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(1) Background: The advancement of technologies has made morphological assessment rapid and reliable. A combination of 3D body scanning (3D-BS) and bioelectrical impedance (BIA) could be essential in monitoring the morphological status of athletes and the general population and their symmetries for coaches, researchers and medical professionals. (2) Methods: The current study presents the use of Inbody-720 BIA and 3D-BS NX-16 for analyzing the asymmetry profile of an athlete in 2 min on a sample of 106 male judo competitors from the following age categories: older boys—U14 (N = 24), younger cadets—U16 (N = 31), cadets—U18 (N = 17), juniors—U21 (N = 19) and seniors (N = 15). Variables observed were arm lean mass, upper arm, elbow, forearm and wrist girth, leg lean mass, thigh length, thigh, knee and calf girth. The paired sample t-test, asymmetry index (AI) and Kruskal–Wallis analysis were used at p ≤ 0.05; (3) Results: Morphological asymmetries were detected in all age categories: seniors—three, U21—four, U18—three, U16—five and U14—four. The most common asymmetrical variable in all categories was the forearm girth, while thigh length, knee girth and upper arm girth presented symmetrical variables in all age categories. AI showed that the size of the asymmetries did not differentiate between the age groups. (4) Conclusions: The current study demonstrated great potential for combining BIA and 3D-BS for rapid asymmetry detection that would allow for monitoring and quick adjustments to the training process in youth to senior age categories.

This paper offers a historical review of the evolution of mathematical methods in economics, tracing their development from the earliest attempts in the 18th century to the sophisticated models of the late 20th century. The study begins by examining the initial integration of mathematical techniques into economic thought, highlighting key milestones that shaped the field. Symmetry concepts are naturally embedded in many of these mathematical frameworks, particularly in the balance and equilibrium found in economic models. Symmetry in economics often reflects proportional relationships and equilibrium conditions that are central to both micro- and macroeconomic analyses. Then, the paper elaborates on the progression of economic growth models, including the foundational Solow–Swan model, which introduced the concept of technological progress (knowledge) as a key factor influencing growth. The review also encompasses the Lucas growth model and the Mankiw–Romer–Weil model, both of which incorporate human capital into the growth equation, highlighting its importance in driving economic development. Finally, the paper addresses the Nonneman–Vanhoudt model, which extends the analysis of growth by integrating multiple types of capital, providing a more comprehensive framework for understanding economic dynamics. By documenting these developments, the paper demonstrates the significant role that mathematical modeling has played in advancing economic theory, providing tools to quantitatively analyze complex economic phenomena and driving the discipline towards greater analytical precision and rigor. This analysis emphasizes how symmetry principles, such as balance between inputs and outputs, equilibrium in supply and demand, and proportionality in growth models, underpin many economic theories.

Brucellosis, as an infectious disease that affects both humans and livestock, poses a serious threat to human health and has a severe impact on economic development. Essentially, brucellosis transmission is a kind of study in biological systems, and the epistemic uncertainty existing in the data of confirmed brucellosis cases in China is realized as significant uncertainty that needs to be addressed. Therefore, this paper proposes an uncertain time series model to explore the confirmed brucellosis cases in China. Then, some methods based on uncertain statistics and symmetry of the biological system are applied, including order estimation, parameter estimation, residual analysis, uncertain hypothesis test, and forecast. The proposed model is practically applied to the data of confirmed brucellosis cases in China from January 2017 to December 2020, and the results show that the uncertain model fits the observed data better than the probabilistic model due to the frequency instability inherent in the data of confirmed brucellosis cases. Based on the proposed model and statistical method, this paper develops an approach to rapidly forecast the number of confirmed brucellosis cases in small sample scenarios, which can contribute to epidemic control in real application.

The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area.

