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14 pages, 1618 KiB  
Article
A Lightweight Deep Learning Network with an Optimized Attention Module for Aluminum Surface Defect Detection
by Yizhe Li, Yidong Xie and Hu He
Sensors 2024, 24(23), 7691; https://doi.org/10.3390/s24237691 (registering DOI) - 30 Nov 2024
Abstract
Aluminum is extensively utilized in the aerospace, aviation, automotive, and other industries. The presence of surface defects on aluminum has a significant impact on product quality. However, traditional detection methods fail to meet the efficiency and accuracy requirements of industrial practices. In this [...] Read more.
Aluminum is extensively utilized in the aerospace, aviation, automotive, and other industries. The presence of surface defects on aluminum has a significant impact on product quality. However, traditional detection methods fail to meet the efficiency and accuracy requirements of industrial practices. In this study, we propose an innovative aluminum surface defect detection method based on an optimized two-stage Faster R-CNN network. A 2D camera serves as the image sensor, capturing high-resolution images in real time. Optimized lighting and focus ensure that defect features are clearly visible. After preprocessing, the images are fed into a deep learning network incorporated with a multi-scale feature pyramid structure, which effectively enhances defect recognition accuracy by integrating high-level semantic information with location details. Additionally, we introduced an optimized Convolutional Block Attention Module (CBAM) to further enhance network efficiency. Furthermore, we employed the genetic K-means algorithm to optimize prior region selection, and a lightweight Ghost model to reduce network complexity by 14.3%, demonstrating the superior performance of the Ghost model in terms of loss function optimization during training and validation as well as in terms of detection accuracy, speed, and stability. The network was trained on a dataset of 3200 images captured by the image sensor, split in an 8:1:1 ratio for training, validation, and testing, respectively. The experimental results show a mean Average Precision (mAP) of 94.25%, with individual Average Precision (AP) values exceeding 80%, meeting industrial standards for defect detection. Full article
(This article belongs to the Special Issue Sensing and Imaging for Defect Detection: 2nd Edition)
19 pages, 6184 KiB  
Article
Ghost Discrimination Method for Broadband Direct Position Determination Based on Frequency Coloring Technology
by Mengling Yu, Long Yang, Yixin Yang, Xionghou Liu and Lu Wang
J. Mar. Sci. Eng. 2024, 12(12), 2182; https://doi.org/10.3390/jmse12122182 - 28 Nov 2024
Viewed by 233
Abstract
Recently proposed direct position determination (DPD) methods have garnered considerable interest in passive localization due to their excellent positioning accuracy. However, in multiple-target environments, error locations generated by wrong associations between different targets and arrays, called ghosts, may lead to incorrect estimations of [...] Read more.
Recently proposed direct position determination (DPD) methods have garnered considerable interest in passive localization due to their excellent positioning accuracy. However, in multiple-target environments, error locations generated by wrong associations between different targets and arrays, called ghosts, may lead to incorrect estimations of the targets, reducing positioning accuracy. To address this, we propose a ghost discrimination method for broadband DPD that exploits the frequency structure differences between various targets. In the frequency coloring strategy proposed in this study, different RGB values are assigned to the spatial spectrum of different frequencies. Then, an RGB color spatial spectrum reflecting the different frequency structures of the signals is formed, which effectively distinguishes between real targets and ghosts visually and enhances multi-target localization accuracy. The probability of correctly distinguishing between targets and ghosts in the proposed method is evaluated using simulation results. It can effectively distinguish multiple targets even at a low SNR level, a significant improvement compared with the original DPD. Furthermore, the SwellEx-96 shallow-water experimental data set is utilized to demonstrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Advances in Underwater Positioning and Navigation Technology)
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<p>Ghosts and targets.</p>
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<p>RGB color space.</p>
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<p>RGB color mapping.</p>
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<p>Two-dimensional spatial spectral value mapping principle.</p>
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<p>Color broadband spatial spectrum mapping.</p>
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<p>The position of the arrays and the targets.</p>
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<p>The spatial spectra of the equivalent intensity targets. (<b>a</b>) Spatial spectrum of the DPD-MVDR method. (<b>b</b>) RGB color spatial spectrum of the proposed method.</p>
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<p>The spatial spectra of the different intensity targets. (<b>a</b>) Spatial spectrum of the DPD-MVDR method. (<b>b</b>) RGB color spatial spectrum of the proposed method.</p>
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<p>The position of the arrays and the targets.</p>
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<p>The spatial spectra of three targets. (<b>a</b>) Spatial spectrum of the DPD-MVDR method. (<b>b</b>) RGB color spatial spectrum of the proposed method.</p>
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<p>The probability of distinguishing between targets and ghosts.</p>
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<p>S59 motion trajectory. (<b>a</b>) The target trajectory of the entire S59 event; the red line indicates the interference trajectory, and the blue line represents the target trajectory, marked at five-minute intervals [<a href="#B42-jmse-12-02182" class="html-bibr">42</a>]. (<b>b</b>) The positions of the targets and the arrays in the period of interest.</p>
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<p>Starting at 12:15, the spectrum of the 10 s signal was intercepted for processing. (<b>a</b>) Time–frequency diagram of HLA North. (<b>b</b>) Time–frequency diagram of HLA South.</p>
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<p>Starting at 12:15, the direct positioning spatial spectrum of the 10 s signal is intercepted. (<b>a</b>) The spatial spectrum of the DPD-MVDR method. (<b>b</b>) The RGB color space spectrum of the proposed method under the same conditions.</p>
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<p>Starting at 11:45, the first 50 min of the S59 event were intercepted and the BTR was drawn. (<b>a</b>) The BTR of HLA North, (<b>b</b>) the BTR of HLA South at the same time.</p>
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29 pages, 16547 KiB  
Article
Research on Shoveling Position Analysis and Recognition of Unmanned Loaders for Gravel Piles
by Hanwen Zhang, Sun Jin, Bing Li, Bo Xu, Yuanbin Xiao and Weixin Zhou
Appl. Sci. 2024, 14(23), 11036; https://doi.org/10.3390/app142311036 - 27 Nov 2024
Viewed by 282
Abstract
Gravel is the most frequently used material in infrastructure construction. However, the irregular shape of the gravel pile makes it challenging for the loader to predict a stable shoveling position, which can easily result in partial collapse or a complete landslide, thereby posing [...] Read more.
