Symmetry, Volume 15, Issue 10 (October 2023) – 157 articles

Lepton flavor universality exists in the Standard Model, and hence any observation of the violation of this universality will be a hint for new physics. Recent experimental searches for processes violating this symmetry have attracted much attention among theorists and experimentalists alike. In recent years, such hints have been observed in flavor changing neutral current weak processes such as $b\to sll$ and charged current weak processes such as $b\to cl\nu$ processes by collider experiments like Belle, Belle II, BaBar, LHCb, ATLAS, and CMS collaborations, where $b,s,c$ are the bottom, strange, and charm quarks, respectively, and $l,\nu$ stand for lepton and the corresponding lepton neutrino, respectively. This article is a review of some of the interesting anomalies observed in the B-sector and includes decays of $B_s$ mesons. Full article

The evolution of smart grids improves the sustainability, controllability, stability, and efficiency of traditional power grids. There is a challenging issue in smart grids with protecting users’ privacy while collecting and controlling individual fine-grained data. To ensure data integrity and address the privacy issue, differential privacy protection is an efficient method to resist differential attacks on aggregated data. However, due to differential noise and faulty smart meters, the problem of differential noise deviation has a great impact on the utility of aggregated data. In this paper, we further supplement the previous work by improving the prediction method, forming a relatively complete DP protection scheme (DPP-UFT) with fault tolerance, and providing a detailed performance evaluation process. The experimental results show that the proposed method of adding differential noise based on the estimated failure rate is related to the estimated failure rate and the noise factor. Compared with several other related literature, it has achieved a higher data utilization effect. Full article

In this study, we utilize the potent generalized Kudryashov method to address the intricate obstacles presented by fractional differential equations in the field of mathematical physics. Specifically, our focus centers on obtaining novel exact solutions for three pivotal equations: the time-fractional seventh-order Sawada-Kotera-Ito equation, the time-fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation, and the time-fractional seventh-order Kaup–Kupershmidt equation. The generalized Kudryashov method, celebrated for its versatility and efficacy in addressing intricate nonlinear problems, plays a central role in our research. This method not only simplifies the equations but also unveils their inner dynamics, rendering them amenable to meticulous analysis. It is worth noting that our fractional derivatives are defined in the context of the conformable fractional derivative, providing a solid foundation for our mathematical investigations. One notable aspect of our study is the visual representation of our findings. Graphical representations of the yielded solutions enliven intricate mathematical structures, providing a concrete insight into the dynamics and behaviors of said equations. This paper highlights the proficiency of the generalized Kudryashov method in resolving complex issues presented by fractional differential equations. Our study not only broadens the range of mathematical methods but also enhances our comprehension of the intriguing realm of nonlinear physical phenomena. Full article

This study aimed to investigate the test–retest reliability of three bilateral jump tests to assess asymmetry and determine the consistency of both the magnitude and direction of asymmetry between two testing sessions. Thirty-three participants performed the countermovement jump (CMJ), drop jump (DJ), and countermovement rebound jump (CMRJ—jump 1: CMRJ1; jump 2: CMRJ2) over two sessions. Inter-limb asymmetry was calculated for kinetic metrics, including the mean propulsive force, net braking impulse, and net propulsive impulse. Test reliability was computed using intraclass correlation coefficients (ICC), coefficients of variation (CV), and standard error of measurement. Furthermore, analysis of variance was used to determine the systematic bias between jump types and sessions. Kappa coefficients were utilised to assess the consistency of asymmetry favouring the same limb. Results showed poor to excellent reliability for all jump tests between sessions (ICC range = 0.19–0.99, CV range = 2.80–11.09%). A significantly higher magnitude of asymmetry was revealed for the net braking impulse during the DJ compared to the CMRJ2 (p ≥ 0.014, g ≤ 0.53). When computing the direction of asymmetry between test sessions, Kappa coefficients revealed that levels of agreement were substantial (Kappa = 0.63–0.70) for the CMJ, moderate to almost perfect (Kappa = 0.59–0.94) for the CMRJ1, moderate to almost perfect (Kappa = 0.58–0.81) for the DJ, and slight to moderate for the CMRJ2 (Kappa = 0.19–0.57). These results underscore the variable nature of both the magnitude and direction of asymmetry during jump testing. Thus, practitioners should carefully choose evaluation methods and metrics characterised by low variability to ensure robust asymmetry assessments. Full article

