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  • Discrete-time Markov Chain
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Articles published on Markov Chain Model

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  • Research Article
  • 10.1038/s41598-026-44230-z
Spatiotemporal evolution and spatial differentiation of carbon emission intensity in the Chinese transport sector.
  • Mar 15, 2026
  • Scientific reports
  • Yongping Tang + 1 more

Accurately identifying the spatiotemporal evolution and spatial differentiation of carbon emission intensity in the transport sector is essential for formulating region-specific carbon reduction policies. This study develops an analytical framework that integrates both static and dynamic perspectives to examine spatial disparities in transport sector carbon emission intensity. From a static perspective, the Dagum Gini coefficient is employed to quantify spatial differences and their sources of transport carbon emission intensity. From a dynamic perspective, kernel density estimation is applied to depict the evolution trajectories of transport carbon emission intensity. Furthermore, the traditional Markov chain model is refined to construct a spatial Markov chain model that accounts for spatial adjacency, enabling identification of persistence and spatial spillover effects. The empirical results indicate that (1) The carbon emission intensity of the transport sector in China presents an overall declining trend with significant spatial heterogeneity among provinces. Regional disparities have expanded, with the largest gap between the eastern and western regions, where inter-regional differences contribute an average of 47.374% to total disparity, representing the main source of variation. (2) The carbon emission intensity in the national, eastern, and central regions tends to converge gradually, while the western region shows a pattern of initial convergence followed by renewed divergence. Within each region, several provinces maintain carbon emission intensity levels significantly higher than the average, forming a clear spatial gradient structure. (3) The traditional Markov chain analysis reveals evident persistence and club convergence in transport carbon emission intensity. The spatial Markov chain analysis further shows that neighboring regions strongly influence local transition probabilities, demonstrating spatial spillover and path dependence effects. Hypothesis testing confirms the necessity of incorporating spatial dependence into the analysis. Based on these findings, this study proposes that carbon reduction strategies in the transport sector should be tailored to regional disparities and spatial interdependencies, aiming to enhance overall mitigation efficiency and foster coordinated governance.

  • Research Article
  • 10.1080/08874417.2026.2637477
Human–Robot Interactive Performance Analysis with Enhanced Metacognition
  • Mar 12, 2026
  • Journal of Computer Information Systems
  • Michael Do + 2 more

ABSTRACT This study investigates integrating metacognition into human–robot interaction (HRI) systems to improve reliability, efficiency, and trust. As HRI deployments expand, performance regulation under uncertainty becomes critical. Prior work has examined metacognition largely through behavioral observation, with limited system-level models that quantify operational impact. We address this gap by proposing a representative Markov chain model to evaluate metacognitive effects under deterministic and stochastic conditions. Using statistical analysis and probabilistic modeling, we measure impacts on machine accuracy and efficiency over extended operation. Experiments show metacognitive-enabled systems achieve a 59.29% reduction in errors and inefficiencies, with an 18.67% increase in execution time, indicating a favorable performance tradeoff. We further conceptualize metacognition as a quantifiable decision-regulation layer rather than an interface-level construct. The framework offers a scalable analytical basis for designing more dependable and trustworthy HRI systems in complex, information-intensive environments.

  • Research Article
  • 10.51594/csitrj.v7i3.2222
Implementing a hybrid compliance–AI cybersecurity model for unified protection of banking and DeFi systems in Brazil
  • Mar 11, 2026
  • Computer Science & IT Research Journal
  • Philip Adu

