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30 pages, 6901 KiB  
Article
EPRNG: Effective Pseudo-Random Number Generator on the Internet of Vehicles Using Deep Convolution Generative Adversarial Network
by Chenyang Fei, Xiaomei Zhang, Dayu Wang, Haomin Hu, Rong Huang and Zejie Wang
Information 2025, 16(1), 21; https://doi.org/10.3390/info16010021 - 3 Jan 2025
Abstract
With the increasing connectivity and automation on the Internet of Vehicles, safety, security, and privacy have become stringent challenges. In the last decade, several cryptography-based protocols have been proposed as intuitive solutions to protect vehicles from information leakage and intrusions. Before generating the [...] Read more.
With the increasing connectivity and automation on the Internet of Vehicles, safety, security, and privacy have become stringent challenges. In the last decade, several cryptography-based protocols have been proposed as intuitive solutions to protect vehicles from information leakage and intrusions. Before generating the encryption keys, a random number generator (RNG) plays an important component in cybersecurity. Several deep learning-based RNGs have been deployed to train the initial value and generate pseudo-random numbers. However, interference from actual unpredictable driving environments renders the system unreliable for its low-randomness outputs. Furthermore, dynamics in the training process make these methods subject to training instability and pattern collapse by overfitting. In this paper, we propose an Effective Pseudo-Random Number Generator (EPRNG) which exploits a deep convolution generative adversarial network (DCGAN)-based approach using our processed vehicle datasets and entropy-driven stopping method-based training processes for the generation of pseudo-random numbers. Our model starts from the vehicle data source to stitch images and add noise to enhance the entropy of the images and then inputs them into our network. In addition, we design an entropy-driven stopping method that enables our model training to stop at the optimal epoch so as to prevent overfitting. The results of the evaluation indicate that our entropy-driven stopping method can effectively generate pseudo-random numbers in a DCGAN. Our numerical experiments on famous test suites (NIST, ENT) demonstrate the effectiveness of the developed approach in high-quality random number generation for the IoV. Furthermore, the PRNGs are successfully applied to image encryption, and the performance metrics of the encryption are close to ideal values. Full article
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Graphical abstract

Graphical abstract
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<p>System model of the proposed PRNG.</p>
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<p>Network model of the IoV.</p>
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<p>Similarity between images.</p>
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<p>Comparison of images before and after stitching.</p>
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<p>Stitching the pixel blocks.</p>
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<p>Raw images before and after adding noise: (<b>a</b>–<b>c</b>) are the raw images; (<b>d</b>–<b>f</b>) are the noise-added images.</p>
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<p>Comparison of images before and after adding noise.</p>
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<p>The noise in 2D.</p>
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<p>DCGAN network model.</p>
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<p>The visual representation of the entropy-driven stopping method.</p>
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<p>Logistic map visualization.</p>
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<p>The statistics of image entropy.</p>
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<p>The datasets collected from multi-sensors in vehicle.</p>
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<p>Comparison of <span class="html-italic">R</span> before and after early stopping.</p>
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<p>The optimal training epochs.</p>
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<p>Comparison of <span class="html-italic">R</span> before and after early stopping on the other datasets. (<b>a</b>) Comparison of <span class="html-italic">R</span> before and after early stopping on the BDD100k dataset; (<b>b</b>) Comparison of <span class="html-italic">R</span> before and after early stopping on the Tsinghua-Tencent100K dataset.</p>
Full article ">Figure 16 Cont.
<p>Comparison of <span class="html-italic">R</span> before and after early stopping on the other datasets. (<b>a</b>) Comparison of <span class="html-italic">R</span> before and after early stopping on the BDD100k dataset; (<b>b</b>) Comparison of <span class="html-italic">R</span> before and after early stopping on the Tsinghua-Tencent100K dataset.</p>
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<p>Optimal <math display="inline"><semantics> <msub> <mi>L</mi> <mrow> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> </mrow> </msub> </semantics></math> with different <span class="html-italic">p</span> and <span class="html-italic">v</span> parameters.</p>
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<p>The sensitivity of the optimal epoch. (<b>a</b>) The sensitivity of the optimal epoch when the target variance changes; (<b>b</b>) The sensitivity of the optimal epoch when the patience changes.</p>
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<p>The encryption and decryption processes of the images.</p>
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<p>The encryption and decryption processes of the images.</p>
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<p>The histogram of the image pair.</p>
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<p>The adjacent pixel correlation of the image pair.</p>
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13 pages, 258 KiB  
Article
On Defining Expressions for Entropy and Cross-Entropy: The Entropic Transreals and Their Fracterm Calculus
by Jan A. Bergstra and John V. Tucker
Entropy 2025, 27(1), 31; https://doi.org/10.3390/e27010031 - 2 Jan 2025
Viewed by 268
Abstract
Classic formulae for entropy and cross-entropy contain operations x0 and log2x that are not defined on all inputs. This can lead to calculations with problematic subexpressions such as 0log20 and uncertainties in large scale calculations; partiality also [...] Read more.
Classic formulae for entropy and cross-entropy contain operations x0 and log2x that are not defined on all inputs. This can lead to calculations with problematic subexpressions such as 0log20 and uncertainties in large scale calculations; partiality also introduces complications in logical analysis. Instead of adding conventions or splitting formulae into cases, we create a new algebra of real numbers with two symbols ± for signed infinite values and a symbol named ⊥ for the undefined. In this resulting arithmetic, entropy, cross-entropy, Kullback–Leibler divergence, and Shannon divergence can be expressed without concerning any further conventions. The algebra may form a basis for probability theory more generally. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
15 pages, 664 KiB  
Article
Few-Shot Graph Anomaly Detection via Dual-Level Knowledge Distillation
by Xuan Li, Dejie Cheng, Luheng Zhang, Chengfang Zhang and Ziliang Feng
Entropy 2025, 27(1), 28; https://doi.org/10.3390/e27010028 - 1 Jan 2025
Viewed by 249
Abstract
Graph anomaly detection is crucial in many high-impact applications across diverse fields. In anomaly detection tasks, collecting plenty of annotated data tends to be costly and laborious. As a result, few-shot learning has been explored to address the issue by requiring only a [...] Read more.
Graph anomaly detection is crucial in many high-impact applications across diverse fields. In anomaly detection tasks, collecting plenty of annotated data tends to be costly and laborious. As a result, few-shot learning has been explored to address the issue by requiring only a few labeled samples to achieve good performance. However, conventional few-shot models may not fully exploit the information within auxiliary sets, leading to suboptimal performance. To tackle these limitations, we propose a dual-level knowledge distillation-based approach for graph anomaly detection, DualKD, which leverages two distinct distillation losses to improve generalization capabilities. In our approach, we initially train a teacher model to generate prediction distributions as soft labels, capturing the entropy of uncertainty in the data. These soft labels are then employed to construct the corresponding loss for training a student model, which can capture more detailed node features. In addition, we introduce two representation distillation losses—short and long representation distillation—to effectively transfer knowledge from the auxiliary set to the target set. Comprehensive experiments conducted on four datasets verify that DualKD remarkably outperforms the advanced baselines, highlighting its effectiveness in enhancing identification performance. Full article
(This article belongs to the Special Issue Robustness of Graph Neural Networks)
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Figure 1

Figure 1
<p>Overall framework of DualKD.</p>
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<p>Detection performance of DualKD and its variants.</p>
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<p>Sensitivity analysis for the number of auxiliary networks <span class="html-italic">P</span> and the weight <math display="inline"><semantics> <mi>α</mi> </semantics></math>, <math display="inline"><semantics> <mi>β</mi> </semantics></math>, and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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16 pages, 4480 KiB  
Article
Evaluation of the Efficiency of Heat Exchanger Channels with Different Flow Turbulence Methods Using the Entropy Generation Minimization Criterion
by Piotr Bogusław Jasiński, Grzegorz Górecki and Zbigniew Cebulski
Energies 2025, 18(1), 132; https://doi.org/10.3390/en18010132 - 31 Dec 2024
Viewed by 251
Abstract
This paper presents the results of an optimization analysis of two types of thermal fluid channels. The selected geometries were evaluated according to the criterion of the Entropy Generation Minimization method as suggested by Adrian Bejan, with reference to a smooth pipe of [...] Read more.