Gravel is the most frequently used material in infrastructure construction. However, the irregular shape of the gravel pile makes it challenging for the loader to predict a stable shoveling position, which can easily result in partial collapse or a complete landslide, thereby posing a serious threat to the equipment. In view of the imperfect method of determining the shoveling position of the pile by the current unmanned loader and the high hardware requirements for the deployment of the identification model, this paper first establishes a mathematical model of the loader, and preliminarily determines the influence of the concave and convex edges of the gravel pile on the shoveling position selection through discrete element joint simulation; secondly, the influence of the pile with different edge curvatures on the loader operation process is analyzed in the simulation software, and the radar map is used to further identify the superior position features; finally, Ghost Net is used as the backbone network, the RFB module is introduced into the Backbone, and the CBAM attention mechanism is integrated into the C3 module to identify the lightweight YOLOv5s shoveling position. Discrete element analysis and a lightweight network model were used in the above study to find the safest and most effective shoveling positions. During the test that mimicked how the loader would actually shovel, the number of parameters in the improved model was cut down to 32.5% of the original, the number of calculations was cut down to about 55.2% of the original, and the average accuracy of finding the shoveling position of the gravel pile reached 98%. Full article
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<p>Overall research methodology framework.</p>
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<p>Overall research methodology framework.</p>
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<p>Loader execution device model, among them: 1. Bucket 2. Linkage 3. Boom 4. Rocker 5. Bucket hydraulic rod 6. Bucket hydraulic cylinder 7. Frame 8. Boom hydraulic cylinder 9. Boom hydraulic rod.</p>
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<p>Loader bucket tip trajectory.</p>
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<p>Crushed stone particle model.</p>
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<p>Modeling convex and concave areas of shoveling gravel in a coupled EDEM and Adams simulation, among them: (<b>a</b>) is the simulation of shoveling the convex part of gravel; (<b>b</b>) simulation of shoveling concave part of gravel.</p>
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<p>The lateral force of crushed stone on the bucket.</p>
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<p>The gravel pile after the shovel is finished.</p>
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<p>Generation of rubble piles with different drop geometries, among them: (<b>a</b>) cylindrical geometry; (<b>b</b>) rectangular geometry.</p>
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<p>Resistance curve during the insertion stage.</p>
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<p>Resistance curve during the lifting stage.</p>
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<p>Comparison of edge curvature for simulation I. The three lines represent the different edges formed by the generation of 3375 kg of rubble. H represents the fitted edge curvature.</p>
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<p>Comparison of edge curvature for simulation II. The three lines represent the different edges formed by the generation of 5063 kg of rubble. H represents the fitted edge curvature.</p>
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<p>Comparison of edge curvature for simulation III. The three lines represent the different edges formed by the generation of 6750 kg of rubble. H represents the fitted edge curvature.</p>
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<p>Radar chart area corresponding to different edge curvatures of 3375 kg stockpile.</p>
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<p>Radar chart area corresponding to different edge curvatures of 5063 kg stockpile.</p>
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<p>Radar chart area corresponding to different edge curvatures of 6750 kg stockpile.</p>
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<p>Data augmentation, among them: (<b>a</b>) add Gaussian noise to the original image; (<b>b</b>) add overexposure to the original image; (<b>c</b>) add fog noise to the original image; (<b>d</b>) the original image is rotated and tilted by <math display="inline"><semantics> <mrow> <mo>±</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to present the uneven working environment.</p>
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<p>Network structure diagram, where: (<b>a</b>) is the original YOLOv5s network structure diagram. (<b>b</b>) is the improved YOLOv5s network structure diagram in this paper.</p>
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<p>(<b>a</b>) Standard convolution module; (<b>b</b>) ghost convolution module.</p>
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<p>The bottleneck structure of ghost module, where: (<b>a</b>) step size is 1; (<b>b</b>) step size is 2.</p>
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<p>RFB module.</p>
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<p>Structure of CBAM.</p>
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<p>C3-CBAM structure diagram, where: (<b>a</b>) C3-CBAM structure diagram; (<b>b</b>) structure diagram of CBAM bottleneck in C3.</p>
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<p>Loss function curve of the improved model.</p>
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<p>The performance advantage of the improved YOLOv5s model. (<b>a</b>) The change in mAP@0.5 performance indicators of different model algorithms on the data set. (<b>b</b>) The classification performance of the improved YOLOv5s model is evaluated based on the P–R curve. In the figure, the closer the curve is to the upper right corner, the better the model performance.</p>
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<p>Test bench for detection device.</p>
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<p>Experimental results: (<b>a</b>) The image labels of this column of images used for training. (<b>b</b>) This column is the detection result of the original YOLOv5s model. (<b>c</b>) This column shows the detection results of the improved YOLOv5s model.</p>
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21 pages, 8183 KiB  
Article
ARSOD-YOLO: Enhancing Small Target Detection for Remote Sensing Images
by Yijuan Qiu, Xiangyue Zheng, Xuying Hao, Gang Zhang, Tao Lei and Ping Jiang
Sensors 2024, 24(23), 7472; https://doi.org/10.3390/s24237472 - 23 Nov 2024
Viewed by 436
Abstract
Remote sensing images play a vital role in domains including environmental monitoring, agriculture, and autonomous driving. However, the detection of targets in remote sensing images remains a challenging task. This study introduces innovative methods to enhance feature extraction, feature fusion, and model optimization. [...] Read more.
Remote sensing images play a vital role in domains including environmental monitoring, agriculture, and autonomous driving. However, the detection of targets in remote sensing images remains a challenging task. This study introduces innovative methods to enhance feature extraction, feature fusion, and model optimization. The Adaptive Selective Feature Enhancement Module (AFEM) dynamically adjusts feature weights using GhostModule and sigmoid functions, thereby enhancing the accuracy of small target detection. Moreover, the Adaptive Multi-scale Convolution Kernel Feature Fusion Module (AKSFFM) enhances feature fusion through multi-scale convolution operations and attention weight learning mechanisms. Moreover, our proposed ARSOD-YOLO optimized the network architecture, component modules, and loss functions based on YOLOv8, enhancing outstanding small target detection capabilities while preserving model efficiency. We conducted experiments on the VEDAI and AI-TOD datasets, showcasing the excellent performance of ARSOD-YOLO. Our algorithm achieved an mAP50 of 74.3% on the VEDAI dataset, surpassing the YOLOv8 baseline by 3.1%. Similarly, on the AI-TOD dataset, the mAP50 reached 47.8%, exceeding the baseline network by 6.1%. Full article
(This article belongs to the Section Sensing and Imaging)
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<p>Some examples of remote sensing images.</p>
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<p>YOLOv8 network architecture.</p>
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<p>ARSOD-YOLO network architecture.</p>
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<p>The basic structure of AFEM. It consists of GhostModule and MLP as the basic components.</p>
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<p>Structural diagrams of AKSFFM, C2f, and Bottleneck.</p>
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<p>Images illustrating the different categories of the dataset [<a href="#B43-sensors-24-07472" class="html-bibr">43</a>].</p>
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<p>Comparison of AI-TOD with other benchmark datasets [<a href="#B44-sensors-24-07472" class="html-bibr">44</a>].</p>
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<p>Visualization of mAP effects of different modules.</p>
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<p>PR curves for categories in the VEDAI dataset.</p>
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<p>PR curves for categories in the AI-TOD dataset.</p>
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<p>Visual comparison of object detection models: ARSOD-YOLO vs. YOLOv3, YOLOv5, and YOLOv10 on VEDAI dataset images.</p>
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13 pages, 341 KiB  
Article
Dr. Cinderella and the Bronze Artifact, Cardinal Napellus and the Copper Globe: Was Gustav Meyrink an Early Adopter of M.R. James’s Ghostly Fiction?
by Martin Voracek
Humanities 2024, 13(6), 162; https://doi.org/10.3390/h13060162 - 21 Nov 2024
Viewed by 428
Abstract
Hitherto unnoticed similarities between two short stories by Gustav Meyrink and two of the most renowned and widely read ghost stories of M.R. James are detailed through comparative literary analysis. Specifically, one early occult horror tale of Meyrink, The Plants of Dr. Cinderella [...] Read more.
