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25 pages, 2758 KiB  
Article
Analysis and Applications of Magnetically Coupled Resonant Circuits
by Stanisław Hałgas, Sławomir Hausman and Łukasz Jopek
Electronics 2025, 14(2), 312; https://doi.org/10.3390/electronics14020312 - 14 Jan 2025
Abstract
Magnetically coupled resonant circuits have been utilized in radio engineering for many years. Recently, these circuits have found new applications, particularly in supplying low- and medium-power devices through medium-range wireless power transmission technology based on magnetic resonance coupling. There is also a growing [...] Read more.
Magnetically coupled resonant circuits have been utilized in radio engineering for many years. Recently, these circuits have found new applications, particularly in supplying low- and medium-power devices through medium-range wireless power transmission technology based on magnetic resonance coupling. There is also a growing need to analyze magnetically coupled resonant circuits in the design of metamaterials, which exhibit specific electromagnetic properties within certain frequency bands. This paper provides a coherent and concise overview of the phenomena associated with magnetically coupled resonant circuits. The results encompass numerous established relations as well as new ones. They can be helpful in the design phase of magnetically coupled resonant circuits. The outcomes include equations for determining the coupling resonant frequencies and some parameters of resonance curves. These analytical results are accompanied by 3D and cross-sectional (contour) graphs for better visualization. Moreover, a lumped-element circuit model that includes magnetically coupled resonant circuits is proposed for the resonators used in metamaterials. Formulas for resonant frequencies are derived in the specific case of exciting such resonators. To validate the accuracy of the derived equations, the analytical results are compared with simulations from SPICE (IsSPICE4 ver. 8.1) and COMSOL 5.4 software, which are widely used tools for circuit analysis and electromagnetic simulations. The results of these comparative analyses indicate that the assumptions employed in the analytical solutions introduce only tiny errors. Full article
(This article belongs to the Section Industrial Electronics)
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of two magnetically coupled resonant circuits with mutual inductance <span class="html-italic">M</span>. The configuration is used to analyze coupling effects in wireless power transfer and RF and microwave filters.</p>
Full article ">Figure 2
<p>Plot of coupling resonance angular frequencies versus coupling factor for two values of <math display="inline"><semantics> <msub> <mi>q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
Full article ">Figure 3
<p>Plots of the RMS value of the secondary circuit current <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> as a function of the relative detuning coefficient <math display="inline"><semantics> <mi>ξ</mi> </semantics></math> under varying coupling conditions: (<b>a</b>) single-peak resonance curves for coupling <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>≤</mo> <msub> <mi>k</mi> <mi>r</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) emergence of dual peaks for over-critical coupling <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>&gt;</mo> <msub> <mi>k</mi> <mi>r</mi> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Plots of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>: (<b>a</b>) 3D plot; (<b>b</b>) contour plot; the straight lines correspond to the considered cases. The plots show how circuit quality factors <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics></math> and resonant frequency tuning <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>2</mn> </msub> </semantics></math> influence resonance characteristics.</p>
Full article ">Figure 5
<p>Plots of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) 3D plot; (<b>b</b>) contour plot; the straight lines correspond to the considered cases. The plots show how circuit quality factors <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics></math> and resonant frequency tuning <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>2</mn> </msub> </semantics></math> influence resonance characteristics.</p>
Full article ">Figure 6
<p>Plots of <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>: (<b>a</b>) 3D plot; (<b>b</b>) contour plot; the straight lines correspond to the considered cases. The plots show how circuit quality factors <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics></math> and resonant frequency tuning <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>ω</mi> <mn>2</mn> </msub> </semantics></math> influence resonance characteristics.</p>
Full article ">Figure 7
<p>Dependence of normalized admittance <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> on detuning parameters <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math> for coupling parameter <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>: (<b>a</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math>; (<b>b</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math>. The plots reflect the effects of coupling on resonance behavior.</p>
Full article ">Figure 8
<p>Dependence of normalized admittance <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> on detuning parameters <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math> for coupling parameter <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>: (<b>a</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math>; (<b>b</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math>. The plots reflect the effects of coupling on resonance behavior.</p>
Full article ">Figure 9
<p>Dependence of normalized admittance <math display="inline"><semantics> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> <msub> <mrow> <msub> <mi>Y</mi> <mn>12</mn> </msub> </mrow> <mi>mm</mi> </msub> </mfrac> </mstyle> </semantics></math> on detuning parameters <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math> for coupling parameter <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>: (<b>a</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>1</mn> </msub> </semantics></math>; (<b>b</b>) variation along <math display="inline"><semantics> <msub> <mi>ζ</mi> <mn>2</mn> </msub> </semantics></math>. The plots reflect the effects of coupling on resonance behavior.</p>
Full article ">Figure 10
<p>Considered structures containing SRR-type resonators: (<b>a</b>) an SRR with dimensions marked; (<b>b</b>) two resonators; (<b>c</b>) three resonators.</p>
Full article ">Figure 11
<p>Plot of the coupling resonance angular frequencies versus coefficient <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>M</mi> <mi>L</mi> </mfrac> </mstyle> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>Lumped -element circuit model of two magnetically coupled resonant circuits.</p>
Full article ">Figure 13
<p>Frequency characteristics of resonant circuits (case 1), showing the RMS values of currents in (<b>a</b>) the primary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>1</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) and (<b>b</b>) the secondary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) under various coupling conditions (<math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>). Markers corresponding to the theoretical calculations have been placed on the plots.</p>
Full article ">Figure 14
<p>Plot of the imaginary part of equivalent impedance <math display="inline"><semantics> <msubsup> <mi>Z</mi> <mn>1</mn> <mo>′</mo> </msubsup> </semantics></math>. Markers corresponding to the theoretical calculations have been placed on the plots.</p>
Full article ">Figure 15
<p>Frequency characteristics of resonant circuits (case 2), showing the RMS values of currents in (<b>a</b>) the primary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>1</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) and (<b>b</b>) the secondary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) under various coupling conditions (<math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>A</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>). Markers corresponding to the theoretical calculations have been placed on the plots.</p>
Full article ">Figure 16
<p>Frequency characteristics of resonant circuits in the general case, illustrating RMS currents in (<b>a</b>) the primary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>1</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) and (<b>b</b>) the secondary circuit (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>I</mi> <mn>2</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) as a function of frequency.</p>
Full article ">Figure 17
<p>Plot of the imaginary part of equivalent impedance <math display="inline"><semantics> <msubsup> <mi>Z</mi> <mn>1</mn> <mo>′</mo> </msubsup> </semantics></math> with coupling resonance frequencies marked.</p>
Full article ">Figure 18
<p>Resonance curves obtained in the model of two resonators (RMS curves of both currents overlap).</p>
Full article ">Figure 19
<p>Resonance curves obtained by analysis of the circuit model of the three resonators: (<b>a</b>) RMS values of the currents in the resonators; (<b>b</b>) imaginary parts of the impedances of the resonators with coupling resonance frequencies marked.</p>
Full article ">Figure 20
<p>Transmission coefficient (<math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>S</mi> <mn>21</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>) obtained via COMSOL simulations, showing a resonance dip at circa 888 GHz. The zoomed-in region represents the frequency range corresponding to the minimum value, reflecting resonator coupling effects.</p>
Full article ">
25 pages, 6587 KiB  
Article
Analysis of Urban Rail Public Transport Space Congestion Using Graph Fourier Transform Theory: A Focus on Seoul
by Cheng-Xi Li and Cheol-Jae Yoon
Sustainability 2025, 17(2), 598; https://doi.org/10.3390/su17020598 - 14 Jan 2025
Abstract
Urban transportation efficiency is critical in densely populated cities, such as Seoul, South Korea, where subway transfer stations are vital. This study investigates the spatial efficiency and passenger flow dynamics of multilayered transfer stations, using triangular Fourier transform as the primary analytical method. [...] Read more.
