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Keywords = high-order line graph

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33 pages, 31456 KiB  
Article
Modeling and Simulation of an Integrated Synchronous Generator Connected to an Infinite Bus through a Transmission Line in Bond Graph
by Gilberto Gonzalez-Avalos, Gerardo Ayala-Jaimes, Noe Barrera Gallegos and Aaron Padilla Garcia
Symmetry 2024, 16(10), 1335; https://doi.org/10.3390/sym16101335 - 9 Oct 2024
Viewed by 787
Abstract
Most electrical energy generation systems are based on synchronous generators; as a result, their analysis always provides interesting findings, especially if an approach different to those traditionally studied is used. Therefore, an approach involving the modeling and simulation of a synchronous generator connected [...] Read more.
Most electrical energy generation systems are based on synchronous generators; as a result, their analysis always provides interesting findings, especially if an approach different to those traditionally studied is used. Therefore, an approach involving the modeling and simulation of a synchronous generator connected to an infinite bus through a transmission line in a bond graph is proposed. The behavior of the synchronous generator is analyzed in four case studies of the transmission line: (1) a symmetrical transmission line, where the resistance and inductance of the three phases (a,b,c) are equal, which determine resistances and inductances in coordinates (d,q,0) as individual decoupled elements; (2) a symmetrical transmission line for the resistances and for non-symmetrical inductances in coordinates (a,b,c) that result in resistances that are individual decoupled elements and in a field of inductances in coordinates (d,q,0); (3) a non-symmetrical transmission line for resistances and for symmetrical inductances in coordinates (a,b,c) that produce a field of resistances and inductances as individual elements decoupled in coordinates (d,q,0); and (4) a non-symmetrical transmission line for resistances and inductances in coordinates (a,b,c) that determine resistances and inductance fields in coordinates (d,q,0). A junction structure based on a bond graph model that allows for obtaining the mathematical model of this electrical system is proposed. Due to the characteristics of a bond graph, model reduction can be carried out directly and easily. Therefore, reduced bond graph models for the four transmission line case studies are proposed, where the transmission line is seen as if it were inside the synchronous generator. In order to demonstrate that the models obtained are correct, simulation results using the 20-Sim software are shown. The simulation results determine that for a symmetrical transmission line, currents in the generator in the d and q axes are −25.87 A and 0.1168 A, while in the case of a non-symmetrical transmission line, these currents are −26.14 A and 0.0211 A, showing that for these current magnitudes, the generator is little affected due to the parameters of the generator and the line. However, for a high degree of non-symmetry of the resistances in phases a, b and c, it causes the generator to reach an unstable condition, which is shown in the last simulation of the paper. Full article
(This article belongs to the Section Engineering and Materials)
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<p>Power supply to an infinite bus.</p>
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<p>Diagram of a synchronous generator.</p>
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<p>Synchronous-generator-equivalent circuits.</p>
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<p>Junction structure with modulated elements.</p>
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<p>BG of case 1.</p>
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<p>RBG of case 1.</p>
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<p>A physical representation of the RBG of case 1.</p>
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<p>BG of case 2.</p>
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<p>RBG for case 2.</p>
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<p>Physical-equivalent model of case 2.</p>
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<p>The BG of case 3.</p>
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<p>The RBG of case 3.</p>
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<p>Reduced physical model of case 3.</p>
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<p>The BG of case 4.</p>
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<p>The RB of case 4.</p>
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<p>Physical meaning of case 4.</p>
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<p>Flow chart for BGs.</p>
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<p>Variables of the SG connected to the infinite bus.</p>
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<p>Currents generated in coordinates <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mfenced> </semantics></math>: (<b>a</b>) time scale from 0 to 80 s; (<b>b</b>) time scale from 1.5 s to 5.5 s; and (<b>c</b>) time scale from 3 s to 3.06 s.</p>
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<p>Generator variables applying case 1.</p>
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<p>SG variables applying case 1.</p>
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<p>SG variables applying case 2.</p>
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<p>SG variables applying case 3.</p>
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<p>Generator behavior of the 4 case studies: (<b>a</b>) currents <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> <mo>;</mo> </mrow> </semantics></math> (<b>b</b>) currents <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> <mo>;</mo> </mrow> </semantics></math> (<b>c</b>) velocities <span class="html-italic">w</span>.</p>
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<p>SG variables with line resistances given by (<a href="#FD86-symmetry-16-01335" class="html-disp-formula">86</a>).</p>
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18 pages, 543 KiB  
Article
AHD-SLE: Anomalous Hyperedge Detection on Hypergraph Symmetric Line Expansion
by Yingle Li, Hongtao Yu, Haitao Li, Fei Pan and Shuxin Liu
Axioms 2024, 13(6), 387; https://doi.org/10.3390/axioms13060387 - 7 Jun 2024
Viewed by 1191
Abstract
Graph anomaly detection aims to identify unusual patterns or structures in graph-structured data. Most existing research focuses on anomalous nodes in ordinary graphs with pairwise relationships. However, complex real-world systems often involve relationships that go beyond pairwise relationships, and insufficient attention is paid [...] Read more.
