Long-range Dependence Research Articles

Analysis of fractional Black-Scholes, Ornstein-Uhlenbeck, and Langevin models: a minimum distance estimation approach

The present research investigates parameter estimation in fractional stochastic models, specifically the Fractional Black-Scholes, Fractional Ornstein-Uhlenbeck, and Fractional Langevin models. These models, driven by fractional Brownian motion (fBm), capture long-memory effects and complex dependencies often observed in financial and physical systems. To efficiently estimate the parameters of these models, we apply the Minimum Distance Estimation (MDE) method. This approach tackles the challenges posed by long-range dependence, ensuring both asymptotic consistency and normality. We analyze the asymptotic properties of the estimators, including their consistency, asymptotic normality, and efficiency. By providing a unified theoretical framework, the current research highlights the robustness and applicability of the MDE method for parameter inference in fractional models. The findings contribute significantly to diverse fields such as quantitative finance, econometrics, and statistical physics.

COMCARE: A Collaborative Ensemble Framework for Context-Aware Medical Named Entity Recognition and Relation Extraction

The rapid expansion of medical information has resulted in named entity recognition (NER) and relation extraction (RE) essential for clinical decision support systems. Medical texts often contain specialized vocabulary, ambiguous abbreviations, synonyms, polysemous terms, and overlapping entities, which introduce significant challenges to the extraction process. Existing approaches, which typically rely on single models such as BiLSTM or BERT, often struggle with these complexities. Although large language models (LLMs) have shown promise in various NLP tasks, they still face limitations in handling token-level tasks critical for medical NER and RE. To address these challenges, we propose COMCARE, a collaborative ensemble framework for context-aware medical NER and RE that integrates multiple pre-trained language models through a collaborative decision strategy. For NER, we combined PubMedBERT and PubMed-T5, leveraging PubMedBERT’s contextual understanding and PubMed-T5’s generative capabilities to handle diverse forms of medical terminology, from standard domain-specific jargon to nonstandard representations, such as uncommon abbreviations and out-of-vocabulary (OOV) terms. For RE, we integrated general-domain BERT with biomedical-specific BERT and PubMed-T5, utilizing token-level information from the NER module to enhance the context-aware entity-based relation extraction. To effectively handle long-range dependencies and maintain consistent performance across diverse texts, we implemented a semantic chunking approach and combined the model outputs through a majority voting mechanism. We evaluated COMCARE on several biomedical datasets, including BioRED, ADE, RDD, and DIANN Corpus. For BioRED, COMCARE achieved F1 scores of 93.76% for NER and 68.73% for RE, outperforming BioBERT by 1.25% and 1.74%, respectively. On the RDD Corpus, COMCARE showed F1 scores of 77.86% for NER and 86.79% for RE while achieving 82.48% for NER on ADE and 99.36% for NER on DIANN. These results demonstrate the effectiveness of our approach in handling complex medical terminology and overlapping entities, highlighting its potential to improve clinical decision support systems.

Patch-Wise Deep Learning Method for Intracranial Stenosis and Aneurysm Detection-the Tromsø Study

Intracranial atherosclerotic stenosis (ICAS) and intracranial aneurysms are prevalent conditions in the cerebrovascular system. ICAS causes a narrowing of the arterial lumen, thereby restricting blood flow, while aneurysms involve the ballooning of blood vessels. Both conditions can lead to severe outcomes, such as stroke or vessel rupture, which can be fatal. Early detection is crucial for effective intervention. In this study, we introduced a method that combines classical computer vision techniques with deep learning to detect intracranial aneurysms and ICAS in time-of-flight magnetic resonance angiography images. The process began with skull-stripping, followed by an affine transformation to align the images to a common atlas space. We then focused on the region of interest, including the circle of Willis, by cropping the relevant area. A segmentation algorithm was used to isolate the arteries, after which a patch-wise residual neural network was applied across the image. A voting mechanism was then employed to identify the presence of atrophies. Our method achieved accuracies of 76.5% for aneurysms and 82.4% for ICAS. Notably, when occlusions were not considered, the accuracy for ICAS detection improved to 85.7%. While the algorithm performed well for localized pathological findings, it was less effective at detecting occlusions, which involved long-range dependencies in the MRIs. This limitation was due to the architectural design of the patch-wise deep learning approach. Regardless, this can, in the future, be mitigated in a multi-scale patch-wise algorithm.