This paper presents the results of an optimization analysis of two types of thermal fluid channels. The selected geometries were evaluated according to the criterion of the Entropy Generation Minimization method as suggested by Adrian Bejan, with reference to a smooth pipe of the same diameter. The aim of this research was to assess the effectiveness of two channels that intensify heat transfer in different ways: with an insert (disrupting the flow in the pipe core) and with internal fins (disrupting the flow at the pipe wall), and to compare the results using the same criterion: the EGM method. The tested insert consisted of spaced streamline-shaped flow turbulizing the elements fixed in the axis of the pipe and spaced at equal distances from each other. The second channel was formed by making a right-angled triangle (rib profile) on the deformation of the pipe wall perimeter. Using computer modeling, the effect of the two geometric parameters of the above-mentioned channels on the flux of entropy generated was studied. These are (a) the diameter of the disturbing element (“droplet”) and the distance between these elements for a channel with a turbulent insert, and (b) the height of the rib and the longitudinal distance between them for a finned channel. The novelty resulting from the research is the discovery that the turbulization of the flow in the pipe wall boundary layer generates significantly less irreversible entropy than the disturbance of the flow in the pipe axis by the insert. Full article
(This article belongs to the Collection Advances in Heat Transfer Enhancement)
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Figure 1

Figure 1
<p>Tube with cross ribs: (<b>a</b>) 3D view, (<b>b</b>) comparison of rib sizes, and (<b>c</b>) tested rib heights.</p>
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<p>Turbulizing insert: (<b>a</b>) 3D view, (<b>b</b>) comparison of the size of the “droplets”, and (<b>c</b>) dimensions of the diameters of the tested elements.</p>
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<p>Mutual proportions of insertion-disturbing elements.</p>
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<p>Diagram of variable designations for Equation (2) in the smooth pipe elementary section.</p>
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<p>The relative entropy generation for forced convection heat transfer in a smooth tube [<a href="#B1-energies-18-00132" class="html-bibr">1</a>].</p>
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<p>Repetitive and periodic segments of the tested pipes as computational domains.</p>
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<p>Repeated and periodic segment of the pipes under study. Heat transfer diagram in the computational domain.</p>
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<p>Total entropy generation rate for dimensionless longitudinal distance <span class="html-italic">L</span>/<span class="html-italic">D</span> = 0.77: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Relative entropy generation rate for dimensionless longitudinal distance <span class="html-italic">L</span>/<span class="html-italic">D</span> = 0.77: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Total entropy generation rate for dimensionless longitudinal distance L/D = 1.38: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Relative entropy generation rate for dimensionless longitudinal distance L/D = 1.38: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Total entropy generation rate for dimensionless longitudinal distance L/D = 3.27: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Relative entropy generation rate for dimensionless longitudinal distance L/D = 3.27: (<b>a</b>) pipe with insert and (<b>b</b>) ribbed pipe.</p>
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<p>Velocity vector map for the two chosen longitudinal distances with marked turbulence zones: <span class="html-italic">L</span>/<span class="html-italic">D</span> = 0.92 and <span class="html-italic">L</span>/<span class="html-italic">D</span> = 1.85, (<b>a</b>) ribbed pipe, and (<b>b</b>) pipe with insert.</p>
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18 pages, 8297 KiB  
Article
Adaptive Asymptotic Shape Synchronization of a Chaotic System with Applications for Image Encryption
by Yangxin Luo, Yuanyuan Huang, Fei Yu, Diqing Liang and Hairong Lin
Mathematics 2025, 13(1), 128; https://doi.org/10.3390/math13010128 - 31 Dec 2024
Viewed by 216
Abstract
In contrast to previous research that has primarily focused on distance synchronization of states in chaotic systems, shape synchronization emphasizes the geometric shape of the attractors of two chaotic systems. Diverging from the existing work on shape synchronization, this paper introduces the application [...] Read more.
In contrast to previous research that has primarily focused on distance synchronization of states in chaotic systems, shape synchronization emphasizes the geometric shape of the attractors of two chaotic systems. Diverging from the existing work on shape synchronization, this paper introduces the application of adaptive control methods to achieve asymptotic shape synchronization for the first time. By designing an adaptive controller using the proposed adaptive rule, the response system under control is able to attain asymptotic synchronization with the drive system. This method is capable of achieving synchronization for models with parameters requiring estimation in both the drive and response systems. The control approach remains effective even in the presence of uncertainties in model parameters. The paper presents relevant theorems and proofs, and simulation results demonstrate the effectiveness of adaptive asymptotic shape synchronization. Due to the pseudo-random nature of chaotic systems and their extreme sensitivity to initial conditions, which make them suitable for information encryption, a novel channel-integrated image encryption scheme is proposed. This scheme leverages the shape synchronization method to generate pseudo-random sequences, which are then used for shuffling, scrambling, and diffusion processes. Simulation experiments demonstrate that the proposed encryption algorithm achieves exceptional performance in terms of correlation metrics and entropy, with a competitive value of 7.9971. Robustness is further validated through key space analysis, yielding a value of 10210×2512, as well as visual tests, including center and edge cropping. The results confirm the effectiveness of adaptive asymptotic shape synchronization in the context of image encryption. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos and Complex Systems)
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Figure 1

Figure 1
<p>Simulation results of asymptotic shape synchronization. (<b>a</b>–<b>c</b>) represent the trajectories of the drive system, which is the original Lorenz system; the Chen system, which is used as the backbone of the response system; and the response system controlled by the proposed controller in Equation (4) and the adaptive rule in Equation (6), respectively. (<b>d</b>–<b>f</b>) depict the projections of the trajectories on three-dimensional planes, the values of the two systems along different axes, and the error of the three projections over time, respectively. (<b>a</b>) Lorenz [<a href="#B62-mathematics-13-00128" class="html-bibr">62</a>] (drive) system; (<b>b</b>) Chen system [<a href="#B63-mathematics-13-00128" class="html-bibr">63</a>]; (<b>c</b>) response system; (<b>d</b>) projections of the drive system and the response system; (<b>e</b>) the values of the systems along different axes; (<b>f</b>) the value of the error in projections.</p>
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<p>The adaptation process of the estimated parameters <math display="inline"><semantics> <mrow> <mover accent="true"> <mo>Φ</mo> <mo stretchy="false">^</mo> </mover> <mo>=</mo> <msup> <mfenced open="[" close="]"> <mtable> <mtr> <mtd> <mi>σ</mi> </mtd> <mtd> <mi>ρ</mi> </mtd> <mtd> <mi>β</mi> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mover accent="true"> <mo>Ψ</mo> <mo stretchy="false">^</mo> </mover> <mo>=</mo> <msup> <mfenced open="[" close="]"> <mtable> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> <mtd> <mi>c</mi> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> </mrow> </semantics></math> by the proposed adaptive rule Equation (6).</p>
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<p>The encryption process using pseudo-random sequences generated by chaotic drive system.</p>
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<p>The decryption process using pseudo-random sequences generated by chaotic response system controlled by the devised adaptive rule and controller.</p>
