Markov Transition Research Articles

Assessing and gauging the carbon emission efficiency in China in accordance with the sustainable development goals

In light of the growing urgency of climate change, carbon emissions reduction has emerged as a pivotal concern within global governance. In this paper, we take carbon emission efficiency (CEE) as the research object to characterize the relationship between economic, social, and environmental development in the context of the Sustainable Development Goals (SDGs). According to the regional division standard of eight comprehensive economic zones in China, this paper analyzed the spatial differences, evolutionary characteristics, and influencing factors of CEE in 257 Chinese cities over the period 2003–2019. The analysis conducted the Dagum Gini Coefficient, Markov Transition Probability Matrix, and geographically and temporally weighted regression model (GTWR). The results demonstrate that: (1) The CEE of Chinese cities exhibits an upward trajectory. (2) The inter-differences among the eight comprehensive economic zones represent the primary spatial source of CEE divergence. (3) The CEE of Chinese cities is a staged process of gradual enhancement with spatial spillover effects. (4) Environmental regulation, energy consumption intensity, and green finances are significant factors affecting CEE, and the direction and intensity of their influence have distinct spatial heterogeneity. Ultimately, this paper proposes measures to narrow the development gap between regions and enhance the CEE across the region. Meanwhile, implementing regional refinement management and formulating differentiated regional sustainable development planning.

Do discrepancies between subjective and objective health shift over time in later life? A markov transition model

Subjective health (SH) deteriorates less rapidly than objective health (OH) in older adults. However, scant evidence exists regarding if discrepancies between SH and OH shift in the same individuals over time. We explore whether such discrepancies change over time in a sample of older adults living in England, through a prospective, observational cohort study design. Using data from the English Longitudinal Study of Ageing, we followed a sample of 6803 older adults, aged 60+ years at baseline, over three waves of data collection (2002–2007), yielding two wave transitions. A ‘health asymmetry’ metric classified older adults into four categories at each wave, based on the level of agreement between their SH and OH scores (‘health pessimist’, ‘health optimist’, ‘good health realist’ and ‘poor health realist’). First-order Markov transition and generalised logit models yielded estimated transition probabilities and odds ratios for health asymmetry transitions over time. At baseline, 36.84% of the sample were ‘good health realists’, 33% were ‘poor health realists’, 14.54% were ‘health optimists’, and 15.62% were ‘health pessimists’. Good and poor health realists were likely to remain health realistic over time. Good health realists who did transition however, were likely to become health optimists. Subsequently, the proportion of health optimists in the sample increased over time. Health pessimists had a high probability of being lost to study attrition. In conclusion, health optimism (i.e. where SH is rated better than OH) becomes more prevalent over time, in later life. Future research should investigate if promoting positive SH appraisals among health pessimists and poor health realists can optimise health and survival outcomes.

Quantitative detection of refrigerant charge faults in multi-unit air conditioning systems based on machine learning algorithms

Refrigerant charging discrepancies constitute the predominant malfunctions in air conditioning systems. Achieving the optimal charging level is crucial for system performance, underscoring the importance of precise refrigerant level prediction. This study introduces an algorithm designed for the quantitative detection of refrigerant charging errors by integrating the Markov Transition Field (MTF), Convolutional Neural Networks (CNN), and Multi-head Self-Attention (MSA) mechanisms. A high-precision enthalpy difference chamber was employed to establish a Variable Refrigerant Flow (VRF) refrigerant charging test bench. This setup facilitated the analysis of system parameter sensitivity to charging faults and aided in the creation of a training dataset for the algorithm. Comparative analysis was conducted against Support Vector Machines (SVM), Random Forests (RF), CNN with Self-Attention (AT), and MTF-CNN-MSA. The findings reveal that our method adeptly captures temporal dependencies and dynamic shifts in time series as visual representations, offering novel insights for discerning fault patterns within such data. Notably, the maximum pressure variations at high-pressure and low-pressure points were 0.25 MPa and 0.07 MPa, respectively, with temperature shifts of 12 °C and 3.5 °C at the high and low-temperature points. The high-pressure and high-temperature points are particularly sensitive to changes in refrigerant charging, and parameters from these sections were utilized to construct the dataset. The CNN-MSA algorithm demonstrates consistent performance across various fault types, effectively delineating fault characteristics. The accuracies achieved by SVM, RF, CNN-AT, and MTF-CNN-MSA were 84.38 %, 73.75 %, 88.13 %, and 93.75 %, respectively. In comparison, the CNN-MSA algorithm was able to more accurately detect refrigerant charge faults at different levels.