Urban transportation efficiency is critical in densely populated cities, such as Seoul, South Korea, where subway transfer stations are vital. This study investigates the spatial efficiency and passenger flow dynamics of multilayered transfer stations, using triangular Fourier transform as the primary analytical method. The research incorporates principal component analysis (PCA) and K-means clustering to classify stations based on structural characteristics and congestion patterns. Data derived from transportation card usage during peak hours and architectural layouts were analysed to identify critical bottlenecks. The results highlighted notable inefficiencies in transfer times and congestion. For example, the analysis revealed that optimising transfer corridors at Seoul Station could reduce average transfer times by over 10 min. Dongdaemun History & Culture Park Station would benefit from ground-level pathways to address inefficiencies caused by its extensive underground network. Sindorim Station’s reorganisation of above-ground and underground connectivity was found to enhance passenger flow. By introducing the concept of the ‘entry baseline for passenger flow in public buildings’, this study offers a novel framework for evaluating and improving urban transit infrastructure. The findings provide actionable insights into transfer station design, supporting strategies for addressing the challenges of urban mobility in megacities while contributing to transit-oriented development. Full article
(This article belongs to the Special Issue Sustainable Transport Research and Railway Network Performance)
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Figure 1

Figure 1
<p>Fundamental Fourier transform theory.</p>
Full article ">Figure 2
<p>Decomposing and calculating complex multilayer transfer structures.</p>
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<p>Results of the cluster analysis using trigonometric Fourier transform functions (1). (<b>a</b>) 3D line plot of 79 multilayer transfer structures with 7 variables by 4 clusters. (<b>b</b>) Cluster analysis location map of Seoul metro stations (79 multilayer transfer structures).</p>
Full article ">Figure 4
<p>Results of the cluster analysis using trigonometric Fourier transform functions (2). (<b>a</b>) 3D scatter plot of clusters (79 multilayer transfer structures). (<b>b</b>) 3D PCA surface plot of 391 clustered metro stations (79 multilayer transfer structures).</p>
Full article ">
21 pages, 2525 KiB  
Article
A Data-Driven Deep Learning Framework for Prediction of Traffic Crashes at Road Intersections
by Mengxiang Wang, Wang-Chien Lee, Na Liu, Qiang Fu, Fujun Wan and Ge Yu
Appl. Sci. 2025, 15(2), 752; https://doi.org/10.3390/app15020752 - 14 Jan 2025
Abstract
Traffic crash prediction (TCP) is a fundamental problem for intelligent transportation systems in smart cities. Improving the accuracy of traffic crash prediction is important for road safety and effective traffic management. Owing to recent advances in artificial neural networks, several new deep-learning models [...] Read more.
Traffic crash prediction (TCP) is a fundamental problem for intelligent transportation systems in smart cities. Improving the accuracy of traffic crash prediction is important for road safety and effective traffic management. Owing to recent advances in artificial neural networks, several new deep-learning models have been proposed for TCP. However, these works mainly focus on accidents in regions, which are typically pre-determined using a grid map. We argue that TCP for roads, especially for crashes at or near road intersections which account for more than 50% of the fatal or injury crashes based on the Federal Highway Administration, has a significant practical and research value and thus deserves more research. In this paper, we formulate TCP at Road Intersections as a classification problem and propose a three-phase data-driven deep learning model, called Road Intersection Traffic Crash Prediction (RoadInTCP), to predict traffic crashes at intersections by exploiting publicly available heterogeneous big data. In Phase I we extract discriminative latent features called topological-relational features (tr-features), of intersections using a neural network model by exploiting topological information of the road network and various relationships amongst nearby intersections. In Phase II, in addition to tr-features which capture some inherent properties of the road network, we also explore additional thematic information in terms of environmental, traffic, weather, risk, and calendar features associated with intersections. In order to incorporate the potential correlation in nearby intersections, we utilize a Graph Convolution Network (GCN) to aggregate features from neighboring intersections based on a message-passing paradigm for TCP. While Phase II serves well as a TCP model, we further explore the signals embedded in the sequential feature changes over time for TCP in Phase III, by exploring RNN or 1DCNN which have known success on sequential data. Additionally, to address the serious issues of imbalanced classes in TCP and large-scale heterogeneous big data, we propose an effective data sampling approach in data preparation to facilitate model training. We evaluate the proposed RoadInTCP model via extensive experiments on a real-world New York City traffic dataset. The experimental results show that the proposed RoadInTCP robustly outperforms existing methods. Full article
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Figure 1
<p>A portion distribution of traffic crashes on NYC road networks in 2016. The solid point means a vehicle crash occurred in the location and the hollow circle means the multiple vehicle crashes occurred in the same location.</p>
Full article ">Figure 2
<p>The Framework of RoadInTCP.</p>
Full article ">Figure 3
<p>The Relationship between Traffic Crashes and Weather Types at Road Intersections from 2014 to 2016.</p>
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<p>(<b>a</b>) The relationship between the number of traffic crashes and one-way road segments. (<b>b</b>) The relationship between the number of traffic crashes and traffic lanes.</p>
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<p>The process of RoadInTCP in Phase II.</p>
Full article ">Figure 6
<p>(<b>a</b>) Weekly traffic crash curves of a specific intersection. (<b>b</b>) Hourly traffic crash curves of a specific intersection.</p>
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<p>An example of input time series to RoadInTCP in Phase III.</p>
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<p>Parameter analysis for RoadInTCP model in Phase I of traffic signal classification.</p>
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<p>Parameter analysis for RoadInTCP model in Phase I of avenue classification.</p>
Full article ">
47 pages, 2512 KiB  
Article
Diagnosis of Cognitive and Mental Disorders: A New Approach Based on Spectral–Spatiotemporal Analysis and Local Graph Structures of Electroencephalogram Signals
by Arezoo Sanati Fahandari, Sara Moshiryan and Ateke Goshvarpour
Brain Sci. 2025, 15(1), 68; https://doi.org/10.3390/brainsci15010068 - 14 Jan 2025
Abstract
Background/Objectives: The classification of psychological disorders has gained significant importance due to recent advancements in signal processing techniques. Traditionally, research in this domain has focused primarily on binary classifications of disorders. This study aims to classify five distinct states, including one control group [...] Read more.