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<p>The process of scrambling utilizes the generated sequences <math display="inline"><semantics> <msub> <mi>S</mi> <mn>2</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>S</mi> <mn>3</mn> </msub> </semantics></math>, while the diffusion process employs sequence <math display="inline"><semantics> <msub> <mi>S</mi> <mn>4</mn> </msub> </semantics></math>. For scrambling, the red and green bit matrices, along with the remaining bit arrays of <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>H</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>L</mi> </mrow> </semantics></math>, as well as parts of the sequences provided by the drive system, are intentionally omitted for simplicity. For diffusion, one step of the operations is illustrated in the figure: for the cyclic XOR operation of <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>H</mi> </mrow> </semantics></math>, the head is first XOR-ed with the tail of the bit array, followed by each bit being XOR-ed with the previous bit. Conversely, for <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>L</mi> </mrow> </semantics></math>, the process is reversed. Finally, the result is XOR-ed with the bit stream produced by <math display="inline"><semantics> <msub> <mi>S</mi> <mn>4</mn> </msub> </semantics></math>. The numbers in this figure are provided for illustrative purposes only.</p>
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<p>Results of the encryption and decryption of colored images, along with their histograms across the RGB channels.</p>
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<p>Correlation analysis of the encrypted Peppers image.</p>
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<p>Decryption of the encrypted material using the wrong key with an error of <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>6</mn> </mrow> </msup> </mrow> </semantics></math> and using the right key, respectively.</p>
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<p>Noise attack simulation results of House image.</p>
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<p>Data loss simulation results via cropping of the House image.</p>
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20 pages, 870 KiB  
Article
Measuring the Inferential Values of Relations in Knowledge Graphs
by Xu Zhang, Xiaojun Kang, Hong Yao and Lijun Dong
Algorithms 2025, 18(1), 6; https://doi.org/10.3390/a18010006 - 31 Dec 2024
Viewed by 232
Abstract
Knowledge graphs, as an important research direction in artificial intelligence, have been widely applied in many fields and tasks. The relations in knowledge graphs have explicit semantics and play a crucial role in knowledge completion and reasoning. Correctly measuring the inferential value of [...] Read more.
Knowledge graphs, as an important research direction in artificial intelligence, have been widely applied in many fields and tasks. The relations in knowledge graphs have explicit semantics and play a crucial role in knowledge completion and reasoning. Correctly measuring the inferential value of relations and identifying important relations in a knowledge graph can effectively improve the effectiveness of knowledge graphs in reasoning tasks. However, the existing methods primarily consider the connectivity and structural characteristics of relations, but neglect the semantics and the mutual influence of relations in reasoning tasks. This leads to truly valuable relations being difficult to fully utilize in long-chain reasoning. To address this problem, this work, inspired by information entropy and uncertainty-measurement methods in knowledge bases, proposes a method called Relation Importance Measurement based on Information Entropy (RIMIE) to measure the inferential value of relations in knowledge graphs. RIMIE considers the semantics of relations and the role of relations in reasoning. Specifically, based on the values of relations in logical chains, RIMIE partitions the logical sample set into multiple equivalence classes, and generates a knowledge structure for each relation. Correspondingly, to effectively measure the inferential values of relations in knowledge graphs, the concept of relation entropy is proposed, and it is calculated according to the knowledge structures. Finally, to objectively assess the effectiveness of RIMIE, a group of experiments are conducted, which compare the influences of the relations selected according to RIMIE and other patterns on the triple classifications by knowledge graph representation learning. The experimental results confirm what is claimed above. Full article
(This article belongs to the Section Analysis of Algorithms and Complexity Theory)
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Figure 1

Figure 1
<p>The knowledge graph of the UEFA European Championship. In the reasoning task of finding the top scorer of the 2016 European Championship, starting from the entity “UEFA”, there are three different choices upon reaching “European Championship”. These three choices lead to three different outcomes. If the relation “final date” is chosen, a time entity will be obtained, which is far from the correct answer. Choosing the relation “responsible person” yields a person entity, but this is also incorrect. Only by choosing the relation “top scorer” can the correct answer be found. Different relations lead to different results, and logical reasoning needs to consider different semantics of relations.</p>
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<p>High-inference value relations. In a burglary case, there are clues pointing to two suspects (<span class="html-italic">A</span> and <span class="html-italic">B</span>), in which the surveillance camera caught <span class="html-italic">A</span> entering the store one hour before the burglary, and <span class="html-italic">B</span> entering the store the day before. Meanwhile, the neighbor saw <span class="html-italic">A</span> entering the store, and frequently appeared around the store in the previous days, and found <span class="html-italic">A</span>’s fingerprint in the store; here, surveillance, witness and fingerprint are all important relations with high inferential value. Changing the relation value of “2024-6-22 13:14:00” will reduce the suspicion of <span class="html-italic">A</span> and may lead to different results.</p>
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<p>The inference chain in a knowledge graph. In a case, according to the clues, the police locks up three suspects <span class="html-italic">A</span>, <span class="html-italic">B</span> and <span class="html-italic">C</span>; there is a conflict between them and the victim <span class="html-italic">S</span>; the severity of the conflict between <span class="html-italic">A</span> and <span class="html-italic">B</span> and <span class="html-italic">S</span> is 1, and the severity of the conflict between <span class="html-italic">C</span> and S is 2; there are three reasoning chains in the figure, that is, the part covered by the shadows.</p>
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<p>RIMIE calculation framework. Circular nodes represent entities and short lines represent relations. The five inference chains are divided by the number of occurrences of <math display="inline"><semantics> <msub> <mi>r</mi> <mn>2</mn> </msub> </semantics></math>, and are divided into three equivalence classes according to the number of occurrences of <math display="inline"><semantics> <msub> <mi>r</mi> <mn>2</mn> </msub> </semantics></math> 0, 1, 2. Then, the relation entropy is calculated according to the probability related to the equivalence classes.</p>
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<p>PR and ROC curves on datasets FB15K-237, NLL-995, YAGO3-10 by TransE. “<b>Raw</b>” represents the experimental result on the original training set with no relation removed. “<b>Random</b>” represents the experimental result on the training set formed after randomly removing a group of relations from the training set. “<b>Max</b>” represents the experimental result on the training set formed after removing the top@<span class="html-italic">k</span> most frequently occurring relations from the training set. “<b>REntropy</b>” represents the experimental result on the training set formed after removing the Top@k relation with the highest relation entropy from the training set.</p>
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<p>PR and ROC curves on datasets FB15K-237, NLL-995, YAGO3-10 by ComplEx. The meanings of “<b>Raw</b>”, “<b>Random</b>”, “<b>Max</b>” and “<b>REntropy</b>” are the same as described above.</p>
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<p>PR and ROC curves on datasets FB15K-237, NLL-995, YAGO3-10 by VLP. The meanings of “<b>Raw</b>”, “<b>Random</b>”, “<b>Max</b>” and “<b>REntropy</b>” are the same as described above.</p>
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<p>Bar chart of the number of triples in the training set obtained after deleting four relations on FB15K-237, NELL-995, YAGO3-10.</p>
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30 pages, 2836 KiB  
Article
Analysis of the Spatiotemporal Heterogeneity and Influencing Factors of Regional Economic Resilience in China
by Qiuyue Zhang, Yili Lin, Yu Cao and Long Luo
Entropy 2025, 27(1), 23; https://doi.org/10.3390/e27010023 - 31 Dec 2024
Viewed by 463
Abstract
This study estimates regional economic resilience in China from 2000 to 2022, focusing on economic resistance resilience, recovery resilience, and reorientation resilience. The entropy method, kernel density estimation, and spatial Durbin model are applied to examine the spatiotemporal evolution and influencing factors. The [...] Read more.
