings emphasize that forecasting in a frontier market requires asset-specific approaches where benchmark selection dictates the interpretation of model superiority. Full article
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17 pages, 999 KB  
Article
A Unified Real Options Framework for Natural Gas Storage: Integrating Market Regimes and Cross-Market Spillovers
by Prosper Lamothe Fernández, Fernando Gallardo Olmedo and Hamidreza Abshenasan
Commodities 2026, 5(2), 11; https://doi.org/10.3390/commodities5020011 - 29 May 2026
Viewed by 275
Abstract
Natural gas markets exhibit violent, non-linear volatility regimes. The 2022 energy crisis introduced persistent supply shocks and cross-Atlantic spillover effects. Traditional valuation models assume single-regime environments; consequently, they systematically misprice storage assets during extreme stress. We propose a valuation framework tailored to these [...] Read more.
Natural gas markets exhibit violent, non-linear volatility regimes. The 2022 energy crisis introduced persistent supply shocks and cross-Atlantic spillover effects. Traditional valuation models assume single-regime environments; consequently, they systematically misprice storage assets during extreme stress. We propose a valuation framework tailored to these specific market volatilities. By integrating a hidden Markov model (HMM) and Diebold–Yilmaz (DY) spillover indices into a stochastic dynamic programming (SDP) engine, the framework isolates the persistence of stressed market conditions. The model captures structural arbitrage opportunities. We demonstrate a 197 percent net present value (NPV) premium over conventional benchmarks using synthetic data. The optimal policy expands inventory holding periods during high spillover intensity. The algorithm executes decisions with sub-millisecond latency. This approach provides a computationally viable tool for high-frequency risk management. Full article
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38 pages, 1157 KB  
Article
Minification Integer-Valued Split-BREAK Process with Power Series Innovations and Application in Fire Safety Dynamics
by Vladica S. Stojanović, Nikola Mitrović, Kristina Tomović, Hassan S. Bakouch and Shuhrah Alghamdi
Axioms 2026, 15(6), 388; https://doi.org/10.3390/axioms15060388 - 22 May 2026
Viewed by 224
Abstract
This manuscript introduces a new class of count time series models, referred to as the minification integer-valued Split-BREAK (MIN–SB) process. The proposed framework extends the Split-BREAK modeling philosophy to the integer-valued setting and provides a flexible mechanism for capturing rare events, zero inflation, [...] Read more.
This manuscript introduces a new class of count time series models, referred to as the minification integer-valued Split-BREAK (MIN–SB) process. The proposed framework extends the Split-BREAK modeling philosophy to the integer-valued setting and provides a flexible mechanism for capturing rare events, zero inflation, and structural regime changes frequently observed in safety-related data. The main stochastic properties of the MIN–SB process are derived, including stationarity conditions, explicit moment structure, and correlation dynamics. A key theoretical result reveals an implicit hidden Markov structure underlying the observable process, providing a structural explanation for zero clustering observed in rare-event count processes. Parameter estimation is developed using a simulated method of moments (SMM) approach based on zero-related statistics, and the asymptotic properties of the resulting estimators are established. A Monte Carlo simulation study demonstrates favorable finite-sample performance of the proposed estimation procedure. The practical usefulness of the model is illustrated through an empirical application to time series of injuries and fatalities caused by fire accidents in Serbia. The results show that the MIN–SB specification provides a flexible and accurate framework for modeling zero-inflated count processes arising in fire safety dynamics. Full article
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30 pages, 4268 KB  
Article
A Bumblebee-Inspired Spatial Memory Navigation Framework for Robotic Odor Source Localization
by Tianyi Xu, Yizhu Guo, Zhigang Wu and Jianing Wu
Biomimetics 2026, 11(5), 350; https://doi.org/10.3390/biomimetics11050350 - 18 May 2026
Viewed by 402
Abstract
Odor source localization in turbulent environments remains a major challenge for autonomous robots, as odor plumes are highly intermittent, spatially fragmented, and often lack stable concentration gradients. Here, we propose a bio-inspired navigation framework that translates key principles of bumblebee olfactory cognition into [...] Read more.