Background/Objectives: The classification of psychological disorders has gained significant importance due to recent advancements in signal processing techniques. Traditionally, research in this domain has focused primarily on binary classifications of disorders. This study aims to classify five distinct states, including one control group and four categories of psychological disorders. Methods: Our investigation will utilize algorithms based on Granger causality and local graph structures to improve classification accuracy. Feature extraction from connectivity matrices was performed using local structure graphs. The extracted features were subsequently classified employing K-Nearest Neighbors (KNN), Support Vector Machine (SVM), AdaBoost, and Naïve Bayes classifiers. Results: The KNN classifier demonstrated the highest accuracy in the gamma band for the depression category, achieving an accuracy of 89.36%, a sensitivity of 89.57%, an F1 score of 94.30%, and a precision of 99.90%. Furthermore, the SVM classifier surpassed the other machine learning algorithms when all features were integrated, attaining an accuracy of 89.06%, a sensitivity of 88.97%, an F1 score of 94.16%, and a precision of 100% for the discrimination of depression in the gamma band. Conclusions: The proposed methodology provides a novel approach for analyzing EEG signals and holds potential applications in the classification of psychological disorders. Full article
(This article belongs to the Section Computational Neuroscience and Neuroinformatics)
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Figure 1

Figure 1
<p>Block diagram of the proposed system.</p>
Full article ">Figure 2
<p>Local graph structure. Decimal calculation steps: (01010110)<sub>2</sub> = (0 × 2<sup>7</sup>) + (1 × 2<sup>6</sup>) + (0 × 2<sup>5</sup>) + (1 × 2<sup>4</sup>) + (0 × 2<sup>3</sup>) + (1 × 2<sup>2</sup>) + (1 × 2<sup>1</sup>) + (0 × 2<sup>0</sup>).</p>
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<p>An illustration of the eight distinct LGSs utilized in the present study. (<b>a</b>) Symmetric local graph structure; (<b>b</b>) Logically extended local graph structure; (<b>c</b>) Vertical local graph structure; (<b>d</b>) Vertical symmetric local graph structure; (<b>e</b>) Zigzag horizontal local graph structure; (<b>f</b>) Zigzag horizontal middle local graph structure; (<b>g</b>) Zigzag vertical local graph structure; (<b>h</b>) Zigzag vertical middle Local graph structure.</p>
Full article ">Figure 3 Cont.
<p>An illustration of the eight distinct LGSs utilized in the present study. (<b>a</b>) Symmetric local graph structure; (<b>b</b>) Logically extended local graph structure; (<b>c</b>) Vertical local graph structure; (<b>d</b>) Vertical symmetric local graph structure; (<b>e</b>) Zigzag horizontal local graph structure; (<b>f</b>) Zigzag horizontal middle local graph structure; (<b>g</b>) Zigzag vertical local graph structure; (<b>h</b>) Zigzag vertical middle Local graph structure.</p>
Full article ">Figure 4
<p>The optimal classification rates: (<b>a</b>) without combined features and (<b>b</b>) with combined features.</p>
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21 pages, 28197 KiB  
Article
Expert Comment Generation Considering Sports Skill Level Using a Large Multimodal Model with Video and Spatial-Temporal Motion Features
by Tatsuki Seino, Naoki Saito, Takahiro Ogawa, Satoshi Asamizu and Miki Haseyama
Sensors 2025, 25(2), 447; https://doi.org/10.3390/s25020447 - 14 Jan 2025
Viewed by 132
Abstract
In sports training, personalized skill assessment and feedback are crucial for athletes to master complex movements and improve performance. However, existing research on skill transfer predominantly focuses on skill evaluation through video analysis, addressing only a single facet of the multifaceted process required [...] Read more.