Graph anomaly detection aims to identify unusual patterns or structures in graph-structured data. Most existing research focuses on anomalous nodes in ordinary graphs with pairwise relationships. However, complex real-world systems often involve relationships that go beyond pairwise relationships, and insufficient attention is paid to hypergraph anomaly detection, especially anomalous hyperedge detection. Some existing methods for researching hypergraphs involve transforming hypergraphs into ordinary graphs for learning, which can result in poor detection performance due to the loss of high-order information. We propose a new method for Anomalous Hyperedge Detection on Symmetric Line Expansion (AHD-SLE). The SLE of a hypergraph is an ordinary graph with pairwise relationships and can be backmapped to the hypergraph, so the SLE is able to preserve the higher-order information of the hypergraph. The AHD-SLE first maps the hypergraph to the SLE; then, the information is aggregated by Graph Convolutional Networks (GCNs) in the SLE. After that, the hyperedge embedding representation is obtained through a backmapping operation. Finally, an anomaly function is designed to detect anomalous hyperedges using the hyperedge embedding representation. Experiments on five different types of real hypergraph datasets show that AHD-SLE outperforms the baseline algorithm in terms of Area Under the receiver operating characteristic Curve(AUC) and Recall metrics. Full article
(This article belongs to the Special Issue Mathematical Modelling of Complex Systems)
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<p>Hypergraph expansions. (<b>a</b>) A hypergraph with 7 nodes and 3 hyperedges. (<b>b</b>) Star expansion. (<b>c</b>) Clique expansion. (<b>d</b>) Line expansion. (<b>e</b>) Symmetric line expansion.</p>
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<p>The bijection between node–hyperedge pairs and SLE graph nodes.</p>
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<p>Anomalous Hyperedge Detection method on hypergraph Symmetric Line Expansion.</p>
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<p>Impact of different anomalous proportions for anomaly detection. (<b>a</b>) is the impact on AUC, (<b>b</b>) is the impact on R@k.</p>
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<p>Impact of different <math display="inline"><semantics> <msub> <mi>w</mi> <mi>v</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>w</mi> <mi>e</mi> </msub> </semantics></math> for detection performance. The x-axis is the value of the <math display="inline"><semantics> <msub> <mi>w</mi> <mi>v</mi> </msub> </semantics></math>. Accordingly, the <math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mi>e</mi> </msub> <mo>=</mo> <mn>2</mn> <mo>−</mo> <msub> <mi>w</mi> <mi>v</mi> </msub> </mrow> </semantics></math>. The y-axis in (<b>a</b>) is the AUC value under different <math display="inline"><semantics> <msub> <mi>w</mi> <mi>v</mi> </msub> </semantics></math>, and the y-axis in (<b>b</b>) is the R@k value under different <math display="inline"><semantics> <msub> <mi>w</mi> <mi>v</mi> </msub> </semantics></math>.</p>
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<p>Impact of different GCN hidden sizes for detection performance. (<b>a</b>) is the impact on AUC, (<b>b</b>) is the impact on R@k.</p>
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22 pages, 1289 KiB  
Article
An Improved Discrete Bat Algorithm for Multi-Objective Partial Parallel Disassembly Line Balancing Problem
by Qi Zhang, Yang Xing, Man Yao, Jiacun Wang, Xiwang Guo, Shujin Qin, Liang Qi and Fuguang Huang
Mathematics 2024, 12(5), 703; https://doi.org/10.3390/math12050703 - 28 Feb 2024
Cited by 3 | Viewed by 1221
Abstract
Product disassembly is an effective means of waste recycling and reutilization that has received much attention recently. In terms of disassembly efficiency, the number of disassembly skills possessed by workers plays a crucial role in improving disassembly efficiency. Therefore, in order to effectively [...] Read more.
Product disassembly is an effective means of waste recycling and reutilization that has received much attention recently. In terms of disassembly efficiency, the number of disassembly skills possessed by workers plays a crucial role in improving disassembly efficiency. Therefore, in order to effectively and reasonably disassemble discarded products, this paper proposes a partial parallel disassembly line balancing problem (PP-DLBP) that takes into account the number of worker skills. In this paper, the disassembly tasks and the disassembly relationships between components are described using AND–OR graphs. In this paper, a multi-objective optimization model is established aiming to maximize the net profit of disassembly and minimize the number of skills for the workers. Based on the bat algorithm (BA), we propose an improved discrete bat algorithm (IDBA), which involves designing adaptive composite optimization operators to replace the original continuous formula expressions and applying them to solve the PP-DLBP. To demonstrate the advantages of IDBA, we compares it with NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA/D. Experimental results show that IDBA outperforms the other five algorithms in real disassembly cases and exhibits high efficiency. Full article
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<p>A ballpoint pen.</p>
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<p>The AND–OR graph of a ballpoint pen.</p>
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<p>A radio.</p>
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<p>The AND–OR graph of a radio.</p>
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<p>Task and skill assignment in the first scheme.</p>
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<p>Task and skill assignment in the second scheme.</p>
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<p>Two skill assignment schemes.</p>
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<p>Encoding scheme.</p>
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<p>Decoding process.</p>
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<p>The process of population initialization.</p>
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<p>Checking and adjusting disassembly process.</p>
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<p>PPX operator.</p>
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<p>Mutation operator.</p>
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<p>The flow chart of IDBA.</p>
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<p>The AND–OR graph of hammer drill.</p>
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<p>The AND–OR graph of another ballpoint.</p>
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<p>The AND–OR graph of desk lamp.</p>
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<p>IGD-metric of each algorithm vs. the number of iterations.</p>
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<p>HV-metric of each algorithm vs. the number of iterations.</p>
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<p>Epsilon-metric of each algorithm vs. the number of iterations.</p>
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<p>IGD-metric of each algorithm vs. population size.</p>
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<p>HV-metric of each algorithm vs. population size.</p>
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<p>Epsilon-metric of each algorithm vs. population size.</p>
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<p>Box plot of IGD-metric for each algorithm.</p>
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<p>Box plot of HV-metric for each algorithm.</p>
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<p>Box plot of Epsilon-metric for each algorithm.</p>
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<p>The Pareto frontier comparison of algorithms.</p>
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<p>A decoding scheme that considers skill assignment.</p>
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20 pages, 4431 KiB  
Article
Including Shield Wires in the Analysis of Transient Processes Occurring in HVAC Transmission Lines
by Andriy Chaban, Andrzej Popenda, Andrzej Szafraniec and Vitaliy Levoniuk
Energies 2023, 16(23), 7870; https://doi.org/10.3390/en16237870 - 1 Dec 2023
Viewed by 1002
Abstract
The article presents an analysis of electromagnetic transient processes in long ultra-high voltage transmission lines, taking into account shield wires. It was shown that EMTP and Matlab/Simulink software are currently widely used in the study of transient processes in power lines. The EMTP [...] Read more.