Vision Transformers for Image Classification: A Comparative Survey

Transformers were initially introduced for natural language processing, leveraging the self-attention mechanism. They require minimal inductive biases in their design and can function effectively as set-based architectures. Additionally, transformers excel at capturing long-range dependencies and enabling parallel processing, which allows them to outperform traditional models, such as long short-term memory (LSTM) networks, on sequence-based tasks. In recent years, transformers have been widely adopted in computer vision, driving remarkable advancements in the field. Previous surveys have provided overviews of transformer applications across various computer vision tasks, such as object detection, activity recognition, and image enhancement. In this survey, we focus specifically on image classification. We begin with an introduction to the fundamental concepts of transformers and highlight the first successful Vision Transformer (ViT). Building on the ViT, we review subsequent improvements and optimizations introduced for image classification tasks. We then compare the strengths and limitations of these transformer-based models against classic convolutional neural networks (CNNs) through experiments. Finally, we explore key challenges and potential future directions for image classification transformers.

An Efficient Retinal Fluid Segmentation Network Based on Large Receptive Field Context Capture for Optical Coherence Tomography Images

Optical Coherence Tomography (OCT) is a crucial imaging modality for diagnosing and monitoring retinal diseases. However, the accurate segmentation of fluid regions and lesions remains challenging due to noise, low contrast, and blurred edges in OCT images. Although feature modeling with wide or global receptive fields offers a feasible solution, it typically leads to significant computational overhead. To address these challenges, we propose LKMU-Lite, a lightweight U-shaped segmentation method tailored for retinal fluid segmentation. LKMU-Lite integrates a Decoupled Large Kernel Attention (DLKA) module that captures both local patterns and long-range dependencies, thereby enhancing feature representation. Additionally, it incorporates a Multi-scale Group Perception (MSGP) module that employs Dilated Convolutions with varying receptive field scales to effectively predict lesions of different shapes and sizes. Furthermore, a novel Aggregating-Shift decoder is proposed, reducing model complexity while preserving feature integrity. With only 1.02 million parameters and a computational complexity of 3.82 G FLOPs, LKMU-Lite achieves state-of-the-art performance across multiple metrics on the ICF and RETOUCH datasets, demonstrating both its efficiency and generalizability compared to existing methods.

A hybrid fault diagnosis scheme for milling tools using MWN-CBAM-PatchTST network with acoustic emission signals

ABSTRACT Milling tools are critical to machining and manufacturing processes. Accurate diagnosis and identification of faults occurring in milling tools during their operation are of utmost importance for maintaining the reliability and availability of these tools, and to minimise machine downtime and overall machining costs. This paper presents a milling tools fault diagnosis network model based on acoustic emission signals. The model integrates a multilayer wavelet CNN (MWN) consisting of a discrete wavelet transform (DWT) and a convolutional neural network (CNN), a convolutional block attention module (CBAM), and a PatchTST module. MWN uses wavelet transformation to withdraw multi-scale features from signals, thus improving sensitivity to small variations in acoustic emission. CBAM improves feature representation by focusing on critical feature channels and regions, while PatchTST uses a self-attention mechanism to optimise processing of long-range feature dependencies. This synergy of mechanisms results in superior performance, outperforming traditional diagnostic methods. Bayesian optimisation is used to select model hyperparameters, eliminating the subjective bias associated with manual range setting. Validation experiments using the milling dataset, including ablation studies and comparative tests, demonstrated that the model achieves an identification accuracy of over 98%, validating its generalisation capability and effectiveness in diagnosing tool faults using acoustic emission signals.

Enhanced Pneumonia Detection in Chest X-Rays Using Hybrid Convolutional and Vision Transformer Networks.

