Symmetry

In recent years, graph neural network algorithm (GNN) for graph semi-supervised classification has made great progress. However, in the task of node classification, the neighborhood size is often difficult to expand. The propagation of nodes always only considers the nearest neighbor nodes. Some algorithms usually approximately classify by message passing between direct (single-hop) neighbors. This paper proposes a simple and effective method, named Graph Mixed Random Network Based on PageRank (PMRGNN) to solve the above problems. In PMRGNN, we design a PageRank-based random propagation strategy for data augmentation. Then, two feature extractors are used in combination to supplement the mutual information between features. Finally, a graph regularization term is designed, which can find more useful information for classification results from neighbor nodes to improve the performance of the model. Experimental results on graph benchmark datasets show that the method of this paper outperforms several recently proposed GNN baselines on the semi-supervised node classification. In the research of over-smoothing and generalization, PMRGNN always maintains better performance. In classification visualization, it is more intuitive than other classification methods. Full article

Many aspects of the asymmetric organ system are controlled by the symmetry model (R&L) of the disease-causing organism pathway, but sensitive matters like somites and limb buds need to be shielded from its influence. Because symmetric and asymmetric structures develop from similar or nearby matters and utilize many of the same signaling pathways, attaining symmetry is made more difficult. On this note, we aim to generalize some important measurements in view of the 2D-quantum calculus (q-calculus, q-analogues or q-disease), including the dimensional of fractals and Tsallis entropy (2D-quantum Tsallis entropy (2D-QTE)). The process is based on producing a generalization of the maximum value of the Tsallis entropy in view of the quantum calculus. Then by considering the maximum 2D-QTE, we design a discrete system. As an application, by using the 2D-QTE, we depict a discrete dynamic system that is afflicted with a disease-causing organism (DCO). We look at the system’s positive and maximum solutions. Studies are done on equilibrium and stability. We will also develop a novel design for the fundamental reproductive ratio based on the 2D-QTE. Full article

The electrolysis of black liquor (BL) has emerged as a new form to valorize this byproduct from the pulp and paper industry. BL electrolysis produces a green fuel, hydrogen, and lignin, a high added-value compound. In opposition to water electrolysis, a symmetric process with two different gases produced at the electrodes, hydrogen and oxygen, BL electrolysis is seen as an asymmetric process, as hydrogen is the only gas generated (at the cathode), while solid lignin is electrodeposited at the anode. The present work intended to develop a model in Aspen Plus^® to simulate BL electrolysis and consequently evaluate the performance of the BL electrolyzer. Aspen Plus^® does not include a package for electrolyzers, so it was necessary to use the Aspen Custom Modeler (ACM) tool. The model developed in ACM is valid for the following conditions: nickel electrodes with 2 cm interelectrode distance, cell voltage between 1.5 V and 2.0 V, and temperatures between 25 and 35 °C for batch operation and 25 and 65 °C for continuous operation. Sensitivity analysis demonstrated that the optimum working temperature for batch operation is 35 °C, whereas it is 45 °C for continuous operation. An economic analysis was carried out, calculating the real gross profit (RGP) for the process and the electricity cost. A 2 kW electrolyzer with 80 cells and an active area of 0.3 m² was simulated. For the electrolyzer in batch operation, RGP values of 1056 €/year and 1867 €/year for the worst and the best scenario were obtained, respectively, and the electricity cost was 1431 €/year. For continuous operation, the RGP values were 2064 €/year and 3648 €/year for the worst and best scenario, respectively, and 2967 €/year for the electricity costs. Full article

The main aim of this study is to define parametric kinds of $\lambda$-Array-type polynomials by using q-trigonometric polynomials and to investigate some of their analytical properties and applications. For this purpose, many formulas and relations for these polynomials, including some implicit summation formulas, differentiation rules, and relations with the earlier polynomials by utilizing some series manipulation method are derived. Additionally, as an application, the zero values of q-Array-type polynomials are presented by the tables and multifarious graphical representations for these zero values are drawn. Full article

Within the framework of the model with quark-gluon strings (color flux tubes) as sources, the properties of the strongly intense variable $\Sigma$, which characterizes the correlations between the number of particles in two observation windows separated in rapidity, are studied. It is shown that, in pp collisions at LHC energies, string fusion effects leading to the formation of string clusters have a significant effect on the behavior of this observable. The experimentally observed changes in this variable with the initial energy and centrality of the pp collision can only be explained by taking into account the formation of string clusters consisting of an increasing number of merged strings. It is demonstrated that the study of the behavior of the $\Sigma$ observable as a function of the rapidity distance between the centers of the observation windows and the width of these windows with variable experimental conditions using different energies and centralities of pp-collisions makes it possible to extract the parameters of string clusters from the experimental data. Full article