Hitherto unnoticed similarities between two short stories by Gustav Meyrink and two of the most renowned and widely read ghost stories of M.R. James are detailed through comparative literary analysis. Specifically, one early occult horror tale of Meyrink, The Plants of Dr. Cinderella (1905), shows no less than about 15 congruences beneath the plot level (concerning specific story requisites) with M.R. James’s ‘Oh, Whistle, and I’ll Come to You, My Lad’ (1904), as does, to the same extent, a later, widely known Meyrink tale (The Cardinal Napellus, 1914) vis-à-vis M.R. James’s Mr Humphreys and His Inheritance (1911). Although direct, conclusive evidence is unavailable, a nexus of circumstantial evidence, building on extensive biographical and bibliographical inquiries, convergently attests to these assumed literary influences on Meyrink: for both cases, the chronology is intact and thus possible; Meyrink was expertly fluent in English and well-connected to England and English literature; and, these borrowings are reminiscent of other, already known originality issues surrounding Meyrink’s work. Altogether, these new discoveries shed fresh light on idiosyncrasies of Meyrink’s creative process, imagination, and literary production; on his still under-researched literary inspirational sources; as well as on the early reception of M.R. James’s ghostly fiction beyond the anglophone sphere. Full article
8 pages, 2186 KiB  
Proceeding Paper
Delicious Cyber Ghost: Using Pepper’s Ghost in Computer-Aided Design to Enhance Cantonese Morning Tea Education
by Song Xu, Peng-Wei Hsiao, Chen Li and Jin-Yu Zhang
Eng. Proc. 2024, 74(1), 78; https://doi.org/10.3390/engproc2024074078 - 21 Nov 2024
Viewed by 242
Abstract
Cantonese morning tea drinking is a cherished intangible cultural heritage in the Guangdong–Hong Kong–Macao Greater Bay Area in China and embodies Guangdong’s culinary tradition. In the digital era, innovative design techniques and digital technology have been applied to preserve and promote this tradition. [...] Read more.
Cantonese morning tea drinking is a cherished intangible cultural heritage in the Guangdong–Hong Kong–Macao Greater Bay Area in China and embodies Guangdong’s culinary tradition. In the digital era, innovative design techniques and digital technology have been applied to preserve and promote this tradition. To enhance heritage education, we designed an augmented reality device for Cantonese morning tea using Pepper’s Ghost technique. Employing field investigations, literature research, and experiments, we showcased Cantonese morning tea drinking. For further developments, affordable materials and professional photos are essential for constructing the model. Full article
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<p>Storyboard.</p>
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<p>The Pepper’s Ghost device’s conceptual design.</p>
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<p>Virtual character “Shrimp Dumpling” and characters in Brother Hao’s dream.</p>
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<p>Filming the performance of the main character “Brother Hao”.</p>
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<p>Filming the lion dance performance.</p>
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<p>Scene compositing of real person and virtual character “Shrimp Dumpling”.</p>
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<p>Scene compositing of real person and virtual characters “Dancing Lion”.</p>
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<p>Effect of the Pepper’s Ghost device.</p>
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26 pages, 14487 KiB  
Article
Accelerating Die Bond Quality Detection Using Lightweight Architecture DSGβSI-Yolov7-Tiny
by Bao Rong Chang, Hsiu-Fen Tsai and Wei-Shun Chang
Electronics 2024, 13(22), 4573; https://doi.org/10.3390/electronics13224573 - 20 Nov 2024
Viewed by 316
Abstract
The die bonding process is one of the most critical steps in the front-end semiconductor packaging process, as it significantly affects the yield of the entire IC packaging process. This research aims to find an efficient, intelligent vision detection model to identify whether [...] Read more.
The die bonding process is one of the most critical steps in the front-end semiconductor packaging process, as it significantly affects the yield of the entire IC packaging process. This research aims to find an efficient, intelligent vision detection model to identify whether each chip correctly adheres to the IC substrate; by utilizing the detection model to classify the type of defects occurring in the die bond images, the engineers can analyze the leading causes, enabling timely adjustments to key machine parameters in real-time, improving the yield of the die bond process, and significantly reducing manufacturing cost losses. This study proposes the lightweight Yolov7-tiny model using Depthwise-Separable and Ghost Convolutions and Sigmoid Linear Unit with β parameter (DSGβSI-Yolov7-tiny), which we can apply for real-time and efficient detection and prediction of die bond quality. The model achieves a maximum FPS of 192.3, a precision of 99.1%, and an F1-score of 0.97. Therefore, the performance of the proposed DSGβSI-Yolov7-tiny model outperforms other methods. Full article
(This article belongs to the Special Issue Novel Methods for Object Detection and Segmentation)
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<p>IC packaging and testing process.</p>
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<p>Yolov4-tiny architecture.</p>
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<p>Yolov5n architecture.</p>
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<p>Yolov7 architecture.</p>
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<p>Yolov7-tiny architecture. Note: k represents kernel size, and s stands for stride.</p>
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<p>Ghost convolution.</p>
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<p>Depthwise separable convolution.</p>
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<p>Depthwise separable and Ghost convolutions.</p>
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<p>DSG-Yolov7 architecture. Note: k represents kernel size, and s stands for stride.</p>
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<p>Sample images of die bond categories. (<b>a</b>,<b>c</b>,<b>e</b>) bond_good; (<b>b</b>,<b>d</b>,<b>f</b>) bond_bad.</p>
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<p>Sample images of die bond categories. (<b>a</b>,<b>c</b>,<b>e</b>) bond_good; (<b>b</b>,<b>d</b>,<b>f</b>) bond_bad.</p>
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<p>Die bond recognition. (<b>a</b>,<b>c</b>,<b>e</b>) bond_good; (<b>b</b>,<b>d</b>,<b>f</b>) bond_bad.</p>
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<p>Die bond recognition. (<b>a</b>,<b>c</b>,<b>e</b>) bond_good; (<b>b</b>,<b>d</b>,<b>f</b>) bond_bad.</p>
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<p>Judgment of categories with bond_good or bond_bad.</p>
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<p>Any combination of the bond detection of the chip’s sides and corners.</p>
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<p>Prediction classification with type of die bond.</p>
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<p>DSG-Yolov7-tiny architecture. Note: k represents kernel size, and s stands for stride.</p>
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<p>DSGβSI-Yolov7-tiny architecture. Note: k represents kernel size, and s stands for stride.</p>
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<p>The workflow of the system.</p>
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<p>The precision–recall curve for the object detection model. (<b>a</b>) Yolov4-tiny; (<b>b</b>) Yolov5n; (<b>c</b>) Yolov7; (<b>d</b>) Yolov7-tiny; (<b>e</b>) DSG-Yolov7; (<b>f</b>) DSG-Yolov7-tiny; (<b>g</b>) DSGSI-Yolov7-tiny; (<b>h</b>) DSGβSI-Yolov7-tiny.</p>
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<p>The precision–recall curve for the object detection model. (<b>a</b>) Yolov4-tiny; (<b>b</b>) Yolov5n; (<b>c</b>) Yolov7; (<b>d</b>) Yolov7-tiny; (<b>e</b>) DSG-Yolov7; (<b>f</b>) DSG-Yolov7-tiny; (<b>g</b>) DSGSI-Yolov7-tiny; (<b>h</b>) DSGβSI-Yolov7-tiny.</p>
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<p>Loss plot of DSGβSI-Yolov7-tiny. (<b>a</b>) Box loss; (<b>b</b>) objectivity loss; (<b>c</b>) classified losses; (<b>d</b>) verify box loss; (<b>e</b>) verify objectivity loss; (<b>f</b>) verify classification losses.</p>
