As network technology evolves, cyberattacks are not only increasing in frequency but also becoming more sophisticated. To proactively detect and prevent these cyberattacks, researchers are developing intrusion detection systems (IDSs) leveraging machine learning and deep learning techniques. However, a significant challenge with these advanced models is the increased training time as model complexity grows, and the symmetry between performance and training time must be taken into account. To address this issue, this study proposes a fast-persistent-contrastive-divergence-based deep belief network (FPCD-DBN) that offers both high accuracy and rapid training times. This model combines the efficiency of contrastive divergence with the powerful feature extraction capabilities of deep belief networks. While traditional deep belief networks use a contrastive divergence (CD) algorithm, the FPCD algorithm improves the performance of the model by passing the results of each detection layer to the next layer. In addition, the mix of parameter updates using fast weights and continuous chains makes the model fast and accurate. The performance of the proposed FPCD-DBN model was evaluated on several benchmark datasets, including NSL-KDD, UNSW-NB15, and CIC-IDS-2017. As a result, the proposed method proved to be a viable solution as the model performed well with an accuracy of 89.4% and an F1 score of 89.7%. By achieving superior performance across multiple datasets, the approach shows great potential for enhancing network security and providing a robust defense against evolving cyber threats.
{"title":"A Study on Network Anomaly Detection Using Fast Persistent Contrastive Divergence","authors":"Jaeyeong Jeong, Seongmin Park, Joonhyung Lim, Jiwon Kang, Dongil Shin, Dongkyoo Shin","doi":"10.3390/sym16091220","DOIUrl":"https://doi.org/10.3390/sym16091220","url":null,"abstract":"As network technology evolves, cyberattacks are not only increasing in frequency but also becoming more sophisticated. To proactively detect and prevent these cyberattacks, researchers are developing intrusion detection systems (IDSs) leveraging machine learning and deep learning techniques. However, a significant challenge with these advanced models is the increased training time as model complexity grows, and the symmetry between performance and training time must be taken into account. To address this issue, this study proposes a fast-persistent-contrastive-divergence-based deep belief network (FPCD-DBN) that offers both high accuracy and rapid training times. This model combines the efficiency of contrastive divergence with the powerful feature extraction capabilities of deep belief networks. While traditional deep belief networks use a contrastive divergence (CD) algorithm, the FPCD algorithm improves the performance of the model by passing the results of each detection layer to the next layer. In addition, the mix of parameter updates using fast weights and continuous chains makes the model fast and accurate. The performance of the proposed FPCD-DBN model was evaluated on several benchmark datasets, including NSL-KDD, UNSW-NB15, and CIC-IDS-2017. As a result, the proposed method proved to be a viable solution as the model performed well with an accuracy of 89.4% and an F1 score of 89.7%. By achieving superior performance across multiple datasets, the approach shows great potential for enhancing network security and providing a robust defense against evolving cyber threats.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The aim of this paper is to examine the L-fuzzy prime filter degrees on lattices and their induced L-fuzzy convex structure. Firstly, the notion of L-fuzzy prime filter degrees on lattices is established using the implication operator when L is a completely distributive lattice. Secondly, an equivalent characterization of L-fuzzy prime filter degrees on lattices is provided. The equivalence relation, through the definitions of reflexivity, symmetry, and transitivity, provides a method for partitioning subsets within a lattice that possesses the prime filter property. Finally, the L-fuzzy convex structure induced by the L-fuzzy prime filter degrees on lattices is examined. Simultaneously, the properties of L-fuzzy prime filter degrees on lattices in relation to images and preimages under homomorphic mappings are discussed.
本文旨在研究网格上的 L-模糊素过滤度及其诱导的 L-模糊凸结构。首先，当 L 是完全分布网格时，利用蕴涵算子建立了网格上的 L-模糊素过滤度概念。其次，提供了网格上 L-模糊素过滤度的等价表征。通过反身性、对称性和反转性的定义，等价关系提供了一种在具有质滤波器性质的网格中划分子集的方法。最后，研究了由网格上的 L-fuzzy prime filter 度引起的 L-fuzzy 凸结构。同时，还讨论了网格上的 L-模糊素滤波度在同态映射下与图像和预图像相关的性质。
{"title":"The L-Fuzzy Prime Filter Degrees on Lattices and Its Induced L-Fuzzy Convex Structure","authors":"Lan Wang, Jing Chen","doi":"10.3390/sym16091215","DOIUrl":"https://doi.org/10.3390/sym16091215","url":null,"abstract":"The aim of this paper is to examine the L-fuzzy prime filter degrees on lattices and their induced L-fuzzy convex structure. Firstly, the notion of L-fuzzy prime filter degrees on lattices is established using the implication operator when L is a completely distributive lattice. Secondly, an equivalent characterization of L-fuzzy prime filter degrees on lattices is provided. The equivalence relation, through the definitions of reflexivity, symmetry, and transitivity, provides a method for partitioning subsets within a lattice that possesses the prime filter property. Finally, the L-fuzzy convex structure induced by the L-fuzzy prime filter degrees on lattices is examined. Simultaneously, the properties of L-fuzzy prime filter degrees on lattices in relation to images and preimages under homomorphic mappings are discussed.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcos E. González Laffitte, Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, Peter F. Stadler
Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.