Forecasting Bitcoin volatility using machine learning techniques

This paper studies the Bitcoin volatility forecasting performance between popular traditional econometric models and machine learning techniques. We compare the 1-day to 2-month ahead forecasting performance of the Long Short-Term Memory (LSTM) and a hybrid Convolutional Neural Network-LSTM (CNN-LSTM) model to the traditional models. We find that neural networks outperform Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models for all forecasting horizons. Furthermore, the LSTM model outperforms the Heterogeneous Autoregressive (HAR) model and by integrating the Markov Transition Field (MTF) into the CNN-LSTM model, we achieve superior forecasting results in the short-term, particularly for the 7-day forecasts.

Forecasting Non-stationary Time Series Using Deep Learning in a Fuzzy Time Series Framework and its Application to Stock Markets

Non-stationary time series prediction is challenging due to its dynamic and complex nature. Fuzzy time series models offer a promising solution for forecasting such data, but a key challenge lies in partitioning the universe of discourse, which significantly impacts forecasting accuracy. Traditional fuzzy time series models often use equal-length interval partitioning, which is more suited for stationary data and limits their adaptability to non-stationary time series. This paper introduces a novel variable-length interval partitioning method designed specifically for non-stationary time series. The developed method combines a Long Short-Term Memory (LSTM) Autoencoder with K-means clustering, enabling dynamic, data-driven partitioning that adapts to the changing characteristics of the data. The LSTM Autoencoder encodes the time series, which is clustered using K-means, and intervals are defined based on cluster centers. Furthermore, the Variable Length Interval Partitioning-based Fuzzy Time Series model (VLIFTS) is developed by incorporating this partitioning method and the concepts of Markov chain and transition probability matrix. In this model, fuzzy sets are viewed as states of a Markov chain, and transition probabilities are used in the forecasting phase. The model is validated on stock market indices Nifty 50, NASDAQ, S&P 500, and Dow Jones. Stationarity and heteroscedasticity are tested using Augmented Dickey-Fuller (ADF) and Levene's tests respectively. Statistical forecast accuracy metrics Root Mean Squared Error (RMSE) and Mean Absolute Percent Error (MAPE) show that VLIFTS significantly improves forecasting accuracy over traditional models. This hybrid approach enhances fuzzy time series modelling and can be applied to various non-stationary time series forecasting problems.

Fusion of Image Transformation Techniques for IoT-based Multivariate Time-Series

The emergence of the Internet of Things (IoT) has ushered in a new era of data generation, with the opportunity for data to become a key element of connected devices. This study investigates new methods to bridge the realms of multivariate time-series data and image analysis, paying special attention to Gramian Angular Summation Field (GASF), Gramian Angular Difference Field (GADF), Markov Transition Field (MTF), and Recurrence Plot (RP) transformation techniques. These techniques serve to convert raw time-series data into visual representations, laying the foundation for deeper analysis and predictive modeling. The study introduces a novel paradigm by not only employing individual image transformation techniques but also fusing them in both horizontal and square orientations. By leveraging Convolutional Neural Networks (CNNs), this study demonstrates the efficiency of innovative fused oriented image transformation techniques in predicting complex patterns within a multivariate time-series dataset related to electricity distribution and transformer oil temperature. Experimental results demonstrate that the fusion of image transformation techniques yields notably enhanced performance compared to employing each technique individually. Fused-Horizontal techniques exhibit the highest performance, while Fused-Square techniques show the second best performance among all fused oriented and individual techniques. This emphasizes the importance of fused oriented image transformation techniques in prediction tasks.