The article presents an analysis of electromagnetic transient processes in long ultra-high voltage transmission lines, taking into account shield wires. It was shown that EMTP and Matlab/Simulink software are currently widely used in the study of transient processes in power lines. The EMTP software package uses the finite element method when integrating the equation that mathematically models the distributed parameter transmission line. The Matlab/Simulink software uses the d’Alembert method. In both cases, it is not known how the boundary conditions for the partial differential equation that mathematically models the transmission line are determined. The power line is analyzed as a distributed parameter system, described by a second-order partial differential equation. The advantage of the proposed method of calculating the boundary conditions for the abovementioned equation is the use of boundary conditions of the second and third types of Neumann and Poincaré, which allowed us to take into account the mutual influence of shield wires and phase conductors of the line in one power system. On this basis, the methodology for obtaining time domain graphs, spatial distributions, and traveling wave distributions of voltages and currents for phase conductors and line shielding wires is presented. The results of a computer simulation of transient processes when switching on the power line, taking into account controlled phase commutation and under single-phase earth fault conditions, are presented. All calculation results of transient processes presented in the article were obtained exclusively using numerical methods. Full article
(This article belongs to the Special Issue Advanced Engineering and Medical Technologies in Energy Exploitation)
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<p>Equivalent circuit of a fragment of the tested electricity transmission system.</p>
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<p>Equivalent circuit of the first discrete section of the line for the shield wires <span class="html-italic">T</span>1.</p>
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<p>Equivalent circuit of the last nodes of <span class="html-italic">T</span>1 and <span class="html-italic">T</span>2 conductors at the end of the discretized line.</p>
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<p>Equivalent circuit of the last discrete section of the line phase conductor (phase A).</p>
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<p>Transient phase voltages in the middle line section.</p>
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<p>Transient phase voltages at the final node (24 km away from the line’s end).</p>
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<p>Transient currents at the beginning of the line.</p>
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<p>Transient currents at the end of the line.</p>
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<p>Transient current in the shield wires <span class="html-italic">T</span>1 at the beginning of the line.</p>
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<p>Transient current in the shield wires <span class="html-italic">T</span>2 at the end of the line.</p>
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<p>Transient voltage of the shield wires <span class="html-italic">T</span>1 at the end of the line.</p>
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<p>Transient voltage of the <span class="html-italic">T</span>2 shield wires at a distance of 24 km from the beginning of the line.</p>
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<p>Spatial distribution of current in shield wires <span class="html-italic">T</span>1 and <span class="html-italic">T</span>2 at the time <span class="html-italic">t</span> = 0.181 s.</p>
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<p>Spatial distribution of voltage in shield wires <span class="html-italic">T</span>1 and <span class="html-italic">T</span>2 at the time <span class="html-italic">t</span> = 0.183 s.</p>
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<p>Voltage traveling wave distribution of the T1 conductor within the time interval <span class="html-italic">t</span> ∈ (0; 0.03) s.</p>
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<p>Current traveling wave distribution of the T2 conductor within the time interval <span class="html-italic">t</span> ∈ (0; 0.03) s.</p>
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15 pages, 4272 KiB  
Article
Precise Cadastral Survey of Rural Buildings Based on Wall Segment Topology Analysis from Dense Point Clouds
by Bo Xu, Zhaochen Han and Min Chen
Appl. Sci. 2023, 13(18), 10197; https://doi.org/10.3390/app131810197 - 11 Sep 2023
Cited by 1 | Viewed by 1292
Abstract
The renewal and updating of the cadastre of real estate is a long and tedious task for land administration, especially for rural buildings that lack unified design and planning. In order to retain the required accuracy of all points in the register, huge [...] Read more.
The renewal and updating of the cadastre of real estate is a long and tedious task for land administration, especially for rural buildings that lack unified design and planning. In order to retain the required accuracy of all points in the register, huge extensive manual editing is often required. In this work, a precise cadastral survey approach is proposed using Unmanned Aerial Vehicle (UAV) imagery-based stereo point clouds. To ensure the accuracy and uniqueness of building outer walls, the non-maximum suppression of wall points that can separate noise and avoid repeated extraction is proposed. Meanwhile, the multiple cue weighted RANSAC, considering both point-to-line distance and normal consistency, is proposed to reduce the influence of building attachments and avoid spurious edges. For a better description of wall topology, the wall line segment topology graph (WLTG), which can guide the connection of adjacent lines and support the searching of closed boundaries through the minimum graph loop analysis, is also built. Experimental results show that the proposed method can effectively detect the building vector contours with high precision and correct topology, and the detection completeness and correctness of the edge corners can reach 84.9% and 93.2% when the mean square error is below 10 cm. Full article
(This article belongs to the Special Issue Advances in 3D Sensing Techniques and Its Applications)
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<p>The overall workflow of proposed approach.</p>
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<p>The workflow of wall segment detection and adjustments. (<b>a</b>) the input point clouds of rural buildings, (<b>b</b>) the projected wall points after density-based clustering and the enlarged region to be processed via non-maximum suppression, (<b>c</b>) the line segments detected by the multiple cues RANSAC algorithm, (<b>d</b>) the global adjustments of edge lines in post processing and (<b>e</b>) the output edge lines.</p>
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<p>The workflow of graph-based wall topology analysis. (<b>a</b>) the input line segments, (<b>b</b>) the extraction of wall-wall topology via TIN-based adjacency, (<b>c</b>) the initial wall line topology graph generated by local analysis among adjacent walls, (<b>d</b>) the connection of line segments based on the topology relationship, (<b>e</b>) the modified wall line topology graph after the analysis of wall topology and (<b>f</b>) the final results for edge boundaries.</p>
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<p>Overall view of the input point cloud and reference vector map. (<b>a</b>) Input color point clouds. (<b>b</b>) Manual reference vector map.</p>
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<p>Overall view of the regularized boundaries detected from dense points. Red lines: boundary edges from wall points, and blue lines: extracted doorway boundaries.</p>
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<p>Comparison of the proposed methods with traditional RANSAC and the polygon boundaries outlined directly from the roof top point clouds. (<b>a</b>,<b>b</b>) are the RMSE and quality index for wall corners defined in Equation (<a href="#FD6-applsci-13-10197" class="html-disp-formula">6</a>), (<b>c</b>,<b>d</b>) are the quality indexes for edges and polygons.</p>
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<p>Comparison of the proposed methods with traditional RANSAC and the polygon boundaries outlined directly from the roof top point clouds. (<b>a</b>,<b>b</b>) are the RMSE and quality index for wall corners defined in Equation (<a href="#FD6-applsci-13-10197" class="html-disp-formula">6</a>), (<b>c</b>,<b>d</b>) are the quality indexes for edges and polygons.</p>
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<p>Comparison of local details. From left to right are input point clouds, ground truth, our results, and results of classical RANSAC and direct output from roof point clouds. For areas A, B, and C, incomplete results will be caused by porches for compared methods; for D and E, roof-based approaches are more likely to produce enlarged boundaries; for G, H, and I, spurious lines are extracted for traditional RANSAC-based methods.</p>
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<p>Limitation of the proposed methods. The left area is selected from area f and the right area is from area a. Location 1: the wall is occluded by the debris; location 2: buildings are connected and no wall exists; and location 3: only one wall plane passes through the boundaries and polygons are detracted.</p>
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16 pages, 2447 KiB  
Article
Identifying Vital Nodes in Hypergraphs Based on Von Neumann Entropy
by Feng Hu, Kuo Tian and Zi-Ke Zhang
Entropy 2023, 25(9), 1263; https://doi.org/10.3390/e25091263 - 25 Aug 2023
Cited by 8 | Viewed by 2037
Abstract
Hypergraphs have become an accurate and natural expression of high-order coupling relationships in complex systems. However, applying high-order information from networks to vital node identification tasks still poses significant challenges. This paper proposes a von Neumann entropy-based hypergraph vital node identification method (HVC) [...] Read more.