In sports training, personalized skill assessment and feedback are crucial for athletes to master complex movements and improve performance. However, existing research on skill transfer predominantly focuses on skill evaluation through video analysis, addressing only a single facet of the multifaceted process required for skill acquisition. Furthermore, in the limited studies that generate expert comments, the learner’s skill level is predetermined, and the spatial-temporal information of human movement is often overlooked. To address this issue, we propose a novel approach to generate skill-level-aware expert comments by leveraging a Large Multimodal Model (LMM) and spatial-temporal motion features. Our method employs a Spatial-Temporal Attention Graph Convolutional Network (STA-GCN) to extract motion features that encapsulate the spatial-temporal dynamics of human movement. The STA-GCN classifies skill levels based on these motion features. The classified skill levels, along with the extracted motion features (intermediate features from the STA-GCN) and the original sports video, are then fed into the LMM. This integration enables the generation of detailed, context-specific expert comments that offer actionable insights for performance improvement. Our contributions are twofold: (1) We incorporate skill level classification results as inputs to the LMM, ensuring that feedback is appropriately tailored to the learner’s skill level; and (2) We integrate motion features that capture spatial-temporal information into the LMM, enhancing its ability to generate feedback based on the learner’s specific actions. Experimental results demonstrate that the proposed method effectively generates expert comments, overcoming the limitations of existing methods and offering valuable guidance for athletes across various skill levels. Full article
(This article belongs to the Section Intelligent Sensors)
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<p>Overview of the proposed method for skill-level-aware expert comment generation. The input video is first processed through a visual encoder, which extracts and tokenizes video features via a shared projection layer. Simultaneously, motion data are derived from the sports video, and an STA-GCN computes skill level attribute probabilities and motion features. Leveraging these visual tokens, skill levels, and motion features, the proposed method generates expert comments through an LMM.</p>
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<p>STGC block configuration. The STGC block is composed of five key network components; Spatial Graph Convolution (S-GC), which captures spatial relationships between joints; batch normalization, which normalizes feature distributions; ReLU, which introduces nonlinearity; Temporal Graph Convolution (T-GC), which captures temporal dependencies; and Dropout, which mitigates overfitting. Together, these components enable effective consideration of spatial-temporal features.</p>
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<p>Examples of a basketball video and the expert comments included in the Ego-Exo4D.</p>
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<p>Comparison of expert comment sentences generated by the PM and CM1-5. The parts highlighted in blue indicate the important human body parts or their surrounding human body parts in the ground truth sentence.</p>
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<p>PM and CM1-5 expert comments on a video of a basketball layup shot when CMs that do not include skill level do not produce valid expert comments. The sentences highlighted in blue indicate actions that require improvement and share similar meanings with those in the ground truth sentence. In contrast, the sections highlighted in red in CM1-5 also indicate actions needing improvement but have different meanings compared to the ground truth sentence.</p>
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<p>PM and CM1-5 expert comments on a video of a basketball layup shot when CMs that do not include motion do not produce valid expert comments. The sentences highlighted in blue represent actions requiring improvement and closely align in meaning with the corresponding ground truth sentence. In contrast, the sections highlighted in red in CM2 and CM3 also identify actions needing improvement but differ in meaning compared to the ground truth sentence.</p>
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<p>PM and CM1-5 expert comments on a video of a basketball layup shot when CMs that do not include video do not produce valid expert comments. The sentences highlighted in blue represent actions requiring improvement and closely align in meaning with the corresponding ground truth sentence. In contrast, the sections highlighted in red in CM4 and CM5 also identify actions needing improvement but differ in meaning compared to the ground truth sentence.</p>
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<p>Examples of expert comments generated by the PM, CM6, and CM7 from a video of a layup shot in basketball. The PM (highlighted in blue) provides comments focused on the arms, closely matching the intended meaning of the ground truth. CM6 (in red) delivers generic advice with irrelevant details, such as dribbling, reflecting a lack of focus on the specific action. CM7 (in light blue) provides relevant yet superficial comments, recognizing good footwork but overlooking opportunities to address hand-eye coordination and targeting accuracy for further improvement.</p>
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<p>Examples of expert comments generated by the PM, CM6, and CM7 from a video of a free throw in basketball. The PM (highlighted in blue) delivers precise and actionable feedback, emphasizing consistent follow-through and relaxed wrist positioning, closely aligning with the meaning of the ground truth sentence. In contrast, CM6 (highlighted in red) provides a broad and generic scene description, often including irrelevant details. At the same time, CM7 (highlighted in light blue) offers relevant but superficial advice, lacking depth and specificity in addressing shooting techniques.</p>
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15 pages, 1904 KiB  
Article
Preventive Effects of Botulinum Neurotoxin Long-Term Therapy: Comparison of the ‘Experienced’ Benefits and ‘Suspected’ Worsening Across Disease Entities
by Harald Hefter and Sara Samadzadeh
J. Clin. Med. 2025, 14(2), 480; https://doi.org/10.3390/jcm14020480 - 14 Jan 2025
Viewed by 176
Abstract
Background: Repetitive intramuscular injections of botulinum neurotoxin (BoNT) have become the treatment of choice for a variety of disease entities. But with the onset of BoNT therapy, the natural course of a disease is obscured. Nevertheless, the present study tries to analyze patients’ [...] Read more.
Background: Repetitive intramuscular injections of botulinum neurotoxin (BoNT) have become the treatment of choice for a variety of disease entities. But with the onset of BoNT therapy, the natural course of a disease is obscured. Nevertheless, the present study tries to analyze patients’ “suspected” course of disease severity under the assumption that no BoNT therapy had been performed and compares that with the “experienced” improvement during BoNT treatment. Methods: For this cross-sectional study, all 112 BoNT long-term treated patients in a botulinum toxin out-patient department were recruited who did not interrupt their BoNT/A therapy for more than two injection cycles during the last ten years. Patients had to assess the remaining severity of their disease as a percentage of the severity at onset of BoNT therapy and to draw three different graphs: (i) the CoDB-graph showing the course of severity of patient’s disease from onset of symptoms to onset of BoNT/A therapy, (ii) the CoDA-graph illustrating the course of severity from onset of BoNT/A therapy until recruitment, and (iii) the CoDS-graph visualizing the suspected development of disease severity from onset of BoNT/A therapy until recruitment under the assumption that no BoNT/A therapy had been performed. Three different types of graphs were distinguished: the R-type indicated a rapid manifestation or improvement, the C-type a continuous worsening or improvement, and the D-type a delayed manifestation or response to BoNT therapy. Four patient subgroups (cervical dystonia, other cranial dystonia, hemifacial spasm, and the migraine subgroup) comprised 91 patients who produced a complete set of graphs which were further analyzed. The “experienced” improvement and “suspected” worsening of disease severity since the onset of BoNT/A therapy were compared and correlated with demographical and treatment related data. Results: Improvement was significant (p < 0.05) and varied between 45 and 70% in all four patient subgroups, the “suspected” worsening was also significantly (p < 0.05) larger than 0, except in the migraine patients and varied between 10 and 70%. The “total benefit” (sum of improvement and prevented “suspected” worsening) was the highest in the other cranial dystonia group and the lowest in the migraine subgroup. The distributions of R-,C-,D-type graphs across CoDB-, CoDS-, and CoDB-graphs and across the four patient subgroups were significantly different. Conclusions: (i) Most BoNT long-term treated patients have the opinion that their disease would have further progressed and worsened if no BoNT/A therapy had been performed, (ii) The type of response to BoNT/A is different across different subgroups of BoNT/A long-term treated patients. Full article
(This article belongs to the Section Clinical Neurology)