The accurate prediction of urban road collapses is of paramount importance for public safety and infrastructure management. However, the complex and variable nature of road subsidence mechanisms, coupled with the inherent noise and non-stationarity in the data, poses significant challenges to the development of precise and real-time prediction models. To address these challenges, this paper develops an Adaptive Difference Least Squares Support Vector Regression (AD-LSSVR) model. The AD-LSSVR model employs a difference transformation to process the input and output data, effectively reducing noise and enhancing model stability. This transformation extracts trends and features from the data, leveraging the symmetrical characteristics inherent within it. Additionally, the model parameters were optimized using grid search and cross-validation techniques, which systematically explore the parameter space and evaluate model performance of multiple subsets of data, ensuring both precision and generalizability of the selected parameters. Moreover, a sliding window method was employed to address data sparsity and anomalies, ensuring the robustness and adaptability of the model. The experimental results demonstrate the superior adaptability and precision of the AD-LSSVR model in predicting road collapse timing, highlighting its effectiveness in handling the complex nonlinear data.

During the preparation of high dilutions, repeated external vibration (shaking) is used. We hypothesized that it was the vibration treatment, and not the negligible content of the initial substance, that underlies the activity of highly diluted preparations. In order to test this, the vibration was separated from the dilution process. After vibrating two tubes together on a vortex mixer (one containing water and the other the initial substance) the electrical conductivity and radio frequency radiation intensity of water differed from the unvibrated control, and the ability to exert a modifying effect on the target solution appeared, as assessed using ELISA and terahertz spectroscopy, appeared. Thus, the properties of the neutral carrier (water) changed after non-contact exposure to the initial substance. We have named this process ‘crossing’ and its products ‘aqueous iterations of the initial substance’. Several aqueous iterations with different physical properties were obtained, some of which have a modifying effect and others cause various chemical (catalytic) and biological (antiviral) effects similar to those of the initial substance. This indicates that during crossing, substances enter into post-vibration supramolecular interactions. At the nanoscale level, aqueous iterations and the initial substance are structurally symmetrical, which allows us to assume that the preservation of the symmetry of substances subjected to vibration treatment is the basis of the post-vibration interaction phenomenon.

Effective and optimal decision-making can enhance system performance, potentially leading to a positive reputation and financial gains. Multi-criteria decision-making (MCDM) is an important research topic widely applied to practical decision-making problems. Using the basic idea of symmetry to balance the arrangement where elements or features have an equality or similarity in distribution, MCDM provides robust decisions in such multi-dimensional complex issues. This study proposes MultiFuzzTOPS, a decision-making model to deal with complexity of multi-criteria decision-making. The proposed MultiFuzzTOPS leverages the fuzzy logic and soft sets such as type-2 soft sets (T2SS) and technique for order preference by similarity to ideal solution (TOPSIS) for decision-making. We validate the proposed model by implementing it to solve the pesticide selection problem in food science by considering various criteria for the selection of pesticides. Our proposed MultiFuzzTOPS recommends the best pesticide compared with its counterparts because it covers the maximum information for the selection of the best alternative. Results are ranked on the basis of the Hamming distance and similarity coefficient. We also validate the effectiveness by performing the sensitivity analysis, and the validation shows the reliability and effectiveness of our proposed model.

This pioneering investigation introduces two innovative estimators crafted to evaluate the finite population distribution function of a study variable, employing auxiliary variables within the framework of stratified random sampling and post-stratification while emphasizing symmetry in the sampling process. The derivation of mathematical expressions for bias and the mean square error up to the first degree of approximation fortifies the credibility of the proposed estimators. Drawing from three distinct datasets, including real-world data capturing student behaviors and exam performances from 500 students, this research highlights the superior efficiency of the proposed estimators compared to existing methods across both sampling schemes. Employing the proposed estimator, we effectively forecast students’ exam scores based on their study hours, backed by empirical evidence showcasing its precision in terms of mean square error and percentage relative efficiency. This study not only introduces inventive solutions to enduring challenges in survey sampling but also provides practical insights into enhancing predictive accuracy in educational assessments.