Test case selection is to minimize the time and effort spent on software testing in real-time practice. During software testing, software firms need techniques to finish the testing in a stipulated time while uncompromising on quality. The motto is to select a subset of test cases rather than take up all available test cases to uncover most bugs. Our proposed model in the research study effort is termed SCARF-RT, which stands for Similarity coefficient (SC), Creating Acronyms, Regression test (RT), and Fuzzy set (FS) with Dataset (DS). Clustering of test cases using ranking and also based on similarity coefficients is to be implemented. This research considered eleven different features for clustering the test cases. Two techniques have been used. Firstly, each cluster will, to a certain extent, encompass a collection of distinct traits. Depending on the coverage of the feature, a cluster of test cases might be chosen. The ranking approach was used to create these groupings. The second methodology finds similarity among test cases based on eleven features. Then, the maxmin composition is used to find fuzzy equivalences upon which clusters are formed. Most similar test cases are clustered. Test cases of every cluster are selected as a test suite. The outcomes of this research show that the selected test cases based on the proposed approaches are better than existing methodologies in selecting test cases with less duration and at the same time not compromising on quality. Both fuzzy rank-based clustering and similarity coefficient-based clustering test case selection approaches have been developed and implemented. With the help of these methods, testers may quickly choose test cases based on the suggested characteristics and complete regression testing more quickly. Full article

This article addresses the issue of information security in the Industrial Internet of Things (IIoT) environment. Information security risk assessment in the IIoT is complicated by several factors: the complexity and heterogeneity of the system, the dynamic nature of the system, the distributed network infrastructure, the lack of standards and guidelines, and the increased consequences of security breaches. Given these factors, information security risk assessment in the IIoT requires a comprehensive approach adapted to the peculiarities and requirements of a particular system and industry. It is necessary to use specialized risk assessment methods and to take into account the context and peculiarities of the system. The method of information security risk assessment in the IIoT, based on the mathematical apparatus of fuzzy set theory, is proposed. This paper analyzes information security threats for IIoT systems, from which the most significant criteria are selected. The rules, based on which decisions are made, are formulated in the form of logical formulas containing input parameters. Three fuzzy inference systems are used: one to estimate the probability of threat realization, another to estimate the probable damage, and a final one to estimate the information security risk for the IIoT system. Based on the proposed method, examples of calculating the information security risk assessment in the IIoT environment are provided. The proposed scientific approach can serve as a foundation for creating expert decision support systems for designing IIoT systems. Full article

This article is devoted to the study of the stability of time-dependent source identification telegraph type differential problems with dependent coefficients. Time-dependent source identification problems (SIPs) for telegraph differential equations (TDEs) with constant coefficients can be solved by classical integral-transform methods. However, these classical methods can be used, basically, in cases where the differential equation has constant coefficients. We establish the basic theorem of the stability of the time-dependent SIPs for the second-order linear differential equation (DE) in a Hilbert space with a self-adjoint positive definite operator (SAPDO) and damping term. In practice, stability estimates for the solution of the three types of SIPs for one-dimensional and for multidimensional TDEs with dependent coefficients and classic and non-classic conditions are obtained. Full article