The objective of this research is to enhance pneumonia detection in chest X-rays by leveraging a novel hybrid deep learning model that combines Convolutional Neural Networks (CNNs) with modified Swin Transformer blocks. This study aims to significantly improve diagnostic accuracy, reduce misclassifications, and provide a robust, deployable solution for underdeveloped regions where access to conventional diagnostics and treatment is limited. The study developed a hybrid model architecture integrating CNNs with modified Swin Transformer blocks to work seamlessly within the same model. The CNN layers perform initial feature extraction, capturing local patterns within the images. At the same time, the modified Swin Transformer blocks handle long-range dependencies and global context through window-based self-attention mechanisms. Preprocessing steps included resizing images to 224x224 pixels and applying Contrast Limited Adaptive Histogram Equalization (CLAHE) to enhance image features. Data augmentation techniques, such as horizontal flipping, rotation, and zooming, were utilized to prevent overfitting and ensure model robustness. Hyperparameter optimization was conducted using Optuna, employing Bayesian optimization (Tree-structured Parzen Estimator) to fine-tune key parameters of both the CNN and Swin Transformer components, ensuring optimal model performance. The proposed hybrid model was trained and validated on a dataset provided by the Guangzhou Women and Children's Medical Center. The model achieved an overall accuracy of 98.72% and a loss of 0.064 on an unseen dataset, significantly outperforming a baseline CNN model. Detailed performance metrics indicated a precision of 0.9738 for the normal class and 1.0000 for the pneumonia class, with an overall F1-score of 0.9872. The hybrid model consistently outperformed the CNN model across all performance metrics, demonstrating higher accuracy, precision, recall, and F1-score. Confusion matrices revealed high sensitivity and specificity with minimal misclassifications. The proposed hybrid CNN-ViT model, which integrates modified Swin Transformer blocks within the CNN architecture, provides a significant advancement in pneumonia detection by effectively capturing both local and global features within chest X-ray images. The modifications to the Swin Transformer blocks enable them to work seamlessly with the CNN layers, enhancing the model's ability to understand complex visual patterns and dependencies. This results in superior classification performance. The lightweight design of the model eliminates the need for extensive hardware, facilitating easy deployment in resource-constrained settings. This innovative approach not only improves pneumonia diagnosis but also has the potential to enhance patient outcomes and support healthcare providers in underdeveloped regions. Future research will focus on further refining the model architecture, incorporating more advanced image processing techniques, and exploring explainable AI methods to provide deeper insights into the model's decision-making process.

TransConv: convolution-infused transformer for protein secondary structure prediction.

Protein secondary structure prediction is essential for understanding protein function and characteristics and can also facilitate drug discovery. Traditional methods for experimentally determining protein structures are both time-consuming and costly. Computational biology offers a viable alternative by predicting protein structures from their sequences. Protein secondary structure is defined by the local spatial arrangement of the protein backbone, resulting from hydrogen bonds between amino acids. In this study, we introduce TransConv, a model that combines transformer models with convolutional blocks to predict protein secondary structures from amino acid sequences. Transformer models are effective at capturing long-range dependencies through self-attention mechanisms. We integrate convolutional blocks into the transformer architecture to improve the detection of important local features. This hybrid model captures both long-range interactions and local features, leading to more accurate predictions of protein secondary structures, thus offering an efficient solution for this critical task. The experimental outcomes on the benchmark datasets depict the superiority of the proposed approach over the state-of-the-art (SOTA) models in the literature.

A Novel Encoder Decoder Architecture with Vision Transformer for Medical Image Segmentation

Brain tumor image segmentation is one of the most critical tasks in medical imaging for diagnosis, treatment planning, and prognosis. Traditional methods for brain tumor image segmentation are mostly based on Convolution Neural Network (CNN), which have been proved very powerful but still have limitations to effectively capture long-range dependencies and complex spatial hierarchies in MRI images. Variability in the shape, size, and location of tumors may affect the performance and may get stuck into suboptimal outcomes. In these regards, new encoder-decoder architecture with the VisionTranscoder(ViT) is proposed, to enhance brain tumor detection and classification. The proposed VisionTranscoder exploits a transformer's ability in modeling global context through self-attention mechanisms, providing more inclusive interpretation of the intricate patterns in medical images and classification by capturing both local and global features. The proposed VisionTranscoder maintains the Vision Transformer in its encoder for processing images as sequences of patches to capture global dependencies often outside the view of traditional CNNs. Then the segmentation map is rebuilt at a high level of fidelity with the decoder through upsampling and skips connections to maintain detailed spatial information. The risk of overfitting is hugely reduced by design and advanced regularization techniques with extensive data augmentation. The dataset contains 7,023 human brain MRI images, all of which are in four different classes: glioma, meningioma, no tumor, and pituitary. Images from the 'no tumor' class, indicating an MRI scan without any detectable tumor, were taken from the Br35H dataset . The results show the efficiency of VisionTranscoder over a wide set of brain MRI scans, producing an accuracy of 98.5% with a loss of 0.05. This performance underlines the ability of it to accurately segment and classify a brain tumor without overfitting.