This study estimates regional economic resilience in China from 2000 to 2022, focusing on economic resistance resilience, recovery resilience, and reorientation resilience. The entropy method, kernel density estimation, and spatial Durbin model are applied to examine the spatiotemporal evolution and influencing factors. The results show significant spatial clustering, with stronger resilience in the east and weaker resilience in the west. While economic resilience has generally improved, regional disparities persist. Key factors such as human capital, urban hospitals, financial development, market consumption, and environmental quality have a positive effect on resilience, with spatial spillover effects. However, human capital and urban hospitals also show a negative indirect impact on surrounding regions. The influence of these factors varies across regions and periods, indicating strong spatiotemporal heterogeneity. Full article
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Figure 1
<p>Moran scatter plot (scatter plot of regional economic resilience for selected years in China under adjacency matrix).</p>
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<p>Spatiotemporal evolution of regional economic resilience in China.</p>
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<p>Spatiotemporal evolution of regional economic resilience in China.</p>
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<p>Dynamic distribution of national and major regional economic resilience (kernel density plot).</p>
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<p>Temporal and spatial evolution of influencing factors. <span class="html-italic">Note</span>: The red dashed lines represent the reference line. The red boxes show the points of the regression coefficients, while the black lines indicate the confidence intervals.</p>
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26 pages, 11904 KiB  
Article
Impact of Outlet Pressure on Internal Flow Characteristics and Energy Loss in Pump-Turbine System Under Pump Operation Conditions
by Tianding Han, Qifei Li, Licheng Feng, Xiangyu Chen, Feng Zhou and Zhenggui Li
Energies 2025, 18(1), 110; https://doi.org/10.3390/en18010110 - 30 Dec 2024
Viewed by 245
Abstract
During pump operation, the pump-turbine system experiences unstable fluctuations in outlet pressure, which induces turbulence and additional energy losses. Understanding the impact of outlet pressure variations on the internal flow field is crucial for the further development of turbine units. This study employs [...] Read more.
During pump operation, the pump-turbine system experiences unstable fluctuations in outlet pressure, which induces turbulence and additional energy losses. Understanding the impact of outlet pressure variations on the internal flow field is crucial for the further development of turbine units. This study employs numerical methods to systematically analyze the effects of outlet pressure changes on flow characteristics and energy loss. The results show that a decrease in outlet pressure to P0.9BEP significantly increases entropy production in the double-row stay guide vane region, primarily due to flow separation and vortex formation. In the flow passage, sealing gap, and tailpipe regions, entropy production is mainly driven by wall effects, while secondary flows influence the spiral case. The vortex distribution in the double-row stay guide vane is complex, with different variation trends observed in the active and fixed guide vane regions. Outlet pressure changes affect the interaction between the flow passage blades and the fluid, leading to localized flow separation and directly impacting energy loss in downstream components. Additionally, the rate of change in outlet pressure significantly influences vortex generation and dissipation. This research provides new theoretical insights and research directions for performance optimization and energy loss control in pump-turbine systems. Full article
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<p>Three-dimensional model of pump-turbine CFD domain.</p>
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<p>Variation of outlet pressure with unit operating time.</p>
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<p>Grid independence verification.</p>
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<p>Vorticity distribution of spiral case.</p>
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<p>Vortex area of volute section.</p>
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<p>Entropy production of volute.</p>
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<p>Vorticity distribution of stay-guide vane.</p>
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<p>Vortex area of double-row cascades.</p>
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<p>Entropy production of double-row cascade.</p>
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<p>Vorticity distribution of runner.</p>
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<p>Vortex area of runner.</p>
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<p>Entropy production of runner.</p>
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<p>Vorticity distribution of tailpipe.</p>
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<p>Vortex area of tailpipe.</p>
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<p>Entropy production of tailpipe.</p>
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<p>Distribution of entropy production rate of spiral case.</p>
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<p>Distribution of entropy production rate of double-row cascade.</p>
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<p>Distribution of entropy production rate of runner.</p>
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<p>Distribution of entropy production rate of tailpipe.</p>
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23 pages, 5881 KiB  
Article
Impact of Wetting-Drying Cycles on Soil Intra-Aggregate Pore Architecture Under Different Management Systems
by Luiz F. Pires, Jocenei A. T. de Oliveira, José V. Gaspareto, Adolfo N. D. Posadas and André L. F. Lourenço
AgriEngineering 2025, 7(1), 9; https://doi.org/10.3390/agriengineering7010009 - 30 Dec 2024
Viewed by 243
Abstract
In many soil processes, including solute and gas dynamics, the architecture of intra-aggregate pores is a crucial component. Soil management practices and wetting-drying (W-D) cycles, the latter having a significant impact on pore aggregation, are two key factors that shape pore structure. This [...] Read more.