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<p>(<b>A</b>): Three different types (R-, C-, D-type) of graphs are presented indicating the course of disease severity before BoNT-therapy (CoDB-graphs) during the time span (DURS) between onset of symptoms (AOS) to onset of BoNT therapy (AOT). Severity of the disease at onset of BoNT therapy was used as reference (=100%). (<b>B</b>): Three different types (R-, C-, D-type) of graphs indicate the “suspected” course of disease severity under the assumption that no BoNT therapy had been performed (CoDS-graphs) during the time span (DURT) between onset of BoNT therapy (AOT) to the day of recruitment (AGE). (<b>C</b>): Three different types (R-, C-, D-type) of graphs indicate the “experienced” course of disease severity (CoDA-graphs) during the time span (DURT) between onset of BoNT therapy (AOT) to the day of recruitment (AGE).</p>
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<p>Comparative analysis of treatment impact across disease entities. This bar chart represents the mean values of benefit (EBEN-D; left light gray bar), “suspected” worsening (SWORS-D; dark gray bar in the middle), and total benefit (TBEN-D = (EBEN-D) + (SWORS-D; right black bar) for patients with cervical dystonia (CD), other cranial dystonia (CRD), hemifacial spasm (HFS), and migraine (MIG) at the day of recruitment. Standard deviations, indicating the variability of the responses within each disease entity, are presented as error bars.</p>
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<p>Highly significant (chi<sup>2</sup>-testing: <span class="html-italic">p</span> &lt; 0.001) difference in the proportional distributions of three response types (R-, C-, D-type) across the three graph categories (CoDB-, CoDS-, CoDA-graphs). The three pie-charts highlight the relative percentages of R-, C-, and D-response types within the overall CoDB, CoDS, and CoDA graph categories.</p>
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<p>Highly significant (chi<sup>2</sup>-testing: <span class="html-italic">p</span> &lt; 0.001) difference in the proportional distributions of the three response types (R-, C-, D-type) across the four disease entities. These four pie-charts illustrate the proportional distribution of R-,C-, and D-types among the four patient groups (cervical dystonia (CD), other cranial dystonia (CRD), hemifacial spasm (HFS), and migraine (MIG).</p>
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<p>Proportional distributions of the three R-, C-, D-response types across the four disease entities (CD = column 1; CRD = column 2; HFS = column 3; MIG = column 4) for all CoDB-graphs (row 1), all CoDS-graphs (row 2) and all CoDA-graphs (row 3).</p>
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32 pages, 5360 KiB  
Article
TempoGRAPHer: Aggregation-Based Temporal Graph Exploration
by Evangelia Tsoukanara, Georgia Koloniari and Evaggelia Pitoura
Information 2025, 16(1), 46; https://doi.org/10.3390/info16010046 - 13 Jan 2025
Viewed by 194
Abstract
Graphs offer a generic abstraction for modeling entities and the interactions and relationships between them. Most real-world graphs, such as social and cooperation networks, evolve over time, and exploring their evolution may reveal important information. In this paper, we present TempoGRAPHer, a system [...] Read more.
Graphs offer a generic abstraction for modeling entities and the interactions and relationships between them. Most real-world graphs, such as social and cooperation networks, evolve over time, and exploring their evolution may reveal important information. In this paper, we present TempoGRAPHer, a system for analyzing and visualizing the evolution of temporal attributed graphs. TempoGRAPHer supports both temporal and attribute aggregation. It also allows graph exploration by identifying periods of significant growth, shrinkage, or stability. Temporal exploration is supported by two complementary strategies, namely skyline- and interaction-based exploration. Skyline-based exploration provides insights into the overall trends in the evolution, while interaction-based exploration offers a closer look at specific parts of the graph evolution history where significant changes occurred. We present experimental results demonstrating the efficiency of TempoGRAPHer. Additionally, we showcase the usefulness of our system in understanding graph evolution by presenting detailed scenarios, including exploring the evolution of a real contact network between primary school students and analyzing the collaborations in a co-authorship network between authors of the same gender over time. Full article
19 pages, 9189 KiB  
Article
NHSH: Graph Hybrid Learning with Node Homophily and Spectral Heterophily for Node Classification
by Kang Liu, Wenqing Dai, Xunyuan Liu, Mengtao Kang and Runshi Ji
Symmetry 2025, 17(1), 115; https://doi.org/10.3390/sym17010115 - 13 Jan 2025
Viewed by 276
Abstract
Graph Neural Network (GNN) is an effective model for processing graph-structured data. Most GNNs are designed to solve homophilic graphs, where all nodes belong to the same category. However, graph data in real-world applications are mostly heterophilic, and homophilic GNNs cannot handle them [...] Read more.
Graph Neural Network (GNN) is an effective model for processing graph-structured data. Most GNNs are designed to solve homophilic graphs, where all nodes belong to the same category. However, graph data in real-world applications are mostly heterophilic, and homophilic GNNs cannot handle them well. To address this, we propose a novel hybrid-learning framework based on Node Homophily and Spectral Heterophily (NHSH) for node classification in graph networks. NHSH is designed to achieve state-of-the-art or superior performance on both homophilic and heterophilic graphs. It includes three core modules: homophilic node extraction (HNE), heterophilic spectrum extraction (HSE) and node feature fusion (NFF). More specifically, HNE identifies symmetric neighborhoods of nodes with the same category, extracting local features that reflect these symmetrical structures. Then, HSE uses filters to analyze the high and low-frequency information of nodes in the graph and extract the global features of the nodes. Finally, NFF fuses the above two node features to obtain the final node features in graphs. Moreover, an elaborate loss function drives the network to preserve critical symmetries and structural patterns in the graph. Experiments on eight benchmark datasets validate that NHSH performs comparably or better than existing methods across diverse graph types. Full article
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<p>Visualization of homophily graph and heterophily graph. (<b>a</b>,<b>b</b>) are homophilic graph, (<b>c</b>,<b>d</b>) are heterophilic graph. Edges represent nodes connected to each other.</p>
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<p>Overview of the NHSH architecture.</p>
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<p>Illustration of node local structure embedding module.</p>
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<p>Illustration of feature extraction module. It is mainly implemented by the dynamic attention mechanism GATv2.</p>
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<p>Illustration of Feedback optimization module. It is mainly implemented by three different loss functions: the Grouploss, Rankloss, and CEloss.</p>
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<p>We visualize the structure of the extracted node from the homophilic node extraction module on cora, citeseer, squirrel, and chameleon, and the image show clusters of 7, 6, 5, and 5, respectively, corresponding to the node classes.</p>
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<p>Visualization of feature information in the form of heat maps. (<b>a</b>,<b>b</b>) are hybrid-learning information heat maps. (<b>c</b>,<b>d</b>) are homophilic node information heat maps. (<b>e</b>,<b>f</b>) are high-frequency information heat maps. (<b>g</b>,<b>h</b>) are low-frequency information heat maps. Furthermore, where (<b>a</b>,<b>c</b>,<b>e</b>,<b>g</b>) are the feature information heat maps obtained after the first epoch, (<b>b</b>,<b>d</b>,<b>f</b>,<b>h</b>) are the feature information heat maps obtained after the last epoch.</p>
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<p>Visualization of intermediate feature information in the form of scatters for citeseer and squirrel. In order to obtain a more intuitive feel for the enhancement of feature information by our model, we visualize the feature information obtained through different numbers of epochs and present it in the form of a scatter plot.</p>
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<p>Accuracy of different number of training layers K on eight datasets. During the experiment, we gradually increased the number of training layers K and adjusted the step size to 1 each time. We present it in the form of a line graph.</p>
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16 pages, 11605 KiB  
Article
Application of Graph Theory and Variants of Greedy Graph Coloring Algorithms for Optimization of Distributed Peer-to-Peer Blockchain Networks
by Miljenko Švarcmajer, Denis Ivanović, Tomislav Rudec and Ivica Lukić
Technologies 2025, 13(1), 33; https://doi.org/10.3390/technologies13010033 - 13 Jan 2025
Viewed by 315
Abstract
This paper investigates the application of graph theory and variants of greedy graph coloring algorithms for the optimization of distributed peer-to-peer networks, with a special focus on private blockchain networks. The graph coloring problem, as an NP-hard problem, presents a challenge in determining [...] Read more.