Exploring the ocean’s resources requires finding underwater objects, which is a challenging task due to blurry images and small, densely packed targets. To improve the accuracy of underwater target detection, we propose an enhanced version of the YOLOv7 network called YOLOv7-SN. Our goal is to optimize the effectiveness and accuracy of underwater target detection by introducing a series of innovations. We incorporate the channel attention module SE into the network’s key part to improve the extraction of relevant features for underwater targets. We also introduce the RFE module with dilated convolution behind the backbone network to capture multi-scale information. Additionally, we use the Wasserstein distance as a new metric to replace the traditional loss function and address the challenge of small target detection. Finally, we employ probe heads carrying implicit knowledge to further enhance the model’s accuracy. These methods aim to optimize the efficacy of underwater target detection and improve its ability to deal with the complexity and challenges of underwater environments. We conducted experiments on the URPC2020, and RUIE datasets. The results show that the mean accuracy (mAP) is improved by 5.9% and 3.9%, respectively, compared to the baseline model.

We investigated the time evolution of the symmetry of symbols constituting alphabets rooted in the Phoenician script. A diversity of quantitative measures of symmetry of graphemes appearing in Phoenician, Western Greek, Etruscan from Marsiliana, Archaic Etruscan, Neo-Etruscan, Euclidian Greek, Archaic and Classical Latin and Proto-Hebrew scripts, constituting the Phoenician script family, were calculated. The same measures were established for the Hebrew/Ashurit and English scripts. The Shannon-like measures of symmetry were computed. The Shannon diversity index was calculated. Our findings indicate that the Shannon diversity index increased with time in a monotonic way for the studied scripts. The diversity of symmetry groups inherent for addressed alphabets grows with time. We also introduced the symmetry factor of the alphabet. The symmetry factor quantifies the averaged level of symmetrization of the alphabet and the possible parsimony of graphical information necessary for the drawing of the entire set of graphemes constituting the alphabet. We found that the symmetry factor is decreased with time for the alphabets rooted in the Phoenician script. This means that the average level of symmetrization of the studied alphabet increases with time. The parsimony of graphical information necessary for writing graphemes is consequently increased with time. The values of the symmetry factor calculated for the addressed scripts are close to one another, with the pronounced exception of the Hebrew/Ashurit script. Our study supplies the arguments for the point of view, according to which the modern Hebrew/Ashurit script did not emerge from the Phoenician one.

The study of multi-time-delay dynamical systems has highlighted many challenges, especially regarding the solution and analysis of multi-time-delay equations. The symmetry and conserved quantity are two important and effective essential properties for understanding complex dynamical behavior. In this study, a multi-time-delay non-conservative mechanical system is investigated. Firstly, the multi-time-delay Hamilton principle is proposed. Then, multi-time-delay non-conservative dynamical equations are deduced. Secondly, depending on the infinitesimal group transformations, the invariance of the multi-time-delay Hamilton action is studied, and Noether symmetry, Noether quasi-symmetry, and generalized Noether quasi-symmetry are discussed. Finally, Noether-type conserved quantities for a multi-time-delay Lagrangian system and a multi-time-delay non-conservative mechanical system are obtained. Two examples in terms of a multi-time-delay non-conservative mechanical system and a multi-time-delay Lagrangian system are given.

In this study, we focused on assessing the symmetry of shapes and quantifying an index of ‘order’ in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was calculated for the distribution of the Casorati curvatures in both segments to determine the similarity between them. This was proposed as an indicator of the ‘order’ exhibited by the shape. To validate the effectiveness of the proposed index, sensory evaluation experiments were conducted on three shapes: extruded, rotated, and vase. For the rotated shape, the coefficient of determination between the proposed index and the sensory evaluation value of ‘order’ on a 5-point Likert scale was found to be less than 0.1. The reason for the poor correlation coefficient of determination may be attributed to the bias in human perception, where individuals tend to perceive mirror symmetry with respect to the plane that includes the vertical axis when recognizing the mirror symmetry of an object. In contrast, for the extruded and vase shapes, the coefficients of determination were 0.36 and 0.66, respectively, supporting the validity of the proposed index. Nonetheless, the coefficient of determination decreased slightly for familiar extruded shapes and asymmetric vase shapes. In future research, our aim is to quantify ‘aesthetic preference’ by combining the ‘order’ and ‘complexity’ indexes.

