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Search Results (489)

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Keywords = time series smoothing

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16 pages, 3200 KB  
Article
Predicting Ransomware Incidents with Time-Series Modeling
by Yaman Roumani and Yazan F. Roumani
J. Cybersecur. Priv. 2025, 5(3), 61; https://doi.org/10.3390/jcp5030061 (registering DOI) - 1 Sep 2025
Abstract
Ransomware attacks pose a serious threat to global cybersecurity, inflicting severe financial and operational damage on organizations, individuals, and critical infrastructure. Despite their pervasive impact, proactive measures to mitigate ransomware threats remain underdeveloped, with most efforts focused on reactive responses. Moreover, prior literature [...] Read more.
Ransomware attacks pose a serious threat to global cybersecurity, inflicting severe financial and operational damage on organizations, individuals, and critical infrastructure. Despite their pervasive impact, proactive measures to mitigate ransomware threats remain underdeveloped, with most efforts focused on reactive responses. Moreover, prior literature reveals a significant gap in systematic approaches for predicting such incidents. This research seeks to address this gap by employing time-series analysis to forecast ransomware attacks. Using 1880 ransomware incidents, we decompose the dataset into trend, seasonal, and residual components, fit a time-series model, and forecast future attacks. The results indicate that time-series analysis is useful for uncovering broad, structural patterns in ransomware data. To gain further insight into these results, we perform sub-analyses based on attacks targeting the top five sectors. The findings reveal reasonable predictive performance for ransomware attacks against government facilities and the healthcare and public health sector, with the latter showing an upward trend in attacks. By providing a predictive lens, our model equips organizations with actionable intelligence, enabling preemptive measures and enhanced situational awareness. Finally, this research underscores the importance of integrating time-series forecasting into cybersecurity strategies and seeks to pave the way for future advancements in predictive analytics for cyber threats. Full article
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10 pages, 2816 KB  
Field Guide
Morphometric Characterization of Bacteria Associated with Bacteremia
by Ladees Al Hafi and Evangelyn C. Alocilja
Encyclopedia 2025, 5(3), 130; https://doi.org/10.3390/encyclopedia5030130 - 27 Aug 2025
Viewed by 828
Abstract
Among the leading causes of bacteremia are Escherichia coli, Klebsiella pneumoniae, and Staphylococcus aureus. E. coli and K. pneumoniae are increasingly exhibiting resistance to last-resort antibiotics, such as carbapenems. Rapid and accurate identification of these pathogens is critical for timely [...] Read more.
Among the leading causes of bacteremia are Escherichia coli, Klebsiella pneumoniae, and Staphylococcus aureus. E. coli and K. pneumoniae are increasingly exhibiting resistance to last-resort antibiotics, such as carbapenems. Rapid and accurate identification of these pathogens is critical for timely treatment and infection control. This paper aimed to develop a computer-aided bacterial morphometric technique for identifying and classifying wild-type E. coli, K. pneumoniae, and S. aureus in a field guide fashion. A 3D laser scanning confocal microscope was used to gather key parameters of each organism: length (L, µm), circular diameter (CD, µm), volume (V, µm3), surface area-to-cross-sectional area ratio (SA/CSA, unitless), surface uniformity ratio (Str), and surface texture ratio (Sdr). Microscope images and measurement results showed that S. aureus was spherical with the shortest length (1.08 µm) and smallest volume (0.52 µm3). E. coli and K. pneumoniae were rod-shaped with lengths >2.0 µm and volumes >1.0 µm3. Carbapenem-resistant (CR) strains exhibited larger volumes than their wild-type counterparts. Surface parameters further differentiated strains: wild-type E. coli had a greater surface texture or a less smooth surface (larger Sdr) than K. pneumoniae (lower Sdr) did. CR E. coli had more surface uniformity (lower Str) than CR K. pneumoniae did. A dichotomous key based on shape, circular diameter, volume, length, and surface characteristics was developed to classify the species using a series of paired, contrasting features. This morphometric analysis can aid researchers in quickly identifying bacteria, leading to faster diagnosis of life-threatening diseases and improved treatment decisions. Full article
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24 pages, 7258 KB  
Article
Experimental Validation of a Rule-Based Energy Management Strategy for Low-Altitude Hybrid Power Aircraft
by Yunfeng She, Kunkun Fu, Bo Diao and Maosheng Sun
Aerospace 2025, 12(9), 758; https://doi.org/10.3390/aerospace12090758 - 24 Aug 2025
Viewed by 390
Abstract
In the electrification of low-altitude aircraft, aviation hybrid power systems have become one of the core research areas in this field due to their significant advantages of low emissions and long endurance. The energy management strategy is an important part of the design [...] Read more.