This paper investigates the application of graph theory and variants of greedy graph coloring algorithms for the optimization of distributed peer-to-peer networks, with a special focus on private blockchain networks. The graph coloring problem, as an NP-hard problem, presents a challenge in determining the minimum number of colors needed to efficiently allocate resources within the network. The paper deals with the influence of different graph density, i.e., the number of links, on the efficiency of greedy algorithms such as DSATUR, Descending, and Ascending. Experimental results show that increasing the number of links in the network contributes to a more uniform distribution of colors and increases the resistance of the network, whereby the DSATUR algorithm achieves the most uniform color saturation. The optimal configuration for a 100-node network has been identified at around 2000 to 2500 links, which achieves stability without excessive redundancy. These results are applied in the context of a private blockchain network that uses optimal connectivity to achieve high resilience and efficient resource allocation. The research findings suggest that adapting network configuration using greedy algorithms can contribute to the optimization of distributed systems, making them more stable and resilient to loads. Full article
(This article belongs to the Section Information and Communication Technologies)
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<p>Impact of graph density on greedy algorithm variants.</p>
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<p>Percentage difference between best and worst case.</p>
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<p>A network with 100 nodes and 99 links.</p>
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<p>Fully connected network with 100 nodes and 4950 links.</p>
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<p>DSATUR 100 nodes 1500 links.</p>
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<p>Descending 100 nodes 1500 links.</p>
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<p>Ascending 100 nodes 1500 links.</p>
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<p>DSATUR 100 nodes 2000 links.</p>
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<p>Descending 100 nodes 2000 links.</p>
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<p>Ascending 100 nodes 2000 links.</p>
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<p>DSATUR 100 nodes 2500 links.</p>
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<p>Descending 100 nodes 2500 links.</p>
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<p>Ascending 100 nodes 2500 links.</p>
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19 pages, 13222 KiB  
Article
Connecting Cities: A Case Study on the Application of Morphological Shortest Paths
by Jorge L. Perez-Ramos, Selene Ramirez-Rosales, Daniel Canton-Enriquez, Luis A. Diaz Jimenez, Herlindo Hernandez-Ramirez, Ana M. Herrera-Navarro and Hugo Jimenez-Hernandez
Symmetry 2025, 17(1), 114; https://doi.org/10.3390/sym17010114 - 13 Jan 2025
Viewed by 257
Abstract
Navigatingdensely connected networks can be complex due to the different connection structures present within a network. No explicit algorithms are designed specifically for this navigation, so heuristic approaches and existing network systems are often employed. However, this task can become computationally asymmetrical, as [...] Read more.
Navigatingdensely connected networks can be complex due to the different connection structures present within a network. No explicit algorithms are designed specifically for this navigation, so heuristic approaches and existing network systems are often employed. However, this task can become computationally asymmetrical, as the complexity of creating a representation of the city is lower than the complexity involved in identifying a set of feasible paths in a combinatorial order. This paper extends the applicability of morphological approaches to compute the shortest path in smart cities, driven by the complexity and size of the vital communication infrastructure. As is well known, this communication infrastructure changes dynamically, particularly with the evolving connection paths due to continuous population growth. Consequently, efficient communication trajectories can quickly become obsolete. The challenge of computing the best trajectories to respond more quickly to the growing population comes with high computational complexity. This paper presents an application that uses a discrete algorithm designed to compute the shortest path through a morphological approach. Specifically, it seeks to identify the best trajectory within a densely populated city based on a complex density graph. By incorporating morphological approaches into path-search algorithms, we can define a new family of methods that operate in discrete spaces with a morphological representation, resulting in approaches that have lower computational requirements. Other well-known applications in this context include the delivery of resources, such as managing electrical power consumption or minimizing time delays in resource delivery. This task is essential but classified as an NP problem, making it an appropriate scenario for applying the proposed algorithm to navigate a dense graph. The paper highlights the well-known problem of finding the shortest path as one of the potential applications of the introduced algorithm. The algorithm aims to identify the optimal path trajectory within a graph representing a dense city’s real scenario. This discussion compares and contrasts the proposal with other established approaches, highlighting the advantages and characteristics of the proposed method. Full article
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<p>Process of encoding a real scenario in a graphical representation of nodes and edges.</p>
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<p>Search space coverage through dilation operator and its convergence to the target node (<b>a</b>–<b>g</b>).</p>
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<p>Reference city used to experimental test [<a href="#B51-symmetry-17-00114" class="html-bibr">51</a>].</p>
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<p>The process used by search algorithms in a graph space involves (<b>a</b>) knowledge of the scenario consisting of avenues, with information on the reference and destination nodes, and (<b>b</b>) the frequency of application of the dilation operator together with the final calculation of the trajectory of the optimal path found.</p>
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<p>Comparison of the search process with covering dilation operator and the search with Dijkstra’s algorithm.</p>
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<p>The distribution resulted of applying the algorithm for delivering resources in a dense city multiple times.</p>
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10 pages, 2010 KiB  
Proceeding Paper
Learnable Weight Graph Neural Network for River Ice Classification
by Yifan Qu, Armina Soleymani, Denise Sudom and Katharine Andrea Scott
Proceedings 2024, 110(1), 30; https://doi.org/10.3390/proceedings2024110030 - 13 Jan 2025
Viewed by 141
Abstract
Monitoring river ice is crucial for planning safe navigation routes, with ice–water classification being one of the most important tasks in ice mapping. While high-resolutions satellite imagery, such as synthetic aperture radar (SAR), is well-suited to this task, manual interpretation of these data [...] Read more.