We demonstrate a symmetry condition for the mixed partial derivatives of measured data when performing a coherent diffraction imaging (CDI) experiment for differentiable samples under scientific investigation. The proposed condition can be used as a physical restriction to improve real data measurements and has been used within the most celebrated phase-retrieval inversion algorithms as an ad hoc constraint without proof. The symmetry relies on John’s ultrahyperbolic equation for the X-ray transform, which is also demonstrated to be valid in the imaging regime for CDI. The obtained conditions are easy to implement and can be used as a constraint by computational imaging methods.

One of the geometric figures that has symmetry properties is the Cassini oval. The Cassini oval is a curve defined as the locus of points in the plane such that the product of the distances to two fixed points is constant. Cassini ovals are named after the astronomer Giovanni Domenico Cassini, who studied them in 1680. Today, the geometric properties of Cassini ovals are used in many fields: analytical geometry, nuclear physics, radiolocation, and industrial applications. The bistatic radar uses Cassini ovals to detect various targets in radiolocation. Until now, there have been no studies on the clustering capabilities of Cassini ovals. As a novelty, it is hypothesized that clustering possibilities could be used for Cassini ovals. In this article, a study of the capabilities of Cassini ovals in radiolocation was carried out, and their suitability for clustering purposes was shown.

This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper.

Power converters can convert the electrical energy output by power source into specific forms required by target device. They are widely used in various fields such as electrification, transportation, and power systems, and are the core components of the systems. Power converters are composed of power semiconductor devices (such as IGBTs), which are prone to failure due to abnormal conditions and aging degradation, leading to power converter faults. Therefore, over the past twenty years, extensive fault diagnosis methods for power converters have been studied and proposed. Among them, symmetry-based methods have the characteristics of rapid diagnosis speed and strong robustness, but so far there’s no systemic summary of such methods. Therefore, this paper reviews the relevant research on fault diagnosis of power converters based on symmetry in recent years, analyzes the mathematical principles of these methods, and compares their diagnostic performance. In addition, two factors that may have an influence on the symmetry are pointed out. This paper provides references and suggestions for the future development and research of power converter fault diagnosis.

The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. The double-center harmonic oscillator is used to formulate the collisions of two nuclei described by harmonic oscillator solutions and traces out the evolution of the cluster structure in the dynamics of the collision process and demonstrates that the symmetries are preserved in this process. The connection between this study and stellar nucleosynthesis is described.

We present experimental results on the formation and evolution of current sheets in two-dimensional magnetic configurations with an X-type null line. Typical features of both the initial magnetic field and the current sheet are their symmetry properties. The experiments were carried out using the CS-3D setup. The formation of a current sheet occurs just after the magneto-sonic wave converges at the null line; then, both the electric current and plasma become compressed in a planar 2D sheet, which accumulates an excess of magnetic energy. The excitation of the Hall currents, which build up the out-of-plane magnetic fields inside the 2D current sheet, brings about the modification of the sheet structure. As a result, the magnetic fields and plasma currents become 3D. The dynamic plasma processes give rise to additional current sheet deformations, which are caused by the excitation of inverse currents at the side edges of the sheet. As a consequence, the out-of-plane magnetic fields are reversed, and strong Ampère’s forces of the opposite directions come into play. These forces slow down the previously accelerated high-speed plasma flows so that the flows become limited in time and space.