In many soil processes, including solute and gas dynamics, the architecture of intra-aggregate pores is a crucial component. Soil management practices and wetting-drying (W-D) cycles, the latter having a significant impact on pore aggregation, are two key factors that shape pore structure. This study examines the effects of W-D cycles on the architecture of intra-aggregate pores under three different soil management systems: no-tillage (NT), minimum tillage (MT), and conventional tillage (CT). The soil samples were subjected to 0 and 12 W-D cycles, and the resulting pore structures were scanned using X-ray micro-computed tomography, generating reconstructed 3D volumetric data. The data analyses were conducted in terms of multifractal spectra, normalized Shannon entropy, lacunarity, porosity, anisotropy, connectivity, and tortuosity. The multifractal parameters of capacity, correlation, and information dimensions showed mean values of approximately 2.77, 2.75, and 2.75 when considering the different management practices and W-D cycles; 3D lacunarity decreased mainly for the smallest boxes between 0 and 12 W-D cycles for CT and NT, with the opposite behavior for MT. The normalized 3D Shannon entropy showed differences of less than 2% before and after the W-D cycles for MT and NT, with differences of 5% for CT. The imaged porosity showed reductions of approximately 50% after 12 W-D cycles for CT and NT. Generally, the largest pores (>0.1 mm3) contributed the most to porosity for all management practices before and after W-D cycles. Anisotropy increased by 9% and 2% for MT and CT after the cycles and decreased by 23% for NT. Pore connectivity showed a downward trend after 12 W-D cycles for CT and NT. Regarding the pore shape, the greatest contribution to porosity and number of pores was due to triaxial-shaped pores for both 0 and 12 W-D cycles for all management practices. The results demonstrate that, within the resolution limits of the microtomography analysis, pore architecture remained resilient to changes, despite some observable trends in specific parameters. Full article
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<p>Location of the State of Paraná on the map of Brazil, the municipality of Ponta Grossa on the map of Paraná, and the experimental area where the samples were collected. IAPAR: “Instituto de Desenvolvimento Rural do Paraná”; CT: conventional tillage; NT: no tillage; MT: minimum tillage.</p>
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<p>Three-dimensional images of the soil pore system (terracotta color) for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 wetting and drying (W-D) cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no tillage for 0 and 12 W-D cycles.</p>
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<p>Three-dimensional Shannon entropy (<math display="inline"><semantics> <mrow> <msup> <mi>H</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>) and lacunarity (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi>n</mi> <mo>(</mo> <mo>Λ</mo> </mrow> </semantics></math>)) curves for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 wetting and drying (W-D) cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no tillage for 0 and 12 W-D cycles. The error bars represent the standard deviation from the mean.</p>
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<p>Variation in the capacity dimension (<math display="inline"><semantics> <msub> <mi>D</mi> <mn>0</mn> </msub> </semantics></math>) as a function of the application of wetting and drying cycles (W-D) for the following conditions: (<b>a</b>) minimum tillage for 0 and 12 W-D cycles; (<b>b</b>) conventional tillage for 0 and 12 W-D cycles; (<b>c</b>) no tillage for 0 and 12 W-D cycles. NS: non-significant differences determined by a <span class="html-italic">t</span>-test (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>).</p>
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<p>Variation in porosity (<math display="inline"><semantics> <mo>Φ</mo> </semantics></math>) and pore size distribution (<math display="inline"><semantics> <mrow> <mo>Φ</mo> <mo>−</mo> <mi>s</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> </mrow> </semantics></math>) as a function of the application of wetting and drying cycles (W-D) for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 W-D cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no-tillage for 0 and 12 W-D cycles. NS: non-significant differences by <span class="html-italic">t</span>-test (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>).</p>
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<p>Variation in the degree of anisotropy (DA) and number of pores (NP) as a function of the application of wetting and drying cycles (W-D) for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 W-D cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no tillage for 0 and 12 W-D cycles. NS: non-significant differences determined by a <span class="html-italic">t</span>-test (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>).</p>
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<p>Variation in pore connectivity (C) and tortuosity (<math display="inline"><semantics> <mi>τ</mi> </semantics></math>) as a function of the application of wetting and drying cycles (W-D) for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 W-D cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no- tillage for 0 and 12 W-D cycles. NS: non-significant differences determined by a <span class="html-italic">t</span>-test (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>).</p>
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<p>Contribution of the different pore shapes to the volume (VP-S) and number of pores (NP-S) for the following conditions: (<b>a</b>,<b>b</b>) minimum tillage for 0 and 12 wetting and drying (W-D) cycles; (<b>c</b>,<b>d</b>) conventional tillage for 0 and 12 W-D cycles; (<b>e</b>,<b>f</b>) no-tillage for 0 and 12 W-D cycles. Eq.: equant; Pr.: prolate; Ob.: oblate; Tr.: triaxial. NS: non-significant differences by <span class="html-italic">t</span>-test (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>&lt;</mo> <mn>0.05</mn> </mrow> </semantics></math>).</p>
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<p>Diagram for extracting the soil aggregate sample. (1) Soil sample inside the cylinder; (2) volume of soil carefully extracted from the cylinder; (3) soil aggregate extracted from the center of the sample.</p>
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<p>Multifractal spectra for samples subjected to different (0 and 12) wetting and drying 565 cycles (W-D). MT: minimum tillage; CT: conventional tillage; NT: no tillage; R: replicate.</p>
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33 pages, 3930 KiB  
Article
The Second Law of Infodynamics: A Thermocontextual Reformulation
by Harrison Crecraft
Entropy 2025, 27(1), 22; https://doi.org/10.3390/e27010022 - 30 Dec 2024
Viewed by 281
Abstract
Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions [...] Read more.
Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions unanswered. This article analyzes and reformulates the law based on thermocontextual interpretation (TCI). The TCI generalizes Hamiltonian mechanics by defining states and transitions thermocontextually with respect to an ambient-temperature reference state. The TCI partitions energy into exergy, which can do work on the ambient surroundings, and entropic energy with zero work potential. The TCI is further generalized here to account for a reference observer’s actual knowledge. This enables partitioning exergy into accessible exergy, which is known and accessible for use, and configurational energy, which is knowable but unknown and inaccessible. The TCI is firmly based on empirically validated postulates. The Second Law of thermodynamics and its information-based analog, MaxEnt, are logically derived corollaries. Another corollary is a reformulated Second Law of Infodynamics. It states that an external agent seeks to increase its access to exergy by narrowing its information gap with a potential exergy source. The principle is key to the origin of self-replicating chemicals and life. Full article
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<p>Perfect measurement of exergy and entropic energy. Perfect measurement is defined with respect to a measurement device in equilibrium with the ambient surroundings. As the system reversibly transitions to its equilibrium ambient state, exergy and entropic energy are the outputs and are recorded by a classical measurement device as exchanges of ambient work w<sub>a</sub> and ambient heat q<sub>a</sub>. Work can be measured by the reversible lifting of a weight in a gravitational field. Absorbed heat can be measured by the work of expansion as a gas isothermally absorbs heat and maintains a fixed ambient temperature and energy.</p>
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<p>TCI energy states. Each system is prepared by applying work w<sub>a</sub> to an ambient gas with zero stored exergy and E = X = Q = 0. (a) The thermal energy state is prepared by the work of reversibly pumping heat from the ambient surroundings into the gas. (b) The mechanical energy state is prepared by applying work to the mechanical battery only. (c) The configurational energy state is prepared by the work of isothermally compressing the gas. (d) Measurement devices record the exergy and entropic energy changes during reversible transitions back to the ARS. (e) The ARS defines the zero-energy levels for exergy and entropic energy. All the transitions are with respect to fixed ambient temperature and pressure.</p>