Acoustic emission-based leakage detection for gas safety valves: Leveraging a multi-domain encoding learning algorithm

Safety valves in gas distribution systems are crucial for preventing excessive pressure buildups. Leakage in these valves compromises system stability, causing equipment damage and environmental pollution. Acoustic emission signal analysis from the valve body is essential for detecting leakage, but these signals are often weak and easily disrupted by noise, complicating detection. This paper proposes a multi-domain encoding learning algorithm to address these challenges. Unlike conventional single-domain methods, it combines two encoding images, the Gramian angular difference field and the Markov transition field, to enhance the comprehensive expression of leakage features. A lightweight convolutional neural network reduces computing resource dependency, and a convolutional block attention mechanism improves feature identification. Experimental results demonstrate that our method detects gas leakage with an accuracy of at least 96.77%. It maintains superior performance even under intense noise interference, offering a promising solution for detecting weak gas leakages in safety valves amidst high background noise.

A lightweight progressive joint transfer ensemble network inspired by the Markov process for imbalanced mechanical fault diagnosis

Owing to safety limitations and data collection costs, scenarios with imbalanced data usually arise, posing a great challenge for precise fault diagnosis. Targeting imbalanced fault diagnosis and the high computational cost of mainstream ensemble learning methods currently used, this article proposes a lightweight and accurate scheme based on a progressive joint-transfer ensemble network (PJTEN) and a Markov-lightweight strategy (MLS). Specifically, a PJTEN is developed, incorporating a multiple excitation-channel attention basic estimator and progressive joint-transfer strategy (PJTS) to maintain diversity of basic estimators better and focus more on key information from minority classes. Besides, the MLS guided by Markov transition probabilities is for the first time constructed for ensemble learning to reduce the network redundancy by alternating optimization. Using a standard dataset and a brand-new dataset of a real ship propulsion system, the proposed method achieves leading results in Accuracy, F1 score and MCC, compared with eight cutting-edge methods, thereby validating its substantial value. In terms of lightweight operation, such as temporal complexity (TC), spatial complexity (SC), and time efficiency, it is also ahead of the latest ensemble-based methods.

Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles.

Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a few slow collective variables (CVs) while treating the remaining fast variables as thermal noise. This enables us to simplify the dynamics and treat it as diffusion in a free-energy landscape spanned by slow CVs, effectively rendering the dynamics Markovian. Our recent statistical learning technique, spectral map [Rydzewski, J. J. Phys. Chem. Lett. 2023, 14(22), 5216-5220], explores this strategy to learn slow CVs by maximizing a spectral gap of a transition matrix. In this work, we introduce several advancements into our framework, using a high-dimensional reversible folding process of a protein as an example. We implement an algorithm for coarse-graining Markov transition matrices to partition the reduced space of slow CVs kinetically and use it to define a transition state ensemble. We show that slow CVs learned by spectral map closely approach the Markovian limit for an overdamped diffusion. We demonstrate that coordinate-dependent diffusion coefficients only slightly affect the constructed free-energy landscapes. Finally, we present how spectral maps can be used to quantify the importance of features and compare slow CVs with structural descriptors commonly used in protein folding. Overall, we demonstrate that a single slow CV learned by spectral map can be used as a physical reaction coordinate to capture essential characteristics of protein folding.

