Symmetry

In this Special Issue, the recent advances in the applications of symmetric functions for mathematics and mathematical physics are reviewed, including many novel techniques in analytic functions, transformation methods, economic growth models, and Hurwitz–Lerch zeta functions that were developed to provide reliable solutions to combinatorial problems [...] Full article

One of expensive stages of the software lifecycle is its maintenance. Software maintenance will be much simpler if its structural models are available. Software module clustering is thought to be a practical reverse engineering method for building software structural models from source code. The most crucial goals in software module clustering are to minimize connections between created clusters, maximize internal connections within clusters, and maximize clustering quality. It is thought that finding the best software clustering model is an NP-complete task. The key shortcomings of the earlier techniques are their low success rates, low stability, and insufficient modularization quality. In this paper, for effective clustering of software source code, a discretized sand cat swarm optimization (SCSO) algorithm has been proposed. The proposed method takes the dependency graph of the source code and generates the best clusters for it. Ten standard and real-world benchmarks were used to assess the performance of the suggested approach. The outcomes show that the quality of clustering is improved when a discretized SCSO algorithm was used to address the software module clustering issue. The suggested method beats the previous heuristic approaches in terms of modularization quality, convergence speed, and success rate. Full article

Using a quark combination model with the equal-velocity combination approximation, we study the production of hadrons with strangeness and charm flavor quantum numbers in Pb+Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV. We present analytical expressions and numerical results for these hadrons’ transverse momentum spectra and yield ratios. Our numerical results agree well with the experimental data available. The features of strange and charm hadron production in the quark–gluon plasma at the early stage of heavy ion collisions are also discussed. Full article

The objective of this paper is to examine the augmentation of the heat transfer rate utilizing graphene (Gr) and multi-walled carbon nanotubes (MWCNTs) as nanoparticles, and water as a host fluid in magnetohydrodynamics (MHD) flow through an upright plate using Caputo fractional derivatives with a Brinkman model on the convective Casson hybrid nanofluid flow. The performance of hybrid nanofluids is examined with various shapes of nanoparticles. The Caputo fractional derivative is utilized to describe the governing fractional partial differential equations with initial and boundary conditions on the flow model. Exact solutions are obtained for flow transport, temperature distribution besides that heat transfer rate and friction drag in terms of Mittag-Leffler function by using Fourier sine and Laplace techniques as hybrid methods. Further, we provided the limiting case solutions for classic partial differential equations on obtained governing fluid flow models. The influence of various physical parameters with different fractional orders are investigated on hybrid nanofluid’s fractional momentum and energy by plotting velocity and energy curves. Few of the findings suggest that fractional parameters have significant effect on flow parameters and that blade-shaped nanoparticles have a high heat transfer rate. The graphical results reveal that the Grashof number shows a symmetry effect in the case of cooling and heating the plate. Furthermore, the performance of hybrid nanofluid is considerably more effective with the Caputo-fractional derivatives rather than in the classic derivative approach. Full article

Drug-drug interaction (DDI) extraction has seen growing usage of deep models, but their effectiveness has been restrained by limited domain-labeled data, a weak representation of co-occurring entities, and poor adaptation of downstream tasks. This paper proposes a novel EMSI-BERT method for drug–drug interaction extraction based on an asymmetrical Entity-Mask strategy and a Symbol-Insert structure. Firstly, the EMSI-BERT method utilizes the asymmetrical Entity-Mask strategy to address the weak representation of co-occurring entity information using the drug entity dictionary in the pre-training BERT task. Secondly, the EMSI-BERT method incorporates four symbols to distinguish different entity combinations of the same input sequence and utilizes the Symbol-Insert structure to address the week adaptation of downstream tasks in the fine-tuning stage of DDI classification. The experimental results showed that EMSI-BERT for DDI extraction achieved a 0.82 F1-score on DDI-Extraction 2013, and it improved the performances of the multi-classification task of DDI extraction and the two-classification task of DDI detection. Compared with baseline Basic-BERT, the proposed pre-training BERT with the asymmetrical Entity-Mask strategy could obtain better effects in downstream tasks and effectively limit “Other” samples’ effects. The model visualization results illustrated that EMSI-BERT could extract semantic information at different levels and granularities in a continuous space. Full article