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<p>Loss plot of DSGβSI-Yolov7-tiny. (<b>a</b>) Box loss; (<b>b</b>) objectivity loss; (<b>c</b>) classified losses; (<b>d</b>) verify box loss; (<b>e</b>) verify objectivity loss; (<b>f</b>) verify classification losses.</p>
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16 pages, 3285 KiB  
Article
Research on the Classification of Sun-Dried Wild Ginseng Based on an Improved ResNeXt50 Model
by Dongming Li, Zhenkun Zhao, Yingying Yin and Chunxi Zhao
Appl. Sci. 2024, 14(22), 10613; https://doi.org/10.3390/app142210613 - 18 Nov 2024
Viewed by 375
Abstract
Ginseng is a common medicinal herb with high value due to its unique medicinal properties. Traditional methods for classifying ginseng rely heavily on manual judgment, which is time-consuming and subjective. In contrast, deep learning methods can objectively learn the features of ginseng, saving [...] Read more.
Ginseng is a common medicinal herb with high value due to its unique medicinal properties. Traditional methods for classifying ginseng rely heavily on manual judgment, which is time-consuming and subjective. In contrast, deep learning methods can objectively learn the features of ginseng, saving both labor and time. This experiment proposes a ginseng-grade classification model based on an improved ResNeXt50 model. First, each convolutional layer in the Bottleneck structure is replaced with the corresponding Ghost module, reducing the model’s computational complexity and parameter count without compromising performance. Second, the SE attention mechanism is added to the model, allowing it to capture feature information more accurately and precisely. Next, the ELU activation function replaces the original ReLU activation function. Then, the dataset is augmented and divided into four categories for model training. A model suitable for ginseng grade classification was obtained through experimentation. Compared with classic convolutional neural network models ResNet50, AlexNet, iResNet, and EfficientNet_v2_s, the accuracy improved by 10.22%, 5.92%, 4.63%, and 3.4%, respectively. The proposed model achieved the best results, with a validation accuracy of up to 93.14% and a loss value as low as 0.105. Experiments have shown that this method is effective in recognition and can be used for ginseng grade classification research. Full article
(This article belongs to the Special Issue Deep Learning and Digital Image Processing)
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<p>Ginseng dataset. (<b>a</b>) Different levels of ginseng images; (<b>b</b>) sample image after data enhancement.</p>
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<p>Group convolution.</p>
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<p>Ghost module.</p>
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<p>Comparison of the ReLU and Leaky ELU functions.</p>
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<p>Squeeze and excitation networks.</p>
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<p>Improved ResNeXt50 model structure.</p>
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<p>Experimental results of each model: (<b>a</b>) Model Accuracy; (<b>b</b>) Model Loss.</p>
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<p>Comparison of thermal characteristic maps before and after model improvement.</p>
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<p>Confusion matrix before and after model improvement. (<b>a</b>) The confusion matrix of improved model; (<b>b</b>) confusion matrix of ResNeXt50.</p>
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<p>Visualization of misclassified samples.</p>
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16 pages, 1989 KiB  
Article
Evaluation of Five Asian Lily Cultivars in Chongqing Province China and Effects of Exogenous Substances on the Heat Resistance
by Ningyu Bai, Yangjing Song, Yu Li, Lijun Tan, Jing Li, Lan Luo, Shunzhao Sui and Daofeng Liu
Horticulturae 2024, 10(11), 1216; https://doi.org/10.3390/horticulturae10111216 - 17 Nov 2024
Viewed by 459
Abstract
Lily is one of the world’s important ornamental flowers. Potted Asiatic lily is a further selected dwarf cultivar suitable for indoor or garden planting. However, there is a lack of relevant research on the cultivation adaptability of potted Asiatic lilies cultivars in the [...] Read more.
Lily is one of the world’s important ornamental flowers. Potted Asiatic lily is a further selected dwarf cultivar suitable for indoor or garden planting. However, there is a lack of relevant research on the cultivation adaptability of potted Asiatic lilies cultivars in the Chongqing region which in the southwest of China. This study selected five potted Asiatic lily cultivars, and the phenological period, stem and leaf characteristics, and flowering traits were assessed through statistical observation. The Asiatic lily ‘Tiny Ghost’ and ‘Tiny Double You’ are well-suited for both spring and autumn planting in Chongqing, while ‘Sugar Love’ and ‘Curitiba’ are best planted in the spring. The ‘Tiny Diamond’ is more appropriate for autumn planting due to its low tolerance to high temperature. The application of exogenous substances, including calcium chloride (CaCl2), potassium fulvic acid (PFA) and melatonin (MT), can mitigate the detrimental effects of high-temperature stress on ‘Tiny Diamond’ by regulating photosynthesis, antioxidant systems, and osmotic substance content. A comprehensive evaluation using the membership function showed that the effect of exogenous CaCl2 treatment is the best, followed by exogenous PFA treatment. CaCl2 acts as a positive regulator of heat stress tolerance in Asian lilies, with potential applications in Asian lily cultivation. This study provides reference for cultivation and application of Asian lily varieties in Chongqing region, and also laid the foundation for further research on the mechanism of exogenous substances alleviating heat stress in lilies. Full article
(This article belongs to the Special Issue Emerging Insights into Horticultural Crop Ecophysiology)
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<p>Asian lily cultivars. (<b>A</b>). ‘Tiny Double You’; (<b>B</b>). ‘Curitiba’; (<b>C</b>). ‘Tiny Diamond’; (<b>D</b>). ‘Sugar Love’; (<b>E</b>). ‘Tiny Ghost’.</p>
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<p>Oxidative stress indexes of ‘Tiny Diamond’ after exogenous application of different substances under high temperature stress. (<b>A</b>). The relative water content of lily. (<b>B</b>). The MDA content of lily. (<b>C</b>). The REL rate of lily. Note: CK: H<sub>2</sub>O; M1: 100 μmol/L MT; M2: 200 μmol/L MT; P1: 0.5 g/L PFA; P2: 1.0 g/L PFA; C1: 20 mmol/L CaCl<sub>2</sub>; C2: 40 mmol/L CaCl<sub>2</sub>. Different lowercase letters indicate significant differences between treatments (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>Chlorophyll content of ‘Tiny Diamond’ after application of exogenous substances. Different lowercase letters indicate significant differences between treatments (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>SOD content of ‘Tiny Diamond’ after application of exogenous substances. Different lowercase letters indicate significant differences between treatments (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>Content of osmoregulatory substances in ‘Tiny Diamond’ after application of exogenous substances. (<b>A</b>). Proline content. (<b>B</b>). Soluble protein content. (<b>C</b>). Total soluble sugar content. Different lowercase letters indicate significant differences between treatments (<span class="html-italic">p</span> &lt; 0.05).</p>
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<p>Correlation analysis of ten indicators under treatment with three exogenous substances. Note: * means correlation is extremely significant at the 0.05 level, ** means correlation is extremely significant at the 0.01 level.</p>
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19 pages, 5488 KiB  
Article
Insulator-YOLO: Transmission Line Insulator Risk Identification Based on Improved YOLOv5
by Nan Zhang, Jingyi Su, Yang Zhao and Hua Chen
Processes 2024, 12(11), 2552; https://doi.org/10.3390/pr12112552 - 15 Nov 2024
Viewed by 383
Abstract
This study introduces an innovative method for detecting risks in transmission line insulators by developing an optimized variant of YOLOv5, named Insulator-YOLO. The model addresses key challenges in small-defect detection, complex backgrounds, and computational efficiency. By incorporating GhostNetV2 in the backbone to streamline [...] Read more.