This study develops and evaluates a hybrid Compliance–AI cybersecurity model for unified protection of traditional banking and decentralized finance (DeFi) systems in Brazil. Using publicly available data from the NIST Cybersecurity Framework, DeFi exploit repositories (REKT and DeFiLlama), Elliptic crypto-transaction graphs, IEEE-CIS fraud data, DARPA Transparent Computing datasets, and Monte Carlo–simulated cross-domain attack scenarios, the research applies hierarchical clustering, supervised learning, Markov chain modeling, and stochastic simulation. Results show that 45% of banking controls are transferable or hybridizable to DeFi, that embedding machine-readable compliance features improves ROC–AUC from 0.842 to 0.914 and reduces false positives by nearly 47%, and that bidirectional orchestration lowers escalation probability by over 54%. Monte Carlo analysis further indicates a 62% reduction in tail financial risk under the hybrid architecture. The study recommends machine-readable regulation, compliance-aware AI deployment, orchestrated enforcement layers, and expanded RegTech and SupTech adoption to strengthen systemic financial cybersecurity. Keywords: Compliance–AI Integration, Financial Cybersecurity, Decentralized Finance, Machine-Readable Regulation, Systemic Cyber Risk.

  • Research Article
  • 10.1007/s11356-026-37607-0
Land use and land cover change dynamics and prediction scenario in the Mahananda River basin: insights into environmental transformations.
  • Mar 10, 2026
  • Environmental science and pollution research international
  • Payel Bhuin + 1 more

Globally, land use land cover (LULC) changes are recognized as a key factor contributing to environmental changes. Understanding the LULC changes in river basin areas is essential for river basin management. The present study aims to analyze LULC changes from 1994 to 2024 in the lower part of the Mahananda River basin and predict future LULC scenarios for 2034. The study cast off Landsat imagery and random forest (RF) classification technique for past LULC classification, while the Cellular Automata Markov Chain (CA-MA) model was employed for future LULC prediction. Furthermore, a statistical technique, Receiver Operating Characteristics (ROC), was utilized for CA-MC model validation. Results highlight a substantial reduction of vegetation cover of 2249.7 km2 and barren land by 1774.08 km2, while cultivated lands, settlement, and water body increased by 3389.75 km2, 831.81 km2, and 440.8 km2, respectively, over the last three decades, revealing the influences of both natural disturbance and anthropogenic activities. The LULC classification's accuracy was assessed using Kappa coefficient and these values are above 80%, indicating that the LULC classifications in this study are highly reliable. The prediction results reveal a further decrease of vegetation cover at 503.53 km2, a continuous increase of cultivation land at 4725.29 km2, and a settlement area of 919.85 km2 over the future decades. The ROC value of 0.71 suggests that the CA-MC model performs reliably in predicting future LULC scenarios, demonstrating acceptable model accuracy. These comprehensive assessments aid in the creation of suitable land management plans and policies to accomplish or uphold sustainable development in the Mahananda River basin.

  • Research Article
  • 10.53894/ijirss.v9i3.11333
Markov-based algorithms for wireless sensor network: Theoretical insights and python implementation
  • Mar 6, 2026
  • International Journal of Innovative Research and Scientific Studies
  • Kian Meng Yap + 3 more

The study concentrates on improving the dependability and operational efficacy of LoRa-based Wireless Sensor Networks (WSNs), which are extensively utilized in IoT applications, especially for long-range private networks. It seeks to deal with the problems that arise when a single node or communication line fails, which can have a big effect on network performance. The research utilizes a Markovian matrix theoretical framework to examine and simulate the behavior of LoRa-based Wireless Sensor Networks (WSNs), incorporating states such as Sleep (S), Idle (I), Transmit (T), and Receive (R) mode. A Python software program was created to put this model into action, allowing for testing and simulation with 50 fake data sets. The method stresses that the network should always be running, that sensor nodes should be replaced quickly, and that the network should be able to handle failures of individual nodes. The simulations indicate that using the Markov chain model in conjunction with detailed step-by-step math computation may yield a more accurate analysis of the data sets. The methodology also helps you evaluate protocols, change control, look at scalability, and make informed choices about how to build a network. This work offers practical benefits for the design, deployment, and maintenance of LoRa-based WSNs in real-world IoT scenarios. It supports network administrators and engineers in predicting power consumption, designing resilient protocols, scaling networks efficiently, and implementing adaptive control measures to ensure continuous and dependable operation. The integration of Markov chain mathematical modeling with Python-based simulation provides a robust solution for ensuring reliable operation of LoRa-based WSNs. The approach mitigates the impact of node failures, supports rapid recovery, and maintains network integrity.