This paper delves into the enhancement of asymptotic and oscillatory behaviors in solutions to even-order neutral differential equations with multiple delays. The main objective is to establish improved inequalities to advance the understanding of oscillation theory for these equations. The paper’s approach is centered on improving the understanding of the intricate relationship between solutions and their corresponding functions. This is achieved by harnessing the modified monotonic properties of positive solutions, which provide valuable insights into oscillation behavior. Furthermore, leveraging the symmetry between positive and negative solutions, we derived criteria that ensure oscillation for all solutions, with a specific emphasis on excluding only positive solutions. To illustrate the significance of our findings, we provide an illustrative example. Full article

Unmanned Aerial Vehicles (UAVs) have become crucial components of building air–ground integrated networks for sixth-generation mobile communications. UAV-related technology has advanced quickly in both military and civilian contexts. Problems with long-distance and dynamic communication need to be fixed in the non-terrestrial transmission channels of high-altitude UAVs. For long-distance UAV dynamic non-terrestrial transmission channel modeling, a spatial statistical channel model–ray tracing (SSCM-RT) hybrid channel model is proposed and verified, and SSCM-RT channel simulations incorporating spatial consistency analysis are carried out to realize the description of the communication process in the dynamic scenario of the non-terrestrial transmission in symmetric and asymmetric situations. The SSCM-RT model can output channel state information continuously, which is helpful for the quantitative description and characterization of the UAV channel in practical settings. Full article

Different from other computer vision tasks, action recognition needs to process larger-scale video data. How to extract and analyze the effective parts from a huge amount of video information is the main difficulty of action recognition technology. In recent years, due to the outstanding performance of Graph Convolutional Networks (GCN) in many fields, a new solution to the action recognition algorithm has emerged. However, in current GCN models, the constant physical adjacency matrix makes it difficult to mine synergistic relationships between key points that are not directly connected in physical space. Additionally, a simple time connection of skeleton data from different frames makes each frame in the video contribute equally to the recognition results, which increases the difficulty of distinguishing action stages. In this paper, the information extraction ability of the model has been optimized in the space domain and time domain, respectively. In the space domain, an Adjacency Matrix Generation (AMG) module, which can pre-analyze node sets and generate an adaptive adjacency matrix, has been proposed. The adaptive adjacency matrix can help the graph convolution model to extract the synergistic information between the key points that are crucial for recognition. In the time domain, the Time Domain Attention (TDA) mechanism has been designed to calculate the time-domain weight vector through double pooling channels and complete the weights of key point sequences. Furthermore, performance of the improved TDA-AMG-GCN modules has been verified on the NTU-RGB+D dataset. Its detection accuracy at the CS and CV divisions reached 84.5% and 89.8%, respectively, with an average level higher than other commonly used detection methods at present. Full article

A new approach to the Dirac equation and the associated hadronic symmetries is proposed. In this approach, we linearize the second Casimir operator of the Lorentz Group, which is defined by the energy–momentum four-vector and the fermion spin, thereby using the spinor-helicity representation instead of the three-vector representation of the particle momentum and spin vector. We then expand the so-obtained standard Dirac equation by employing an inner abstract “hadronic” isospin, initially describing a $SU\left(2\right)$ fermion doublet. Application of the spin-helicity representation of that isospin leads to the occurrence of a quadruplet of inner states, revealing the $SU\left(4\right)$ symmetry via the isospin helicity operator. This further leads to two independent fermion state spaces, specifically, singlet and triplet states, which we interpret as $U\left(1\right)$ symmetry of the leptons and $SU\left(3\right)$ symmetry of the three quarks, respectively. These results indicate the genuinely very different physical nature of the strong $SU\left(4\right)$ symmetry in comparison to the chiral $SU\left(2\right)$ symmetry. While our approach does not require the a priori concept of grand unification, such a notion arises naturally from the formulation with the isospin helicity. We then apply the powerful procedures developed for the electroweak interactions in the SM, in order to break the $SU\left(4\right)$ symmetry by means of the Higgs mechanism involving a scalar Higgs field as an $SU\left(4\right)$ quadruplet. Its finite vacuum creates the masses of the three vector bosons involved, which can change the three quarks into a lepton and vice versa. Finally, we consider a toy model for calculation of the strong coupling constant of a Yukawa potential. Full article