This study introduces an innovative method for detecting risks in transmission line insulators by developing an optimized variant of YOLOv5, named Insulator-YOLO. The model addresses key challenges in small-defect detection, complex backgrounds, and computational efficiency. By incorporating GhostNetV2 in the backbone to streamline feature extraction and introducing SE and CBAM attention mechanisms, the model enhances its focus on critical features. The Bibi-directional Feature feature Pyramid pyramid Network network (BiFPN) is applied to enhance multi-scale feature fusion, and the integration of CIoU and NWD loss functions optimizes bounding box regression, achieving higher accuracy. Additionally, focal loss mitigates the imbalance between positive and negative samples, leading to more accurate and robust defect detection. Extensive evaluations demonstrate that Insulator-YOLO significantly improves detection accuracy and efficiency in real-world power line insulator defects, providing a reliable solution for maintaining the integrity of transmission systems. Full article
(This article belongs to the Special Issue AI-Based Modelling and Control of Power Systems)
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<p>FPN + PAN network structure.</p>
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<p>YOLOv5 network structure.</p>
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<p>Network structure diagram of our Insulator-YOLO algorithm.</p>
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<p>GhostNetV2 bottleneck.</p>
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<p>Schematic diagram of SE attention mechanism.</p>
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<p>The modular structure of CBAM.</p>
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<p>Structure comparison of PANet (<b>left</b>) and BiFPN (<b>right</b>).</p>
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<p>Part of the insulator self-explosion defect data.</p>
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<p>Model mAP curve comparison diagram.</p>
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<p>Model loss curve comparison diagram.</p>
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<p>Partial visualization results.</p>
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23 pages, 10156 KiB  
Article
GFS-YOLO11: A Maturity Detection Model for Multi-Variety Tomato
by Jinfan Wei, Lingyun Ni, Lan Luo, Mengchao Chen, Minghui You, Yu Sun and Tianli Hu
Agronomy 2024, 14(11), 2644; https://doi.org/10.3390/agronomy14112644 - 9 Nov 2024
Viewed by 774
Abstract
In order to solve the problems that existing tomato maturity detection methods struggle to take into account both common tomato and cherry tomato varieties in complex field environments (such as light change, occlusion, and fruit overlap) and the model size being too large, [...] Read more.
In order to solve the problems that existing tomato maturity detection methods struggle to take into account both common tomato and cherry tomato varieties in complex field environments (such as light change, occlusion, and fruit overlap) and the model size being too large, this paper proposes a lightweight tomato maturity detection model based on improved YOLO11, named GFS-YOLO11. In order to achieve a lightweight network, we propose the C3k2_Ghost module to replace the C3K2 module in the original network, which can ensure a feature extraction capability and reduce model computation. In order to compensate for the potential feature loss caused by the light weight, this paper proposes a feature-refining module (FRM). After embedding each feature extraction module in the trunk network, it improves the feature expression ability of common tomato and cherry tomato in complex field environments by means of depth-separable convolution, multi-scale pooling, and channel attention and spatial attention mechanisms. In addition, in order to further improve the detection ability of the model for tomatoes of different sizes, the SPPFELAN module is also proposed in this paper. In combining the advantages of SPPF and ELAN, multiple parallel SPPF branches are used to extract features of different levels and perform splicing and fusion. To verify the validity of the method, this study constructed a dataset of 1061 images of common and cherry tomatoes, covering tomatoes in six ripened categories. The experimental results show that the performance of the GFS-YOLO11 model is significantly improved compared with the original model; the P, R, mAP50, and MAP50-95 increased by 5.8%, 4.9%, 6.2%, and 5.5%, respectively, and the number of parameters and calculation amount were reduced by 35.9% and 22.5%, respectively. The GFS-YOLO11 model is lightweight while maintaining high precision, can effectively cope with complex field environments, and more conveniently meet the needs of real-time maturity detection of common tomatoes and cherry tomatoes. Full article
(This article belongs to the Section Precision and Digital Agriculture)
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<p>In order to create a dataset of ordinary tomatoes and cherry tomatoes with a variety of light environments, shooting angles, and occlusion conditions, we paid special attention to the following scenarios when capturing images: (1) shooting from above under bright light; (2) the shooting angle when the object is partially occluded or overlapped; (3) shooting from the side under sufficient lighting conditions; (4) shooting from the front in a low-light environment.</p>
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<p>Examples of data enhancement techniques: random processing of images, including rotation in the range of 15 to 45 degrees, horizontal flipping, introduction of random noise, and horizontal or vertical translation.</p>
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<p>Model structure diagram of GFS-YOLO11.</p>
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<p>Network structure of the C3K2_Ghost module.</p>
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<p>Model structure diagram of FRM.</p>
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<p>SPPFELAN model structure diagram.</p>
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<p>Experimental results of GFS-YOLO11 model.</p>
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<p>F1 fraction curve of GFS-YOLO11 model.</p>
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<p>Precision–Recall curve of GFS-YOLO11 model.</p>
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<p>This figure shows a performance comparison of 12 models on multiple evaluation indicators, including the mAP50, MAP50-95, model volume, number of parameters, computational complexity, and average inference time. In the radar map, each curve represents a model, and the closer the intersection of the curve and the axis is to the edge, the better the model performs on the corresponding indicator. The larger the area enclosed by the curve, the stronger the overall performance of the model.</p>
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<p>This figure shows the detection results of the original model and GFS-YOLO11 on common tomatoes. The first image shows the real labels, the second image shows the detection results of the original model, and the third image shows the detection results of GFS-YOLO11. The red arrows indicate false detections, and the yellow arrows indicate missed detections.</p>
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<p>This figure shows the detection results of the original model and GFS-YOLO11 on cherry tomatoes. The first image shows the real labels, the second image shows the detection results of the original model, and the third image shows the detection results of GFS-YOLO11. The red arrows indicate false detections, and the yellow arrows indicate missed detections.</p>
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<p>The first row is the feature visualizations of the YOLO11 backbone network, and the second row is the feature visualizations of the GFS-YOLO11 backbone network.</p>
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<p>This figure shows the difference between the model with the SPPFELAN module and the original model in feature extraction.</p>
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16 pages, 5783 KiB  
Article
LG-YOLOv8: A Lightweight Safety Helmet Detection Algorithm Combined with Feature Enhancement
by Zhipeng Fan, Yayun Wu, Wei Liu, Ming Chen and Zeguo Qiu
Appl. Sci. 2024, 14(22), 10141; https://doi.org/10.3390/app142210141 - 6 Nov 2024
Viewed by 541
Abstract
In the realm of construction site monitoring, ensuring the proper use of safety helmets is crucial. Addressing the issues of high parameter values and sluggish detection speed in current safety helmet detection algorithms, a feature-enhanced lightweight algorithm, LG-YOLOv8, was introduced. Firstly, we introduce [...] Read more.