  • Research Article
  • 10.1093/sysbio/syag017
Tensor cores unlock efficient and lower-energy massive parallelization on phylogenetic trees.
  • Mar 3, 2026
  • Systematic biology
  • Karthik Gangavarapu + 6 more

Massively parallel algorithms leveraging graphics processing units (GPUs) have significantly accelerated inference in statistical phylogenetics, with applications in understanding pathogen evolution, population dynamics, natural selection, and evolutionary timescales using ancient genomes. Continued advancements in GPU hardware necessitate innovative algorithms to fully exploit their potential. Here, we introduce three novel algorithms that accelerate matrix multiplication operations using tensor cores on NVIDIA GPUs to calculate the observed sequence data likelihood and the gradient of the log-likelihood with respect to branch-length-specific parameters under continuous-time Markov chain models of evolution. The algorithms presented in this paper deliver 2 to 3-fold gains in performance for amino acid and codon models compared to existing GPU-based massively parallel algorithms. Notably, these performance gains are accompanied by a ~2-fold reduction in energy usage, demonstrating the potential of these algorithms to lower the carbon footprint of evolutionary computing. We make our new algorithms available to the broader phylogenetics community through the high-performance, open source library BEAGLE v4.0.0.

  • Research Article
  • 10.64497/jssci.137
A Bayesian two-state Markov chain model with categorical responses: An application to climatic conditions for crop growth
  • Feb 27, 2026
  • Journal of Statistical Sciences and Computational Intelligence
  • V Adah + 3 more

In this study, Bayesian estimation procedure is presented especially for a binary Markov chain model under the assumption that the prior for had non- informative and informative prior distribution when the number of unfavourable climatic periods for the growth of the crop is more than the favourable period. Thus, a sequence of logical connectives was used to combine climatic variable namely , rainfall and temperature to obtain favourable and unfavourable crop growth conditions for the Pearl millet. Bayed factor revealed the that probability estimates obtained using the informative prior performed better than those obtained using the non-informative prior. There is a lower probability, 0.4227 of a favourable climate for the pearl millet growth, indicating that climate change has an adverse effect on the crop.

  • Research Article
  • 10.1287/trsc.2024.0690
Digging Deep: Finding and Maximizing the Throughput Capacity of Multideep Storage Systems
  • Feb 24, 2026
  • Transportation Science
  • Timo Lehmann + 1 more

Multideep storage systems are space-efficient storage solutions for a variety of industries and applications, such as in retail, spare parts and pharmaceutical logistics, and container terminals. They include robotic compact storage and retrieval (RCS/R) and multideep automated storage and retrieval (AS/R) systems. In such systems, multiple loads can be stored behind or above each other in a single lane, which leads to high space utilization. However, loads must be reshuffled if they block a requested load. This increases the command cycle time. We use Markov-chain models to estimate the steady state of the storage system and derive the travel time, which is then used in a closed queueing network to estimate the throughput capacity with a given number of robots. We built these models using four storage assignment strategies, three load reshuffling strategies, and two retrieval load selection strategies, incorporating the access frequency of the products and allowing multiple stored loads per product. Four strategy combinations are analyzed, including the current AutoStore strategy. We find that when information about the access frequency and number of loads per product is available, the throughput capacity can be increased significantly by properly storing and reshuffling loads to better positions. Based on the throughput models, we optimize the rack layout yielding maximum throughput capacity for two industry cases. Furthermore, we provide managerial insights on storage assignment, reshuffle, and retrieval load selection strategies for multideep storage systems. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0690 .