This article extends the application of fractional-order time derivatives to replace their integer-order counterparts within a system comprising two singular one-dimensional coupled partial differential equations. The resulting model proves invaluable in representing radially symmetric deformation and temperature distribution within a unit disk. The incorporation of fractional-order derivatives in mathematical models is shown to significantly enhance their capacity for characterizing real-life phenomena in comparison to their integer-order counterparts. To address the studied system numerically, we employ the q-homotopy analysis transform method (q-HATM). We evaluate the efficiency of this method in solving the problem through a series of illustrative examples. The convergence of the derived scheme is assessed visually, and we compare the performance of the q-HATM with that of the Laplace decomposition method (LDM). While both methods excel in resolving the majority of the presented examples, a notable divergence arises in the final example: the numerical solutions obtained using q-HATM converge, whereas those derived from LDM exhibit divergence. This discrepancy underscores the remarkable efficiency of the q-HATM in addressing this specific problem. Full article

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated here using the symmetry approach. Symmetry groups for the mean momentum and the Reynolds stress equations of ASL are searched under random dilation transformations, which, with different leading order balances in different flow regions, lead to a set of specific scalings for the characteristic length ${\ell }_{13}$ (defined by Reynolds shear stress and mean shear). In particular, symmetry analysis shows that in the shear-dominated region, ${\ell }_{13}$ scales linearly with the surface height z, which corresponds to the classical log law of mean velocity. In the buoyancy-dominated region, ${\ell }_{13}/L\sim {\left(z,/,L\right)}^{4/3}$ for unstably stratified ASL and ${\ell }_{13}/L\sim const$ for stably stratified ASL, where L is the Obukhov length. The specific formula of the celebrated Monin–Obukhov similarity function is obtained, and hence an algebraic model of mean velocity profiles in ASL is derived, showing good agreement with the datum from the QingTu Lake observation array (QLOA) in China. Full article

A deterministic model for the transmission dynamics of SIRS-type malaria in hosts and SI in mosquito populations is proposed. The host population is differentiated between naive, primary, and secondary susceptible individuals. Primary and secondary infected individuals (and also recovered) are differentiated from each other according to their degree of infectiousness. The impact of changing the relative susceptibilities of primary and secondary (with respect to naive) susceptible individuals on the dynamics is investigated. Also, the impact of changing the relative infectiousness of secondary infected, primary, and secondary recovered individuals (with respect to primary infected) on the transmission dynamics of malaria is studied. Full article

In this work, we analyze a bilinear optimal control problem related to a 2D parabolic–elliptic chemo-repulsion system with a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a generic result on the existence of Lagrange multipliers in Banach spaces, we obtain first-order necessary optimality conditions and derive an optimality system for a local optimal solution. Full article

In this paper, we present two machine learning algorithms to identify D mesons produced in a colour singlet state from radiative W boson decays at the LHC. The combined network algorithm is able to identify D mesons via its hadronic decays with an efficiency of 47% while suppressing a background of quark and gluon jets by a factor of 100. Using the developed algorithm, we perform a prospective study for the measurement of $\mathcal{B}(W\to D_s\gamma )$. Full article

With stereo cameras becoming widely used in invasive surgery systems, stereo endoscopic images provide important depth information for delicate surgical tasks. However, the small size of sensors and their limited lighting conditions lead to low-quality and low-resolution endoscopic images and videos. In this paper, we propose a stereo endoscopic video super-resolution method using transformer with a hybrid attention mechanism named HA-VSR. Stereo video SR aims to reconstruct high-resolution (HR) images from corresponding low-resolution (LR) videos. In our method, the stereo correspondence and temporal correspondence are incorporated into the HA-VSR model. Specifically, the Swin transformer architecture is utilized in proposed framework with hybrid attention mechanisms. The parallel attention mechanism is utilized by using the symmetry and consistency of left and right images, and the temporal attention mechanism is utilized by using the consistency of consecutive frames. Detailed quantitative evaluation and experiments on two datasets show the proposed model achieves advanced SR reconstruction performance, showing that the proposed stereo VSR framework outperforms alternative approaches. Full article