Odor source localization in turbulent environments remains a major challenge for autonomous robots, as odor plumes are highly intermittent, spatially fragmented, and often lack stable concentration gradients. Here, we propose a bio-inspired navigation framework that translates key principles of bumblebee olfactory cognition into robotic decision-making. First, classical conditioning and olfactorily triggered spatial memory experiments demonstrated that bumblebees could form robust odor memories and that training frequency is positively correlated with both proboscis extension response retention and spatial directional preference. Based on these biological findings, a bio-inspired navigation framework, termed Bio-Nav, is constructed by integrating a Partially Observable Markov Decision Process, a Hidden Markov Model, short-term memory, long-term directional reference memory, fuzzy inference, and value iteration. High-fidelity two-dimensional turbulent simulations show that the proposed algorithm substantially outperforms moth-inspired search, Infotaxis, and standard POMDP-based navigation. In 100 Monte Carlo trials, Bio-Nav achieved a success rate of 96.0%, an average of 20.3 search steps, an average path length of 155.1 cm, and a path-to-straight-line distance ratio of 1.6. Even under strong turbulence, the success rate remained above 91%. These results indicate that memory–perception coupling, inspired by bumblebee navigation, provides an effective and robust strategy for odor source localization in complex turbulent environments, offering a generalizable principle for bio-inspired robotic search under uncertainty. Full article
(This article belongs to the Special Issue Bio-Inspired Robotics and Applications 2026)
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19 pages, 5117 KB  
Article
SD-Fuzz: A State-Aware Industrial Control Protocol Fuzzing Framework Based on Diffusion Models
by Hao Tang, Zhiyong Zhang, Kejing Zhao and Zhi Liang
Electronics 2026, 15(10), 2156; https://doi.org/10.3390/electronics15102156 - 17 May 2026
Viewed by 305
Abstract
Current fuzzing techniques for industrial control protocols (ICPs) encounter notable challenges, including model training instability, limited sample diversity, and the inability to manage complex state dependencies in protocol interactions. To address these issues, this paper presents SD-Fuzz, a state-aware fuzzing framework that integrates [...] Read more.
Current fuzzing techniques for industrial control protocols (ICPs) encounter notable challenges, including model training instability, limited sample diversity, and the inability to manage complex state dependencies in protocol interactions. To address these issues, this paper presents SD-Fuzz, a state-aware fuzzing framework that integrates a discrete denoising diffusion probabilistic model (DDPM) with an online Hidden Markov Model (HMM). The discrete DDPM is designed to generate syntactically valid and diverse protocol messages using cosine noise scheduling and Denoising Diffusion Implicit Model (DDIM) sampling, while the HMM performs unsupervised learning of state transitions from real traffic to guide the creation of logically consistent multi-step interaction sequences. The framework is evaluated on three representative Modbus/TCP slave implementations. Evaluations based on 5 h benchmark campaigns across multiple independent runs indicate that SD-Fuzz achieves a mean test case recognition rate (TCRR) of 91.3% and an HMM-inferred state transition coverage of 50.1%, exhibiting statistically significant improvements over the evaluated baselines. Furthermore, an extended 8 h vulnerability mining campaign demonstrates its capability to trigger deep-seated exceptions, including buffer overflows and protocol state violations, which are typically challenging to access using traditional stateless approaches. This work illustrates the feasibility of combining diffusion-based generation with lightweight state inference for automated vulnerability discovery in industrial control systems. Directions for future work include validation on physical programmable logic controller (PLC) hardware to acquire internal code coverage feedback. Full article
(This article belongs to the Section Computer Science & Engineering)
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28 pages, 1475 KB  
Article
Authentic SEC Data and Regime-Aware Ensemble Learning for Corporate Cash Flow Forecasting
by Amjed Mohammed Fahad and Naeem Sabah Jearah
J. Risk Financial Manag. 2026, 19(5), 333; https://doi.org/10.3390/jrfm19050333 - 5 May 2026
Viewed by 795
Abstract
Financial forecasting research often prioritizes methodological sophistication over the authenticity of underlying training data. This study quantifies the “estimation–reality divide” by comparing models trained on estimated quarterly data versus genuine, re-stated SEC-reported cash flows. Using 244 firm-quarter observations from five large-cap U.S. technology [...] Read more.