Anorexia nervosa (AN) and bulimia nervosa (BN) are eating diseases characterized by extreme eating behaviours impacting both mental and physical health. Aberrant musculoskeletal adaptations due to malnutrition affect motor abilities such as postural control and gait. To date, limited data is available with regards to gait symmetry in AN and BN. The aim of this study was to characterize inter-limb asymmetry during gait in two cohorts affected by AN and BN, respectively, using the synchronized cyclograms and to compare it with a healthy weight group. A total of 14 AN, 17 BN, and 11 healthy-weight females were assessed via 3D gait analysis. Gait spatio-temporal parameters were computed together with angle–angle diagrams, which were characterized in terms of their geometric features. Individuals with AN and BN were characterized by reduced speed and cadence and an abnormal increase in the duration of the double support phase with respect to the healthy controls. With respect to inter-limb symmetry, asymmetries were detected in both groups, with individuals with BN exhibiting significantly larger cyclogram areas at the hip joint with respect to the other groups (323.43 degrees2 vs. 253.74 degrees2 vs. 136.37 degrees2) and significantly higher orientation angle and Trend Symmetry at both knee and ankle joint. The cyclogram analysis suggests the presence of an altered gait symmetry in individuals with BN. In the AN group, it is possible to observe a similar trend; however, this is not statistically significant. Overall, the findings of this study may provide a novel perspective on the motor control dysfunction linked to eating disorders and aid clinicians in selecting a suitable rehabilitation scheme targeted at enhancing motor stability and control.

The behavior and bifurcations of solutions to three-dimensional (three-phase) quadratic polynomial dynamical systems (DSs) are considered. The integrability in elementary functions is proved for a class of autonomous polynomial DSs. The occurrence of bifurcations of the type-twisted fold is discovered on the basis and within the frames of the elements of the developed DS qualitative theory. The discriminant criterion applied originally to two-phase quadratic polynomial DSs is extended to three-phase DSs investigated in terms of their coefficient matrices. Specific classes of D- and S-vectors are introduced and a complete description of the symmetry relations inherent to the DS coefficient matrices is performed using the discriminant criterion.

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes.

With the continuous improvement in human awareness of environmental protection, energy savings, and emission reduction, as well as the vigorous development of precision machinery and process technology, energy-saving and efficient diaphragm pumps have become a hot research topic at home and abroad. The diaphragm pump is a membrane-isolated reciprocating transport pump that isolates the transport medium from the piston through the diaphragm and can be used to transport high-viscosity, volatile, and corrosive media, and the symmetrical structure can make it easier for the diaphragm pump to achieve stable operation, reduce vibration and noise, and extend the life of the pump. This paper summarizes the development and research status of diaphragm pumps in recent years, including diaphragm pump structure, working principle, category, cavitation research, wear research, fault diagnosis research, vibration and noise research, fluid–solid-interaction research, and optimum research on one-way valves and diaphragms. It also puts forward some reasonable and novel viewpoints, such as applying the theory of entropy production to explore the motion mechanism of diaphragm pumps, optimizing the performance of diaphragm pumps, using new technologies to study new materials for diaphragm pumps, and designing diaphragm protection devices. This review provides valuable references and suggestions for the future development and research of diaphragm pumps.

In this paper, we first study the uniqueness and symmetry of solution of nonlinear Schrödinger–Kirchhoff equations with constant coefficients. Then, we show the uniqueness of the solution of nonlinear Schrödinger–Kirchhoff equations with the polynomial potential. In the end, we investigate the asymptotic behaviour of the positive least energy solutions to nonlinear Schrödinger–Kirchhoff equations with vanishing potentials. The vanishing potential means that the zero set of the potential is non-empty. The uniqueness results of Schrödinger equations and the scaling technique are used in our proof. The elliptic estimates and energy analysis are applied in the proof of the asymptotic behaviour of the above Schrödinger–Kirchhoff-type equations.

The manuscript presents an innovative approach for the engineering design of resonant DC/AC converters used as sources of high-frequency electricity for a variety of needs: industrial and domestic applications, wireless power transmission, high-performance lighting, and more. The methodology is based on the generalized consideration of electromagnetic processes in a series resonant RLC circuit fed by a square-wave voltage source. Due to the symmetry in the form of the current in the AC circuit of the DC/AC converter, it is possible to generalize all their possible operating modes. This was realized by applying the quasi-boundary method to the analysis of resonant DC/AC converters with and without reverse diodes operating in soft and hard switching modes. On this basis, the transfer functions of the devices, which give the relationship between their output and input voltages, are defined and analytically determined. Additionally considered are cases of resonant DC/AC converters with complex output circuits, which are applied to match the load needs and the capabilities of the power electronic device. In this sense, the basic dependencies for designing the main types of resonant DC/AC converters using series and parallel load compensation are given. The effectiveness of the proposed methods is demonstrated through several examples, and their verification and validation is achieved with simulations and prototypes. The proposed innovative design approach is applicable not only in power electronics education, but also in the design and prototyping of a whole class of power electronic devices. The unification of design methodologies formalizes and algorithmizes the design process, which is an important step for its automation and for applying various optimization procedures to achieve certain goals.