原子到原子图谱（AAM）是建立化学反应中反应物和生成物原子对应关系的双射。它们捕捉了反应机理的关键特征，因此在图变换层面的化学建模中发挥着核心作用。AAM 等同于所谓的 "假想过渡态"（ITS）图，因此可以将 AAM 的计算比较等任务简化为测试图的同构性。然而，在许多应用场景中，只有部分信息可用，即只知道部分映射，或者等同于只知道 ITS 图的子图。在此，我们将研究是否可以、如何以及在多大程度上完成并比较这些部分化学数据。本文的重点完全在于为分析部分 AAM 及其相关的部分 ITS 图奠定坚实的数学基础。
{"title":"Partial Imaginary Transition State (ITS) Graphs: A Formal Framework for Research and Analysis of Atom-to-Atom Maps of Unbalanced Chemical Reactions and Their Completions","authors":"Marcos E. González Laffitte, Klaus Weinbauer, Tieu-Long Phan, Nora Beier, Nico Domschke, Christoph Flamm, Thomas Gatter, Daniel Merkle, Peter F. Stadler","doi":"10.3390/sym16091217","DOIUrl":"https://doi.org/10.3390/sym16091217","url":null,"abstract":"Atom-to-atom maps (AAMs) are bijections that establish the correspondence of reactant and product atoms across chemical reactions. They capture crucial features of the reaction mechanism and thus play a central role in modeling chemistry at the level of graph transformations. AAMs are equivalent to so-called “imaginary transition state” (ITS) graphs, making it possible to reduce tasks such as the computational comparison of AAMs to testing graph isomorphisms. In many application scenarios, nonetheless, only partial information is available, i.e., only partial maps or, equivalently, only subgraphs of the ITS graphs, are known. Here, we investigate whether and how, and to what extent, such partial chemical data can be completed and compared. The focus of this contribution is entirely on the development of a solid mathematical foundation for the analysis of partial AAMs and their associated partial ITS graphs.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"593 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Unsupervised domain adaptation (UDA) methods, based on adversarial learning, employ the means of implicit global and class-aware domain alignment to learn the symmetry between source and target domains and facilitate the transfer of knowledge from a labeled source domain to an unlabeled target domain. However, these methods still face misalignment and poor target generalization due to small inter-class domain discrepancy and large intra-class discrepancy of target features. To tackle these challenges, we introduce a novel adversarial learning-based UDA framework named Coding Rate Reduction Adversarial Domain Adaptation (CR2ADA) to better learn the symmetry between source and target domains. Integrating conditional domain adversarial networks with domain-specific batch normalization, CR2ADA learns robust domain-invariant features to implement global domain alignment. For discriminative class-aware domain alignment, we propose the global and local coding rate reduction methods in CR2ADA to maximize inter-class domain discrepancy and minimize intra-class discrepancy of target features. Additionally, CR2ADA combines minimum class confusion and mutual information to further regularize the diversity and discriminability of the learned features. The effectiveness of CR2ADA is demonstrated through experiments on four UDA datasets. The code can be obtained through email or GitHub.
