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20 pages, 49658 KB  
Article
Dead Chicken Identification Method Based on a Spatial-Temporal Graph Convolution Network
by Jikang Yang, Chuang Ma, Haikun Zheng, Zhenlong Wu, Xiaohuan Chao, Cheng Fang and Boyi Xiao
Animals 2026, 16(3), 368; https://doi.org/10.3390/ani16030368 - 23 Jan 2026
Viewed by 343
Abstract
In intensive cage rearing systems, accurate dead hen detection remains difficult due to complex environments, severe occlusion, and the high visual similarity between dead hens and live hens in a prone posture. To address these issues, this study proposes a dead hen identification [...] Read more.
In intensive cage rearing systems, accurate dead hen detection remains difficult due to complex environments, severe occlusion, and the high visual similarity between dead hens and live hens in a prone posture. To address these issues, this study proposes a dead hen identification method based on a Spatial-Temporal Graph Convolutional Network (STGCN). Unlike conventional static image-based approaches, the proposed method introduces temporal information to enable dynamic spatial-temporal modeling of hen health states. First, a multimodal fusion algorithm is applied to visible light and thermal infrared images to strengthen multimodal feature representation. Then, an improved YOLOv7-Pose algorithm is used to extract the skeletal keypoints of individual hens, and the ByteTrack algorithm is employed for multi-object tracking. Based on these results, spatial-temporal graph-structured data of hens are constructed by integrating spatial and temporal dimensions. Finally, a spatial-temporal graph convolution model is used to identify dead hens by learning spatial-temporal dependency features from skeleton sequences. Experimental results show that the improved YOLOv7-Pose model achieves an average precision (AP) of 92.8% in keypoint detection. Based on the constructed spatial-temporal graph data, the dead hen identification model reaches an overall classification accuracy of 99.0%, with an accuracy of 98.9% for the dead hen category. These results demonstrate that the proposed method effectively reduces interference caused by feeder occlusion and ambiguous visual features. By using dynamic spatial-temporal information, the method substantially improves robustness and accuracy of dead hen detection in complex cage rearing environments, providing a new technical route for intelligent monitoring of poultry health status. Full article
(This article belongs to the Special Issue Welfare and Behavior of Laying Hens)
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17 pages, 649 KB  
Article
Bi-Symmetric Polyhedral Cages with Three, Four, Five or Six Connected Faces and Small Holes
by Bernard Piette
Symmetry 2025, 17(9), 1537; https://doi.org/10.3390/sym17091537 - 15 Sep 2025
Cited by 1 | Viewed by 1072
Abstract
Polyhedral cages (p-cages) are Euclidean geometric structures corresponding to polyhedra with holes. They are a good example of the geometry of some artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces, where the face [...] Read more.
Polyhedral cages (p-cages) are Euclidean geometric structures corresponding to polyhedra with holes. They are a good example of the geometry of some artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces, where the face of one family is attached to three other faces while the faces of the other family are attached to three, four, five or six other faces. To restrict ourselves to p-cages with small holes, we consider p-cages where each hole comprises at most four faces. The construction starts from planar graphs made out of two families of equivalent nodes. One can then construct the dual of the solid corresponding to that graph and tile its faces with regular or nearly regular polygons. An energy function is then defined to quantify the amount of irregularity of the p-cages which is then minimised using a simulated annealing algorithm. We have analysed nearly 100,000 possible configurations, ruling out the p-cages made out of faces with deformations exceeding 10%. We then present graphically some of the most interesting geometries. Full article
(This article belongs to the Section Physics)
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18 pages, 1062 KB  
Article
Using Causality-Driven Graph Representation Learning for APT Attacks Path Identification
by Xiang Cheng, Miaomiao Kuang and Hongyu Yang
Symmetry 2025, 17(9), 1373; https://doi.org/10.3390/sym17091373 - 22 Aug 2025
Viewed by 1867
Abstract
In the cybersecurity attack and defense space, the “attacker” and the “defender” form a dynamic and symmetrical adversarial pair. Their strategy iterations and capability evolutions have long been in a symmetrical game of mutual restraint. We will introduce modern Intrusion Detection Systems (IDSs) [...] Read more.