In the electrification of low-altitude aircraft, aviation hybrid power systems have become one of the core research areas in this field due to their significant advantages of low emissions and long endurance. The energy management strategy is an important part of the design of aviation hybrid power systems and has a significant impact on the performance and safety.This paper first develops a 200 kW dual DC-bus series hybrid power system prototype for low-altitude aircraft and its Simulink simulation model; then, it proposes a rule-based energy management strategy that uses the smoothness of the state of charge (SOC) of energy storage batteries as a coordination criterion. The strategy is validated via ground tests, where the battery SOC remains above 30%, the system response time is within 5 s, and the DC-bus voltage fluctuation is within 1%. These results demonstrate the strategy’s feasibility, providing a reference for designing and implementing series hybrid power systems. Full article
(This article belongs to the Section Aeronautics)
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24 pages, 3024 KB  
Article
Varying-Coefficient Additive Models with Density Responses and Functional Auto-Regressive Error Process
by Zixuan Han, Tao Li, Jinhong You and Narayanaswamy Balakrishnan
Entropy 2025, 27(8), 882; https://doi.org/10.3390/e27080882 - 20 Aug 2025
Viewed by 268
Abstract
In many practical applications, data collected over time often exhibit autocorrelation, which, if unaccounted for, can lead to biased or misleading statistical inferences. To address this issue, we propose a varying-coefficient additive model for density-valued responses, incorporating a functional auto-regressive (FAR) error process [...] Read more.
In many practical applications, data collected over time often exhibit autocorrelation, which, if unaccounted for, can lead to biased or misleading statistical inferences. To address this issue, we propose a varying-coefficient additive model for density-valued responses, incorporating a functional auto-regressive (FAR) error process to capture serial dependence. Our estimation procedure consists of three main steps, utilizing spline-based methods after mapping density functions into a linear space via the log-quantile density transformation. First, we obtain initial estimates of the bivariate varying-coefficient functions using a B-spline series approximation. Second, we estimate the error process from the residuals using spline smoothing techniques. Finally, we refine the estimates of the additive components by adjusting for the estimated error process. We establish theoretical properties of the proposed method, including convergence rates and asymptotic behavior. The effectiveness of our approach is further demonstrated through simulation studies and applications to real-world data. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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17 pages, 8985 KB  
Article
Assessing Geomorphological Changes and Oil Extraction Impacts in Abandoned Yellow River Estuarine Tidal Flats Using Cloud Coverage in Region of Interest (CCROI) and WDM
by Lianjie Zhang, Jishun Yan, Pan Zhang, Bo Zhao, Xia Lin and Quanming Wang
Appl. Sci. 2025, 15(16), 9097; https://doi.org/10.3390/app15169097 - 18 Aug 2025
Viewed by 290
Abstract
Waterline extraction is a key step in applying the Waterline Detection Method (WDM) to Digital Elevation Model (DEM) generation. Cloud interference remains a major challenge for achieving high-quality extraction of waterlines. This study developed an image filtering method termed “Cloud Coverage in Region [...] Read more.