Hypergraphs have become an accurate and natural expression of high-order coupling relationships in complex systems. However, applying high-order information from networks to vital node identification tasks still poses significant challenges. This paper proposes a von Neumann entropy-based hypergraph vital node identification method (HVC) that integrates high-order information as well as its optimized version (semi-SAVC). HVC is based on the high-order line graph structure of hypergraphs and measures changes in network complexity using von Neumann entropy. It integrates s-line graph information to quantify node importance in the hypergraph by mapping hyperedges to nodes. In contrast, semi-SAVC uses a quadratic approximation of von Neumann entropy to measure network complexity and considers only half of the maximum order of the hypergraph’s s-line graph to balance accuracy and efficiency. Compared to the baseline methods of hyperdegree centrality, closeness centrality, vector centrality, and sub-hypergraph centrality, the new methods demonstrated superior identification of vital nodes that promote the maximum influence and maintain network connectivity in empirical hypergraph data, considering the influence and robustness factors. The correlation and monotonicity of the identification results were quantitatively analyzed and comprehensive experimental results demonstrate the superiority of the new methods. At the same time, a key non-trivial phenomenon was discovered: influence does not increase linearly as the s-line graph orders increase. We call this the saturation effect of high-order line graph information in hypergraph node identification. When the order reaches its saturation value, the addition of high-order information often acts as noise and affects propagation. Full article
(This article belongs to the Special Issue Maximal Entropy Random Walk)
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<p>Hypergraph and corresponding <math display="inline"><semantics> <mi>s</mi> </semantics></math>-line graph. (<b>a</b>) A hypergraph with 11 nodes and 4 hyperedges; (<b>b</b>–<b>d</b>) represent the line graph with the order from 1 to 3, respectively.</p>
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<p>Distribution of the <math display="inline"><semantics> <mi>s</mi> </semantics></math>-overlap between hyperedges in hypergraphs. Both axes represent the hyperedge index, and the color indicates the s-overlap between hyperedges. Maximum s-overlap of the hypergraphs (<b>a</b>–<b>f</b>) were 14, 14, 63, 8, 19, 57, respectively. To clearly demonstrate the distribution, (<b>a</b>–<b>e</b>) selected approximately half of the maximum <math display="inline"><semantics> <mi>s</mi> </semantics></math>-overlap, and (<b>e</b>) selected the <math display="inline"><semantics> <mi>s</mi> </semantics></math>-overlap starting from <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>.</p>
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<p>Mapping of the simplicial propagation model to hypergraph the nonlinear propagation model. (<b>a</b>) is a simplicial propagation model in 2-simplex with 3 nodes, the infection rate <math display="inline"><semantics> <mrow> <mn>2</mn> <msub> <mi>β</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>β</mi> <mn>2</mn> </msub> </mrow> </semantics></math> is related to both the infected nodes and “triangles”. (<b>b</b>) represents the hypergraph nonlinear propagation model, and the infection rate <math display="inline"><semantics> <mrow> <mi>β</mi> <mfenced> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>η</mi> </mrow> </mfenced> </mrow> </semantics></math> is variable, where <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>Nonlinear propagation experiment with the top 1% ranked nodes in the hypergraphs. <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> and <math display="inline"><semantics> <mi>t</mi> </semantics></math> represent the influence and time step, respectively. In (<b>f</b>), the subplot shows the influence variation of different identification methods on the initial stage of propagation.</p>
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<p>Relationship between the influence of the top 1% ranked nodes identified by the HVC and adjustable parameters <math display="inline"><semantics> <mi>α</mi> </semantics></math> as well as nonlinear exponent <math display="inline"><semantics> <mi>κ</mi> </semantics></math>. The range of variation for <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>κ</mi> </semantics></math> was <math display="inline"><semantics> <mrow> <mn>2</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> <mo>~</mo> <mn>9.8</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>~</mo> <mn>3</mn> </mrow> </semantics></math>, respectively, where the color denotes the node influence value at the fifth time step. The results for other methods were similar.</p>
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<p>Nonlinear propagation of the top 1% ranked nodes identified by the HVC with different order of the <math display="inline"><semantics> <mi>s</mi> </semantics></math>-line graph in hypergraphs. <math display="inline"><semantics> <mi>i</mi> </semantics></math>-order refers to the maximum order used by the HVC. This is the result of 100 repeated simulations with the experimental parameters <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>κ</mi> <mo>=</mo> <mn>1.25</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>. In (<b>f</b>), the subplot shows the influence variation of HVC with different orders of the <math display="inline"><semantics> <mi>s</mi> </semantics></math>-line graph on the initial stage of propagation.</p>
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<p>Correlation matrix of vital node identification methods in the hypergraphs. The color of the matrix elements corresponds to the Pearson correlation coefficient values between different methods, ranging from bright green to blue.</p>
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<p>The largest component size after removing the top 10%, 20%, and 30% nodes using different methods in the hypergraphs. The color in the 3-D cone plot represents the proportion of removed nodes. As the removal proportion increases, the largest component size decreases.</p>
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18 pages, 1556 KiB  
Article
The Effects of Climate Change to Weather-Related Environmental Hazards: Interlinkages of Economic Factors and Climate Risk
by George Halkos and Argyro Zisiadou
J. Risk Financial Manag. 2023, 16(5), 264; https://doi.org/10.3390/jrfm16050264 - 5 May 2023
Cited by 5 | Viewed by 2639
Abstract
Climate change has become an increasingly intense global phenomenon in recent years. A great number of researchers support the idea that climate change is strongly connected to some environmental hazards, and specifically, those correlated to extreme weather events. Following the Paris Agreement, and [...] Read more.