In the cybersecurity attack and defense space, the “attacker” and the “defender” form a dynamic and symmetrical adversarial pair. Their strategy iterations and capability evolutions have long been in a symmetrical game of mutual restraint. We will introduce modern Intrusion Detection Systems (IDSs) from the defender’s side to counter the techniques designed by the attacker (APT attack). One major challenge faced by IDS is to identify complex attack paths from a vast provenance graph. By constructing an attack behavior tracking graph, the interactions between system entities can be recorded, but the malicious activities of attackers are often hidden among a large number of normal system operations. Although traditional methods can identify attack behaviors, they only focus on the surface association relationships between entities and ignore the deep causal relationships, which limits the accuracy and interpretability of detection. Existing graph anomaly detection methods usually assign the same weight to all interactions, while we propose a Causal Autoencoder for Graph Explanation (CAGE) based on reinforcement learning. This method extracts feature representations from the traceability graph through a graph attention network(GAT), uses Q-learning to dynamically evaluate the causal importance of edges, and highlights key causal paths through a weight layering strategy. In the DARPA TC project, the experimental results conducted on the selected three datasets indicate that the precision of this method in the anomaly detection task remains above 97% on average, demonstrating excellent accuracy. Moreover, the recall values all exceed 99.5%, which fully proves its extremely low rate of missed detections. Full article
(This article belongs to the Special Issue Advanced Studies of Symmetry/Asymmetry in Cybersecurity)
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23 pages, 925 KB  
Article
Bi-Symmetric Polyhedral Cages with Nearly Maximally Connected Faces and Small Holes
by Bernard Piette
Symmetry 2025, 17(6), 940; https://doi.org/10.3390/sym17060940 - 12 Jun 2025
Cited by 2 | Viewed by 1840
Abstract
Polyhedral cages (p-cages) provide a good description of the geometry of some families of artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces/protein rings, where each face has at least four neighbours and where [...] Read more.
Polyhedral cages (p-cages) provide a good description of the geometry of some families of artificial protein cages. In this paper we identify p-cages made out of two families of equivalent polygonal faces/protein rings, where each face has at least four neighbours and where the holes are contributed by at most four faces. We start the construction from a planar graph made out of two families of equivalent nodes. We construct the dual of the solid corresponding to that graph, and we tile its faces with regular or nearly regular polygons. We define an energy function describing the amount of irregularity of the p-cages, which we then minimise using a simulated annealing algorithm. We analyse over 600,000 possible geometries but restrict ourselves to p-cages made out of faces with deformations not exceeding 10%. We then present graphically some of the most promising geometries for protein nanocages. Full article
(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)
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18 pages, 1717 KB  
Article
Development of Attractive Toxic Sugar Baits (ATSBs) System and Its Effectiveness in Mosquito Control
by Ruixiang Zhang, Teng Zhao, Dan Xing, Xinyu Zhou, Haotian Yu, Dongfen Geng, Zhihua Fan, Kai Wang, Xinan Huang and Chunxiao Li
Insects 2025, 16(3), 258; https://doi.org/10.3390/insects16030258 - 2 Mar 2025
Cited by 3 | Viewed by 4567
Abstract
Background: Attractive Toxic Sugar Baits (ATSBs) are an innovative vector control strategy based on the “attract-and-kill” principle. The core of ATSBs lies in the preparation of attractive and toxic baits through the mixing and proportioning of luring and active ingredients. Although previous studies [...] Read more.