Symmetry in a differential evolution (DE) transforms a solution without impacting the family of solutions. For symmetrical problems in differential equations, DE is a strong evolutionary algorithm that provides a powerful solution to resolve global optimization problems. DE/best/1 and DE/rand/1 are the two most commonly used mutation strategies in DE. The former provides better exploitation while the latter ensures better exploration. DE/Neighbor/1 is an improved form of DE/rand/1 to maintain a balance between exploration and exploitation which was used with a random neighbor-based differential evolution (RNDE) algorithm. However, this mutation strategy slows down convergence. It should achieve a global minimum by using 1000 × D, where D is the dimension, but due to exploration and exploitation balancing trade-offs, it can not achieve a global minimum within the range of 1000 × D in some of the objective functions. To overcome this issue, a new and enhanced mutation strategy and algorithm have been introduced in this paper, called DE/Neighbor/2, as well as an improved random neighbor-based differential evolution algorithm. The new DE/Neighbor/2 mutation strategy also uses neighbor information such as DE/Neighbor/1; however, in addition, we add weighted differences after various tests. The DE/Neighbor/2 and IRNDE algorithm has also been tested on the same 27 commonly used benchmark functions on which the DE/Neighbor/1 mutation strategy and RNDE were tested. Experimental results demonstrate that the DE/Neighbor/2 mutation strategy and IRNDE algorithm show overall better and faster convergence than the DE/Neighbor/1 mutation strategy and RNDE algorithm. The parametric significance test shows that there is a significance difference in the performance of RNDE and IRNDE algorithms at the 0.05 level of significance.

This paper proposes a novel robust model predictive control (RMPC) scheme for constrained linear discrete-time systems with bounded disturbance. Firstly, the adjustable error tube set, which is affected by local error and error variety rate, is introduced to overcome uncertainties and disturbances. Secondly, the auxiliary control rate associated with the cost function is designed to minimize the discrepancy between the actual system and the nominal system. Finally, a constrained deep neural network (DNN) architecture with symmetry properties is developed to address the optimal control problem (OCP) within the constrained system while conducting a thorough convergence analysis. These innovations enable more flexible adjustments of state and control tube cross-sections and significantly improve optimization speed compared to the homothetic tube MPC. Moreover, the effectiveness and practicability of the proposed optimal control strategy are illustrated by two numerical simulations. In practical terms, for 2-D systems, this approach achieves a remarkable 726.23-fold improvement in optimization speed, and for 4-D problems, it demonstrates an even more impressive 7218.07-fold enhancement.

Deep learning techniques have found applications across diverse fields, enhancing the efficiency and effectiveness of decision-making processes. The integration of these techniques underscores the significance of interdisciplinary research. In particular, decisions often rely on the output’s projected value or probability from neural networks, considering different values of the relevant output factor. This interdisciplinary review examines the impact of deep learning on decision-making systems, analyzing 25 relevant papers published between 2017 and 2022. The review highlights improved accuracy but emphasizes the need for addressing issues like interpretability, generalizability, and integration to build reliable decision support systems. Future research directions include transparency, explainability, and real-world validation, underscoring the importance of interdisciplinary collaboration for successful implementation.

The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other.