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<p>TCI energy states and their preparations in an X−Q space. (a) The thermal state’s energy, <b>E<sub>q</sub></b>, has an exergy equal to its work of preparation, w, and positive entropic energy, Q, equal to the ambient heat reversibly pumped from the ambient surroundings. (b) The mechanical state’s energy, <b>E<sub>m</sub></b>, has an exergy equal to its work of preparation and zero entropic energy. (c) The configurational state’s energy, <b>E</b><sub>c</sub>, has an exergy equal to its applied work, w, and negative entropic energy, equal to the ambient heat expelled during isothermal compression. (d) Measurements of the energy states are defined by the changes in measurable work and ambient heat as the systems reversibly transition to the ARS.</p>
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<p>Thermocontextual state description and macrostate model. The thermocontextual state is completely defined by its energy-state measurement with respect to the ambient reference and by its microstate description by a perfect ambient observer. The macrostate model, in contrast, is defined with respect to a reference at a fixed reference temperature, T<sub>ref</sub> ≥ T<sub>a</sub>, and by a generally imperfect observer with incomplete information.</p>
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<p>Accessibility and configurational energy. Configurational energy C is unavailable to the reference observer for work due to T<sub>ref</sub> &gt; T<sub>a</sub> or due to incomplete microstate information. Accessibility A is the balance of exergy X that is reversibly available to the reference observer for work.</p>
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<p>Quasistatic transition types. The figure illustrates the three types of transitions from ambient gas to compressed gas by the application of ambient work, w<sub>a</sub>. The transitions are quasistatic, with no frictional losses. The equilibrium transitions, L and R, reversibly and deterministically compress the gas from either the left or right side and produce a definite and known microstate, L or R. Transition M is reversible but statistical, and it produces a mixed macrostate M<sub>LR</sub>, with a single definite but unknown microstate L or R. Transition Q irreversibly but deterministically compresses the gas and produces a single thermalized microstate, Q<sub>LR</sub>. The macrostate model and transactional properties for each are shown in the tables on the right side.</p>
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<p>Dissipative network diagram for the reactions A + X → B + Y and Y → X. States are represented as horizontal lines with specific exergy per unit of component. Transitions between states are represented by dotted lines and numbered nodes. Transition 1 extracts exergy from input A as it transitions to output B. Exergy is transferred to the coupled transition node 2, which does the internal work of converting X to the higher-exergy state Y. Transition 3 takes state Y back to X and uses the extracted exergy for external work on the surroundings.</p>
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<p>Stationary dissipative processes and homeostates. Each path represents a homeostate and the process of transitioning source components to the ambient surroundings. Observation reduces the observer’s information gap by revealing information on the network nodes, transitions, and the internal work of increasing the system’s accessibility. An external device measures the outputs of reference work (mechanical work plus accessible energy) and heat to the fixed reference. Perfect observation and measurement are in the quasistatic limit of zero frictional losses of exergy and information.</p>
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<p>Double-slit experiment. The microstate configurations are defined by the resolution of the detector screen. If the which-switch detector (WSD) is disabled, an individual transition passes through the double slits symmetrically and randomly instantiates an impact and definite configuration on the detector screen (state B). Multiple transitions generate a statistically mixed macrostate C, represented by a probability distribution of instantiated microstates. With the WSD activated, the particle passes asymmetrically through one slit or the other, and the interference pattern for C changes to a single broad peak.</p>
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<p>Probability distribution profiles for particle detection from double slits, with and without wave interference, and from single slits.</p>
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<p>The work of adding an A or B to an array is equal to Δw.</p>
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25 pages, 271 KiB  
Article
Evaluation of the Degree of Synergy in High-Quality Development Among Inter-Provincial Adjacent Districts and Planning Recommendations: The Case Study of Anhui Province and Its Surrounding Provinces
by Qiguo Li, Yafei Zhang, Linfeng Zhu, Xiaohan Geng and Jia Liu
Sustainability 2025, 17(1), 197; https://doi.org/10.3390/su17010197 - 30 Dec 2024
Viewed by 391
Abstract
As China’s economy accelerates its transition toward high-quality development, various regions are actively tapping into their distinctive resources to unlock economic potential and exploring pathways to achieve high-quality collaborative development with neighboring areas. This study endeavors to provide both theoretical insights and practical [...] Read more.
As China’s economy accelerates its transition toward high-quality development, various regions are actively tapping into their distinctive resources to unlock economic potential and exploring pathways to achieve high-quality collaborative development with neighboring areas. This study endeavors to provide both theoretical insights and practical recommendations for the actual development of Anhui Province and its adjacent regions, through an in-depth analysis of their collaborative pursuit of high-quality growth. Employing the entropy weight method and the coupled coordination degree model, this research rigorously evaluates the extent of coordinated high-quality development between Anhui Province and its neighboring provinces, and offers effective planning suggestions grounded in the evaluation results. The findings reveal that (1) coastal cities generally demonstrate a higher level of comprehensive development compared to those located further inland; (2) cities with superior comprehensive development also tend to excel in economic growth, scientific and technological innovation, ecological advancement, and coupling coordination; (3) nevertheless, a higher level of comprehensive development does not necessarily imply better social service provision. Full article
27 pages, 4677 KiB  
Review
Weak Physycally Unclonable Functions in CMOS Technology: A Review
by Massimo Vatalaro, Raffaele De Rose, Marco Lanuzza and Felice Crupi
Chips 2025, 4(1), 3; https://doi.org/10.3390/chips4010003 - 30 Dec 2024
Viewed by 203
Abstract
Physically unclonable functions (PUFs) represent emerging cryptographic primitives that exploit the uncertainty of the CMOS manufacturing process as an entropy source for generating unique, random and stable keys. These devices can be potentially used in a wide variety of applications ranging from secret [...] Read more.
Physically unclonable functions (PUFs) represent emerging cryptographic primitives that exploit the uncertainty of the CMOS manufacturing process as an entropy source for generating unique, random and stable keys. These devices can be potentially used in a wide variety of applications ranging from secret key generation, anti-counterfeiting, and low-cost authentications to advanced protocols such as oblivious transfer and key exchange. Unfortunately, guaranteeing adequate PUF stability is still challenging, thus often requiring post-silicon stability enhancement techniques. The latter help to contrast the raw sensitivity to on-chip noise and variations in the environmental conditions (i.e., voltage and temperature variations), but their area and energy costs are not always feasible for IoT devices that operate with constrained budgets. This pushes the demand for ever more stable, area- and energy-efficient solutions at design time. This review aims to provide an overview of several weak PUF solutions implemented in CMOS technology, discussing their performance and suitability for being employed in security applications. Full article
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<p>Some of the most important Figures of Merit (FOMs) for PUFs.</p>
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<p>Some of the most relevant (<b>a</b>–<b>d</b>) mismatch-based, and (<b>e</b>,<b>f</b>) non mismatch-based PUF classes.</p>