Climate change has become an increasingly intense global phenomenon in recent years. A great number of researchers support the idea that climate change is strongly connected to some environmental hazards, and specifically, those correlated to extreme weather events. Following the Paris Agreement, and due to the increased concern regarding climate change impacts, several indices have been established. The Climate Change Performance Index (CCPI) includes 59 countries and the EU, which cumulatively emit 92% of global greenhouse gases (GHGs), while the Global Climate Risk Index (CRI) analyzes to what extend countries have been affected by impacts of weather-related loss events. Both indices provide annual scores to each country and rank them based on those scores indicating the existing environmental situation. Our main purpose is to examine whether there is an interconnection between those two indices as well as testify whether economic growth is a great contributor to country’s environmental performance and as a result to climate risk. Using a sample of the reported countries for the year 2019, the latest reported year for both indices, and following a cross-sectional econometric analysis, we provide evidence regarding the connection of CCPI and CRI by using graphs, mapping visualization and econometric estimations in order to draw lines between indices. Moreover, we examine the interlinkages, and we estimate the influence caused by socio-economic factors and emissions levels per country. We provide evidence regarding the high-ranked and low-ranked countries and how they perform not only to an environmental base, but also to an economic base. Regarding the major finding, based on our analysis, no proven causality between CRI and CCPI was observed. Economic growth appears to have a significant impact on CRI but not on the CCPI, for the year 2019, while population density has an impact on both indices. Regarding greenhouse gas emissions, the econometric estimations provide evidence of significance for CRI but not for CCPI. An in-depth understanding of the current situation as well as of the factors affecting the climate conditions will give us the needed elements in order to minimize the adverse impact, if not improve the current situation. It is well known and stated that climate action should be taken so that we bequeath a safer and more sustainable planet to the next generations. Full article
(This article belongs to the Special Issue Macroeconomic Modelling)
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<p>Carbon Dioxide Emissions (CO<sub>2</sub>)—Year 2019. <italic>Conducted by the authors</italic>.</p>
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<p>Methane Emissions (CH<sub>4</sub>- kt CO<sub>2</sub> equivalent)—Year 2019. <italic>Conducted by the authors</italic>.</p>
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<p>Nitrous Oxide Emissions (N<sub>2</sub>O- kt CO<sub>2</sub> equivalent)—Year 2019. <italic>Conducted by the authors</italic>.</p>
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<p>Sea Surface Temperature Anomaly (1992–2022). <italic>Conducted by the authors</italic>.</p>
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<p>Comparison of CRI 2019 and Average CRI 2000–2019. <italic>Conducted by the authors</italic>.</p>
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<p>Comparison between CCPI 2019 and CCPI 2022. <italic>Conducted by the authors</italic>.</p>
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27 pages, 5493 KiB  
Review
Processing of Metal Waste—Sludge from the Galvanizing Plants
by Jaromír Drápala, Hana Rigoulet, Silvie Brožová, Jitka Malcharcziková, Šárka Langová, Jiřina Vontorová, Václav Nétek, Jaroslav Kubáč and Dominik Janáček
Metals 2022, 12(11), 1947; https://doi.org/10.3390/met12111947 - 14 Nov 2022
Cited by 1 | Viewed by 3165
Abstract
This paper deals with the possibility of obtaining zinc from waste galvanic sludge, which is formed during galvanic plating. The aim of the experimental and practical part was to obtain zinc after the leaching of galvanic sludge. Leaching was performed in sulfuric acid, [...] Read more.