{"title":"Towards Discriminative Class-Aware Domain Alignment via Coding Rate Reduction for Unsupervised Adversarial Domain Adaptation","authors":"Jiahua Wu, Yuchun Fang","doi":"10.3390/sym16091216","DOIUrl":"https://doi.org/10.3390/sym16091216","url":null,"abstract":"Unsupervised domain adaptation (UDA) methods, based on adversarial learning, employ the means of implicit global and class-aware domain alignment to learn the symmetry between source and target domains and facilitate the transfer of knowledge from a labeled source domain to an unlabeled target domain. However, these methods still face misalignment and poor target generalization due to small inter-class domain discrepancy and large intra-class discrepancy of target features. To tackle these challenges, we introduce a novel adversarial learning-based UDA framework named Coding Rate Reduction Adversarial Domain Adaptation (CR2ADA) to better learn the symmetry between source and target domains. Integrating conditional domain adversarial networks with domain-specific batch normalization, CR2ADA learns robust domain-invariant features to implement global domain alignment. For discriminative class-aware domain alignment, we propose the global and local coding rate reduction methods in CR2ADA to maximize inter-class domain discrepancy and minimize intra-class discrepancy of target features. Additionally, CR2ADA combines minimum class confusion and mutual information to further regularize the diversity and discriminability of the learned features. The effectiveness of CR2ADA is demonstrated through experiments on four UDA datasets. The code can be obtained through email or GitHub.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Event extraction is a complex and challenging task in the field of information extraction. It aims to identify event types, triggers, and argument information from the text. In recent years, overlapping event extraction has attracted the attention of researchers because of its higher challenge and practicability, and some work has carried out in-depth research on overlapping event extraction and achieved remarkable results. But these works (1) ignore the role of ontology knowledge in event extraction; (2) use the same semantic encoding for multi-stage models, lacking consideration for the independent characteristics of extraction tasks such as event types, triggers, and arguments; and (3) face issues in the training process of multi-stage models, such as error cascading and slow convergence. To address the above issues, we propose an ontology-guided and scheduled-sampling approach for overlapping event extraction, termed as OGSS. First, we design a symmetric matrix for event ontology knowledge representation and integrate it into the semantic encoding process, infusing ontology knowledge into event extraction. Second, for extraction targets such as event types, triggers, and arguments, we process the semantic encoding according to the characteristics of each extraction target, obtaining semantic representations tailored for each subtask. Finally, we view multi-stage predictions as sequential outputs of a joint model, using a scheduled sampling strategy between subtasks to effectively mitigate the cascading propagation of errors during training and accelerate model convergence. We conduct extensive experiments on the FewFc event extraction benchmark dataset. The results show that OGSS achieves significant improvements in overlapping event extraction tasks compared to previous methods.
{"title":"OGSS: An Ontology-Guided and Scheduled-Sampling Approach for Overlapping Event Extraction","authors":"Jizhao Zhu, Hualong Wen, Xinlong Pan, Xiang Li","doi":"10.3390/sym16091214","DOIUrl":"https://doi.org/10.3390/sym16091214","url":null,"abstract":"Event extraction is a complex and challenging task in the field of information extraction. It aims to identify event types, triggers, and argument information from the text. In recent years, overlapping event extraction has attracted the attention of researchers because of its higher challenge and practicability, and some work has carried out in-depth research on overlapping event extraction and achieved remarkable results. But these works (1) ignore the role of ontology knowledge in event extraction; (2) use the same semantic encoding for multi-stage models, lacking consideration for the independent characteristics of extraction tasks such as event types, triggers, and arguments; and (3) face issues in the training process of multi-stage models, such as error cascading and slow convergence. To address the above issues, we propose an ontology-guided and scheduled-sampling approach for overlapping event extraction, termed as OGSS. First, we design a symmetric matrix for event ontology knowledge representation and integrate it into the semantic encoding process, infusing ontology knowledge into event extraction. Second, for extraction targets such as event types, triggers, and arguments, we process the semantic encoding according to the characteristics of each extraction target, obtaining semantic representations tailored for each subtask. Finally, we view multi-stage predictions as sequential outputs of a joint model, using a scheduled sampling strategy between subtasks to effectively mitigate the cascading propagation of errors during training and accelerate model convergence. We conduct extensive experiments on the FewFc event extraction benchmark dataset. The results show that OGSS achieves significant improvements in overlapping event extraction tasks compared to previous methods.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The process of symmetrical multidirectional pressure was adopted to inhibit the macrosegregation of eutectic Si in squeeze cast A356 alloy. Five pressure modes were applied to study the effects of multidirectional pressure and the timing of pressure application on the macrosegregation of eutectic Si. The results show that the directional movement of the solute-rich liquid phase could be inhibited by symmetrical multidirectional pressure. Therefore, the macrosegregation of eutectic Si in the casting part was inhibited. Moreover, the timing of pressure application should be matched with the local pressure position. After the effective inhibition of the macrosegregation of eutectic Si, the elongation of the alloy was significantly improved, reaching up to 7.12%. In addition, the plastic deformation region was observed at the local pressure position. The grains in the plastic deformation region were refined. The proportion of low-angle grain boundaries in the deformed region was about 30%, which was much higher than that in the other undeformed region. The size of the Fe-containing intermetallics in the deformed region decreased to 5–10 μm, which is favorable for the mechanical properties of the alloy.