Symmetry has long been viewed as a feature of objects that facilitates ease of perception. Three experiments investigated 4- to 5-month-old infants’ detection and processing of vertical symmetry, oblique symmetry, and asymmetry in novel patterns and faces. In Experiment 1, infants showed the fewest shifts in visual fixations to vertical symmetry in patterns and faces, supporting the view that vertical symmetry is processed more efficiently than oblique symmetry or asymmetry. In Experiment 2, stimulus presentation disallowed more than a single visual fixation, and infants looked longer at a face that is vertically symmetrical compared to obliquely symmetrical or asymmetrical, and they looked equally to patterns regardless of symmetry. In Experiment 3, where pattern exposures were prolonged and inverted faces viewed, infants discriminated vertical symmetry in patterns but lost the advantage with vertical symmetry in faces. Thus, symmetry in patterns requires more processing time from infants, and inverting the face costs infants the normal perceptual advantage of symmetry, even though components of the face remain symmetrical. These findings suggest that infants are prepared to exploit symmetry in their everyday perceptual worlds.

Data mining is an analytical approach that contributes to achieving a solution to many problems by extracting previously unknown, fascinating, nontrivial, and potentially valuable information from massive datasets. Clustering in data mining is used for splitting or segmenting data items/points into meaningful groups and clusters by grouping the items that are near to each other based on certain statistics. This paper covers various elements of clustering, such as algorithmic methodologies, applications, clustering assessment measurement, and researcher-proposed enhancements with their impact on data mining thorough grasp of clustering algorithms, its applications, and the advances achieved in the existing literature. This study includes a literature search for papers published between 1995 and 2023, including conference and journal publications. The study begins by outlining fundamental clustering techniques along with algorithm improvements and emphasizing their advantages and limitations in comparison to other clustering algorithms. It investigates the evolution measures for clustering algorithms with an emphasis on metrics used to gauge clustering quality, such as the F-measure and the Rand Index. This study includes a variety of clustering-related topics, such as algorithmic approaches, practical applications, metrics for clustering evaluation, and researcher-proposed improvements. It addresses numerous methodologies offered to increase the convergence speed, resilience, and accuracy of clustering, such as initialization procedures, distance measures, and optimization strategies. The work concludes by emphasizing clustering as an active research area driven by the need to identify significant patterns and structures in data, enhance knowledge acquisition, and improve decision making across different domains. This study aims to contribute to the broader knowledge base of data mining practitioners and researchers, facilitating informed decision making and fostering advancements in the field through a thorough analysis of algorithmic enhancements, clustering assessment metrics, and optimization strategies.

A polygon with n nodes can be divided into two subpolygons by an internal diagonal through node n. Splitting the polygon along diagonal δi,n and diagonal δn−i,n, i∈{2,…,⌊n/2⌋} results in mirror images. Obviously, there are ⌊n/2⌋−1 pairs of these reflectively symmetrical images. The influence of the observed symmetry on polygon triangulation is studied. The central result of this research is the construction of an efficient algorithm used for generating convex polygon triangulations in minimal time and without generating repeat triangulations. The proposed algorithm uses the diagonal values of the Catalan triangle to avoid duplicate triangulations with negligible computational costs and provides significant speedups compared to known methods.

The aim of this text is to present the covariant confined quark model (CCQM) and review its applications in the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we also review. The physics principles are, in detail, exposed for the CCQM; the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering, successively, three categories of decay processes: leptonic, semileptonic and non-leptonic.

A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.

Further exploration into the influence of a memristor on the behavior of chaotic systems deserves attention. When constructing memristor chaotic systems, it is commonly believed that increasing the number of memristors will lead to better system performance. This paper proposes a class of chaotic maps with different discrete memristors, achieved through internal perturbation based on the Sine map. The I-V curve of the discrete memristor has a symmetrical structure. The dynamic characteristics of the designed system are analyzed using the chaotic attractor phase diagram, Lyapunov exponent (LE) spectrum, and bifurcation diagram. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map’s chaotic characteristics, expand the chaos range, and improve the ergodicity and LE value. Moreover, the type of discrete memristors has a significant impact on the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, in this paper, a direction for the design of a discrete memristor chaotic system is provided. Finally, a discrete memristor chaotic map with a simple structure and better performance is selected. Based on this, a pseudo-random sequence generator is designed, and the generated sequence passes the National Institute of Standards and Technology (NIST) test.