Background: Attractive Toxic Sugar Baits (ATSBs) are an innovative vector control strategy based on the “attract-and-kill” principle. The core of ATSBs lies in the preparation of attractive and toxic baits through the mixing and proportioning of luring and active ingredients. Although previous studies have investigated the effects of ATSBs on mosquitoes, significant challenges remain for broader field application. Methods: This study evaluated five fruit juices as ATSBs for mosquitoes, focusing on feeding preferences. Preservative concentrations were assessed by measuring antimicrobial activity over time. Two commercial traps were tested for mosquito entry rates. The optimal insecticide species and concentration were determined based on mortality rates. An optimized ATSBs system was developed and tested under a semi-field cage. Statistical analysis was performed using GraphPad Prism. Results: Within 24 h, apple juice-based ATSBs had the highest attractant index for Culex quinquefasciatus and Anopheles sinensis, while a pear juice-based ATSB was most effective for Aedes albopictus. A 0.1% preservative concentration best maintained juice stability. The LC50 values of dinotefuran-based ATSBs for Cx. quinquefasciatus, Ae. albopictus, and An. sinensis were 1.18 × 10−3, 4.06 × 10−4, and 5.20 × 10−5 g/L, respectively. The Spodoptera frugiperda trap outperformed the Drosophilidae trap. Simulated semi-field cage tests showed 48 h mortality rates of 86.00% for Cx. quinquefasciatus and 95.67% for Ae. albopictus. Conclusion: This study optimized an ATSB system by screening various fruit juices, preservative concentrations, insecticides, and trap devices. The system’s efficacy in mosquito control was evaluated under a semi-field cage. These findings provide a strong foundation for the future application and refinement of ATSB-based mosquito control strategies. Full article
(This article belongs to the Section Medical and Livestock Entomology)
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30 pages, 4214 KB  
Article
Spectral Polynomials and Spectra of Graphs Beyond Cubic and Icosahedral Symmetries: n-Octahedra, n-Cubes, Symmetric and Semi-Symmetric Graphs, Giant Fullerene Cages and Generalized Petersen Graphs
by Krishnan Balasubramanian
Symmetry 2025, 17(2), 247; https://doi.org/10.3390/sym17020247 - 7 Feb 2025
Viewed by 3354
Abstract
We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expanded forms. The coefficients of these polynomials contain a [...] Read more.
We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expanded forms. The coefficients of these polynomials contain a wealth of combinatorial information that finds a number of applications in many areas including nanomaterials, genetic networks, dynamic stereochemistry, chirality, and so forth. This study focuses on a number of symmetric and semi-symmetric graphs with automorphism groups of high order. In particular, Heawood, Coxeter, Pappus, Möbius–Kantor, Tutte–Coxeter, Desargues, Meringer, Dyck, n-octahedra, n-cubes, icosahedral fullerenes such as C80(Ih), golden supergiant C240(Ih), Archimedean (Ih), and generalized Petersen graphs up to 720 vertices, among others, have been studied. The spectral polynomials are computed in fully expanded forms as opposed to factored forms. Several applications of these polynomials are briefly discussed. Full article
(This article belongs to the Collection Feature Papers in Chemistry)
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20 pages, 731 KB  
Article
Bi-Symmetric Polyhedral Cages with Maximally Connected Faces and Small Holes
by Bernard Piette and Árpad Lukács
Symmetry 2025, 17(1), 101; https://doi.org/10.3390/sym17010101 - 10 Jan 2025
Cited by 3 | Viewed by 1136
Abstract
Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and P1 edges, while those of the [...] Read more.
Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of one family have five neighbors and P1 edges, while those of the other family have six neighbors and P2 edges. We restrict ourselves to polyhedral cages where the holes are adjacent to four faces at most. We characterize all p-cages with a deformation of the faces, compared to regular polygons, not exceeding 10%. Full article
(This article belongs to the Section Mathematics)
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22 pages, 693 KB  
Article
Biequivalent Planar Graphs
by Bernard Piette
Axioms 2024, 13(7), 437; https://doi.org/10.3390/axioms13070437 - 28 Jun 2024
Cited by 4 | Viewed by 1603
Abstract
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an [...] Read more.
We define biequivalent planar graphs, which are a generalisation of the uniform polyhedron graphs, as planar graphs made out of two families of equivalent nodes. Such graphs are required to identify polyhedral cages with geometries suitable for artificial protein cages. We use an algebraic method, which is followed by an algorithmic method, to determine all such graphs with up to 300 nodes each with valencies ranging between three and six. We also present a graphic representation of every graph found. Full article
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
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29 pages, 756 KB  
Article
Near-Miss Bi-Homogenous Symmetric Polyhedral Cages
by Bernard Piette and Árpad Lukács
Symmetry 2023, 15(9), 1804; https://doi.org/10.3390/sym15091804 - 21 Sep 2023
Cited by 5 | Viewed by 2109
Abstract
Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of [...] Read more.