In the realm of construction site monitoring, ensuring the proper use of safety helmets is crucial. Addressing the issues of high parameter values and sluggish detection speed in current safety helmet detection algorithms, a feature-enhanced lightweight algorithm, LG-YOLOv8, was introduced. Firstly, we introduce C2f-GhostDynamicConv as a powerful tool. This module enhances feature extraction to represent safety helmet wearing features, aiming to improve the efficiency of computing resource utilization. Secondly, the Bi-directional Feature Pyramid (BiFPN) was employed to further enrich the feature information, integrating feature maps from various levels to achieve more comprehensive semantic information. Finally, to enhance the training speed of the model and achieve a more lightweight outcome, we introduce a novel lightweight asymmetric detection head (LADH-Head) to optimize the original YOLOv8-n’s detection head. Evaluations on the SWHD dataset confirm the effectiveness of the LG-YOLOv8 algorithm. Compared to the original YOLOv8-n algorithm, our approach achieves a mean Average Precision (mAP) of 94.1%, a 59.8% reduction in parameters, a 54.3% decrease in FLOPs, a 44.2% increase in FPS, and a 2.7 MB compression of the model size. Therefore, LG-YOLOv8 has high accuracy and fast detection speed for safety helmet detection, which realizes real-time accurate detection of safety helmets and an ideal lightweight effect. Full article
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<p>Network structure of YOLOv8.</p>
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<p>Conventional convolution and Ghost module. (<b>a</b>) The convolutional layer; (<b>b</b>) The Ghost module.</p>
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<p>The structure of DynamicConv.</p>
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<p>Comparison of C2f and C2f-GhostDynamicConv modules: (<b>a</b>) C2f module; (<b>b</b>) C2f-GhostDynamicConv module.</p>
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<p>(<b>a</b>) FPN introduces a top-down path to fuse multiscale features from the third to the seventh level (P3–P7); (<b>b</b>) PANet enhances the FPN (Feature Pyramid Network) by incorporating an additional bottom-up pathway; and (<b>c</b>) BiFPN offers a superior balance between accuracy and efficiency.</p>
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<p>YOLOv8-n Detection Head.</p>
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<p>Network structure of the lightweight asymmetric detection head (LADH-Head).</p>
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<p>Example of experimental dataset (Reprinted from [<a href="#B35-applsci-14-10141" class="html-bibr">35</a>]).</p>
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<p>Changes in key metrics during YOLOv 8-n and LG-YOLOv8 trainings.</p>
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<p>Changes in loss during YOLOv8-n and LG-YOLOv8 training.</p>
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<p>Histogram comparison of results of different algorithms.</p>
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<p>Visualization results for different scenarios (adapted from ref. [<a href="#B35-applsci-14-10141" class="html-bibr">35</a>]). (<b>a</b>) The pictures in the original dataset and the helmet detection pictures in different scenarios; (<b>b</b>) Base model YOLOv8-n; (<b>c</b>) Improved model LG-YOLOv8.</p>
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19 pages, 14846 KiB  
Article
The Effect of Heating Rate on the Microstructure Evolution and Hardness of Heterogeneous Manganese Steel
by Wubin Ren, Peiyu Zhao, Menghu Wang, Shuai Tong, Xiaokai Liang, Xinjun Sun and Huibin Wu
Materials 2024, 17(21), 5321; https://doi.org/10.3390/ma17215321 - 31 Oct 2024
Viewed by 452
Abstract
The use of a rapid heating method to achieve heterogeneity of Mn in medium-manganese steel and improve its comprehensive performance has been widely studied and these techniques have been widely applied. However, the heating rate (from α to γ) has not received sufficient [...] Read more.