The lack of operation and maintenance data brings difficulties to traditional risk assessment based on probability methods. Therefore, experts are invited to evaluate the key performance indicators related to system risk. These evaluation results are usually described by ambiguous language, so they have epistemic uncertainty. Uncertainty theory is a branch of mathematics used to model experts’ degrees of belief. The uncertain measure has duality, that is, some symmetry, which means that the sum of the uncertain measure of an event and the uncertain measure of its complementary set is equal to 1. Therefore, the risk occurrence time of each basic event evaluated by experts is modeled by the uncertain variable in this article. Then, the risk assessment method of systems with epistemic uncertainty is proposed based on an uncertain fault tree analysis. Furthermore, two risk-based maintenance optimization models for systems with epistemic uncertainty are established. In particular, the leakage risk assessment method and the two risk-based maintenance optimization models for a subsea production system are considered, and the optimization results are given. The optimization results can help practitioners to warn of the leakage risk and make scientific maintenance decisions based on expert knowledge, so as to extend the service life of subsea production systems. Full article

With the continuous innovation and development of technologies for breeding varieties of fruits, there are more than 8000 varieties of apples in existence. The accurate identification of apple varieties can promote the healthy and stable development of the global apple industry and protect the breeding property rights of rights-holders. To avoid economic losses due to the improper identification of varieties at the seedling-procurement stage, this paper proposes the classification of varieties using images of apple leaves in conjunction with the network models of traditional classification methods, supplemented with deep-learning methods, such as AlexNet, VGG, and ResNet, to account for their shortcomings in robustness and generalizability. We used the Multi-Attention Fusion Convolutional Neural Network (MAFNet) classification method for apple leaf images. The convolutional block distribution pattern of [2,2,2,2] is used to drive the feature extraction layer to have a symmetric structure. According to the characteristics of the dataset, the model is based on the ResNet model to optimize the feature extraction module and integrate a variety of attention mechanisms to achieve the weight distribution of channel features, reduce the interference information before and after feature extraction, complete the accurate extraction of image features, from low-dimensional to high-dimensional, and finally obtain the apple classification results through the Softmax function. The experiments were conducted on a mixture of leaves from 30 apple varieties at 2 growth stages: tender and mature. A total of 14,400 images were used for training, 2400 for validation, and 7200 for testing. The model’s classification accuracy was 98.14%, which improved the accuracy and reduced the classification imputation time as compared with the previous model. Among them, the accuracy rate of “Red General”, “SinanoGold”, and “Jonagold” reached 100%, and the accuracy rate of the bud variant of the Fuji line (“Fuji 2001”, “Red General”, “Yanfu 0”. and “Yanfu 3”) also had an accuracy rate of over 90%. The method proposed in this paper not only significantly improves the classification accuracy of apple cultivars, but it also achieves this with a low cost and a high efficiency level, providing a new way of thinking and an essential technical reference for apple cultivar identification by growers, operators, and law enforcement supervisors in the production practice. Full article

In computer science, and especially in computer vision, the contour of an object is used to describe its features; thus, the shape descriptor plays an indispensable role in target detection and recognition. Further, Fourier is an important mathematical description method, and the Fourier transform of a shape contour has symmetry. This paper will demonstrate the symmetry of shape contour in the frequency domain. In recent years, increasing numbers of shape descriptors have come to the fore, but many descriptors ignore the details of shape. It is found that the most fundamental reason affecting the performance of shape descriptors is structural restraints, especially feature structure restraint. Therefore, in this paper, the restraint of feature structure that intrinsically deteriorates recognition performance is shown, and a fast shape recognition method via the Bone Point Segment (BPS) restraint reduction is proposed. An approach using the inner distance to find bone shapes and segment the shape contour by these bones is proposed. Then, Fourier transform is performed on each segment to form the shape feature. Finally, the restraints of the shape feature are reduced in order to build a more effective shape feature. What is commendable is that its discriminability and robustness is strong, the process is simple, and matching speed is fast. More importantly, the experiment results show that the shape descriptor has higher recognition accuracy and the matching speed runs up to more than 1000 times faster than the existing description methods like CBW and TCD. More importantly, it is worth noting that the recognition accuracy approaches 100% in the self-build dataset. Full article