Cryogenic cavitation exhibits complexities primarily represented by the coupled interactions of thermodynamic effects, vortices, and cavities during the cavitation process. To further investigate this coupling mechanism, this study employed the DDES turbulence model and Sauer–Schnerr cavitation model to perform unsteady numerical simulations of liquid nitrogen cavitation flow around the NACA0015 Hydrofoil. Numerical validation of the model utilized a symmetrical Hord hydrofoil. The results reveal that the upstream development of the recirculation flow under inverse pressure gradients is the fundamental cause of the detachment in the primary cavitation region. At a cavitation number of 0.616, thermodynamic effects noticeably suppress the formation of cavities and alter the range of adverse pressure gradients, consequently influencing the detachment behavior in the primary cavitation region. Full article

This paper discusses complexity theory, that is, the many theories that have been proposed for emergence of complexity from the underlying physics. Our aim is to identify which aspects have turned out to be the more fundamental ones as regards the emergence of biology, engineering, and digital computing, as opposed to those that are in fact more peripheral in these contexts. In the cases we consider, complexity arises via adaptive modular hierarchical structures that are open systems involving broken symmetries. Each emergent level is causally effective because of the meshing together of upwards and downwards causation that takes place consistently with the underlying physics. Various physical constraints limit the outcomes that can be achieved. The underlying issue concerns the origin of consciousness and agency given the basis of life in physics, which is structured starting from symmetries and variational principles with no trace of agency. A possible solution is to admit that consciousness is an irreducible emergent property of matter. Full article

Rare decays of the Higgs boson into a pair of diquarks $cc\left(bb\right)$ and $\overline{c}\overline{c}$$\left(\overline{b}\overline{b}\right)$ are studied within the perturbative Standard Model and relativistic quark model. The relativistic corrections determined by the relative motion of quarks are calculated using the production amplitude and the diquark wave functions. Numerical values of the decay widths of the Higgs boson into a baryon pair $ccq$$\left(bbq\right)$ and $\overline{c}\overline{c}\overline{q}$$\left(\overline{b}\overline{b}\overline{q}\right)$ are obtained. Full article

In this article, we delve into the study of fuzzy triple controlled metric spaces, investigating their properties and presenting a range of illustrative examples. We emphasize the broader applicability of this concept in comparison to fuzzy rectangular metric spaces and fuzzy rectangular b-metric spaces. By introducing the novel concept of ($\alpha$-$\psi$)-fuzzy contractive mappings, we derive fixed point results specifically designed for complete fuzzy triple controlled metric spaces. Our theorems extend and enrich previous findings in this field. Additionally, we demonstrate the practical significance of our study by applying our findings to the solution of an integral equation and providing an example of its application. Furthermore, we propose potential avenues for future research endeavors. Full article

In the Lagrangian approach, the transport processes in the ocean and atmosphere are studied by tracking water or air parcels, each of which may carry different tracers. In the ocean, they are salt, nutrients, heat, and particulate matter, such as plankters, oil, radionuclides, and microplastics. In the atmosphere, the tracers are water vapor, ozone, and various chemicals. The observation and simulation reveal highly complex patterns of advection of tracers in turbulent-like geophysical flows. Transport barriers are material surfaces across which the transport is minimal. They can be classified into elliptic, parabolic, and hyperbolic barriers. Different diagnostics in detecting transport barriers and the analysis of their role in the dynamics of oceanic and atmospheric flows are reviewed. We discuss the mathematical tools, borrowed from dynamical systems theory, for detecting transport barriers in simple kinematic and dynamic models of vortical and jet-like flows. We show how the ideas and methods, developed for simple model flows, can be successfully applied for studying the role of barriers in oceanic and atmospheric flows. Special attention is placed on the significance of transport barriers in important practical issues: anthropogenic and natural pollution, advection of plankton, cross-shelf exchange, and propagation of upwelling fronts in coastal zones. Full article