采用对称多向压力工艺抑制挤压铸造 A356 合金中共晶 Si 的宏观偏析。采用五种压力模式研究了多向压力和加压时间对共晶 Si 大偏析的影响。结果表明，对称多向压力可抑制富溶质液相的定向移动。因此，铸件中共晶 Si 的宏观偏析受到了抑制。此外，加压时间应与局部压力位置相匹配。在有效抑制了共晶 Si 的宏观偏析后，合金的伸长率得到了显著提高，达到了 7.12%。此外，在局部压力位置观察到了塑性变形区。塑性变形区内的晶粒被细化。变形区中低角度晶界的比例约为 30%，远高于其他未变形区。变形区中含铁金属间化合物的尺寸减小到 5-10 μm，这有利于合金的机械性能。
{"title":"Inhibiting Eutectic Si Macrosegregation in Squeeze Cast A356 Alloy by Symmetrical Multidirectional Pressure","authors":"Weitao Cai, Xiaozu Zhang, Dongtao Wang, Wenping Weng, Zibin Wu, Hiromi Nagaumi","doi":"10.3390/sym16091213","DOIUrl":"https://doi.org/10.3390/sym16091213","url":null,"abstract":"The process of symmetrical multidirectional pressure was adopted to inhibit the macrosegregation of eutectic Si in squeeze cast A356 alloy. Five pressure modes were applied to study the effects of multidirectional pressure and the timing of pressure application on the macrosegregation of eutectic Si. The results show that the directional movement of the solute-rich liquid phase could be inhibited by symmetrical multidirectional pressure. Therefore, the macrosegregation of eutectic Si in the casting part was inhibited. Moreover, the timing of pressure application should be matched with the local pressure position. After the effective inhibition of the macrosegregation of eutectic Si, the elongation of the alloy was significantly improved, reaching up to 7.12%. In addition, the plastic deformation region was observed at the local pressure position. The grains in the plastic deformation region were refined. The proportion of low-angle grain boundaries in the deformed region was about 30%, which was much higher than that in the other undeformed region. The size of the Fe-containing intermetallics in the deformed region decreased to 5–10 μm, which is favorable for the mechanical properties of the alloy.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Insect wing vein networks facilitate blood transport with unknown haemodynamic effects on their structures. Fruit flies have the posterior cross vein (PCV) that disrupts the symmetry of the network topology and reduces the total pressure loss during blood transport; however, the impact of its various positions among species has not been examined. This study investigated the haemodynamic effects of this vein with various connecting positions. By analogising venous networks to hydraulic circuits, the flow rates and pressure losses within the veins were derived using Poiseuille’s and Kirchhoff’s laws. The results showed that the total pressure loss decreased for both PCV connections near the wing’s base. In an idealised circuit imitating the network topology, applied high hydraulic resistances as one-sided as those along the edge of the wing, the same pressure loss response as that in the actual network was demonstrated, but not within a symmetric resistance distribution. Therefore, the most proximal PCV minimises the pressure loss within the asymmetric resistance distribution, indicating an evolutionary adaptation to reducing the pressure loss in certain species with this vein near the base. Our findings highlight the possible optimisation of the flies’ wing morphology to maintain the functions of the liquid transport networks and flight devices simultaneously.
{"title":"Positional Effects of a Fly’s Wing Vein in the Asymmetric Distribution of Hydraulic Resistances","authors":"Kazuki Sugiyama, Yoshihiro Kubota, Osamu Mochizuki","doi":"10.3390/sym16091212","DOIUrl":"https://doi.org/10.3390/sym16091212","url":null,"abstract":"Insect wing vein networks facilitate blood transport with unknown haemodynamic effects on their structures. Fruit flies have the posterior cross vein (PCV) that disrupts the symmetry of the network topology and reduces the total pressure loss during blood transport; however, the impact of its various positions among species has not been examined. This study investigated the haemodynamic effects of this vein with various connecting positions. By analogising venous networks to hydraulic circuits, the flow rates and pressure losses within the veins were derived using Poiseuille’s and Kirchhoff’s laws. The results showed that the total pressure loss decreased for both PCV connections near the wing’s base. In an idealised circuit imitating the network topology, applied high hydraulic resistances as one-sided as those along the edge of the wing, the same pressure loss response as that in the actual network was demonstrated, but not within a symmetric resistance distribution. Therefore, the most proximal PCV minimises the pressure loss within the asymmetric resistance distribution, indicating an evolutionary adaptation to reducing the pressure loss in certain species with this vein near the base. Our findings highlight the possible optimisation of the flies’ wing morphology to maintain the functions of the liquid transport networks and flight devices simultaneously.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"211 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The authors of this paper introduce and discuss three weaker forms of soft faint continuity: soft faint semi-continuity, soft faint pre-continuity, and soft faint β-continuity. They characterize each of them in several ways. They also demonstrate how they are preserved under some restrictions. Moreover, they prove that a soft function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) if its soft graph function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous). Moreover, they show that a soft function is soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) iff it is soft semi-continuous provided that it has a soft regular codomain. Finally, the symmetry between our new ideas and their analogous topological ones is investigated.