Due to the abundant natural resources of the underwater world, autonomous exploration using underwater robots has become an effective technological tool in recent years. Real-time object detection is critical when employing robots for independent underwater exploration. However, when a robot detects underwater, its computing power is usually limited, which makes it challenging to detect objects effectively. To solve this problem, this study presents a novel algorithm for underwater object detection based on YOLOv4-tiny to achieve better performance with less computational cost. First, a symmetrical bottleneck-type structure is introduced into the YOLOv4-tiny’s backbone network based on dilated convolution and 1 × 1 convolution. It captures contextual information in feature maps with reasonable computational cost and improves the mAP score by 8.74% compared to YOLOv4-tiny. Second, inspired by the convolutional block attention module, a symmetric FPN-Attention module is constructed by integrating the channel-attention module and the spatial-attention module. Features extracted by the backbone network can be fused more efficiently by the symmetric FPN-Attention module, achieving a performance improvement of 8.75% as measured by mAP score compared to YOLOv4-tiny. Finally, this work proposed the YOLO-UOD for underwater object detection through the fusion of the YOLOv4-tiny structure, symmetric FPN-Attention module, symmetric bottleneck-type dilated convolutional layers, and label smoothing training strategy. It can efficiently detect underwater objects in an embedded system environment with limited computing power. Experiments show that the proposed YOLO-UOD outperforms the baseline model on the Brackish underwater dataset, with a detection mAP of 87.88%, 10.5% higher than that of YOLOv4-tiny’s 77.38%, and the detection result exceeds YOLOv5s’s 83.05% and YOLOv5m’s 84.34%. YOLO-UOD is deployed on the embedded system Jetson Nano 2 GB with a detection speed of 9.24 FPS, which shows that it can detect effectively in scenarios with limited computing power. Full article

This paper mainly proposes a new disturbance observer (DO) for a secure communication system (SCS) of the chaos-based system (CBS). First, the fractional-order (FO) Chen chaotic system is remodeled by a Takagi–Sugeno (T–S) fuzzy system with the aim of softening in calculation. Second, the robust fixed-time was designed to synchronize two nonidentical chaotic systems. Third, a new disturbance observer was proposed to compensate for the disturbance and uncertainty of the secure communication system. Fourth, the proof of the proposed method based on Lyapunov condition together with simulation are given to illustrate the correctness and effectiveness of the proposed theory. The tested disturbance on the public channel was mostly compensated by the appropriately estimated disturbance value. The states of master and slave systems (MSSs) were closed to each other in fixed-time. These factors are used to confirm that the symmetry of two chaotic systems were obtained by the proposed control methods. Full article

Appropriate task offloading management strategy is a challenging problem for high delay-sensitive and heavy-task applications. This paper proposes a fuzzy-based mobile edge manager with task partitioning, which can handle the multi-criteria decision-making process by considering multiple parameters in the MEC network framework and make appropriate offloading decisions for incoming tasks of IoT applications. Considering that the mobile devices are becoming more and more powerful, this paper also takes WLAN delay and the computing power of mobile devices into account, forming a three-level fuzzy logic system. In addition, since many tasks of Internet of Things applications are composed of several independent modules, this paper also sets two optimal task partitioning ratios, which have symmetry, so that each module can be independently executed in each layer of the MEC network. In addition, results will return to the mobile devices after execution, so as to minimize the service time and improve QoS. Finally, several indexes such as task failure rate and service time are simulated, and the results show that the proposed scheme has better performance compared with the other four comparison schemes, especially for high-latency sensitivity and heavy-task applications. Full article

Human–object interaction (HOI) is a human-centered object detection task that aims to identify the interactions between persons and objects in an image. Previous end-to-end methods have used the attention mechanism of a transformer to spontaneously identify the associations between persons and objects in an image, which effectively improved detection accuracy; however, a transformer can increase computational demands and slow down detection processes. In addition, the end-to-end method can result in asymmetry between foreground and background information. The foreground data may be significantly less than the background data, while the latter consumes more computational resources without significantly improving detection accuracy. Therefore, we proposed an input-controlled transformer, “ratio-transformer” to solve an HOI task, which could not only limit the amount of information in the input transformer by setting a sampling ratio, but also significantly reduced the computational demands while ensuring detection accuracy. The ratio-transformer consisted of a sampling module and a transformer network. The sampling module divided the input feature map into foreground versus background features. The irrelevant background features were a pooling sampler, which were then fused with the foreground features as input data for the transformer. As a result, the valid data input into the Transformer network remained constant, while irrelevant information was significantly reduced, which maintained the foreground and background information symmetry. The proposed network was able to learn the feature information of the target itself and the association features between persons and objects so it could query to obtain the complete HOI interaction triplet. The experiments on the VCOCO dataset showed that the proposed method reduced the computational demand of the transformer by 57% without any loss of accuracy, as compared to other current HOI methods. Full article