The chirality of the interaction between the local magnetic moments in small transition-metal alloy clusters is investigated in the framework of density-functional theory. The Dzyaloshinskii–Moriya (DM) coupling vectors ${\mathit{D}}_{ij}$ between the Fe atoms in Fe₂X and Fe₃X with X = Cu, Pd, Pt, and Ir are derived from independent ground-state energy calculations for different noncollinear orientations of the local magnetic moments. The local-environment dependence of ${\mathit{D}}_{ij}$ and the resulting relative stability of different chiral magnetic orders are analyzed by contrasting the results for different adatoms X and by systematically varying the distance between the adatom X and the Fe clusters. One observes that the adatoms trigger most significant DM couplings in Fe₂X, often in the range of 10–30 meV. Thus, the consequences of breaking the inversion symmetry of the Fe dimer are quantified. Comparison between the symmetric and antisymmetric Fe-Fe couplings shows that the DM couplings are about two orders of magnitude weaker than the isotropic Heisenberg interactions. However, they are in general stronger than the anisotropy of the symmetric couplings. In Fe₃X, alloying induces interesting changes in both the direction and strength of the DM couplings, which are the consequence of breaking the reflection symmetry of the Fe trimer and which depend significantly on the adatom-trimer distance. A local analysis of the chirality of the electronic energy shows that the DM interactions are dominated by the spin-orbit coupling at the adatoms and that the contribution of the Fe atoms is small but not negligible. Full article

Images are frequently disrupted by noise of all kinds, making image restoration very challenging. There have been many different image denoising models proposed over the last few decades. Some models preserve the image’s smooth region, while others preserve the texture margin. One of these methods is by using quantum calculus. Quantum calculus is a branch of mathematics that deals with the manipulation of functions and operators in a quantum mechanical setting. It has been used in image processing to improve the speed and accuracy of image-processing algorithms. In quantum computing, entropy can be defined as a measure of the disorder or randomness of a quantum state. The concept of local fractional entropy has been used to study a wide range of quantum systems. In this study, an image denoising model is proposed based on the quantum calculus of local fractional entropy (QC-LFE) to remove a Gaussian noise. The local fractional entropy is used to estimate the image pixel probability, while the quantum calculus is used to estimate the convolution window mask for image denoising. A processing fractional mask with n x n elements was used in the suggested denoising algorithm. The proposed image denoising algorithm uses mask convolution to process each corrupted pixel one at a time. The proposed denoising algorithm’s effectiveness is assessed using peak signal-to-noise ratio and visual perception (PSNR). The experimental findings show that, compared to other similar fractional operators, the proposed method can better preserve texture details when denoising. Full article

The World Wide Web has revolutionized the way we live, causing the number of web pages to increase exponentially. The web provides access to a tremendous amount of information, so it is difficult for internet users to locate accurate and useful information on the web. In order to categorize pages accurately based on the queries of users, methods of categorizing web pages need to be developed. The text content of web pages plays a significant role in the categorization of web pages. If a word’s position is altered within a sentence, causing a change in the interpretation of that sentence, this phenomenon is called polysemy. In web page categorization, the polysemy property causes ambiguity and is referred to as the polysemy problem. This paper proposes a fine-tuned model to solve the polysemy problem, using contextual embeddings created by the symmetry multi-head encoder layer of the Bidirectional Encoder Representations from Transformers (BERT). The effectiveness of the proposed model was evaluated by using the benchmark datasets for web page categorization, i.e., WebKB and DMOZ. Furthermore, the experiment series also fine-tuned the proposed model’s hyperparameters to achieve 96.00% and 84.00% F1-Scores, respectively, demonstrating the proposed model’s importance compared to baseline approaches based on machine learning and deep learning. Full article

The manuscript solves a modified Kawahara equation (mKE) within two cases with and without a damping term by applying the Laplace homotopy perturbation method (LHPM). Since the damped mKE is non-integrable (i.e., it does not have analytic integrals) and does not have exact initial conditions, this challenge makes many numerical methods fail to solve non-integrable equations. In this article, we suggested a new modification at LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for mKE as the initial condition for non-damped mKE. The results proved that this mathematical approach is an effective method for solving damped mKE. Thus, we believe that the presented method will be helpful for solving many non-integrable equations that describe phenomena in sciences, such as nonlinear symmetrical wave propagation in plasma. Full article

Privacy security and property rights protection have gradually attracted the attention of people. Users not only hope that the images edited by themselves will not be forensically investigated, but also hope that the images they share will not be tampered with. Aiming at the problem that inpainted images can be located by forensics, this paper proposes a general anti-forensics framework for image inpainting with copyright protection. Specifically, we employ a hierarchical attention model to symmetrically reconstruct the inpainting results based on existing deep inpainting methods. The hierarchical attention model consists of a structural attention stream and a texture attention stream in parallel, which can fuse hierarchical features to generate high-quality reconstruction results. In addition, the user’s identity information can be symmetrically embedded and extracted to protect copyright. The experimental results not only had high-quality structural texture information, but also had homologous features with the original region, which could mislead the detection of forensics analysis. At the same time, the protection of users’ privacy and property rights is also achieved. Full article