Waterline extraction is a key step in applying the Waterline Detection Method (WDM) to Digital Elevation Model (DEM) generation. Cloud interference remains a major challenge for achieving high-quality extraction of waterlines. This study developed an image filtering method termed “Cloud Coverage in Region of Interest” (CCROI). By integrating the CCROI method with the Otsu algorithm and noise smoothing techniques, this study enabled high-quality batch and automated extraction of waterlines within the Google Earth Engine (GEE) platform. Using the WDM, DEMs were established to evaluate recent geomorphological changes in the estuarine tidal flats of the abandoned Diaokou Course (ETFADC). The results confirm that the erosional trend of the ETFADC has persisted throughout nearly 50 years of natural adjustment. In areas distant from oil extraction zones, erosion dominates the high-tide zone, while accretion prevails in the low-tide zone, indicating a slope-flattening process. However, in areas near the oil extraction zone, tree-shaped embankments have acted to inhibit erosion rather than exacerbate it, with strong accretion even occurring in wave-sheltered areas. By enhancing the quality of the selected images and reducing the waterline false detection rate, the CCROI method demonstrates significant potential for time-series studies of small regions. Full article
(This article belongs to the Special Issue New Technologies for Observation and Assessment of Coastal Zones)
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21 pages, 5536 KB  
Article
Analyzing and Forecasting Vessel Traffic Through the Panama Canal: A Comparative Study
by Mitzi Cubilla-Montilla, Anabel Ramírez, William Escudero and Clara Cruz
Appl. Sci. 2025, 15(15), 8389; https://doi.org/10.3390/app15158389 - 29 Jul 2025
Viewed by 515
Abstract
The Panama Canal, inaugurated in 1914, continues to play a pivotal role in global maritime connectivity. In 2016, the Canal underwent a significant expansion, reshaping maritime transit by accommodating larger vessels and reinforcing its strategic importance in international trade. The objective of this [...] Read more.
The Panama Canal, inaugurated in 1914, continues to play a pivotal role in global maritime connectivity. In 2016, the Canal underwent a significant expansion, reshaping maritime transit by accommodating larger vessels and reinforcing its strategic importance in international trade. The objective of this study is to identify a suitable time series statistical model to forecast the number of vessels transiting the Panama Canal. The three approaches employed were the following: the Autoregressive Integrated Moving Average (ARIMA) model, the Holt–Winters (HW) exponential smoothing method, and the Neural Network Autoregressive (NNAR) model. The models were compared based on forecasting errors to evaluate their predictive accuracy. Overall, the NNAR model exhibited slightly better predictive performance than the SARIMA (1,0,1) (0,1,1) model in terms of error, with both outperforming the Holt–Winters model by a significant margin. Full article
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16 pages, 855 KB  
Article
Evaluating Time Series Models for Monthly Rainfall Forecasting in Arid Regions: Insights from Tamanghasset (1953–2021), Southern Algeria
by Ballah Abderrahmane, Morad Chahid, Mourad Aqnouy, Adam M. Milewski and Benaabidate Lahcen
Geosciences 2025, 15(7), 273; https://doi.org/10.3390/geosciences15070273 - 20 Jul 2025
Viewed by 544
Abstract
Accurate precipitation forecasting remains a critical challenge due to the nonlinear and multifactorial nature of rainfall dynamics. This is particularly important in arid regions like Tamanghasset, where precipitation is the primary driver of agricultural viability and water resource management. This study evaluates the [...] Read more.