Financial forecasting research often prioritizes methodological sophistication over the authenticity of underlying training data. This study quantifies the “estimation–reality divide” by comparing models trained on estimated quarterly data versus genuine, re-stated SEC-reported cash flows. Using 244 firm-quarter observations from five large-cap U.S. technology firms (Microsoft, Apple, Amazon, Alphabet, Meta; 2011–2024), this case study shows that, within this specific set of firms, models trained on estimated data exhibit a large optimistic bias. For a state-of-the-art ensemble, this bias appears as a 43% lower error rate (4.5% vs. 7.9%) compared to the same model trained on authentic data. To address this, we introduce a forecasting framework that combines (i) a Hidden Markov Model for detecting economic regimes, (ii) models tailored to each regime (XGBoost and LSTM with attention), and (iii) a dynamic ensemble that adapts to recent performance. In realistic out-of-sample tests, our framework achieves a 7.9% error rate on authentic data, significantly outperforming standard benchmarks. We also show that a meta-learning approach reduces the data needed for a new firm by about 35% while improving accuracy by 24%. In plain terms, using real SEC data leads to more honest and useful forecasts than relying on estimated data. All claims are strictly limited to the five large-cap U.S. technology firms analyzed (Microsoft, Apple, Amazon, Alphabet, Meta). No claims of generalizability to other sectors, firm sizes, or markets are made or implied. Validation on broader samples is required before extending these findings. Full article
(This article belongs to the Section Financial Technology and Innovation)
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22 pages, 1001 KB  
Review
Antivirus Systems: Detection Methods and Architectures
by Paul A. Gagniuc
Algorithms 2026, 19(5), 345; https://doi.org/10.3390/a19050345 - 1 May 2026
Viewed by 1184
Abstract
Antivirus systems have evolved from static pattern matchers into complex algorithmic ecosystems that encapsulate the broader logic of modern cybersecurity. This review deconstructs their internal architecture, tracing the transition from deterministic string-matching automata to probabilistic, behavioral, and cloud-assisted paradigms. Foundational modules such as [...] Read more.
Antivirus systems have evolved from static pattern matchers into complex algorithmic ecosystems that encapsulate the broader logic of modern cybersecurity. This review deconstructs their internal architecture, tracing the transition from deterministic string-matching automata to probabilistic, behavioral, and cloud-assisted paradigms. Foundational modules such as scanners, heuristic analyzers, behavioral monitors, and sandbox environments operate as interconnected computational strata, forming adaptive feedback loops that mirror principles of distributed intelligence. Signature-based methods, such as Aho-Corasick, Boyer-Moore, and Wu-Manber, remain core to real-time filtering, while probabilistic reasoning through Bayesian inference, Markov modeling, and Hidden Markov Models extends detection to polymorphic and metamorphic threats. Behavioral analysis, empowered by Support Vector Machines, deep neural architectures, and temporal models, enables semantic inference over system-call graphs and runtime telemetry. Moreover, cloud-assisted frameworks integrate federated learning and global reputation graphs, which transform detection into a collective intelligence process. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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27 pages, 3810 KB  
Article
Real-Time Energy Management of a Series Hybrid Wheel Loader Using Operating-Stage Recognition and ISSA-Optimized ECMS
by Tao Yu, Zhiguo Lei, Yubo Xiao and Xuesheng Shen
Energies 2026, 19(9), 2149; https://doi.org/10.3390/en19092149 - 29 Apr 2026
Viewed by 480
Abstract
Driven by increasingly stringent requirements for energy saving and emission reduction in non-road machinery, hybrid wheel loaders have attracted growing attention as a practical pathway toward cleaner construction equipment. However, conventional energy management strategies often show limited adaptability to highly transient operating cycles [...] Read more.