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<p>Some of the most relevant delay-based solutions: (<b>a</b>) current-integrated differential NAND PUF [<a href="#B15-chips-04-00003" class="html-bibr">15</a>], (<b>b</b>) configurable RO solution proposed in [<a href="#B18-chips-04-00003" class="html-bibr">18</a>], and (<b>c</b>) thyristor-based solution proposed in [<a href="#B19-chips-04-00003" class="html-bibr">19</a>].</p>
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<p>Some of the most relevant SRAM-based solutions: (<b>a</b>–<b>c</b>) monostable-based cells proposed in [<a href="#B23-chips-04-00003" class="html-bibr">23</a>,<a href="#B24-chips-04-00003" class="html-bibr">24</a>,<a href="#B25-chips-04-00003" class="html-bibr">25</a>], (<b>d</b>) metastable-based 11T cell proposed in [<a href="#B31-chips-04-00003" class="html-bibr">31</a>], (<b>e</b>,<b>f</b>) delay-based cells proposed in (<b>e</b>) [<a href="#B32-chips-04-00003" class="html-bibr">32</a>] and (<b>f</b>) [<a href="#B33-chips-04-00003" class="html-bibr">33</a>].</p>
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<p>Some of the most relevant metastable-based bitcells: (<b>a</b>,<b>b</b>) cross-coupled comparators [<a href="#B35-chips-04-00003" class="html-bibr">35</a>,<a href="#B36-chips-04-00003" class="html-bibr">36</a>], (<b>c</b>) cross-coupled inverters proposed in [<a href="#B37-chips-04-00003" class="html-bibr">37</a>], and (<b>d</b>) cross-coupled NAND proposed in [<a href="#B39-chips-04-00003" class="html-bibr">39</a>], (<b>e</b>,<b>f</b>) transient effect ring oscillator (TERO) solutions [<a href="#B41-chips-04-00003" class="html-bibr">41</a>,<a href="#B42-chips-04-00003" class="html-bibr">42</a>].</p>
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<p>Some of the most relevant monostable-based bitcells based on (<b>a</b>) regulated cascode current mirrors [<a href="#B44-chips-04-00003" class="html-bibr">44</a>] (<b>b</b>) 2T amplifiers [<a href="#B49-chips-04-00003" class="html-bibr">49</a>], (<b>c</b>) subthreshold inverters [<a href="#B51-chips-04-00003" class="html-bibr">51</a>], (<b>d</b>) dual entropy [<a href="#B52-chips-04-00003" class="html-bibr">52</a>], (<b>e</b>) cross-coupled impedance [<a href="#B55-chips-04-00003" class="html-bibr">55</a>], and (<b>f</b>) cascode NAND gates [<a href="#B56-chips-04-00003" class="html-bibr">56</a>].</p>
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<p>(<b>a</b>) Conceptual diagram of the sub-threshold voltage divider-based PUF bitcell. (<b>b</b>) 2T- [<a href="#B58-chips-04-00003" class="html-bibr">58</a>], (<b>c</b>) 4T- [<a href="#B59-chips-04-00003" class="html-bibr">59</a>], (<b>d</b>) 6T-, (<b>e</b>) 8T-core based bitcell [<a href="#B60-chips-04-00003" class="html-bibr">60</a>].</p>
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<p>Some of the most relevant active PUF bitcells based on (<b>a</b>,<b>b</b>) hard oxide breakdown proposed in [<a href="#B61-chips-04-00003" class="html-bibr">61</a>,<a href="#B62-chips-04-00003" class="html-bibr">62</a>], respectively, (<b>c</b>) soft oxide breakdown proposed in [<a href="#B65-chips-04-00003" class="html-bibr">65</a>], and (<b>d</b>) quantum tunneling mechanism proposed in [<a href="#B66-chips-04-00003" class="html-bibr">66</a>].</p>
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<p>Some of the most relevant via PUF bitcells based on (<b>a</b>) contact formation probability [<a href="#B67-chips-04-00003" class="html-bibr">67</a>] and (<b>b</b>) metal via resistance [<a href="#B69-chips-04-00003" class="html-bibr">69</a>].</p>
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<p>Some of the most common PUF applications.</p>
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<p>Block diagram for (<b>a</b>) cryptographic key generation, (<b>b</b>) anti-counterfeiting, and (<b>c</b>) entity authentication.</p>
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<p>Comparison table among weak PUF solutions.</p>
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16 pages, 3804 KiB  
Article
Ring Oscillators with Additional Phase Detectors as a Random Source in a Random Number Generator
by Łukasz Matuszewski, Mieczysław Jessa and Jakub Nikonowicz
Entropy 2025, 27(1), 15; https://doi.org/10.3390/e27010015 - 28 Dec 2024
Viewed by 313
Abstract
In this paper, we propose a method to enhance the performance of a random number generator (RNG) that exploits ring oscillators (ROs). Our approach employs additional phase detectors to extract more entropy; thus, RNG uses fewer resources to produce bit sequences that pass [...] Read more.
In this paper, we propose a method to enhance the performance of a random number generator (RNG) that exploits ring oscillators (ROs). Our approach employs additional phase detectors to extract more entropy; thus, RNG uses fewer resources to produce bit sequences that pass all statistical tests proposed by National Institute of Standards and Technology (NIST). Generating a specified number of bits is on-demand, eliminating the need for continuous RNG operation. This feature enhances the security of the produced sequences, as eavesdroppers are unable to observe the continuous random bit generation process, such as through monitoring power lines. Furthermore, our research demonstrates that the proposed RNG’s perfect properties remain unaffected by the manufacturer of the field-programmable gate arrays (FPGAs) used for implementation. This independence ensures the RNG’s reliability and consistency across various FPGA manufacturers. Additionally, we highlight that the tests recommended by the NIST may prove insufficient in assessing the randomness of the output bit streams produced by RO-based RNGs. Full article
(This article belongs to the Section Signal and Data Analysis)
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<p>Jitter oscillator sampling method for producing random bits.</p>
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<p>Successive restarts of RO-based RNG from <a href="#entropy-27-00015-f001" class="html-fig">Figure 1</a>. During a single restart, an <span class="html-italic">M</span>-bit sequence is produced.</p>
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<p>Successive restarts of RO-based RNG from <a href="#entropy-27-00015-f001" class="html-fig">Figure 1</a>. During a single restart, an <span class="html-italic">M</span>-bit sequence is produced.</p>
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<p>A start–stop combined RNG with phase detectors.</p>
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<p>A scheme of the phase detector PD used in the start–stop combined RNG from <a href="#entropy-27-00015-f004" class="html-fig">Figure 4</a>.</p>
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<p>Comparison of the spectrum on the output of RO-based generator without phase detector (<b>left</b>) and with phase detector (<b>right</b>) for K = 2.</p>
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<p>Comparison of the spectrum on the output of RO-based generator without phase detector (<b>left</b>) and with phase detector (<b>right</b>) for K = 4.</p>
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<p>Comparison of the spectrum on the output of RO-based generator without phase detector (<b>left</b>) and with phase detector (<b>right</b>) for K = 8.</p>
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<p><math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> as a function of <span class="html-italic">K</span> for sampling frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math> MHz.</p>
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<p><math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> as a function of <span class="html-italic">K</span> for sampling frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> MHz.</p>
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<p><math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> as a function of <span class="html-italic">K</span> for sampling frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>200</mn> </mrow> </semantics></math> MHz.</p>
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<p><math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> as a function of <span class="html-italic">K</span> for sampling frequency <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>L</mi> </msub> <mo>=</mo> <mn>300</mn> </mrow> </semantics></math> MHz.</p>
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<p>Comparison of <math display="inline"><semantics> <msub> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> values as a function of <span class="html-italic">K</span> for two vendors of FPGAs and two solutions of RNG: classic and with additional phase detectors. The sampling frequency was set to 50 MHz.</p>
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35 pages, 4965 KiB  
Article
A Novel IVBPRT-ELECTRE III Algorithm Based on Bidirectional Projection and Its Application
by Juxiang Wang, Min Xu, Yanjun Wang and Ziqi Zhu
Symmetry 2025, 17(1), 26; https://doi.org/10.3390/sym17010026 - 26 Dec 2024
Viewed by 330
Abstract
Fuzzy semantics have a wide range of applications in life, and especially when expressing people’s evaluation information, it is more specific. As people increasingly prefer to express their personal opinions through media platforms, the opinions of the general public have become an indispensable [...] Read more.