Accurate precipitation forecasting remains a critical challenge due to the nonlinear and multifactorial nature of rainfall dynamics. This is particularly important in arid regions like Tamanghasset, where precipitation is the primary driver of agricultural viability and water resource management. This study evaluates the performance of several time series models for monthly rainfall prediction, including the autoregressive integrated moving average (ARIMA), Exponential Smoothing State Space Model (ETS), Seasonal and Trend decomposition using Loess with ETS (STL-ETS), Trigonometric Box–Cox transform with ARMA errors, Trend and Seasonal components (TBATS), and neural network autoregressive (NNAR) models. Historical monthly precipitation data from 1953 to 2020 were used to train and test the models, with lagged observations serving as input features. Among the approaches considered, the NNAR model exhibited superior performance, as indicated by uncorrelated residuals and enhanced forecast accuracy. This suggests that NNAR effectively captures the nonlinear temporal patterns inherent in the precipitation series. Based on the best-performing model, rainfall was projected for the year 2021, providing actionable insights for regional hydrological and agricultural planning. The results highlight the relevance of neural network-based time series models for climate forecasting in data-scarce, climate-sensitive regions. Full article
(This article belongs to the Section Climate and Environment)
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23 pages, 1983 KB  
Article
CoTD-VAE: Interpretable Disentanglement of Static, Trend, and Event Components in Complex Time Series for Medical Applications
by Li Huang and Qingfeng Chen
Appl. Sci. 2025, 15(14), 7975; https://doi.org/10.3390/app15147975 - 17 Jul 2025
Viewed by 387
Abstract
Interpreting complex clinical time series is vital for patient safety and care, as it is both essential for supporting accurate clinical assessment and fundamental to building clinician trust and promoting effective clinical action. In complex time series analysis, decomposing a signal into meaningful [...] Read more.
Interpreting complex clinical time series is vital for patient safety and care, as it is both essential for supporting accurate clinical assessment and fundamental to building clinician trust and promoting effective clinical action. In complex time series analysis, decomposing a signal into meaningful underlying components is often a crucial means for achieving interpretability. This process is known as time series disentanglement. While deep learning models excel in predictive performance in this domain, their inherent complexity poses a major challenge to interpretability. Furthermore, existing time series disentanglement methods, including traditional trend or seasonality decomposition techniques, struggle to adequately separate clinically crucial specific components: static patient characteristics, condition trend, and acute events. Thus, a key technical challenge remains: developing an interpretable method capable of effectively disentangling these specific components in complex clinical time series. To address this challenge, we propose CoTD-VAE, a novel variational autoencoder framework for interpretable component disentanglement. CoTD-VAE incorporates temporal constraints tailored to the properties of static, trend, and event components, such as leveraging a Trend Smoothness Loss to capture gradual changes and an Event Sparsity Loss to identify potential acute events. These designs help the model effectively decompose time series into dedicated latent representations. We evaluate CoTD-VAE on critical care (MIMIC-IV) and human activity recognition (UCI HAR) datasets. Results demonstrate successful component disentanglement and promising performance enhancement in downstream tasks. Ablation studies further confirm the crucial role of our proposed temporal constraints. CoTD-VAE offers a promising interpretable framework for analyzing complex time series in critical applications like healthcare. Full article
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21 pages, 5559 KB  
Article
The Use of Minimization Solvers for Optimizing Time-Varying Autoregressive Models and Their Applications in Finance
by Zhixuan Jia, Wang Li, Yunlong Jiang and Xingshen Liu
Mathematics 2025, 13(14), 2230; https://doi.org/10.3390/math13142230 - 9 Jul 2025
Viewed by 337
Abstract
Time series data are fundamental for analyzing temporal dynamics and patterns, enabling researchers and practitioners to model, forecast, and support decision-making across a wide range of domains, such as finance, climate science, environmental studies, and signal processing. In the context of high-dimensional time [...] Read more.