The transition point from a two-dimensional (2D) to a three-dimensional (3D) structure in a series of small gold clusters remains a topic of continuing debate. In the present study, coupled-cluster CCSD(T) and DFT calculations are performed to re-examine the relative energies of several low-lying isomers of Au₁₂, aiming to shed new light on this issue. At odds with many previous reports on the preference of a planar di-capped elongated-hexagon structure, the Au₁₂ size is found to energetically prefer a globular cup-like form with C_2v symmetry. While DFT results are not able to assign the most stable form of Au₁₂ as the relative energies between the lowest-lying isomers are strongly functional-dependent, coupled-cluster theory calculations point out the preference of a 3D structure for having a D_3h symmetry. Such a prediction is further supported by a comparison of the vibrational spectra computed using the revTPSS density functional with the available experimental infrared ones that were previously recorded from the far-IR multiple photon dissociation (FIR-MPD) experiment. Full article

In a traditional electronic auction, the centralized auctioneer and decentralized bidders are in an asymmetric structure, where the auctioneer has more ability to decide the auction result. This asymmetric auction structure is not fair to the participants and not suitable for data auctions in the Internet of Things (IoT). The blockchain-based auction system, with participant equality and fairness, is typically symmetrical and particularly suitable for IoT data sharing. However, when applied to IoT data sharing in reality, it faces privacy and efficiency problems. In this context, how to guarantee privacy and break the inherent performance bottleneck of blockchain is still a major challenge. In this paper, a consensus-based distributed auction scheme is proposed for data sharing, which enforces privacy preservation and collusion resistance. A reverse auction-based decentralized data trading model is introduced to solve the trust problem without a centralized auctioneer, where bidders reach consensus on the auction result. Specifically, we devise a differentially private auction mechanism to incentivize data owners to participate in data sharing. An effective hybrid consensus algorithm is constructed among bidders to reach consensus on the auction result with improved security and efficiency. Theoretical analysis shows that the proposed scheme ensures the properties of privacy preservation, incentive compatibility and collusion resistance. Experimental results reveal that the proposed mechanism guarantees the data sharing efficiency and has certain scalability. Full article

The purpose of this paper is to develop coupled fixed point theorems by C-class functions with mixed monotonicity, discuss the existence of the coupled fixed point of two mappings and obtain a coupled coincidence point theorem via inverse $C_k$-class functions in partially ordered H-metric spaces. This improves the existing results. In addition, some instances and an application are given to illustrate the usability and validity of the results. Full article

To reduce the waste of energy in communications, unequal error protection (UEP) is used to provide asymmetric protection for messages with different levels of importance. This paper proposes new efficient strategies of UEP based on bilayer protograph-based low-density parity check (PLDPC) codes in decoding-and-forward (DF) relay systems. In particular, we jointly utilize source coding and channel coding to design UEP strategies and then save transmission energy. According to the different levels of importance of discrete cosine transform (DCT) coefficients of image and variance statistical characteristics of image sub-blocks, bilayer-lengthened PLDPC codes are exploited to protect the transmitted image information with different importance levels at the half-duplex relay system. In the end, the simulation result shows that the proposed UEP schemes achieve excellent performance gains compared to conventional equal error protection (EEP) scheme. Additionally, the complexity analysis of the UEP strategies is given. Full article

This study numerically investigated the symmetric breakup of bubble within a heated microfluidic Y-junction. The established three-dimensional model was verified with the results in the literature. Two crucial variables, Reynolds number (Re) and heat flux (q), were considered. Numerical results demonstrated that the bubble breakup was significantly affected by phase change under the heated environment. The “breakup with tunnel” and “breakup with obstruction” modes respectively occurred at the low and high q. The breakup rate in pinch-off stage was much larger than that in squeezing stage. As Re increased, the bubble broke more rapidly, and the critical neck thickness tended to decrease. The bubble annihilated the vortices existing in the divergence region and made the fluid flow more uniform. The heat transfer was enhanced more drastically as Re was decreased or q was increased, where the maximum Nusselt number under two-phase case was 6.53 times larger than single-phase case. The present study not only helps understanding of the physical mechanisms of bubble behaviors and heat transfer within microfluidic Y-junction, but also informs design of microfluidic devices. Full article

In this paper, we construct new nonstandard finite difference schemes to approximate a set of positive solutions for the predator–prey model, which contains different functional responses. The organization of the denominator of the discrete derivative and nonlocal approximations of nonlinear terms are employed to design the new schemes. The approach results in significant qualitative improvements in how the numerical solution behaves. We establish that the proposed nonstandard finite difference methods are elementary stable and satisfy the positivity requirement. In addition, the instances of applying PESN methods to some predator–prey systems using the Beddington–DeAngelis and Nicholson–Bailey functional responses are provided here. Finally, some numerical comparisons are presented to illustrate our findings. Our results indicate that the proposed methods are very suitable for the symmetric model of predator–prey. Full article