{"title":"Three Weaker Forms of Soft Faint Continuity","authors":"Samer Al-Ghour, Dina Abuzaid","doi":"10.3390/sym16091211","DOIUrl":"https://doi.org/10.3390/sym16091211","url":null,"abstract":"The authors of this paper introduce and discuss three weaker forms of soft faint continuity: soft faint semi-continuity, soft faint pre-continuity, and soft faint β-continuity. They characterize each of them in several ways. They also demonstrate how they are preserved under some restrictions. Moreover, they prove that a soft function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) if its soft graph function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous). Moreover, they show that a soft function is soft faint semi-continuous (resp. soft faint pre-continuous, soft faint β-continuous) iff it is soft semi-continuous provided that it has a soft regular codomain. Finally, the symmetry between our new ideas and their analogous topological ones is investigated.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A two-step simplified modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem. According to general matrix splitting and special matrix splitting, a general convergence analysis and a specific convergence analysis are described, respectively. Numerical experiments show that the iteration method is effective and that the convergence theories are valid.
{"title":"Two-Step Simplified Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems","authors":"Ximing Fang","doi":"10.3390/sym16091210","DOIUrl":"https://doi.org/10.3390/sym16091210","url":null,"abstract":"A two-step simplified modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem. According to general matrix splitting and special matrix splitting, a general convergence analysis and a specific convergence analysis are described, respectively. Numerical experiments show that the iteration method is effective and that the convergence theories are valid.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zihan Zhao, Tao Yu, Shang Wang, Huadong Li, Zhi Wang
Inertial sensors act as inertial references in space gravitational wave detection missions, necessitating that their internal test mass (TM) maintains minimal residual acceleration noise. High-energy particles and cosmic rays in space, along with ion pumps in ground-based torsion pendulum experiments, can cause charge accumulation on the TM surface, leading to increased residual acceleration noise. Consequently, a charge management system was introduced to control the TM’s charge. The complex light path propagation within the electrode housing (EH) makes the TM’s charging and discharging process difficult to theoretically calculate and fully simulate. To address this issue, we propose a simulation method for charging and discharging inertial sensors within ultraviolet (UV) charge management systems. This method innovatively considers the impact of photoelectron emission angle and the TM’s position offset from symmetry on performance. The method also simulates charging and discharging rates over time under conditions of symmetry and preliminarily examines factors affecting the TM’s equilibrium potential. Simulation results indicate that this method effectively models the charge management system’s operation, providing a valuable reference for system design.
{"title":"Charging and Discharging Modeling of Inertial Sensors Based on Ultraviolet Charge Management","authors":"Zihan Zhao, Tao Yu, Shang Wang, Huadong Li, Zhi Wang","doi":"10.3390/sym16091209","DOIUrl":"https://doi.org/10.3390/sym16091209","url":null,"abstract":"Inertial sensors act as inertial references in space gravitational wave detection missions, necessitating that their internal test mass (TM) maintains minimal residual acceleration noise. High-energy particles and cosmic rays in space, along with ion pumps in ground-based torsion pendulum experiments, can cause charge accumulation on the TM surface, leading to increased residual acceleration noise. Consequently, a charge management system was introduced to control the TM’s charge. The complex light path propagation within the electrode housing (EH) makes the TM’s charging and discharging process difficult to theoretically calculate and fully simulate. To address this issue, we propose a simulation method for charging and discharging inertial sensors within ultraviolet (UV) charge management systems. This method innovatively considers the impact of photoelectron emission angle and the TM’s position offset from symmetry on performance. The method also simulates charging and discharging rates over time under conditions of symmetry and preliminarily examines factors affecting the TM’s equilibrium potential. Simulation results indicate that this method effectively models the charge management system’s operation, providing a valuable reference for system design.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142261469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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