Salient object detection with non-local feature enhancement and edge reconstruction

The salient object detection task based on deep learning has made significant advances. However, the existing methods struggle to capture long-range dependencies and edge information in complex images, which hinders precise prediction of salient objects. To this end, we propose a salient object detection method with non-local feature enhancement and edge reconstruction. Firstly, we adopt self-attention mechanisms to capture long-range dependencies. The non-local feature enhancement module uses non-local operation and graph convolution to model and reason the region-wise relations, which enables to capture high-order semantic information. Secondly, we design an edge reconstruction module to capture essential edge information. It aggregates various image details from different branches to better capture and enhance edge information, thereby generating saliency maps with more exact edges. Extensive experiments on six widely used benchmarks show that the proposed method achieves competitive results, with an average of Structure-Measure and Enhanced-alignment Measure values of 0.890 and 0.931, respectively.

Some empirical studies for the applications of fractional $ G $-Brownian motion in finance

<p>Since the fractional $ G $-Brownian motion (fGBm) generalizes the concepts of the standard Brownian motion, fractional Brownian motion, and $ G $-Brownian motion, while it can exhibit long-range dependence or antipersistence and feature the volatility uncertainty simultaneously, it can be a better alternative stochastic process in the financial applications. Thus, in this paper, some empirical studies for the financial applications of the fGBm were carried out, where the recent high-frequency data for some selected assets in the financial market are from the Oxford-Man Institute of Quantitative Finance Realized Library. There are two main empirical findings. One was that the H-$ G $-normal distributions associated with the fGBm are more suitable in describing the dynamics of daily returns and increments of log-volatility for these assets than the usual distributions, since they not only characterize the properties of skewness, excess kurtosis, and long-range dependence $ \left(\frac{1}{2} < H < 1\right) $ or antipersistence $ \left(0 < H < \frac{1}{2}\right) $, but also feature the volatility uncertainty. The other one was that the daily return and log-volatility both behave essentially as fGBm with different $ \underline{\sigma}^2 $ and $ \overline{\sigma}^2 $, but Hurst parameters $ H < \frac{1}{2} $, at any reasonable time scale. Then a generalized stochastic model for the dynamics of the assets called rough fractional stochastic volatility model driven by fGBm (RFSV-fGBm) was developed. Finally, some parameter estimates and numerical experiments for the RFSV-fGBm model were investigated and carried out.</p>

Cross-scale hierarchical spatio-temporal transformer for video enhancement

The diversity and complexity of degradations in low-quality videos pose non-trivial challenges on video enhancement to reconstruct the high-quality counterparts. Prevailing sliding window based methods represent poor performance due to the limitation of window size. Recurrent networks take advantage of long-term modeling to aggregate more information, resulting in significant performance improvements. However, most of them are trained on simple degraded data and can only tackle specific degradation. To break through the limitation, we propose a progressive alignment network, namely Cross-scale Hierarchical Spatio-Temporal Transformer (CHSTT), which leverages cross-scale tokenization to generate multi-scale visual tokens in the entire sequence to capture extensive long-range temporal dependencies. To enhance the spatial and temporal interactions, we introduce an innovative hierarchical Transformer, facilitating the computation of mutual multi-head attention across both spatial and temporal dimensions. Quantitative and qualitative assessments substantiate the superior performance of CHSTT compared to several state-of-the-art benchmarks across three distinct video enhancement tasks, including video super-resolution, video denoising, and video deblurring.

Multi-view brain functional connectivity and hierarchical fusion for EEG-based emotion recognition

Emotional states evolve gradually from their onset to full manifestation, reflected in changes in brain functional connectivity. Existing research often focuses only on the final emotional state, missing the rich, dynamic information of emotional evolution. This paper proposes a novel network framework leveraging global and local brain functional connectivity through a multi-view approach. We introduce a global and local connectivity modeling method using electroencephalogram signals to simulate brain connectivity changes across time and specific moments. A residual-based local detail feature extractor combined with a coordinate attention module captures long-range dependencies and maintains positional accuracy. A global feature extractor is also designed for the effective extraction of emotional information. Finally, a hierarchical multi-scale cross-attention feature fusion module integrates features across different levels to enhance emotion recognition performance and robustness. Extensive experiments on three publicly available datasets demonstrate the framework’s superiority and generalization capability.