  • Research Article
  • 10.1080/00207543.2026.2632695
Enhancing operational performance in textile manufacturing: impact of deep learning-based defect detection
  • Feb 18, 2026
  • International Journal of Production Research
  • Artur Carvalho + 2 more

Quality performance in manufacturing has a direct influence on efficiency, generated waste, and costs. In collaboration with a textile manufacturer as a case study, this paper develops an automated defect detection system for a weaving process and evaluates its impact on operational performance. The system identifies defects immediately at their onset and prevents their propagation to subsequent fabric and production stages. A deep learning image classification model is developed, with six well-established network architectures being compared, leveraging a non-invasive image acquisition method that averts machinery disturbances for data collection. Based on the best-performing model, key indicators of operational performance are estimated using Markov Chain modelling, addressing a gap in linking model performance to operational impacts. Notable operational gains are demonstrated, namely a cost reduction of 1.3% and over 90% of waste reduction. A sensitivity analysis guides the definition of the image acquisition frame rate to minimise false alarms and shows that different operational indicators are impacted differently by different predictive performance metrics, affecting model selection. This research not only underscores the potential of integrating deep learning into textile production but also guarantees the effective communication of its impact to industry stakeholders, thus offering valuable practical insights to enhance operational performance.

  • Research Article
  • 10.1038/s41598-026-39708-9
Research on online EDI order scheduling optimization strategy in manufacturing enterprises based on time-varying Markov chains.
  • Feb 10, 2026
  • Scientific reports
  • Qiqige Wulan

In the era of Industry 5.0 and artificial intelligence, with the continuous development of online EDI orders, manufacturing enterprises adopting a combined online and offline order acceptance model face the challenge of optimizing production scheduling for online EDI production lines. The primary difficulties stem from time-varying order demand and the unique service paradigm of online scheduling. To address this decision-making problem, this study first models the online EDI production line service system within the ERP framework as a resource-sharing queue. Time-varying Markov chains and the uniformization method are employed to model and analyze key performance indicators, including order sojourn time, queue length, and production line overtime. Subsequently, building upon this system evaluation methodology, a heuristic algorithm based on Variable Neighborhood Search (VNS) is proposed to solve the production line scheduling problem. Finally, numerical experiments are conducted using real production order data from a traditional manufacturing enterprise to validate the accuracy of the time-varying Markov chain modeling. The results demonstrate that the proposed algorithm yields scheduling solutions superior to the actual schedules generated by the factory's ERP system. This leads to more rational allocation of production line working hours, reduced order sojourn times, controlled order backlog within the system, and exhibits strong robustness. The research presented holds practical significance for enhancing the operational management of online EDI order systems in traditional industrial manufacturing enterprises. .

  • Research Article
  • 10.1038/s41598-026-38544-1
Remote sensing and GIS-based modelling of land use dynamics and urban flood risk in Lagos megacity for future flood mitigation.
  • Feb 10, 2026
  • Scientific reports
  • Opeyemi Aniramu + 2 more

This study investigates changes in land use and land cover (LULC) and their impact on flood risk in Lagos Megacity using an integrated geospatial approach. Multi-temporal Landsat TM1984, ETM + 2002, OLI 2023, and Sentinel-2 images were used for LULC classification. Flood depth mapping was conducted using terrain models and hydro-climatic datasets to assess surface inundation dynamics. Rainfall-runoff modelling and flood hydrograph simulations were performed using HEC-HMS 4.12, while Markov Chain Model predicted future LULC dynamics and flood receptors by 2050 within the megacity. Results revealed significant urbanization, with light vegetation (18.87%) and built-up areas (37.68%) expanded between 1984 and 2023. Meanwhile, forests (- 31.55%) and waterbodies (- 11.26%) declined rapidly, reducing the natural flood buffering capacity of Lagos Megacity. Flood impact analysis revealed that 46, 018.18ha were affected within 12-24h; 125, 218.43ha over 5-7days; and 211, 230.22ha were severely affected for up to 30days. By the year 2050, extreme flooding will significantly impact built-up area, totaling 236,810.7ha (66.20%), while natural flood buffers including forest (1.35%), light vegetation (7.64%), and waterbodies (10.86%) will decline drastically over the predicted year, indicating noticeable environmental changes and high flood vulnerability in the future. The spatial modelling highlighted the need for robust disaster reduction framework, emphasizing the interaction between land use dynamics and hydro-climatic responses in flood-prone areas of Lagos. The study is timely and crucial for informing sustainable land use frameworks and the implementation of future flood mitigations in fast-growing African cities such as Lagos.