This paper presents an initial proposal for the utilization of mediative fuzzy logic in control problems. Mediative fuzzy logic (MFL) was originally proposed with the idea of modeling situations in which there exists contradictory knowledge among several experts in an application domain. In this situation, a mediative solution may be a better choice in this particular decision-making situation. In this paper, we are extending the concept of fuzzy control to the realm of MFL for situations in which we have two or more control experts, and the design of the fuzzy controller has to be based on their knowledge. In this situation, we are taking advantage of the symmetrical nature of membership functions in reducing the complexity of designing the fuzzy controllers. The goal of this study was to improve control results by combining the knowledge of several experts, which MFL is aimed at executing. The initial architecture of mediative fuzzy control for type-1 fuzzy logic is presented, and an illustrative example is used to better comprehend the proposed approach. Later, we extend type-1 MFL to the realms of type-2 and type-3 fuzzy logic, and we also provide a comparative study that exhibits that the type-3 version surpasses the type-2 and type-1 versions of mediative fuzzy control. The idea of utilizing type-2 and type-3 is to improve the capabilities of the fuzzy controller in handling uncertainty coming from noise in the control process. Full article

The Earth’s ionosphere experiences forcing from above and below and varies in different periods. We analyzed the dynamics of the ionospheric global and regional electron contents (GEC and REC) in solar cycles 23/24 (SC23/SC24) and the first part of solar cycle 25 (SC25). We considered several methodological issues for GEC calculations and created a tool to compute GEC and made it available through SIMuRG (System for Ionosphere Monitoring and Research from GNSS). The paper shows the asymmetry of GEC dynamics in different solar cycles. The mid-latitude summer evening anomaly disrupted the diurnal REC variation in the Siberian region under solar minima. The mean GEC showed similar dependence on the F10.7 index in SC25 and SC23/SC24. The difference in solar cycles could prevent reliable forecasting for GEC for the next solar cycle. Our model, based on a neural network, could predict GEC dynamics in SC25 accurately when we input the F10.7 index. Full article

In this research, we employ a dual-approach that combines the Laplace residual power series method and the novel iteration method in conjunction with the Caputo operator. Our primary objective is to address the solution of two distinct, yet intricate partial differential equations: the Foam Drainage Equation and the nonlinear time-fractional Fisher’s equation. These equations, essential for modeling intricate processes, present analytical challenges due to their fractional derivatives and nonlinear characteristics. By amalgamating these distinctive methodologies, we derive precise and efficient solutions substantiated by comprehensive figures and tables showcasing the accuracy and reliability of our approach. Our study not only elucidates solutions to these equations, but also underscores the effectiveness of the Laplace Residual Power Series Method and the New Iteration Method as potent tools for grappling with intricate mathematical and physical models, thereby making significant contributions to advancements in diverse scientific domains. Full article