Driven by increasingly stringent requirements for energy saving and emission reduction in non-road machinery, hybrid wheel loaders have attracted growing attention as a practical pathway toward cleaner construction equipment. However, conventional energy management strategies often show limited adaptability to highly transient operating cycles and struggle to balance fuel economy, real-time applicability, and battery charge sustainability. To address these issues, this study proposes an improved sparrow-search-algorithm-based equivalent consumption minimization strategy (ISSA-ECMS) for a series hybrid wheel loader. A quasi-static powertrain model was established, while ISSA was used to optimize both the hyperparameters of a Convolutional Neural Network-Long Short-Term Memory (CNN–LSTM) stage-recognition model and the stage-dependent ECMS parameters. A hidden Markov model (HMM)-based post-processing framework was further introduced to improve temporal consistency in operating-stage recognition. The results show that the optimized ISSA-CNN–LSTM achieved 93.22% accuracy, 93.08% Macro-F1, and 93.21% Weighted-F1, while HMM refinement further improved recognition accuracy from 94.02% to 97.92%. In energy management simulations, ISSA-ECMS maintained the terminal state of charge (SOC) at 50.0069%, reduced fuel consumption by 2.1% and 1.4% compared with conventional ECMS and A-ECMS, respectively, and increased the proportion of engine operating points in the economical region to 77.549%. Compared with dynamic programming, its fuel-consumption increase was only 0.28%, while retaining online applicability. These results demonstrate that the proposed method provides an effective and practical solution for real-time energy management of series hybrid wheel loaders. Full article
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31 pages, 878 KB  
Article
A Class of Causal 2D Markov-Switching ARMA Models: Probabilistic Properties and Variational Estimation
by Khudhayr A. Rashedi, Soumia Kharfouchi, Abdullah H. Alenezy and Tariq S. Alshammari
Axioms 2026, 15(5), 302; https://doi.org/10.3390/axioms15050302 - 22 Apr 2026
Viewed by 304
Abstract
This paper introduces a rigorous class of two-dimensional Markov-switching autoregressive moving-average (2D MS-ARMA) models for spatial lattice data exhibiting regime-dependent dynamics. The switching mechanism is governed by a latent causal Markov random field that drives spatial transitions between regime-specific autoregressive and moving-average structures. [...] Read more.
This paper introduces a rigorous class of two-dimensional Markov-switching autoregressive moving-average (2D MS-ARMA) models for spatial lattice data exhibiting regime-dependent dynamics. The switching mechanism is governed by a latent causal Markov random field that drives spatial transitions between regime-specific autoregressive and moving-average structures. We provide sufficient conditions for the existence of a strictly stationary solution through the top Lyapunov exponent associated with a sequence of random matrices obtained from a state-space representation constructed along the lexicographic order. For the first-order bidirectional specification, we derive explicit spectral conditions linking stationarity to the regime-dependent spectral radii. Sufficient conditions ensuring the existence of finite second-order moments are also provided. Parameter estimation is carried out using a variational expectation–maximization (VEM) algorithm based on a mean-field approximation of the posterior distribution of the hidden regimes. The E-step yields closed-form coordinate ascent updates, while the M-step relies on gradient-based numerical optimization with derivatives computed via recursive differentiation. Under increasing-domain asymptotics, we discuss the consistency and asymptotic behavior of the variational estimator. The proposed framework fills a methodological gap between classical one-dimensional Markov-switching ARMA models and spatial autoregressive structures by extending regime-switching theory to multi-indexed processes with rigorous probabilistic foundations. It provides a comprehensive basis for statistical inference, model diagnostics, and prediction in spatially heterogeneous environments. Full article
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