  • Research Article
  • 10.1007/s11069-025-07820-0
Assessment of dynamic drought risk and transition characteristics by combining an indicator-based approach and Markov chain model
  • Feb 1, 2026
  • Natural Hazards
  • Bin Huang + 11 more

Assessment of dynamic drought risk and transition characteristics by combining an indicator-based approach and Markov chain model

  • Research Article
  • 10.1016/j.mbs.2025.109597
Quantifying the risk of long-term chikungunya persistence in Miami-Dade county.
  • Feb 1, 2026
  • Mathematical biosciences
  • Antonio Gondim + 3 more

Quantifying the risk of long-term chikungunya persistence in Miami-Dade county.

  • Research Article
  • 10.1016/j.crmeth.2025.101294
Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains.
  • Feb 1, 2026
  • Cell reports methods
  • Jordan M Culp + 5 more

Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains.

  • Research Article
  • 10.1016/j.ress.2026.112369
Resilience Analysis of Four-state Engineering Systems Under the Framework of Continuous-time Markov Chain Model
  • Feb 1, 2026
  • Reliability Engineering & System Safety
  • Xiaohu Li + 2 more

Resilience Analysis of Four-state Engineering Systems Under the Framework of Continuous-time Markov Chain Model

  • Research Article
  • 10.1016/j.indic.2026.101189
Multi-scale analysis based on spatial Markov chain model provides insights into long-term and short-term SO2 control in China
  • Feb 1, 2026
  • Environmental and Sustainability Indicators
  • Zhe Yin + 3 more

Multi-scale analysis based on spatial Markov chain model provides insights into long-term and short-term SO2 control in China

  • Research Article
  • 10.1016/j.mbs.2026.109639
A partition method for bounding continuous-time Markov chain models of general reaction network.
  • Feb 1, 2026
  • Mathematical biosciences
  • Guillaume Ballif + 2 more

A partition method for bounding continuous-time Markov chain models of general reaction network.

  • Research Article
  • 10.3390/resources15020024
Spatio-Temporal Dynamics of Land Use and Land Cover Change and Ecosystem Service Value Assessment in Citarum Watershed, Indonesia: A Multi-Scenario and Multi-Scale Approach
  • Jan 31, 2026
  • Resources
  • Irmadi Nahib + 13 more

Rapid land use and land cover (LULC) changes in densely populated watersheds pose serious challenges to the sustainability of ecosystem services (ES), yet their spatially explicit economic consequences remain insufficiently understood. This study analyzes the spatio-temporal dynamics of LULC and ecosystem service values (ESVs) in the Citarum Watershed, Indonesia, one of the country’s most critical and intensively transformed watersheds. Multi-temporal Landsat imagery from 2003, 2013, and 2023 was classified using a Random Forest algorithm, while future LULC conditions for 2043 were projected using a Multi-layer Perceptron–Markov Chain (MLP–MC) model under three scenarios: Business-as-Usual (BAU), Protecting Paddy Field (PPF), and Protecting Forest Area (PFA). ESVs were quantified at multiple spatial scales (county, 250 m grids, and 100 m grids) using both the Traditional Benefit Transfer (TBT) method and a Spatial Benefit Transfer (SBT) approach that integrates biophysical indicators with socio-economic variables. The contribution of LULC transitions to ESV dynamics was further assessed using the Ecosystem Service Change Intensity (ESCI) index. The results reveal substantial historical forest and shrubland losses, alongside rapid expansion of settlements and dryland agriculture, indicating intensifying anthropogenic pressure on watershed functions. Scenario analysis shows continued degradation under BAU, limited mitigation under PPF, and improved forest retention under PFA; although settlement expansion persists across all scenarios. Total ESV declined from USD 2641.33 million in 2003 to USD 1585.01 million in 2023, representing a cumulative loss of 46.13%. Projections indicate severe ESV losses under BAU and PPF by 2043, while PFA substantially reduces, but does not eliminate economic degradation. ESCI results identify forest and shrubland conversion to settlements and dryland agriculture as the dominant drivers of ESV decline. These findings demonstrate that integrating multi-scenario LULC modeling with spatially explicit ESV assessment provides a more robust basis for ecosystem-based spatial planning and supports sustainable watershed management under increasing development pressure.