The use of a rapid heating method to achieve heterogeneity of Mn in medium-manganese steel and improve its comprehensive performance has been widely studied and these techniques have been widely applied. However, the heating rate (from α to γ) has not received sufficient attention with respect to its microstructure-evolution mechanism. In this study, the effect of heating rate on the microstructure evolution and hardness of heterogeneous medium-manganese steel was investigated by using X-ray diffraction (XRD), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and DICTRA simulation. The results showed that the Mn distribution was heterogeneous in the initial microstructure of pearlite due to strong partitioning of Mn between ferrite and cementite. At low heating rates (<10 °C/s), the heterogeneity of Mn distribution was diminished to some extent due to the long-distance diffusion of Mn in high-temperature austenite. Contrastingly, at high heating rates, the initial heterogeneity of the Mn element could be largely preserved due to insufficient diffusion of Mn, which resulted in more ghost pearlite (GP: pearlite-like microstructure with film martensite/RA). Moreover, the high heating rate not only refines the prior austenite grain but also increases the total RA content, which is mainly composed of additional film RA. As the heating rate increases, the hardness gradually increases from 628.1 HV to 663.3 HV, due to grain refinement and increased dislocation density. Dynamic simulations have also demonstrated a strong correlation between this interesting microstructure and the non-equilibrium diffusion of Mn. Full article
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<p>Calculation results using the TCFE10 database by Thermo-Calc software: (<b>a</b>) phase diagram, in which vertical dotted lines represent the chemical composition of the designed steel; (<b>b</b>) step diagram.</p>
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<p>Pearlite pretreatment and quenching process after heating of the tested steels at different rates.</p>
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<p>(<b>a</b>) SEM characterization of initial microstructure and (<b>b</b>) TEM characterization of pearlite. (<b>c</b>) Mn profiles along the scanning line in (<b>b</b>).</p>
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<p>Prior austenite grains at different heating rates: (<b>a</b>) 0.3 °C/s, (<b>b</b>) 10 °C/s, (<b>c</b>) 50 °C/s, and (<b>d</b>) 200 °C/s.</p>
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<p>Distribution statistics of PAGs at different heating rates: (<b>a</b>) 0.3 °C/s, (<b>b</b>) 10 °C/s, (<b>c</b>) 50 °C/s, and (<b>d</b>) 200 °C/s.</p>
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<p>XRD pattern (<b>a</b>) and RA content variation curve with heating rate (<b>b</b>).</p>
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<p>SEM microstructure at different heating rates: (<b>a</b>) 0.3 °C/s, (<b>b</b>) 10 °C/s, (<b>c</b>) 50 °C/s, and (<b>d</b>) 200 °C/s.</p>
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<p>EBSD phase distribution of the tested steels (<b>a</b>–<b>d</b>) after heating at different rates; the red phase is RA, and the gray phase is martensite: IPF diagram (<b>e</b>–<b>h</b>); (<b>a</b>,<b>e</b>) 0.3 °C/s; (<b>b</b>,<b>f</b>) 10 °C/s; (<b>c</b>,<b>g</b>) 50 °C/s; and (<b>d</b>,<b>h</b>) 200 °C/s.</p>
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<p>Polar diagram of the martensite and austenite within the selected white box in <a href="#materials-17-05321-f008" class="html-fig">Figure 8</a>d.</p>
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<p>TEM microstructure characterization of the tested steels heated at a rate of 0.3~200 °C/s: bright field image after heating at 0.3 °C/s (<b>a</b>), 10 °C/s (<b>d</b>), 50 °C/s (<b>e</b>), and 200 °C/s (<b>h</b>). Images (<b>b</b>,<b>f</b>) are the SAED patterns from the white circles in (<b>a</b>,<b>e</b>), respectively; images (<b>c</b>,<b>g</b>,<b>i</b>) are the energy spectra of the Mn content in the red-lined area in (<b>a</b>,<b>e</b>,<b>h</b>), respectively.</p>
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<p>KAM diagrams and average KAM values of the tested steels heated at different rates: (<b>a</b>) 0.3 °C/s, (<b>b</b>) 10 °C/s, (<b>c</b>) 50 °C/s, (<b>d</b>) 200 °C/s, and (<b>e</b>) average KAM values.</p>
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<p>Vickers hardness and microhardness of test steels after heating at different rates. (<b>a</b>) Macro hardness variation curve with heating rate (<b>b</b>) The variation curve of microhardness of ghost pearlite and martensite with heating rate.</p>
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<p>Microhardness indentation images of the tested steels heated at 10 °C/s (<b>a</b>) and 200 °C/s (<b>b</b>).</p>
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<p>The volume fraction of film and blocky RA after heating at different rates.</p>
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<p>Hypothetical lamellar pearlite model: initial pearlite state (<b>a</b>), and austenite growth in pearlite (<b>b</b>).</p>
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<p>Evolution of Mn (<b>a</b>) and C (<b>b</b>) profiles during continuous heating at 10 °C/s and holding for 3 s. Solid lines of different colors represent different stages of heating and insulation.</p>
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20 pages, 8544 KiB  
Article
DCS-YOLOv5s: A Lightweight Algorithm for Multi-Target Recognition of Potato Seed Potatoes Based on YOLOv5s
by Zhaomei Qiu, Weili Wang, Xin Jin, Fei Wang, Zhitao He, Jiangtao Ji and Shanshan Jin
Agronomy 2024, 14(11), 2558; https://doi.org/10.3390/agronomy14112558 - 31 Oct 2024
Viewed by 490
Abstract
The quality inspection of potato seed tubers is pivotal for their effective segregation and a critical step in the cultivation process of potatoes. Given the dearth of research on intelligent tuber-cutting machinery in China, particularly concerning the identification of bud eyes and defect [...] Read more.
The quality inspection of potato seed tubers is pivotal for their effective segregation and a critical step in the cultivation process of potatoes. Given the dearth of research on intelligent tuber-cutting machinery in China, particularly concerning the identification of bud eyes and defect detection, this study has developed a multi-target recognition approach for potato seed tubers utilizing deep learning techniques. By refining the YOLOv5s algorithm, a novel, lightweight model termed DCS-YOLOv5s has been introduced for the simultaneous identification of tuber buds and defects. This study initiates with data augmentation of the seed tuber images obtained via the image acquisition system, employing strategies such as translation, noise injection, luminance modulation, cropping, mirroring, and the Cutout technique to amplify the dataset and fortify the model’s resilience. Subsequently, the original YOLOv5s model undergoes a series of enhancements, including the substitution of the conventional convolutional modules in the backbone network with the depth-wise separable convolution DP_Conv module to curtail the model’s parameter count and computational load; the replacement of the original C3 module’s Bottleneck with the GhostBottleneck to render the model more compact; and the integration of the SimAM attention mechanism module to augment the model’s proficiency in capturing features of potato tuber buds and defects, culminating in the DCS-YOLOv5s lightweight model. The research findings indicate that the DCS-YOLOv5s model outperforms the YOLOv5s model in detection precision and velocity, exhibiting superior detection efficacy and model compactness. The model’s detection metrics, including Precision, Recall, and mean Average Precision at Intersection over Union thresholds of 0.5 (mAP1) and 0.75 (mAP2), have improved to 95.8%, 93.2%, 97.1%, and 66.2%, respectively, signifying increments of 4.2%, 5.7%, 5.4%, and 9.8%. The detection velocity has also been augmented by 12.07%, achieving a rate of 65 FPS. The DCS-YOLOv5s target detection model, by attaining model compactness, has substantially heightened the detection precision, presenting a beneficial reference for dynamic sample target detection in the context of potato-cutting machinery. Full article
(This article belongs to the Special Issue Advances in Data, Models, and Their Applications in Agriculture)
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<p>Selected Augmented Images.</p>
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<p>Schematic of the YOLOv5 Network Architecture.</p>
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<p>Illustration of Depth-wise Separable Convolution.</p>
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<p>Illustration of the Ghost Module.</p>
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<p>Illustration of the GhostConv Module.</p>
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<p>Illustration of the SimAM Attention Mechanism.</p>
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<p>Architecture of the DCS-YOLOv5s Model.</p>
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<p>Illustration of Intersection over Union (IOU).</p>
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<p>Accuracy Metric Trend Lines for Various Detection Models on the Validation Dataset.</p>
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<p>Ablation Study Outcome Graph.</p>
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<p>Category Precision Comparison in DCS-YOLOv5s Model Detection.</p>
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<p>Multi-Object Detection Heatmaps for Seed Potatoes: (<b>a</b>) 20th Layer Prediction Heatmap of the YOLOv5s Model, (<b>b</b>) 21st Layer Prediction Heatmap of the DCS-YOLOv5s Model.</p>
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<p>Seed Potato Test Image Annotation Files. (The □ symbol in the image represents the detection target, and the labels in the image represent detection categories).</p>
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<p>YOLOv5s Model Detection Illustrations. (The ☐ symbol in the image represents the detection target, the labels in the image represent detection categories and confidence values, the <b><span style="color:#00B050">○</span></b> in the image represents a missed target, and the <b><span style="color:#7030A0">○</span></b> in the image represents the false detection target).</p>
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<p>DCS-YOLOv5s Model Detection Illustrations. (The ☐ symbol in the image represents the detection target, the labels in the image represent detection categories and confidence values, and the <b>○</b> in the image represents the false detection target).</p>
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23 pages, 3287 KiB  
Article
Relational Lorentzian Asymptotically Safe Quantum Gravity: Showcase Model
by Renata Ferrero and Thomas Thiemann
Universe 2024, 10(11), 410; https://doi.org/10.3390/universe10110410 - 31 Oct 2024
Viewed by 518
Abstract
In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or [...] Read more.