Identifying loci in mobility networks with applications in New Zealand work commutes: a statistical test for identifying extreme stationary distribution values in Markov transition matrices

Human mobility describes physical patterns of movement of people within a spatial system. Many of these patterns, including daily commuting, are cyclic and quantifiable. These patterns capture physical phenomena tied to processes studied in urban planning, epidemiology, and other social, behavioral, and economic sciences. This paper advances human mobility research by proposing a statistical method for identifying locations that individual move to and through at a rate proportionally higher than other locations, using commuting data for the country of New Zealand as a case study. We term these locations mobility loci and they capture a global property of communities in which people commute. The method makes use of a directed-graph representation where vertices correspond to locations, and traffic between locations correspond to edge weights. Following a normalization, the graph can be regarded as a Markov chain whose stationary distribution can be calculated. The proposed permutation procedure is then applied to determine which stationary distribution values are larger than what would be expected, given the structure of the directed graph and traffic between locations. The results of this method are evaluated, including a comparison to what is already known about commuting patterns in the area as well as a comparison with similar features.

Predicting odor from vibrational spectra: a data-driven approach

This study investigates olfaction, a complex and not well-understood sensory modality. The chemical mechanism behind smell can be described by so far proposed two theories: vibrational and docking theories. The vibrational theory has been gaining acceptance lately but needs more extensive validation. To fill this gap for the first time, we, with the help of data-driven classification, clustering, and Explainable AI techniques, systematically analyze a large dataset of vibrational spectra (VS) of 3018 molecules obtained from the atomistic simulation. The study utlizes image representations of VS using Gramian Angular Fields and Markov Transition Fields, allowing computer vision techniques to be applied for better feature extraction and improved odor classification. Furthermore, we fuse the PCA-reduced fingerprint features with image features, which show additional improvement in classification results. We use two clustering methods, agglomerative hierarchical (AHC) and k-means, on dimensionality reduced (UMAP, MDS, t-SNE, and PCA) VS and image features, which shed further insight into the connections between molecular structure, VS, and odor. Additionally, we contrast our method with an earlier work that employed traditional machine learning on fingerprint features for the same dataset, and demonstrate that even with a representative subset of 3018 molecules, our deep learning model outperforms previous results. This comprehensive and systematic analysis highlights the potential of deep learning in furthering the field of olfactory research while confirming the vibrational theory of olfaction.

Patterns of poly tobacco use among adults in the Population Assessment of Tobacco and Health (PATH) study, 2013–2017: a multistate Markov transition analysis

BackgroundA better understanding of sociodemographic transition patterns between single, dual and poly tobacco product use may help improve tobacco control policy interventions.MethodsHRs of transition between never, non-current (no past 30-day...

Exploring Inner Speech Recognition via Cross-Perception Approach in EEG and fMRI

Multimodal brain signal analysis has shown great potential in decoding complex cognitive processes, particularly in the challenging task of inner speech recognition. This paper introduces an innovative I nner Speech Recognition via Cross-Perception (ISRCP) approach that significantly enhances accuracy by fusing electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data. Our approach comprises three core components: (1) multigranularity encoders that separately process EEG time series, EEG Markov Transition Fields, and fMRI spatial data; (2) a cross-perception expert structure that learns both modality-specific and shared representations; and (3) an attention-based adaptive fusion strategy that dynamically adjusts the contributions of different modalities based on task relevance. Extensive experiments on the Bimodal Dataset on Inner Speech demonstrate that our model outperforms existing methods across accuracy and F1 score.

Classification and identification of extreme wind events by CNNs based on Shapelets and improved GASF-GADF