Following the discovery of an artificial protein cage with a paradoxical geometry, we extend the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages, for which all the faces are equivalent, and define bi-homogeneous symmetric polyhedral cages made of two different types of faces, where all the faces of a given type are equivalent. We parametrise the possible connectivity configurations for such cages, analytically derive p-cages that are regular, and numerically compute near-symmetric p-cages made of polygons with 6 to 18 edges and with deformation not exceeding 10%. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Nature-Inspired, Bio-Based Materials)
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21 pages, 16913 KB  
Article
Einstein Model of a Graph to Characterize Protein Folded/Unfolded States
by Steve Tyler, Christophe Laforge, Adrien Guzzo, Adrien Nicolaï, Gia G. Maisuradze and Patrick Senet
Molecules 2023, 28(18), 6659; https://doi.org/10.3390/molecules28186659 - 16 Sep 2023
Cited by 2 | Viewed by 2835
Abstract
The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related [...] Read more.
The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randić resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states. Full article
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9 pages, 1056 KB  
Article
Indoxyl Sulfate Administration during Pregnancy Contributes to Renal Injury and Increased Blood–Brain Barrier Permeability
by Ashley Griffin, Brittany Berry, Shauna-Kay Spencer, Teylor Bowles and Kedra Wallace
Int. J. Mol. Sci. 2023, 24(15), 11968; https://doi.org/10.3390/ijms241511968 - 26 Jul 2023
Cited by 4 | Viewed by 3317
Abstract
Rates of pregnancy-related acute kidney injury (PR-AKI) have increased in the U.S over the past two decades, but how PR-AKI affects the blood–brain barrier (BBB) is understudied. AKI is associated with increased amounts of uremic toxins, like indoxyl sulfate (I.S), whose chronic administration [...] Read more.
Rates of pregnancy-related acute kidney injury (PR-AKI) have increased in the U.S over the past two decades, but how PR-AKI affects the blood–brain barrier (BBB) is understudied. AKI is associated with increased amounts of uremic toxins, like indoxyl sulfate (I.S), whose chronic administration leads to BBB and cognitive changes. This study’s objective was to determine if (1) PR-AKI increases I.S and (2) if administration of I.S during pregnancy elicits renal injury and/or increases BBB permeability. From gestational day (GD) 11 to GD19, Sprague Dawley rats were given either 100 or 200 mg/kg body-weight dose of I.S. PR-AKI was induced on GD18 via 45 min bilateral renal ischemic reperfusion surgery. On GD18, metabolic cage metrics and metabolic waste was collected and on GD19 blood pressure, and BBB permeability (by Evan’s Blue infusion) were measured. I.S and creatinine were measured in both urine and circulation, respectively. One-way ANOVA or student t-tests were performed using GraphPad Prism with a p < 0.05 significance. I.S and PR-AKI led to oliguria. I.S administration led to increased BBB permeability compared to normal pregnant and PR-AKI animals. These results suggest that I.S administration during pregnancy leads to increased BBB permeability and evidence of renal injury comparable to PR-AKI animals. Full article
(This article belongs to the Special Issue Pathogenesis of Pregnancy-Related Complication 2023)
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28 pages, 825 KB  
Article
Near-Miss Symmetric Polyhedral Cages
by Bernard M. A. G. Piette and Árpad Lukács
Symmetry 2023, 15(3), 717; https://doi.org/10.3390/sym15030717 - 13 Mar 2023
Cited by 7 | Viewed by 4637
Abstract
Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons [...] Read more.
Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for P=6 to P=20 with deformation of up to 10%. Full article
(This article belongs to the Section Mathematics)
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22 pages, 459 KB  
Article
Edge Data Center Organization and Optimization by Using Cage Graphs
by Pedro Juan Roig, Salvador Alcaraz, Katja Gilly, Cristina Bernad and Carlos Juiz
Network 2023, 3(1), 93-114; https://doi.org/10.3390/network3010005 - 18 Jan 2023
Cited by 5 | Viewed by 3036
Abstract
Data center organization and optimization are increasingly receiving attention due to the ever-growing deployments of edge and fog computing facilities. The main aim is to achieve a topology that processes the traffic flows as fast as possible and that does not only depend [...] Read more.
Data center organization and optimization are increasingly receiving attention due to the ever-growing deployments of edge and fog computing facilities. The main aim is to achieve a topology that processes the traffic flows as fast as possible and that does not only depend on AI-based computing resources, but also on the network interconnection among physical hosts. In this paper, graph theory is introduced, due to its features related to network connectivity and stability, which leads to more resilient and sustainable deployments, where cage graphs may have an advantage over the rest. In this context, the Petersen graph cage is studied as a convenient candidate for small data centers due to its small number of nodes and small network diameter, thus providing an interesting solution for edge and fog data centers. Full article
(This article belongs to the Special Issue Advances in Edge and Cloud Computing)
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16 pages, 3609 KB  
Article
Does the Presence of a Bond Path Really Mean Interatomic Stabilization? The Case of the Ng@Superphane (Ng = He, Ne, Ar, and Kr) Endohedral Complexes
by Mirosław Jabłoński
Symmetry 2021, 13(12), 2241; https://doi.org/10.3390/sym13122241 - 24 Nov 2021
Cited by 16 | Viewed by 2993
Abstract
Using a fairly structurally flexible and, therefore, very suitable for this type of research, superphane molecule, we demonstrate that the inclusion of a noble gas atom (Ng = He, Ne, Ar, and Kr) inside it and, thus, the formation of the Ng@superphane endohedral [...] Read more.
Using a fairly structurally flexible and, therefore, very suitable for this type of research, superphane molecule, we demonstrate that the inclusion of a noble gas atom (Ng = He, Ne, Ar, and Kr) inside it and, thus, the formation of the Ng@superphane endohedral complex, leads to its ‘swelling’. Positive values of both the binding and strain energies prove that encapsulation and in turn ‘swelling’ of the superphane molecule is energetically unfavorable and that the Ng⋯C interactions in the interior of the cage are destabilizing, i.e., repulsive. Additionally, negative Mayer Bond Orders indicate the antibonding nature of Ng⋯C contacts. This result in combination with the observed Ng⋯C bond paths shows that the presence of a bond path in the molecular graph does not necessarily prove interatomic stabilization. It is shown that the obtained conclusions do not depend on the computational methodology, i.e., the method and the basis set used. However, on the contrary, the number of bond paths may depend on the methodology. This is yet another disadvantageous finding that does not favor the treatment of bond paths on molecular graphs as indicators of chemical bonds. The Kr@superphane endohedral complex features one of the longest C–C bonds ever reported (1.753 Å). Full article
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17 pages, 397 KB  
Article
On the Wiener Complexity and the Wiener Index of Fullerene Graphs
by Andrey A. Dobrynin and Andrei Yu Vesnin
Mathematics 2019, 7(11), 1071; https://doi.org/10.3390/math7111071 - 7 Nov 2019
Cited by 12 | Viewed by 3771
Abstract
Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the [...] Read more.
Fullerenes are molecules that can be presented in the form of cage-like polyhedra, consisting only of carbon atoms. Fullerene graphs are mathematical models of fullerene molecules. The transmission of a vertex v of a graph is a local graph invariant defined as the sum of distances from v to all the other vertices. The number of different vertex transmissions is called the Wiener complexity of a graph. Some calculation results on the Wiener complexity and the Wiener index of fullerene graphs of order n 232 and IPR fullerene graphs of order n 270 are presented. The structure of graphs with the maximal Wiener complexity or the maximal Wiener index is discussed, and formulas for the Wiener index of several families of graphs are obtained. Full article
(This article belongs to the Special Issue Graph Theory at Work in Carbon Chemistry)
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