Pairs of lepton and antilepton (dilepton) in a continuous mass range are one of the most experimentally challenging and golden probes of the quark-gluon plasma (QGP) produced in heavy ion collisions because they do not strongly interact with the hot and dense medium, and reflect the properties of the medium at the time the dilepton is generated. The measurements of dileptons require lepton identification with high purity and high efficiency at large detector acceptance. STAR is one of two large experiments at the relativistic heavy ion collider with a primary goal of searching for the QGP and studying its properties. The STAR experiment launched a comprehensive dielectron ($e^{+}{e}^{-}$) program enabled by the time-of-flight (TOF) detector that had been fully installed in 2010. In this article, we review the decade-long $R\&D$, the construction and performance of the STAR TOF detector, and dielectron measurements, including thermal dielectron production and dielectron production from the Breit–Wheeler process. Future perspectives are also discussed. Full article

The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville–Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions $\left({\Delta _a^{\mathrm{LC}}}^{\mu }f\right)(a+J_0+1-\mu )\ge (1-\mu )f(a+J_0)$ and $\left({\Delta _a^{\mathrm{LC}}}^{\mu }f\right)(a+J_0+1-\mu )\le (1-\mu )f(a+J_0)$ to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results. Full article

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether’s theorem) on the (pre)multisymplectic phase spaces. Full article

In this paper, a new analytical technique is proposed for solving fractional partial differential equations. This method is referred to as the general conformal multiple Laplace transform decomposition method. It is a combination of the multiple Laplace transform method and the Adomian decomposition method. The main theoretical results of using this method are presented. In addition, illustrative examples are provided to demonstrate the validity and symmetry of the presented method. Full article

A review of computational–theoretical and experimental works devoted to the study of the flow of bodies by two-phase (dispersed) flows is carried out. The features of particle motion in the vicinity of bodies of various shapes, as well as the effect of the dispersed phase on resistance and heat transfer, are considered. Some consequences of the interaction of particles and droplets with the surface of streamlined bodies (erosive destruction, gas-dynamic spraying, icing, glowing) are analyzed. Full article

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public’s focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use $k$-means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers’ evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai “6.18” Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper. Full article

We review the status of dark matter (DM) candidates in supersymmetric Twin Higgs models in light of the first results of the LUX-ZEPLIN (LZ) experiment. We found that, for twin bino-dominated DM, the new results strengthened the lower bound on the higgsino mass. However, a large part of the parameter space consistent with natural electroweak symmetry breaking is still allowed. In the case of twin-stau DM, the new results imply that, if the thermal abundance of the twin-stau LSP fits the observed density of DM, the twin stau cannot have a large left-handed component anymore. Full article

The current analysis discusses Jeffery nanofluid’s thermally radiative flow with convection over a stretching wedge. It takes into account the Brownian movement and thermophoresis of the Buongiorno nanofluid model. The guiding partial differential equations (PDEs) are modified by introducing the symmetry variables, leading to non-dimensional ordinary differential equations (ODEs). To solve the generated ODEs, the MATLAB function bvp4c is implemented. Examined are the impacts of different flow variables on the rate of transmission of heat transfer (HT), temperature, mass, velocity, and nanoparticle concentration (NC). It has been noted that the velocity and mass transfer were increased by the pressure gradient factor. Additionally, the thermal boundary layer (TBL) and nanoparticle concentration are reduced by the mixed convection (MC) factor. In order to validate the present research, the derived numerical results were compared to previous findings from the literature while taking into account the specific circumstances. It was found that there was good agreement in both sets of data. Full article

This work investigates the containment control for linear multiagent systems. We assume that the systems are subject to periodic energy-limited denial-of-service (DoS) attacks, which prevent agent-to-agent data transmission. It is assumed that the DoS attacks occur periodically based on the time sequence method. It is also assumed that some devices can be used to predict the duration of DoS attacks and uniform lower bound of communication areas. To achieve containment control, state and disturbance estimators are proposed for each following agent to estimate the relative state information. Under suitable conditions, the containment control problem can be solved with the designed controllers and observers. Finally, we provide a simulation result to confirm the theoretical analysis. Full article