In this manuscript, we propose an automatic classification and recognition method for extreme wind events based on Convolutional Neural Networks (CNNs) and combining the Shapelet Transform (ST) algorithm with the improved Gramian Angular Summation Field - Gramian Angular Difference Field (GASF-GADF) 2D images construction format. First, a CNN model suitable for wind speed time series 2D images classification and recognition among five mainstream CNNs (ResNet-50, ShuffleNet0.5 × , DenseNet-121, EfficientNet-B2, and EfficientNetV2-S) is preferred based on the basic Gramian Angular Field (GAF) method; then, the improved GASF-GADF images construction format is proposed, and the optimal CNN is used to compare the classification and recognition results based on other three image conversion methods: Markov Transition Field (MTF), GASF, GADF. Last, it is proposed to utilize the ST algorithm to extract the feature subsequence Shapelets of wind speed time series to further improve the classification and recognition effect on extreme wind events. The effectiveness and applicability of the proposed method were verified through three extreme wind event datasets in this paper.The results show that the combination of Shapelets and the improved GASF-GADF images transformation method proposed in this paper can effectively enhance the classification and recognition of extreme wind events by CNNs. Among them, EfficientNetV2-S combined with the method proposed in this paper achieves 99.50%, 99.50% and 97.50% recognition Accuracy for thunderstorm, gust front and typhoon, respectively. Meanwhile, it still has good robustness for extreme wind events disturbed by noise.

A Cross-Working Condition-Bearing Diagnosis Method Based on Image Fusion and a Residual Network Incorporating the Kolmogorov–Arnold Representation Theorem

With the optimization and advancement of industrial production and manufacturing, the application scenarios of bearings have become increasingly diverse and highly coupled. This complexity poses significant challenges for the extraction of bearing fault features, consequently affecting the accuracy of cross-condition fault diagnosis methods. To improve the extraction and recognition of fault features and enhance the diagnostic accuracy of models across different conditions, this paper proposes a cross-condition bearing diagnosis method. This method, named MCR-KAResNet-TLDAF, is based on image fusion and a residual network that incorporates the Kolmogorov–Arnold representation theorem. Firstly, the one-dimensional vibration signals of the bearing are processed using Markov transition field (MTF), continuous wavelet transform (CWT), and recurrence plot (RP) methods, converting the resulting images to grayscale. These grayscale images are then multiplied by corresponding coefficients and fed into the R, G, and B channels for image fusion. Subsequently, fault features are extracted using a residual network enhanced by the Kolmogorov–Arnold representation theorem. Additionally, a domain adaptation algorithm combining multiple kernel maximum mean discrepancy (MK-MMD ) and conditional domain adversarial network with entropy conditioning (CDAN+E ) is employed to align the source and target domains, thereby enhancing the model’s cross-condition diagnostic accuracy. The proposed method was experimentally validated on the Case Western Reserve University (CWRU) dataset and the Jiangnan University (JUN) dataset, which include the 6205-2RS JEM SKF, N205, and NU205 bearing models. The method achieved accuracy rates of 99.36% and 99.889% on the two datasets, respectively. Comparative experiments from various perspectives further confirm the superiority and effectiveness of the proposed model.

Interpretable coal-rock cutting vibration recognition with Markov transition field and selective neural networks

Interpretable coal-rock cutting vibration recognition with Markov transition field and selective neural networks

Participation in Physical, Cognitive, and Social Activities and the Association with Mobility Disability Transitions in Older Adults.

Development of late-life mobility disability is a dynamic process of transitions between worsening and improving. We tested associations between participation in physical, social, and cognitive activity with mobility disability transitions. Participants (N=2,758, age 78.1 years [SD: 7.7]) from two Rush Alzheimer's Disease Center cohorts completed annual mobility disability questionnaires for 7.6 (SD: 4.4) years. First-order Markov transition models tested associations between baseline self-reported physical, social, and cognitive activity with bidirectional transitions in mobility disability score increases (worsening) and decreases (improving) between consecutive visits. Overall, 75.5% of participants experienced ≥1 transition among 18,318 pairs of consecutive visits-4,174 of which were worsening and 2,606 were improving transitions. Adjusting for covariates, higher participation in each activity type was associated with lower odds of worsening (physical OR=0.71, 95% CI: 0.67-0.75; social OR=0.64, 95% CI: 0.58-0.70; and cognitive OR=0.79, 95% CI: 0.74-0.85), and higher odds of improving (physical OR=1.20, 95% CI: 1.11-1.28; social OR=1.45, 95% CI: 1.30-1.61; and cognitive OR=1.12, 95% CI: 1.03-1.22) in separate models. In combined models, physical and social activity remained associated with worsening and improving; cognitive activity was only associated with worsening. Physical, social, and cognitive activity engagement contributes to lower odds of worsening mobility disability and may promote recovery.