Fuzzy semantics have a wide range of applications in life, and especially when expressing people’s evaluation information, it is more specific. As people increasingly prefer to express their personal opinions through media platforms, the opinions of the general public have become an indispensable reference. However, information asymmetry can have a significant impact on the rationality of decision-making. Based on the above considerations, this paper extends bidirectional projection to probabilistic linguistic term sets to preserve the completeness of information as much as possible. The large-scale group decision-making problem under the probabilistic linguistic environment is extended to limited interval values, and a new group decision-making method named IVBPRT-ELECTRE III algorithm (ELECTRE III based on bidirectional projection and regret theory under limited interval-valued probabilistic linguistic term set) is proposed. The method is an extended ELECTRE III method based on limited interval-valued probabilistic linguistic term set (l-IVPLTS) bidirectional projection by regret theory approach. Firstly, this involves mining the online text comment information on social media about an emergency and considering the effect of the number of fans, determining the attributes and their initial weights for judging the strengths and weaknesses of the emergency management alternative using the TF-IDF and the Word2vec technology, and using the entropy value to adjust the initial weight of attributes, not only considering the real opinions of the public, but also combining with the views of experts, making the decision-making alternative selection more scientific and reasonable. Secondly, this paper fills the gap of bidirectional projection under l-IVPLTS environment; then, combining l-IVPLTS bidirectional projection and regret theory to determine the objective weights of experts, combines the differences in individual expertise of experts to obtain the comprehensive weights of experts, and uses the extended ELECTRE III method to rank the alternatives. Finally, the feasibility and validity of the provided method is verified through the Yanjiao explosion incident as a case. Full article
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<p><inline-formula><mml:math id="mm523"><mml:semantics><mml:mrow><mml:mi mathvariant="normal">L</mml:mi><mml:mi mathvariant="normal">D</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> model diagram.</p>
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<p>Emergency decision-making flow chart.</p>
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<p>Word cloud of ‘3.13’ Yanjiao deflagration accident.</p>
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<p>Topic consistency.</p>
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<p><inline-formula><mml:math id="mm524"><mml:semantics><mml:mrow><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> value of clustering for mass data.</p>
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<p>Silhouette coefficient of clustering for mass data.</p>
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<p>Visualization of clustering results for mass data.</p>
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<p><inline-formula><mml:math id="mm525"><mml:semantics><mml:mrow><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> value of clustering for official data.</p>
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<p>Silhouette coefficient of clustering for official data.</p>
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<p>Visualization of clustering results for official data.</p>
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<p>Comparison of the results of the six methods [<xref ref-type="bibr" rid="B21-symmetry-17-00026">21</xref>,<xref ref-type="bibr" rid="B31-symmetry-17-00026">31</xref>].</p>
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<p>Visualization of the results of the <inline-formula><mml:math id="mm526"><mml:semantics><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> sensitivity analysis.</p>
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<p>Visualization of the results of the <inline-formula><mml:math id="mm527"><mml:semantics><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> sensitivity analysis.</p>
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<p>Visualization of the results of the <inline-formula><mml:math id="mm528"><mml:semantics><mml:mrow><mml:mi>γ</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> sensitivity analysis.</p>
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20 pages, 1940 KiB  
Article
Study on the Performance of Filters Under Biogas Slurry Drip Irrigation Systems
by Shuaijie Wang, Haitao Wang, Xuefeng Qiu, Jiandong Wang, Shuji Wang, Hang Wang and Tao Shen
Agriculture 2025, 15(1), 30; https://doi.org/10.3390/agriculture15010030 - 26 Dec 2024
Viewed by 263
Abstract
Filters are essential components for maintaining the stability of drip irrigation systems, effectively reducing the risk of clogging. However, when applied to slurry drip irrigation systems, the complexity of slurry water quality makes it unclear how different filter types and their combinations affect [...] Read more.
Filters are essential components for maintaining the stability of drip irrigation systems, effectively reducing the risk of clogging. However, when applied to slurry drip irrigation systems, the complexity of slurry water quality makes it unclear how different filter types and their combinations affect the hydraulic performance of the system. This study provides a comprehensive performance evaluation of two common filter types and their combinations, considering various flow rates and biogas slurry-to-water ratios under drip irrigation conditions. The results revealed the following key findings: (1) In the application of biogas slurry drip irrigation, an increase in the concentration or flow rate of the slurry significantly affects the hydraulic performance of the filter, increasing the risk of clogging and shortening the operational lifespan. Notably, the impact of changes in slurry concentration on the hydraulic performance of the filter is much greater than that of the flow rate. Compared to mesh filters, disk filters offer better hydraulic performance, with the contaminant capacity of disk filters being approximately three times that of mesh filters. (2) In biogas slurry drip irrigation, the filter combination generally outperforms single filters in terms of hydraulic performance and contaminant removal capacity. Due to the unique nature of the water source in biogas slurry, a selection process for filter combinations was conducted. It was found that when a disk filter is used as the pre-filter and a mesh filter as the post-filter, the overall rate of head loss change is the smallest, and the clogging uniformity is the least. (3) In the entropy weight-TOPSIS comprehensive evaluation, the filter’s operating time and contaminant capacity are key factors affecting its overall performance. From the perspective of improving the operational stability of the biogas slurry drip irrigation system, it is recommended to use a disk filter + mesh filter combination. This study conducts practical measurements on the hydraulic performance, contaminant removal capacity, filtration accuracy, and other indicators of commonly used mesh and disk filters, aiming to provide useful references for the practical application of biogas slurry drip irrigation filters. Full article
(This article belongs to the Special Issue Livestock Waste Sustainable Management and Applications)
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<p>Filter hydraulic performance testing platform. 1. Water pump. 2. Check valve. 3. Reflux valve. 4. Flow regulating ball valve. 5. Flow regulating diaphragm valve. 6. Electromagnetic flow meter. 7. Pressure gauge. 8. 80 screen mesh filter. 9. 80 disk filter. 10. 120 screen mesh filter. 11. 120 disk filter. 12. S80 + S120. 13. S80 + D120. 14. D80 + S120. 15. D80 + D120. 16. Tail pressure regulating valve. 17. Water bucket. 18. Water pump inlet valve. 19. Bucket outlet valve.</p>
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<p>Effect of univariate cleaning on the hydraulic performance of the filter screen.</p>
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<p>Changes in head loss of each filter under three different flow rates (biogas slurry:clean water 1:14).</p>
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<p>Changes in head loss of each filter under three different concentrations of biogas slurry (flow rate 2.5 m<sup>3</sup>/h).</p>
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<p>The variation pattern of running time of each filter. (<b>a</b>) The variation law of operating time of each filter under three different flow rates and (<b>b</b>) the variation law of operating time of each filter combination under three different concentrations.</p>
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<p>The variation law of pollutant carrying capacity of each filter element at different flow rates (volume ratio of biogas slurry to water 1:14). Different letters represent different treatments with significant differences under <span class="html-italic">p</span> &lt; 0.05.</p>
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<p>The variation pattern of pollutant carrying capacity of each filter element under different concentrations of biogas slurry (flow rate 2.5 m<sup>3</sup>/h), Different letters represent different treatments with significant differences under <span class="html-italic">p</span> &lt; 0.05.</p>
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