Time series data are fundamental for analyzing temporal dynamics and patterns, enabling researchers and practitioners to model, forecast, and support decision-making across a wide range of domains, such as finance, climate science, environmental studies, and signal processing. In the context of high-dimensional time series, the Vector Autoregressive model (VAR) is widely used, wherein each variable is modeled as a linear combination of lagged values of all variables in the system. However, the traditional VAR framework relies on the assumption of stationarity, which states that the autoregressive coefficients remain constant over time. Unfortunately, this assumption often fails in practice, especially in systems subject to structural breaks or evolving temporal dynamics. The Time-Varying Vector Autoregressive (TV-VAR) model has been developed to address this limitation, allowing model parameters to vary over time and thereby offering greater flexibility in capturing non-stationary behavior. In this study, we propose an enhanced modeling approach for the TV-VAR framework by incorporating minimization solvers in generalized additive models and one-sided kernel smoothing techniques. The effectiveness of the proposed methodology is assessed using simulations based on non-homogeneous Markov chains, accompanied by a detailed discussion of its advantages and limitations. Finally, we illustrate the practical utility of our approach using an application to real-world financial data. Full article
(This article belongs to the Section E5: Financial Mathematics)
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19 pages, 2774 KB  
Article
Numerical Modeling on the Damage Behavior of Concrete Subjected to Abrasive Waterjet Cutting
by Xueqin Hu, Chao Chen, Gang Wang and Jenisha Singh
Buildings 2025, 15(13), 2279; https://doi.org/10.3390/buildings15132279 - 28 Jun 2025
Viewed by 326
Abstract
Abrasive waterjet technology is a promising sustainable and green technology for cutting underground structures. Abrasive waterjet usage in demolition promotes sustainable and green construction practices by reduction of noise, dust, secondary waste, and disturbances to the surrounding infrastructure. In this study, a numerical [...] Read more.
Abrasive waterjet technology is a promising sustainable and green technology for cutting underground structures. Abrasive waterjet usage in demolition promotes sustainable and green construction practices by reduction of noise, dust, secondary waste, and disturbances to the surrounding infrastructure. In this study, a numerical framework based on a coupled Smoothed Particle Hydrodynamics (SPH)–Finite Element Method (FEM) algorithm incorporating the Riedel–Hiermaier–Thoma (RHT) constitutive model is proposed to investigate the damage mechanism of concrete subjected to abrasive waterjet. Numerical simulation results show a stratified damage observation in the concrete, consisting of a crushing zone (plastic damage), crack formation zone (plastic and brittle damage), and crack propagation zone (brittle damage). Furthermore, concrete undergoes plastic failure when the shear stress on an element exceeds 5 MPa. Brittle failure due to tensile stress occurs only when both the maximum principal stress (σ1) and the minimum principal stress (σ3) are greater than zero at the same time. The damage degree (χ) of the concrete is observed to increase with jet diameter, concentration of abrasive particles, and velocity of jet. A series of orthogonal tests are performed to analyze the influence of velocity of jet, concentration of abrasive particles, and jet diameter on the damage degree and impact depth (h). The parametric numerical studies indicates that jet diameter has the most significant influence on damage degree, followed by abrasive concentration and jet velocity, respectively, whereas the primary determinant of impact depth is the abrasive concentration followed by jet velocity and jet diameter. Based on the parametric analysis, two optimized abrasive waterjet configurations are proposed: one tailored for rock fragmentation in tunnel boring machine (TBM) operations; and another for cutting reinforced concrete piles in shield tunneling applications. These configurations aim to enhance the efficiency and sustainability of excavation and tunneling processes through improved material removal performance and reduced mechanical wear. Full article
(This article belongs to the Section Building Structures)
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21 pages, 1288 KB  
Article
Intrusion Alert Analysis Method for Power Information Communication Networks Based on Data Processing Units
by Rui Zhang, Mingxuan Zhang, Yan Liu, Zhiyi Li, Weiwei Miao and Sujie Shao
Information 2025, 16(7), 547; https://doi.org/10.3390/info16070547 - 27 Jun 2025
Viewed by 328
Abstract
Leveraging Data Processing Units (DPUs) deployed at network interfaces, the DPU-accelerated Intrusion Detection System (IDS) enables microsecond-latency initial traffic inspection through hardware offloading. However, while generating high-throughput alerts, this mechanism amplifies the inherent redundancy and noise issues of traditional IDS systems. This paper [...] Read more.