Monitoring river ice is crucial for planning safe navigation routes, with ice–water classification being one of the most important tasks in ice mapping. While high-resolutions satellite imagery, such as synthetic aperture radar (SAR), is well-suited to this task, manual interpretation of these data is challenging due to the large data volume. Machine learning approaches are suitable methods to overcome this; however, training the models might not be time-effective when the desired result is a narrow structure, such as a river, within a large image. To address this issue, we proposed a model incorporating a graph neural network (GNN), called learnable weights graph convolution network (LWGCN). Focusing on the winters of 2017–2021 with emphasis on the Beauharnois Canal and Lake St Lawrence regions of the Saint Lawrence River. The model first converts the SAR image into graph-structured data using simple linear iterative clustering (SLIC) to segment the SAR image, then connecting the centers of each superpixel to form graph-structured data. For the training model, the LWGCN learns the weights on each edge to determine the relationship between ice and water. By using the graph-structured data as input, the proposed model training time is eight times faster, compared to a convolution neural network (CNN) model. Our findings also indicate that the LWGCN model can significantly enhance the accuracy of ice and water classification in SAR imagery. Full article
(This article belongs to the Proceedings of The 31st International Conference on Geoinformatics)
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<p>The study region consists of the Beauharnois Canal and Lake Saint Lawrence. The central coordinates for the Beauharnois Canal are approximately 45.26° N and 73.94° W. The central coordinates for Lake Saint Lawrence are approximately 44.99° N and 74.88° W.</p>
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<p>The process of generating graphs from SAR imagery for an arbitrary chosen date (2017-01-12) in the Beauharnois Canal. (<b>a</b>) Sentinel-1 SAR image. (<b>b</b>) Use simple linear iterative clustering (SLIC) to segment the image into superpixels. (<b>c</b>) Connect the centers of each superpixel. (<b>d</b>) Remove the land area (this is the graph structure used in the LWGCN model).</p>
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<p>(<b>a</b>) Sentinel-1 VV SAR image of Lake Saint Lawrence (see <a href="#proceedings-110-00030-f001" class="html-fig">Figure 1</a> for location within larger study region), (<b>b</b>) ground truth from manually labeled shapefile, where blue indicates water and red indicates ice, and (<b>c</b>) LWGCN model output, where the colors are represented in <a href="#proceedings-110-00030-t005" class="html-table">Table 5</a>. The arbitrary chosen date is 2018-01-07.</p>
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17 pages, 4632 KiB  
Article
Chinese Mathematical Knowledge Entity Recognition Based on Linguistically Motivated Bidirectional Encoder Representation from Transformers
by Wei Song, He Zheng, Shuaiqi Ma, Mingze Zhang, Wei Guo and Keqing Ning
Information 2025, 16(1), 42; https://doi.org/10.3390/info16010042 - 13 Jan 2025
Viewed by 284
Abstract
We assessed whether constructing a mathematical knowledge graph for a knowledge question-answering system or a course recommendation system, Named Entity Recognition (NER), is indispensable. The accuracy of its recognition directly affects the actual performance of these subsequent tasks. In order to improve the [...] Read more.
We assessed whether constructing a mathematical knowledge graph for a knowledge question-answering system or a course recommendation system, Named Entity Recognition (NER), is indispensable. The accuracy of its recognition directly affects the actual performance of these subsequent tasks. In order to improve the accuracy of mathematical knowledge entity recognition and provide effective support for subsequent functionalities, this paper adopts the latest pre-trained language model, LERT, combined with a Bidirectional Gated Recurrent Unit (BiGRU), Iterated Dilated Convolutional Neural Networks (IDCNNs), and Conditional Random Fields (CRFs), to construct the LERT-BiGRU-IDCNN-CRF model. First, LERT provides context-related word vectors, and then the BiGRU captures both long-distance and short-distance information, the IDCNN retrieves local information, and finally the CRF is decoded to output the corresponding labels. Experimental results show that the accuracy of this model when recognizing mathematical concepts and theorem entities is 97.22%, the recall score is 97.47%, and the F1 score is 97.34%. This model can accurately recognize the required entities, and, through comparison, this method outperforms the current state-of-the-art entity recognition models. Full article
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<p>The whole model architecture.</p>
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<p>The structure of LERT.</p>
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<p>The structure of the encoder.</p>
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<p>The structure of the GRU unit.</p>
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<p>Changes in the CNN expansion. The receptive field in the left image is 3 × 3; in the middle image, it is 7 × 7; and in the right image, it is 15 × 15.</p>
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<p>The structure of the IDCNN unit.</p>
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<p>Model effect.</p>
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<p>Model loss.</p>
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<p>Precision comparison of the models.</p>
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<p>Recall comparison of the models.</p>
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<p>F1 comparison of the models.</p>
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<p>Comparison of training times between the BiGRU and BiLSTM.</p>
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15 pages, 376 KiB  
Article
Dynamic Spatial–Temporal Graph Neural Network for Cooling Capacity Prediction in HVDC Systems
by Hao Sun, Shaosen Li, Jianxiang Huang, Hao Li, Guanxin Jing, Ye Tao and Xincui Tian
Energies 2025, 18(2), 313; https://doi.org/10.3390/en18020313 - 12 Jan 2025
Viewed by 495
Abstract
Predicting the cooling capacity of converter valves is crucial for maintaining the stability and efficiency of high-voltage direct current (HVDC) systems. This task involves handling complex, multi-dimensional time-series data with strong inter-variable dependencies and temporal dynamics. Traditional machine learning methods, while effective in [...] Read more.