SecEdge: A novel deep learning framework for real-time cybersecurity in mobile IoT environments.

The rapid growth of Internet of Things (IoT) devices presents significant cybersecurity challenges due to their diverse and resource-constrained nature. Existing security solutions often fall short in addressing the dynamic and distributed environments of IoT systems. This study aims to propose a novel deep learning framework, SecEdge, designed to enhance real-time cybersecurity in mobile IoT environments. The SecEdge framework integrates transformer-based models for efficient handling of long-range dependencies and Graph Neural Networks (GNNs) for modeling relational data, coupled with federated learning to ensure data privacy and reduce latency. The adaptive learning mechanism continuously updates model parameters to counter evolving cyber threats. The framework's performance was evaluated in a simulation environment using the NSL-KDD, UNSW-NB15, and CICIDS2017 datasets. Results demonstrated that SecEdge outperformed state-of-the-art methods with a detection rate of 98.8% for DoS attacks on NSL-KDD, 98.5% for MitM attacks on UNSW-NB15, and 98.7% for data injection attacks on CICIDS2017.

FusionMamba: dynamic feature enhancement for multimodal image fusion with Mamba

Multimodal image fusion aims to integrate information from different imaging techniques to produce a comprehensive, detail-rich single image for downstream vision tasks. Existing methods based on local convolutional neural networks (CNNs) struggle to capture global features efficiently, while Transformer-based models are computationally expensive, although they excel at global modeling. Mamba addresses these limitations by leveraging selective structured state space models (S4) to effectively handle long-range dependencies while maintaining linear complexity. In this paper, we propose FusionMamba, a novel dynamic feature enhancement framework that aims to overcome the challenges faced by CNNs and Vision Transformers (ViTs) in computer vision tasks. The framework improves the visual state-space model Mamba by integrating dynamic convolution and channel attention mechanisms, which not only retains its powerful global feature modeling capability, but also greatly reduces redundancy and enhances the expressiveness of local features. In addition, we have developed a new module called the dynamic feature fusion module (DFFM). It combines the dynamic feature enhancement module (DFEM) for texture enhancement and disparity perception with the cross-modal fusion Mamba module (CMFM), which focuses on enhancing the inter-modal correlation while suppressing redundant information. Experiments show that FusionMamba achieves state-of-the-art performance in a variety of multimodal image fusion tasks as well as downstream experiments, demonstrating its broad applicability and superiority.

Robust Image Forgery Detection and Localization Framework using Vision Transformers (ViTs)

Image forgery detection has become increasingly critical with the proliferation of image editing tools capable of generating realistic forgeries. Traditional deep learning approaches, such as convolutional neural networks (CNNs), often struggle with capturing global dependencies and subtle inconsistencies across larger image contexts. To address these challenges, this paper proposes a novel Vision Transformer(ViT)- based framework for robust image forgery detection and localization. Leveraging the self-attention mechanism of transformers, our approach effectively models long-range dependencies and detects even subtle tampered regions with high precision. The proposed framework processes images as patch embeddings, extracting both local and global features, and outputs a detailed forgery map for accurate localization. We evaluate our method on multiple benchmark datasets containing diverse forgery types, including splicing, cloning, and inpainting. Experimental results demonstrate that the Vit based model outperforms state-of-the-art CNN and GAN-based methods, achieving superior accuracy, precision, and recall. Additionally, qualitative analyses highlight its capability to localize forgeries in complex scenarios. The results underscore the potential of Vision Transformers as a powerful tool for advancing the field of image forgery detection.

Optimizing electric vehicle charging strategies using multi-layer perception-based spatio-temporal prediction of charging station load

The production and sales of electric vehicles have been increasing in line with the gradual adaptation of consumers to electric vehicles, driven by various government policies and subsidies over the past decade. As a result, the deployment of charging facilities, which are essential for supporting electric vehicles, has also been extensive. However, despite the rapid development in scale, charging facilities face challenges such as low utilization during off-peak hours and excessive congestion during peak hours, leading to resource wastage and a diminished user charging experience. To address these issues, this study proposes a spatio-temporal prediction model for charging station load. The model introduces a global spatial enhancement module to simultaneously learn short-range and long-range spatial dependencies in the data, resulting in improved prediction accuracy. The aim of this research is to provide practical guidance in terms of conserving charging resources and enhancing user charging experience based on spatio-temporal prediction effectiveness.