Leveraging Data Processing Units (DPUs) deployed at network interfaces, the DPU-accelerated Intrusion Detection System (IDS) enables microsecond-latency initial traffic inspection through hardware offloading. However, while generating high-throughput alerts, this mechanism amplifies the inherent redundancy and noise issues of traditional IDS systems. This paper proposes an alert correlation method using multi-similarity factor aggregation and a suffix tree model. First, alerts are preprocessed using LFDIA, employing multiple similarity factors and dynamic thresholding to cluster correlated alerts and reduce redundancy. Next, an attack intensity time series is generated and smoothed with a Kalman filter to eliminate noise and reveal attack trends. Finally, the suffix tree models attack activities, capturing key behavioral paths of high-severity alerts and identifying attacker patterns. Experimental evaluations on the CPTC-2017 and CPTC-2018 datasets validate the proposed method’s effectiveness in reducing alert redundancy, extracting critical attack behaviors, and constructing attack activity sequences. The results demonstrate that the method not only significantly reduces the number of alerts but also accurately reveals core attack characteristics, enhancing the effectiveness of network security defense strategies. Full article
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23 pages, 5955 KB  
Article
Remaining Useful Life Interval Prediction for Lithium-Ion Batteries via Periodic Time Series and Trend Filtering Segmentation-Based Fuzzy Information Granulation
by Chunsheng Cui, Guangshu Xia, Chenyu Jia and Jie Wen
World Electr. Veh. J. 2025, 16(7), 356; https://doi.org/10.3390/wevj16070356 - 26 Jun 2025
Viewed by 396
Abstract
The accurate prediction of remaining useful life (RUL) is crucial in order to reasonably and efficiently utilize lithium-ion batteries (LiBs). In this paper, a construction method of periodic time series is applied to the degradation data of LiBs to address the issues of [...] Read more.
The accurate prediction of remaining useful life (RUL) is crucial in order to reasonably and efficiently utilize lithium-ion batteries (LiBs). In this paper, a construction method of periodic time series is applied to the degradation data of LiBs to address the issues of insufficient training data and smooth degradation in the RUL interval prediction method based on trend filtering segmentation and fuzzy information granulation. The construction method for periodic time series is used to form a new dataset from the original data, based on which the fusion model, by combining the variational mode decomposition (VMD) and gated recurrent unit (GRU), is used as the RUL interval prediction model of LiBs. Moreover, the effectiveness and advantage of the RUL interval prediction method proposed in this paper was verified and analyzed by utilizing the CALCE battery dataset and NCA battery dataset. Full article
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16 pages, 2271 KB  
Article
A Data Reconstruction Method for Inspection Mode in GBSAR Monitoring Using Sage–Husa Adaptive Kalman Filtering and RTS Smoothing
by Yaolong Qi, Jialiang Guo, Jiaxin Hui, Ting Hou, Pingping Huang, Weixian Tan and Wei Xu
Sensors 2025, 25(13), 3937; https://doi.org/10.3390/s25133937 - 24 Jun 2025
Viewed by 365
Abstract
Ground-based synthetic aperture radar (GBSAR) has been widely used in the fields of early warning of geologic hazards and deformation monitoring of engineering structures due to its characteristics of high spatial resolution, zero spatial baseline, and short revisit period. However, in the continuous [...] Read more.