In recent years, the incidence rate of lumbar diseases has been progressively increasing. The conventional lumbar fusion cages used in existing lumbar interbody fusion surgery are not able to take into account the multiple characteristics of cushioning, vibration reduction, support, cell adhesion, and bone tissue growth. Therefore, in this work, based on the CT data of a lumbar intervertebral disc plain scan, a combined symmetric lumbar fusion cage structure was innovatively designed. The core was made of lightweight TC4 medical titanium alloy flexible microporous metal rubber (LTA-FMP MR), and the outer frame was made of cobalt–chromium–molybdenum alloy. Its comprehensive biomechanical performance was comprehensively evaluated through finite element simulation, static and dynamic mechanics, and impact resistance tests. The three-dimensional model of the L3/L4 lumbar segment was established by reverse engineering, and a Mises stress analysis was conducted on the lumbar fusion cage by importing it into Ansys to understand its structural advantages compared to the traditional lumbar fusion cage. Through static experiments, the influence of the internal nucleus of a symmetrical lumbar fusion cage with different material parameters on its static performance was explored. At the same time, to further explore the superior characteristics of this symmetrical structure in complex human environments, a biomechanical test platform was established to analyze its biomechanical performance under sinusoidal excitation of different amplitudes and frequencies, as well as impact loads of different amplitudes and pulse widths. The results show that under different amplitudes and frequencies, the lumbar fusion cage with a symmetrical structure has a small loss factor, a high impact isolation coefficient, and a maximum energy consumption of 422.8 N·mm, with a maximum kinetic energy attenuation rate of 0.43. Compared to existing traditional lumbar fusion cages in clinical practice, it not only has sufficient stiffness, but also has good vibration damping, support, and impact resistance performance, and has a lower probability of postoperative settlement, which has broad application prospects. Full article

As the efficiency of advanced aero engines improves, the operational speed of their rotors increases. This heightened operational speed makes the rotor dynamics highly sensitive to changes in the rotor’s mass asymmetry state, or unbalance state. During the use of a dual-spool turbofan engine, when its supercritical high-pressure rotor (HPR) exceeds a certain operational speed, the rotor’s vibration spikes and continues to increase with the operational speed until it drops sharply near the maximum operational speed. Analysis of the bolt joints in the faulty rotor reveals various phenomena such as joint interface damage, changes in bolt loosening torque distribution, and alterations in rotor initial unbalance. This paper proposes that at high operational speeds, the bolt joint of the HPR undergoes sudden angular deformation, resulting in the slanting of the principal axis of inertia of the turbine disk. This slant leads to changes in the unbalanced state of the HPR. The additional unbalance causes a sudden rotational inertia load excitation, triggering the rotor vibration failure. Subsequently, a rotor dynamic model that incorporates the angular deformation of the joints is established to simulate how this joint deformation influences the dynamic response of the rotor. The simulation results align well with the observed failure phenomenon and validate the proposed failure mechanism. Finally, troubleshooting measures are proposed and implemented in the faulty engine, effectively mitigating the vibration fault. Full article

We have studied a class of $(1+1)$-dimensional equations that models phenomena with heterogeneous diffusion, advection, and reaction. We have analyzed these fourth-order partial differential equations within the framework of group methods. In this class, the diffusion coefficient is constant, while the coefficients of advection and the reaction term are assumed to depend on the unknown density $u(t,x)$. We have identified the Lie symmetries extending the Principal Algebra along with all the conservation laws corresponding to the different forms of the coefficients, and have derived several brief applications. Full article

Concept drift (CD) refers to a phenomenon where the data distribution within datasets changes over time, and this can have adverse effects on the performance of prediction models in software engineering (SE), including those used for tasks like cost estimation and defect prediction. Detecting CD in SE datasets is difficult, but important, because it identifies the need for retraining prediction models and in turn improves their performance. If the concept drift is caused by symmetric changes in the data distribution, the model adaptation process might need to account for this symmetry to maintain accurate predictions. This paper explores the impact of CD within the context of cross-version defect prediction (CVDP), aiming to enhance the reliability of prediction performance and to make the data more symmetric. A concept drift detection (CDD) approach is further proposed to identify data distributions that change over software versions. The proposed CDD framework consists of three stages: (i) data pre-processing for CD detection; (ii) notification of CD by triggering one of the three flags (i.e., CD, warning, and control); and (iii) providing guidance on when to update an existing model. Several experiments on 30 versions of seven software projects reveal the value of the proposed CDD. Some of the key findings of the proposed work include: (i) An exponential increase in the error-rate across different software versions is associated with CD. (ii) A moving-window approach to train defect prediction models on chronologically ordered defect data results in better CD detection than using all historical data with a large effect size $(\delta \ge 0.427)$. Full article