This paper deals with the possibility of obtaining zinc from waste galvanic sludge, which is formed during galvanic plating. The aim of the experimental and practical part was to obtain zinc after the leaching of galvanic sludge. Leaching was performed in sulfuric acid, nitric acid and hydrochloric acid at different temperatures and time intervals with the addition of oxidizing agents as hydrogen peroxide or ozone. A separation of the leach and filtrate using filtration followed. The leach was further processed by a precipitation of iron and other metals using various agents. After a further filtration, the electrolysis was performed in order to obtain pure zinc on the cathode at the electrical voltage of approximately 3.5 V. Leaching using a solution of sodium hydroxide or potassium hydroxide was also performed when the prior dissolving of a major part of zinc into the leach occurred, while iron and non-ferrous metals remained in the leaching residue. After the filtration of the leach, the electrolysis with a high zinc yield of a purity of more than 99% followed. This way seems to be an optimal one for building a semi-industrial line for galvanic sludge recycling. All the partial products, i.e., the leach, the leaching residue, the filtrate, the solid precipitate and the separated metal on the cathode were subjected to chemical analyses. The analyses results are presented in tables and graphs. Full article
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<p>Block diagram of “MAR-Process” technology for galvanic sludge processing [<a href="#B19-metals-12-01947" class="html-bibr">19</a>].</p>
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<p>Preparation of samples for leaching—on the left: the delivered samples, on the right: sludge after milling and drying-up. Source: own.</p>
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<p>X-ray diffraction analysis for a presence of phases in the sludge sample from P20 supplier.</p>
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<p>Effectiveness of leaching of Zn and Fe (sludge) D20 depending on the type of leaching agent, additives and temperature (g/L).</p>
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<p>AAS analyses of leaches after sludge leaching in 20% H<sub>2</sub>SO<sub>4</sub> after 2 and 5 h.</p>
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<p>Photo documentation of the precipitated zinc on the cathode after the electrolysis [<a href="#B40-metals-12-01947" class="html-bibr">40</a>]—sample B21. The appearance of cathode zinc with dendritic formations after the electrolysis has been documented. Conditions at the electrolysis are above in the text. Source: own.</p>
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<p>Segregated zinc on the graphite cathode (the electrolyte: HCl solution) on the left side—sample M (see <a href="#metals-12-01947-t012" class="html-table">Table 12</a>). Cathode zinc in the flask for ED-XRF analysis. Source: own.</p>
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<p>The temperature dependence of zinc content in leaches during leaching in 500 mL of 20% NaOH solution (a sludge weighed amount was always 125 g).</p>
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<p>A photo documentation of the zinc product segregated on a stainless plate after electrolysis—sample H22. Condition at the electrolysis: cathode—stainless plate, anode—nickel plate, electrolyte—20% solution of NaOH, voltage 4 V, current 2.5 A, time 4 h and temperature 23 °C.</p>
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<p>Results of laser diffraction analysis (device Mastersizer 3000—producer: firm Malvern) for Zn powder obtained at the electrolysis process. Radionuclide Co was used. Conditions are described in <a href="#metals-12-01947-t020" class="html-table">Table 20</a> above. Time of ultrasonic mixing: 60 min at 3000 rpm. Dv(50) = 40.9 μm.</p>
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<p>Microstructure of Zn powder (SEM analysis) after electrolysis process at various enlargement—sample D22. (<b>a</b>) Zinc particles at low magnification. (<b>b</b>) Dendritic structure of the sample at higher magnification. (<b>c</b>) Small whiskers are visible on the surface of the zinc particles. The thickness of the lamellae is about 10 nm. (<b>d</b>) The zinc particles are very thin. The surface was indented, and the arrangement resembles a fine dendritic structure.</p>
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<p>An influence of the electric voltage of the electrolytic cell upon the efficiency of the cathode zinc obtaining.</p>
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24 pages, 11839 KiB  
Article
An Improved Method of an Image Mosaic of a Tea Garden and Tea Tree Target Extraction
by Jinzhu Lu, Yishan Xu and Zongmei Gao
AgriEngineering 2022, 4(1), 231-254; https://doi.org/10.3390/agriengineering4010017 - 25 Feb 2022
Cited by 3 | Viewed by 2672
Abstract
UAV may be limited by its flight height and camera resolution when aerial photography of a tea garden is carried out. The images of the tea garden contain trees and weeds whose vegetation information is similar to tea tree, which will affect tea [...] Read more.
UAV may be limited by its flight height and camera resolution when aerial photography of a tea garden is carried out. The images of the tea garden contain trees and weeds whose vegetation information is similar to tea tree, which will affect tea tree extraction for further agricultural analysis. In order to obtain a high-definition large field-of-view tea garden image that contains tea tree targets, this paper (1) searches for the suture line based on the graph cut method in the image stitching technology; (2) improves the energy function to realize the image stitching of the tea garden; and (3) builds a feature vector to accurately extract tea tree vegetation information and remove unnecessary variables, such as trees and weeds. By comparing this with the manual extraction, the algorithm in this paper can effectively distinguish and eliminate most of the interference information. The IOU in a single mosaic image was more than 80% and the omissions account was 10%. The extraction results in accuracies that range from 84.91% to 93.82% at the different height levels (30 m, 60 m and 100 m height) of single images. Tea tree extraction accuracy rates in the mosaic images are 84.96% at a height of 30 m, and 79.94% at a height of 60 m. Full article
(This article belongs to the Special Issue Hyperspectral Imaging Technique in Agriculture)
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<p>Photograph of the tea garden and the drone operator.</p>
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<p>Raw image datasets of the tea garden. (<b>a</b>) Images of the tea garden dataset; (<b>b</b>) one image from 30 m high (“Group 1”); (<b>c</b>) one image from 60 m high (“Group 2”); (<b>d</b>) the image from 100 m high (“Group 3”).</p>
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<p>Flowchart of the image registration.</p>
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<p>HSV model and components. (<b>a</b>) RGB model; (<b>b</b>) HSV model; (<b>c</b>) H component; (<b>d</b>) S component; and (<b>e</b>) V component.</p>
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<p>Flowchart of tea tree extraction.</p>
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<p>SIFT feature points in the tea garden images.</p>
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<p>Matching effects of the (<b>a</b>) rough match and (<b>b</b>) exact match.</p>
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<p>Tea garden image registration by the AANAP algorithm. (<b>a</b>) Reference image; (<b>b</b>) target image; (<b>c</b>) image with extracted feature points by the SIFT algorithm; (<b>d</b>) image with selected feature points; (<b>e</b>) mesh division and deformation; (<b>f</b>) image transformation result; and (<b>g</b>) results by the AANAP algorithm.</p>