Ground-based synthetic aperture radar (GBSAR) has been widely used in the fields of early warning of geologic hazards and deformation monitoring of engineering structures due to its characteristics of high spatial resolution, zero spatial baseline, and short revisit period. However, in the continuous monitoring process of GBSAR, due to the sudden failure of radar equipment, such as power failure, or the influence of alternating work between multiple regions, it often leads to discontinuous data collection, and this problem caused by missing data is collectively called “inspection mode”. The problem of missing data in the inspection mode not only destroys the spatial and temporal continuity of the data but also affects the accuracy of the subsequent deformation analysis. In order to solve this problem, in this paper, we propose a data reconstruction method that combines Sage–Husa Kalman adaptive filtering and the Rauch–Tung–Striebel (RTS) smoothing algorithm. The method is based on the principle of Kalman filtering and solves the problem of “model mismatch” caused by the fixed noise statistics of traditional Kalman filtering by dynamically adjusting the noise covariance to adapt to the non-stationary characteristics of the observed data. Subsequently, the Rauch–Tung–Striebel (RTS) smoothing algorithm is used to process the preliminary filtering results to eliminate the cumulative error during the period of missing data and recover the complete and smooth deformation time series. The experimental and simulation results show that this method successfully restores the spatial and temporal continuity of the inspection data, thus improving the overall accuracy and stability of deformation monitoring. Full article
(This article belongs to the Section Remote Sensors)
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19 pages, 4327 KB  
Article
Research on a Two-Stage Human-like Trajectory-Planning Method Based on a DAC-MCLA Network
by Hao Xu, Guanyu Zhang and Huanyu Zhao
Vehicles 2025, 7(3), 63; https://doi.org/10.3390/vehicles7030063 - 24 Jun 2025
Viewed by 560
Abstract
Due to the complexity of the unstructured environment and the high-level requirement of smoothness when a tracked transportation vehicle is traveling, making the vehicle travel as safely and smoothly as when a skilled operator is maneuvering the vehicle is a critical issue worth [...] Read more.
Due to the complexity of the unstructured environment and the high-level requirement of smoothness when a tracked transportation vehicle is traveling, making the vehicle travel as safely and smoothly as when a skilled operator is maneuvering the vehicle is a critical issue worth studying. To this end, this study proposes a trajectory-planning method for human-like maneuvering. First, several field equipment operators are invited to manipulate the model vehicle for obstacle avoidance driving in an outdoor scene with densely distributed obstacles, and the manipulation data are collected. Then, in terms of the lateral displacement, by comparing the similarity between the data as well as the curvature change degree, the data with better smoothness are screened for processing, and a dataset of human manipulation behaviors is established for the training and testing of the trajectory-planning network. Then, using the dynamic parameters as constraints, a two-stage planning approach utilizes a modified deep network model to map trajectory points at multiple future time steps through the relationship between the spatial environment and the time series. Finally, after the experimental test and analysis with multiple methods, the root-mean-square-error and the mean-average-error indexes between the planned trajectory and the actual trajectory, as well as the trajectory-fitting situation, reveal that this study’s method is capable of planning long-step trajectory points in line with human manipulation habits, and the standard deviation of the angular acceleration and the curvature of the planned trajectory show that the trajectory planned using this study’s method has a satisfactory smoothness. Full article
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19 pages, 1355 KB  
Article
Mathematical Evaluation of Classical and Quantum Predictive Models Applied to PM2.5 Forecasting in Urban Environments
by Jesús Cáceres-Tello and José Javier Galán-Hernández
Mathematics 2025, 13(12), 1979; https://doi.org/10.3390/math13121979 - 16 Jun 2025
Cited by 1 | Viewed by 368
Abstract
Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed [...] Read more.
Air quality modeling has become a strategic area within data science, particularly in urban contexts where pollution exhibits high variability and nonlinear dynamics. This study provides a mathematical and computational comparison between two predictive paradigms: the classical Long Short-Term Memory (LSTM) model, designed for sequential analysis of time series, and the quantum model Quantum Support Vector Machine (QSVM), based on kernel methods applied in Hilbert spaces. Both approaches are applied to real PM2.5 concentration data collected at the Plaza Castilla monitoring station (Madrid) over the period 2017–2024. The LSTM model demonstrates moderate accuracy for smooth seasonal trends but shows limited performance in detecting extreme pollution events. In contrast, the QSVM achieves perfect binary classification through a quantum kernel based on angle encoding, with significantly lower training time and computational cost. Beyond the empirical results, this work highlights the growing potential of Quantum Artificial Intelligence as a hybrid paradigm capable of extending the boundaries of classical models in complex environmental prediction tasks. The implications point toward a promising transition to quantum-enhanced predictive systems aimed at advancing urban sustainability. Full article
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