Predicting the cooling capacity of converter valves is crucial for maintaining the stability and efficiency of high-voltage direct current (HVDC) systems. This task involves handling complex, multi-dimensional time-series data with strong inter-variable dependencies and temporal dynamics. Traditional machine learning methods, while effective in static scenarios, struggle to capture these dependencies, and existing deep learning models often lack the ability to jointly model spatial and temporal relationships. To address these challenges, we propose a novel framework that integrates Graph Neural Networks (GNNs) with temporal dynamics. The GNN component captures spatial dependencies by representing the data as a graph, where nodes correspond to system variables, and edges encode their relationships. Temporal dependencies are modeled using temporal convolutional layers and recurrent neural networks (RNNs), enabling the framework to learn both short-term variations and long-term trends. Additionally, a graph attention mechanism dynamically adjusts the importance of variable relationships, improving prediction accuracy and interoperability. The proposed method demonstrates superior performance over traditional machine learning and deep learning baselines on real-world cooling system data. These results validate the effectiveness of the framework for industrial applications such as cooling system monitoring and predictive maintenance. Full article
(This article belongs to the Topic Advances in Power Science and Technology, 2nd Edition)
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<p>The proposed framework for cooling capacity prediction. The framework consists of four main components: graph construction, Temporal Graph Convolutional Network (TGCN), graph attention mechanism (GAT), and temporal dependency modeling. Input data (e.g., voltage, current, temperature) are first transformed into a graph structure, where nodes represent variables, and edges encode relationships. The TGCN combines graph convolution and temporal convolution to extract spatial–temporal features, which are refined by the GAT for dynamic edge weighting. Finally, the temporal dependencies are captured using LSTM to predict the cooling capacity.</p>
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<p>Histogram of cooling capacity distribution in the HVDC cooling system dataset.</p>
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<p>Comparison of the proposed method and the baseline (GCN) in terms of prediction accuracy, prediction time, and prediction efficiency. (<b>a</b>) Prediction accuracy comparison: The proposed method achieves a significantly higher accuracy, with an average accuracy of 94.62%, compared to 92.12% for the baseline. (<b>b</b>) Prediction time comparison: The proposed method demonstrates a reduced prediction time, with an average of 3.54 s, compared to 6 s for the baseline. (<b>c</b>) Prediction efficiency comparison: The proposed method achieves a higher prediction efficiency, averaging 91.80%, compared to 86.74% for the baseline. These results highlight the superior accuracy, efficiency, and computational performance of the proposed method in predicting the cooling capacity of converter valves.</p>
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<p>Heatmap visualization of attention weights learned by the graph attention mechanism (GAT). Rows represent the source variables, and columns represent the target variables. Higher attention weights (darker colors) indicate stronger influence of the source variable on the target variable. The heatmap highlights the dominant roles of ambient temperature and coolant flow rate in cooling capacity prediction, consistent with the physical principles of heat exchange.</p>
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12 pages, 275 KiB  
Article
Graceful Local Antimagic Labeling of Graphs: A Pattern Analysis Using Python
by Luqman Alam , Andrea Semaničová-Feňovčíková and Ioan-Lucian Popa
Symmetry 2025, 17(1), 108; https://doi.org/10.3390/sym17010108 - 12 Jan 2025
Viewed by 245
Abstract
Graph labeling is the process of assigning labels to vertices and edges under certain conditions. This paper investigates the graceful local antimagic labeling of various graph families, excluding symmetric labelings, using computational experiments and Python-based algorithms. Through these experiments, we identify new results [...] Read more.
Graph labeling is the process of assigning labels to vertices and edges under certain conditions. This paper investigates the graceful local antimagic labeling of various graph families, excluding symmetric labelings, using computational experiments and Python-based algorithms. Through these experiments, we identify new results and patterns within specific graph classes. The study expands on the existing literature by offering computational evidence, proposing algorithms for the verification of labelings, and exploring the relationship between the local antimagic labeling and the chromatic number. Our results increase the understanding of graph labeling and offer insights into its computational aspects. Full article
(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)
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<p>Graceful local antimagic labelings of <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>P</mi> <mn>6</mn> </msub> </semantics></math> and a tree <math display="inline"><semantics> <msub> <mi>T</mi> <mn>6</mn> </msub> </semantics></math>, which are not graceful antimagic.</p>
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<p>Graceful local antimagic labeling of 5 vertces.</p>
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<p>Graceful local antimagic labeling of 6 vertces.</p>
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<p>Graceful local antimagic labeling of 7 vertces.</p>
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<p>Graceful local antimagic labeling of 8 vertces.</p>
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<p>Graceful local antimagic labeling of 9 vertces.</p>
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<p>Graceful local antimagic labeling of 10 vertces.</p>
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<p>Graceful local antimagic labeling of 11 vertces.</p>
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<p>Graceful local antimagic labeling of 12 vertces.</p>
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<p>Graceful local antimagic labelings of 13 vertces.</p>
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<p>Graceful local antimagic labelings of 14 vertces.</p>
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<p>Graceful local antimagic labeling of cycles.</p>
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<p>All graceful antimagic trees on 9 vertices.</p>
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<p>All graceful antimagic trees on 9 vertices.</p>
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<p>All graceful antimagic trees on 9 vertices.</p>
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<p>Graceful local antimagic labeling of <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>.</p>
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14 pages, 450 KiB  
Article
Consumer Transactions Simulation Through Generative Adversarial Networks Under Stock Constraints in Large-Scale Retail
by Sergiy Tkachuk, Szymon Łukasik and Anna Wróblewska
Electronics 2025, 14(2), 284; https://doi.org/10.3390/electronics14020284 - 12 Jan 2025
Viewed by 349
Abstract
In the rapidly evolving domain of large-scale retail data systems, envisioning and simulating future consumer transactions has become a crucial area of interest. It offers significant potential to fortify demand forecasting and fine-tune inventory management. This paper presents an innovative application of Generative [...] Read more.
In the rapidly evolving domain of large-scale retail data systems, envisioning and simulating future consumer transactions has become a crucial area of interest. It offers significant potential to fortify demand forecasting and fine-tune inventory management. This paper presents an innovative application of Generative Adversarial Networks (GANs) to generate synthetic retail transaction data, specifically focusing on a novel system architecture that combines consumer behavior modeling with stock-keeping unit (SKU) availability constraints to address real-world assortment optimization challenges. We diverge from conventional methodologies by integrating SKU data into our GAN architecture and using more sophisticated embedding methods (e.g., hyper-graphs). This design choice enables our system to generate not only simulated consumer purchase behaviors but also reflects the dynamic interplay between consumer behavior and SKU availability—an aspect often overlooked, among others, because of data scarcity in legacy retail simulation models. Our GAN model generates transactions under stock constraints, pioneering a resourceful experimental system with practical implications for real-world retail operation and strategy. Preliminary results demonstrate enhanced realism in simulated transactions measured by comparing generated items with real ones using methods employed earlier in related studies. This underscores the potential for more accurate predictive modeling. Full article
(This article belongs to the Special Issue Data Retrieval and Data Mining)
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<p>Proposed augmentation of conditional GAN.</p>
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<p>Stabilization of discriminator training process (illustrative example).</p>
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