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<p>Tea garden image registration by the AANAP algorithm. (<b>a</b>) Reference image; (<b>b</b>) target image; (<b>c</b>) image with extracted feature points by the SIFT algorithm; (<b>d</b>) image with selected feature points; (<b>e</b>) mesh division and deformation; (<b>f</b>) image transformation result; and (<b>g</b>) results by the AANAP algorithm.</p>
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<p>Results of the suture lines with different energy functions (<b>a</b>) based on the “color” feature, (<b>b</b>) “gradient” feature, and (<b>c</b>) “color + gradient” feature (<b>d</b>) in this study.</p>
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<p>Results of the suture lines with different energy functions (<b>a</b>) based on the “color” feature, (<b>b</b>) “gradient” feature, and (<b>c</b>) “color + gradient” feature (<b>d</b>) in this study.</p>
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<p>Results of AutoStitch, AANAP and the algorithms used in this study. (<b>a</b>) Reference images; (<b>b</b>) target image; (<b>c</b>) suture line results of (<b>a</b>,<b>b</b>) in this study; (<b>d</b>) results in AutoStitch; (<b>e</b>) magnified images in red frames of (<b>d</b>); (<b>f</b>) results in AANAP; (<b>g</b>) magnified images in red frames of (<b>f</b>); (<b>h</b>) results in this study; and (<b>i</b>) magnified images in red frames of (<b>h</b>).</p>
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<p>Results of AutoStitch, AANAP and the algorithms used in this study. (<b>a</b>) Reference images; (<b>b</b>) target image; (<b>c</b>) suture line results of (<b>a</b>,<b>b</b>) in this study; (<b>d</b>) results in AutoStitch; (<b>e</b>) magnified images in red frames of (<b>d</b>); (<b>f</b>) results in AANAP; (<b>g</b>) magnified images in red frames of (<b>f</b>); (<b>h</b>) results in this study; and (<b>i</b>) magnified images in red frames of (<b>h</b>).</p>
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<p>Original image (<b>a</b>) and the image with RGRI features (<b>b</b>).</p>
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<p>Point set extraction and filtering. (<b>a</b>) Raw image; (<b>b</b>) image by point set extraction; (<b>c</b>) binary mask image calculated by RGRI indices; and (<b>d</b>) image after filtering.</p>
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<p>Mean shift clustering results of different image examples.</p>
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<p>KNN classification and tea tree extraction. (<b>a</b>) Mean shift clustering results; (<b>b</b>) KNN classification results; (<b>c</b>) contour fitting result; and (<b>d</b>) extraction results.</p>
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<p>KNN classification and tea tree extraction. (<b>a</b>) Mean shift clustering results; (<b>b</b>) KNN classification results; (<b>c</b>) contour fitting result; and (<b>d</b>) extraction results.</p>
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<p>Comparison images of the ground truth and method in this study. (<b>a</b>) Raw image; (<b>b</b>) tea tree extracted by humans; (<b>c</b>) tea tree extracted in this study; and (<b>d</b>) result of the contrast between (<b>b</b>,<b>c</b>).</p>
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<p>Contrastive example of the tea tree extraction from the tea garden mosaic images. (<b>a</b>) mosaic image 1; (<b>b</b>) tea tree extracted as the ground truth of (<b>a</b>); (<b>c</b>) tea tree extracted in this study; (<b>d</b>) result of the contrast between (<b>b</b>) and (<b>c</b>); (<b>e</b>) mosaic image 2; (<b>f</b>) tea tree extracted as the ground truth of (<b>e</b>); (<b>g</b>) tea tree extracted in this study of (<b>e</b>); and (<b>h</b>) the result of the contrast between (<b>f</b>,<b>g</b>).</p>
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22 pages, 1566 KiB  
Article
Revealing the Role of Divergent Thinking and Fluid Intelligence in Children’s Semantic Memory Organization
by Clara Rastelli, Antonino Greco and Chiara Finocchiaro
J. Intell. 2020, 8(4), 43; https://doi.org/10.3390/jintelligence8040043 - 14 Dec 2020
Cited by 11 | Viewed by 6045
Abstract
The current theories suggest the fundamental role of semantic memory in creativity, mediating bottom-up (divergent thinking) and top-down (fluid intelligence) cognitive processes. However, the relationship between creativity, intelligence, and the organization of the semantic memory remains poorly-characterized in children. We investigated the ways [...] Read more.
The current theories suggest the fundamental role of semantic memory in creativity, mediating bottom-up (divergent thinking) and top-down (fluid intelligence) cognitive processes. However, the relationship between creativity, intelligence, and the organization of the semantic memory remains poorly-characterized in children. We investigated the ways in which individual differences in children’s semantic memory structures are influenced by their divergent thinking and fluid intelligence abilities. The participants (mean age 10) were grouped by their levels (high/low) of divergent thinking and fluid intelligence. We applied a recently-developed Network Science approach in order to examine group-based semantic memory graphs. Networks were constructed from a semantic fluency task. The results revealed that divergent thinking abilities are related to a more flexible structure of the semantic network, while fluid intelligence corresponds to a more structured semantic network, in line with the previous findings from the adult sample. Our findings confirm the crucial role of semantic memory organization in creative performance, and demonstrate that this phenomenon can be traced back to childhood. Finally, we also corroborate the network science methodology as a valid approach to the study of creative cognition in the developmental population. Full article
(This article belongs to the Special Issue Intelligence and Creativity)
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<p>Semantic networks and bootstrapped results for DT. (<b>A</b>) 2D graph visualizations of the DT groups (high and low). The graphs are unweighted and undirected, with nodes (word responses) represented as circles, and the links between them (edges) represented as symmetrical similarities between two nodes; (<b>B</b>) Plots of the bootstrapped partial network measures (1000 samples per nodes remaining percentage). The density plots are above the scatterplots (individual dots depict a single sample), with a black dot representing the mean. The y-axis denotes the percentage of nodes remaining, with the legend of the DT groups (low and high) below the plots. All <span class="html-italic">p</span> &lt; 0.001.</p>
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<p>Semantic networks and bootstrapped results for Gf. (<b>A</b>) 2D graph visualizations of the Gf groups (high and low). The graphs are unweighted and undirected, with nodes (word responses) represented as circles, and the links between them (edges) represented as symmetrical similarities between two nodes. (<b>B</b>) Plots of the bootstrapped partial network measures (1000 samples per nodes remaining percentage). The density plots are above the scatterplots (individual dots depict a single sample), with a black dot representing the mean. The y-axis denotes the percentage of nodes remaining, with the legend of the Gf’ groups (low and high) below the plots. All <span class="html-italic">p</span> &lt; 0.001, with the exception of ASPL at 50% which were not significant.</p>
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13 pages, 1066 KiB  
Article
Optimal Resilience Enhancement of Water Distribution Systems
by Imke-Sophie Lorenz and Peter F. Pelz
Water 2020, 12(9), 2602; https://doi.org/10.3390/w12092602 - 17 Sep 2020
Cited by 14 | Viewed by 4175
Abstract
Water distribution systems (WDSs) as critical infrastructures are subject to demand peaks due to daily consumption fluctuations, as well as long term changes in the demand pattern due to increased urbanization. Resilient design of water distribution systems is of high relevance to water [...] Read more.