A Hybrid Model for Soybean Yield Prediction Integrating Convolutional Neural Networks, Recurrent Neural Networks, and Graph Convolutional Networks

Soybean yield prediction is one of the most critical activities for increasing agricultural productivity and ensuring food security. Traditional models often underestimate yields because of limitations associated with single data sources and simplistic model architectures. These prevent complex, multifaceted factors influencing crop growth and yield from being captured. In this line, this work fuses multi-source data—satellite imagery, weather data, and soil properties—through the approach of multi-modal fusion using Convolutional Neural Networks and Recurrent Neural Networks. While satellite imagery provides information on spatial data regarding crop health, weather data provides temporal insights, and the soil properties provide important fertility information. Fusing these heterogeneous data sources embeds an overall understanding of yield-determining factors in the model, decreasing the RMSE by 15% and improving R2 by 20% over single-source models. We further push the frontier of feature engineering by using Temporal Convolutional Networks (TCNs) and Graph Convolutional Networks (GCNs) to capture time series trends, geographic and topological information, and pest/disease incidence. TCNs can capture long-range temporal dependencies well, while the GCN model has complex spatial relationships and enhanced the features for making yield predictions. This increases the prediction accuracy by 10% and boosts the F1 score for low-yield area identification by 5%. Additionally, we introduce other improved model architectures: a custom UNet with attention mechanisms, Heterogeneous Graph Neural Networks (HGNNs), and Variational Auto-encoders. The attention mechanism enables more effective spatial feature encoding by focusing on critical image regions, while the HGNN captures interaction patterns that are complex between diverse data types. Finally, VAEs can generate robust feature representation. Such state-of-the-art architectures could then achieve an MAE improvement of 12%, while R2 for yield prediction improves by 25%. In this paper, the state of the art in yield prediction has been advanced due to the employment of multi-source data fusion, sophisticated feature engineering, and advanced neural network architectures. This provides a more accurate and reliable soybean yield forecast. Thus, the fusion of Convolutional Neural Networks with Recurrent Neural Networks and Graph Networks enhances the efficiency of the detection process.

A Lightweight Small Target Detection Algorithm for UAV Platforms

The targets in the aerial view of UAVs are small, scenes are complex, and background noise is strong. Additionally, the low computational capability of UAVs is challenged when trying to meet the requirements of large neural networks. Therefore, a lightweight object detection algorithm tailored for UAV platforms, called RSG-YOLO, is proposed. The algorithm introduces an attention module constructed with receptive field attention and coordinate attention, which helps reduce background noise interference while improving long-range information dependency. It also introduces and refines a fine-grained downsampling structure to minimize the loss of target information during the downsampling process. A general efficient layer aggregation network enhances the base feature extraction module, improving gradient flow information. Additionally, a detection layer rich in small target information is added, while redundant large object detection layers are removed, achieving a lightweight design while enhancing detection accuracy. Experimental results show that, compared to the baseline algorithm, the improved algorithm increases the P, R, mAP@0.5, and mAP@0.5:0.95 by 6.9%, 7.2%, 8.4%, 5.8%, respectively, on the VisDrone 2019 dataset, and by 5.7%, 9%, 9.3%, 3.6%, respectively, on the TinyPerson dataset, while reducing the number of parameters by 23.3%. This significantly enhances the model’s detection performance and robustness, making it highly suitable for object detection tasks on low-computing-power UAV platforms.

Techniques for Data Augmentation and Their Impact on Long-Range Dependence and Applications

Data augmentation is a common approach to enhance datasets for training machine learning models. This study employs five distinct techniques to generate augmented datasets. Furthermore, eight measures are applied to assess datasets both before and after augmentation techniques. A critical requirement is that any augmentation should preserve the fundamental properties of the original dataset. The study reveals that certain augmentation methods can disrupt the long-range dependence on Internet traffic data (ITD) with distributed denial of service (DDoS) attacks (DDoS ITD). These DDoS ITDs originate from stochastic and bursty environments, affecting the probability mass function (PMF) and data labeling.