In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation. Full article
(This article belongs to the Section Foundations of Quantum Mechanics and Quantum Gravity)
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<p>Projected flow diagram of the real (<b>left</b>) and imaginary (<b>right</b>) part in the <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>−</mo> <mi>g</mi> </mrow> </semantics></math> plane. The purple dot represents the fixed point in (<a href="#FD64-universe-10-00410" class="html-disp-formula">64</a>). The arrows point towards an increasing <span class="html-italic">k</span>, hence at <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math> the fixed point is attractive in both projections.</p>
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<p>Flow diagram of the <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>real</mi> </msub> <mo>−</mo> <msub> <mi>g</mi> <mi>imaginary</mi> </msub> </mrow> </semantics></math> (<b>left</b>) and <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>imaginary</mi> </msub> <mo>−</mo> <msub> <mi>g</mi> <mi>real</mi> </msub> </mrow> </semantics></math> (<b>right</b>) part. The arrows along the trajectories point towards an increasing value of <span class="html-italic">k</span>, and that means that the trajectories flow into the fixed point (<a href="#FD64-universe-10-00410" class="html-disp-formula">64</a>) (purple dot) in the UV.</p>
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<p>Flow diagram in the <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>real</mi> </msub> <mo>−</mo> <msub> <mi>λ</mi> <mi>imaginary</mi> </msub> </mrow> </semantics></math> (<b>left</b>, projected to <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <msub> <mi>g</mi> <mo>*</mo> </msub> </mrow> </semantics></math>) and in the <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mi>real</mi> </msub> <mo>−</mo> <msub> <mi>g</mi> <mi>imaginary</mi> </msub> </mrow> </semantics></math> (<b>right</b>, projected to <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <msub> <mi>λ</mi> <mo>*</mo> </msub> </mrow> </semantics></math>) space. The purple dot depicted is the fixed point in (<a href="#FD64-universe-10-00410" class="html-disp-formula">64</a>). The arrows point towards <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math>.</p>
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<p>Graphic method for the proof of the existence of an admissible trajectory for a given set of real initial conditions. At fixed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> we choose the fixed point set of initial conditions <math display="inline"><semantics> <mrow> <msub> <mi>g</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1.013</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.460</mn> </mrow> </semantics></math>, we integrate down the flow to <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and we plot the surface of the dimensionful imaginary part of <span class="html-italic">G</span> and <math display="inline"><semantics> <mo>Λ</mo> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>. The two surfaces intersect exactly in one point on the plane <math display="inline"><semantics> <mrow> <mi>Im</mi> <mrow> <mo>[</mo> <msub> <mo>Λ</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>]</mo> </mrow> <mo>=</mo> <mi>Im</mi> <mrow> <mo>[</mo> <msub> <mi>G</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mo>]</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>: the intersection point furnishes the corresponding pair of imaginary initial conditions at <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> for <math display="inline"><semantics> <msub> <mi>g</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>i</mi> </msub> </semantics></math> giving rise to an admissible trajectory.</p>
Full article ">Figure 5
<p>Admissible trajectory with <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>0.460</mn> <mo>+</mo> <mn>0.015</mn> <mi>i</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>1.013</mn> <mo>+</mo> <mn>0.079</mn> <mi>i</mi> </mrow> </semantics></math>. The flow of the imaginary parts of the dimensionful coupling constants are vanishing for <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Admissible trajectory with <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>0.460</mn> <mo>+</mo> <mn>0.015</mn> <mi>i</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>1.013</mn> <mo>+</mo> <mn>0.079</mn> <mi>i</mi> </mrow> </semantics></math>. The real part of the dimensionful coupling constants is well behaved and reaches a finite value (vanishes for <math display="inline"><semantics> <msub> <mo>Λ</mo> <mi>real</mi> </msub> </semantics></math>) when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Admissible trajectory with <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>0.460</mn> <mo>+</mo> <mn>0.015</mn> <mi>i</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>1.013</mn> <mo>+</mo> <mn>0.079</mn> <mi>i</mi> </mrow> </semantics></math>. The flow of the real and imaginary parts of the dimensionless coupling <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>k</mi> </msub> </semantics></math> reaches the UV fixed point when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math>. Note the divergence for vanishing <span class="html-italic">k</span> due to the approximation (<a href="#FD51-universe-10-00410" class="html-disp-formula">51</a>) performed in the evaluation of the integrals.</p>
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<p>Admissible trajectory with <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>0.460</mn> <mo>+</mo> <mn>0.015</mn> <mi>i</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>(</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>)</mo> <mo>=</mo> <mn>1.013</mn> <mo>+</mo> <mn>0.079</mn> <mi>i</mi> </mrow> </semantics></math>. The real and imaginary parts of the dimensionless coupling <math display="inline"><semantics> <msub> <mi>g</mi> <mi>k</mi> </msub> </semantics></math> flow into the UV fixed point when <math display="inline"><semantics> <mrow> <mi>k</mi> <mo>→</mo> <mo>∞</mo> </mrow> </semantics></math>. In the IR, both parts vanish.</p>
Full article ">Figure 9
<p>Plot of the functions <math display="inline"><semantics> <msub> <mi>f</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>f</mi> <mn>2</mn> </msub> </semantics></math> defined in (<a href="#FD66-universe-10-00410" class="html-disp-formula">66</a>) and (67) (here we fixed <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>k</mi> <mo stretchy="false">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>). Points on the two surfaces realize admissible trajectories. Those exist for increasing values of <math display="inline"><semantics> <msub> <mi>λ</mi> <mi>r</mi> </msub> </semantics></math> and cease to exist in the regime where no surface is depicted. Furthermore, we see that the surfaces are regular, hinting at the unicity of the admissible trajectories at fixed initial conditions.</p>
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