Simulation of geological uncertainty based on improved three-dimensional coupled Markov chain model

The natural stratigraphic distribution is uncertain due to the geological tectonic movements and sedimentation. It is a challenge for traditional deterministic models to capture geological uncertainty. The objective of this study is to develop an improved three-dimensional coupled Markov chain (ICMC3D) model based on limited boreholes. The proposed method enhances the traditional three-dimensional coupled Markov chain model by modifying the transition probability equation for predicting unknown elements. The dip data is added to estimate the transition probability matrix with the borehole information. On this basis, a back analysis method is proposed for estimating the horizontal transition probability matrics. The method makes the predicted results more suitable for the possible stratigraphic distribution. The accuracy of the proposed method is verified through some applications. In this paper, an improved three-dimensional coupled Markov chain model and transition probability matrix estimation method are illustrated by the borehole data collected from a tunnel project in Qingdao. The results show that the presented method can reflect the asymmetry, continuity and anisotropy of the three-dimensional stratum. The exceedance probability is proposed to predict the fault zone development range in order to reduce the geological uncertainty.

Research on the coupling coordination characteristics and convergence of digital finance and regional sustainable development: evidence from Chinese city clusters

The study examines the digital finance (DF) and regional sustainable development (RSD) across 90 cities within six major city clusters in China over the period from 2011 to 2020. By constructing an evaluation index system for DF and RSD, we employed the entropy value method to assess their levels, and the coupling coordination degree (CCD) model to evaluate their interplay. Our analysis extended to temporal and spatial disparities, distribution dynamics, and the convergence of CCD through kernel density estimation, Markov chain analysis, σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document}-convergence, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-convergence techniques. The results indicate a consistent upward trend in CCD, yet it remains at a low level with pronounced regional disparities and temporal characteristics. The kernel density distribution’s central tendency has shifted rightward progressively, albeit with a decelerating pace annually. The Markov transition probability matrix suggests a stable CCD across various levels, hinting at “club convergence”. Furthermore, both σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document}-convergence and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-convergence analyses reveal significant convergence trends in CCD, enhanced by economic growth factors. Using the Quadratic Assignment Procedure (QAP) method, we found that regional economic growth disparities significantly influence the CCD’s regional variances.

A new dual-channel convolutional neural network and its application in rolling bearing fault diagnosis

Abstract Recently, deep learning has received widespread attention in the field of bearing fault diagnosis due to its powerful feature learning capability. However, when the actual working conditions are complex and variable, the fault information in a single domain is limited, making it difficult to achieve high accuracy. To overcome these challenges, this paper proposes a bearing fault diagnosis method based on the Markov transition field, continuous wavelet transform (CWT), and dual-channel convolutional neural network (CNN). The method combines the descriptive ability of the Markov model for state transfer, the time-frequency analysis ability of CWT for signal, and the excellent performance of CNN with attention mechanism in feature extraction and classification. Specifically, we first propose a multi-channel Markov transition field method, which is combined with CWT to obtain two different representations of two-dimensional (2D) images. To comprehensively mine fault information, we further propose a dual-channel CNN with an attention mechanism. The design of this network structure aims to extract multi-level features from two types of 2D images. At the same time, we designed and embedded an attention mechanism to enable the network to focus more on extracting effective features, thereby improving the performance and accuracy of the network. To verify the effectiveness of the proposed method, three datasets were used for empirical research. The results show that this method exhibits superior performance in bearing fault diagnosis and has higher accuracy compared to traditional methods.