Water distribution systems (WDSs) as critical infrastructures are subject to demand peaks due to daily consumption fluctuations, as well as long term changes in the demand pattern due to increased urbanization. Resilient design of water distribution systems is of high relevance to water suppliers. The challenging combinatorial problem of high-quality and, at the same time, low-cost water supply can be assisted by cost-benefit optimization to enhance the resilience of existing main line WDSs, as shown in this paper. A Mixed Integer Linear Problem, based on a graph-theoretical resilience index, is implemented considering WDS topology. Utilizing parallel infrastructures, specifically those of the urban transport network and the water distribution network, makes allowances for physical constraints, in order to adjust the existing WDS and to enhance resilience. Therefore, decision-makers can be assisted in choosing the optimal adjustment of WDS depending on their investment budget. Furthermore, it can be observed that, for a specific urban structure, there is a convergence of resilience enhancement with higher costs. This cost-benefit optimization is conducted for a real-world main line WDS, considering also the limitations of computational expenses. Full article
(This article belongs to the Special Issue Management of Urban Water Services)
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<p>Existing main line water distribution system marked by solid lines and possible adaptations marked by dashed lines. Consumer and junction nodes are marked by dots and the source is marked by the tank image.</p>
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<p>Optimal main line water distribution system adaptations for different optimization instances, differing in the maximum length of added pipes <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mi>max</mi> </msub> </mrow> </semantics></math> for (<b>a</b>) 200 m, (<b>b</b>) 500 m, (<b>c</b>) 1000 m, and (<b>d</b>) 1750 m. The existing main line WDS is marked by blue edges while all chosen edges to be added are marked in yellow.</p>
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<p>Cost-benefit resilience analysis given as the Pareto front of the existing WDS embedded in its urban structure.</p>
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1 pages, 152 KiB  
Abstract
Investigation of the Effects of Momordica charantia Extract on Cell Survival and Migration in U87G Glioblastoma Cell Line
by Kubra Erdogan and Onur Eroglu
Proceedings 2019, 40(1), 18; https://doi.org/10.3390/proceedings2019040018 - 26 Dec 2019
Cited by 2 | Viewed by 1284
Abstract
Glioblastoma multiforme (GBM) is a type of cancer which has the highest mortality rate among brain cancers (1–2). Momordica charantia, known as bitter melon, is a plant its pharmacological activities and nutritional properties. Due to contains bioactive compounds, M. charantia is used [...] Read more.
Glioblastoma multiforme (GBM) is a type of cancer which has the highest mortality rate among brain cancers (1–2). Momordica charantia, known as bitter melon, is a plant its pharmacological activities and nutritional properties. Due to contains bioactive compounds, M. charantia is used for cancer treatments, inflammation-related diseases and diabetes (3–4). In this study, it was aimed to investigate the effects of M. charantia extract on cell viability, cytotoxicity and migration capacity in U87G cell line. U87G was cultured in DMEM-high glucose containing FBS 10% (v/v) and penisillin-streptomicin 1% (v/v). Cells were incubated at 37 °C in a humidified 5% CO2 incubator. The cytotoxic effect of M. charantia extract was determined by MTT analysis, cell viability by survival analysis and migration by wound-healing analysis. The results were evaluated by using ANOVA and GraphPad Prism7.0 program (GraphPad Software, La Jolla, CA, USA) in three replicates. IC50 value of M. charantia extract was found 750 μg/mL which is statistically significant (* p < 0.05). The extract had an increasing lethal effect at the 16.6% (24 h), 42.6% (48 h), 79.3% (72 h) and 91.6% (96 h). According to the wound-healing analysis, the wound closed at 24 h in the control group and the wound gradually increased depending on time in the extract treated group. According to the results, M. charantia extract has a cytotoxic and a significant anti-proliferative effect on U87G. It might be used as therapeutic agent against to GBM. However, in order to understand the effect of M. charantia in living organisms, in vivo experiments must be determined. Full article
1279 KiB  
Article
Urban Extreme Weather: A Challenge for a Healthy Living Environment in Akure, Ondo State, Nigeria
by Olabode Abiodun Daniel
Climate 2015, 3(4), 775-791; https://doi.org/10.3390/cli3040775 - 30 Sep 2015
Cited by 12 | Viewed by 13207
Abstract
The increasing rate of heat in the climate in urban areas has become one of the striking problems in many developing countries. This study examined the relationships between the monthly temperature, rainfall and incidence of heat-rash between 2003 and 2012 in order to [...] Read more.
The increasing rate of heat in the climate in urban areas has become one of the striking problems in many developing countries. This study examined the relationships between the monthly temperature, rainfall and incidence of heat-rash between 2003 and 2012 in order to determine the impact of climate on occurrence of heat-rash in Akure, Ondo state, Nigeria. Data were obtained from Ondo State Specialist Hospital and Ondo State Meteorological Center. A line graph analysis was employed to identify the trend of the temperature, rainfall and incidence of this weather-based disease. Correlation analysis determined the relationship existing between the monthly temperature and the heat-rash. Tables and graphs were generally used for data presentation. The result shows that; the monthly temperature is low between the month of May and October when the minimum and maximum temperature is at 20.6 °C and 34.1 °C respectively; high temperature was recorded during the month of January, February, March and slightly different in April, November and December ranging from 24.6 °C to 35.1 °C.; the monthly temperature descends sharply during the month of March and remains low in April, May, June and July that characterized with high peak of rainfall; heat-rash has significant increase in 2003 (September), 2004 (September), 2007 (December), 2011 (November) and 2012 (October). The study recommends that people in this area and other related environments should engage in sensitizing the public on awareness of temperature—rash relationship and put up a measure of avoiding the heat effect during the periods of high temperature. Full article
(This article belongs to the Special Issue Climate Impacts on Health)
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<p>Nigeria showing Ondo State.</p>
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<p>Ondo State showing Akure.</p>
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<p>Trend of monthly minimum temperature of Akure from 2003 to 2012.</p>
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<p>Trend of monthly maximum temperature of Akure from 2003 to 2012.</p>
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<p>Monthly Incidence of heat-rash in Akure from 2003 to 2012.</p>
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<p>Graph showing trend of temperature, rainfall and heat-rash.</p>
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