  • Research Article
  • 10.3390/su18031283
Mapping the Coupling Coordination Between China’s Digital Economy and Carbon Emissions: Spatiotemporal Patterns and Spatial Markov Transitions
  • Jan 27, 2026
  • Sustainability
  • Chen Gao + 3 more

Against the backdrop of accelerating global digitalization and mounting climate pressures, enabling digital-economy growth while simultaneously controlling carbon emissions has become a critical challenge for China. This study constructs a Digital Economy Development Index (DEI) and a Carbon Emissions Index (CEI) to examine the spatiotemporal evolution and spatial heterogeneity of coordinated development between the digital economy and carbon emissions. We employ global and local Moran’s I, a spatial Markov chain model, and kernel density estimation to investigate spatiotemporal autocorrelation, interregional transition patterns, and the dynamic evolution of the coupling coordination degree over 2011–2022. The results indicate that China’s eastern region performs notably better in achieving coordinated development, maintaining persistently higher coupling coordination levels. In contrast, the central and western regions face substantial challenges; in particular, low-value areas exhibit considerable potential to transition toward higher-value states, suggesting substantial room for improvement. The spatiotemporal analysis further reveals pronounced regional disparities and provides a scientific basis for policymaking aimed at advancing green and low-carbon development strategies tailored to regional characteristics.

  • Research Article
  • 10.1093/annweh/wxaf088
A Markov model for fate and transport of Staphylococcus aureus at a swine barn and proposed interventions to reduce worker exposures.
  • Jan 21, 2026
  • Annals of work exposures and health
  • Melissa G Edmondson + 2 more

Swine workers may be occupationally exposed to Staphylococcus aureus (S. aureus) during time spent inside swine barns. Exposure may occur by inhaling S. aureus-containing particles or by touching contaminated surfaces or infected animals. Despite strong evidence that swine production work is a risk factor for increased nasal carriage of S. aureus, pathways of worker exposure within the swine barn setting have not been well characterized. We developed a Markov chain model to address this research gap by first describing the fate and transport of S. aureus-containing particles within a swine finishing barn. We defined 7 possible physical locations in and around the barn in which S. aureus-containing particles may exist and used published data to determine the probability that a particle will transition from any of these locations to the other locations during a 1-s time interval. We then used our model to estimate worker exposure to S. aureus during a period of 1 s to 30 min spent inside the swine barn. Finally, we modified inputs to simulate interventions to protect workers, such as ventilation controls, respirator use, and handwashing. Increasing the ventilation rate (ie the rate at which outdoor air replaces indoor air in the barn) in our model from the recommended rate for cold weather to the rate for mild weather resulted in a 59% decrease in the number of S. aureus-containing particles in the worker's respiratory system after 30 min. Increasing ventilation rates further to the recommended rate for hot weather resulted in an additional 58% decrease. Models simulating floor and surface cleaning prior to the worker's entry into the barn had little impact on the air concentration of S. aureus (<1% change) but reduced worker exposure to facial membranes by up to 13%. Simulations of N-95 respirator wearing had the greatest impact on worker exposure. As modeled, a well-fitting N-95 respirator may reduce worker inhalation exposure from 1,772 to 72 S. aureus-containing particles after 30 min in the barn, a 96% reduction. In our model, a poorly fitting N-95 respirator reduced exposure by about 30%, indicating that the type and fit of respirator worn has an important impact on the level worker protection.

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