Analytical modeling presents symmetries and aesthetic-mathematical characteristics which are not catchable in numerical computation for science and technology; nanoscience plays a significant role in unification attempts, considering also models including holistic aspects of reality. In this paper we present new discovered results about the complete analytical quantum-relativistic form of the mean square deviation of position R2(t) related to a recently introduced Drude–Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function R2(t) gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds application from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating process in nature. Examples of application and suggestions supplement this paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on vacuum energy.

The Raman scattering, infrared absorption, and reflection spectra of hexagonal non-centrosymmetric BaZnBO3F and BaAlBO3F2 and centrosymmetric BaZn3BO3F2 and BaZnCO3F2 are calculated using the standard procedures of the CRYSTAL package with the basis of localized orbitals and the B3LYP hybrid functional within the framework of the Hartree-Fock conjugate perturbation method. It is shown that the layered structure of crystals manifests itself in the spectra of vibrational modes polarized along and perpendicular to the c axis with wavenumbers for the lattice region formed by displacements of atoms in [BaF]∞ and [MAO3]∞ (M: Zn, Al; A: B, C) layers, for molecular deformation outside and in the plane of anions BO3 and CO3. The quantitative and qualitative composition of the spectra is determined by the symmetry of the crystal lattice.

Box jumps are often included in training programs as an introductory exercise to novice athletes and untrained individuals and are an efficient option of lower-body explosiveness training. However, it is unclear whether the use of boxes of differing heights affect the inter-limb asymmetry during this exercise. The purpose of this study is to investigate the effect of box height in inter-limb asymmetry during box jumps. Recreationally active young males (n = 14) and females (n = 16) performed three jumps at boxes that corresponded to approximately 0, 20, 40, 60, and 80% of their individual countermovement jumps. The selected performance variables were peak force (PF), peak power (PP), rate of force development (RFD), and time to take-off (TToff). The intraclass correlation coefficients ranged from 0.76 to 0.99, and the coefficient of variation ranged from 4.03 to 16.52%. A series of one-way repeated measures ANOVA tests were used to test for significant differences of the performance variables and inter-limb asymmetries. The females’ PF at 80% was significantly higher from 0% (p < 0.05). No significant differences were observed for inter-limb asymmetry across box heights (p ≥ 0.25). This study shows that the box height does not affect the overall intra-session inter-limb asymmetries in recreationally active individuals.

In dense Wi-Fi networks, achieving load balancing is critical to optimize network utilization and provide equitable network consumption among the users. Traditional Wi-Fi networks have issues in attaining effective load balancing. Software-Defined Networking (SDN) has presented a viable solution by isolating the data plane and control plane, enabling more agile and cost-effective networks. In this paper we put forward an Adaptive Symmetrical Load Balancing (ASLB) scheme to ensure fairness of load symmetry in Software Defined Wi-Fi Networks (SD-Wi-Fi), while also optimizing the flows transition process using an Analytical Hierarchal Process (AHP). User activity is monitored by access points (APs), which operate under OpenFlow standards. Three essential features, packet volume, packet category and delay hindrance, are used for flow assignment to various controllers. The controllers are arranged in two tiers, universal and regional controllers. The universal controller (UC) handles the workload statistics of regional controllers (RC) in the form of clusters. Extensive simulations using OMNeT++ simulator are performed. The performance parameters taken into consideration are throughput, delay, packet loss rate, network transition count and workload distribution. Our findings demonstrate that the ASLB technique effectively optimizes the network utilization and ensures equitable network consumption among the end users. The proposed scheme outperforms the Mean Probe Delay scheme (MPD), Channel Measurement-based Access Selection scheme (CMAS), Received Signal Strength Indicator-based scheme (RSSI) and Distributed Antenna Selection scheme (DASA), being 40% higher in throughput and 25% lower in delay.

Image block matching is one of the representative methods for image detection and motion compensation in MPEG. Block matching between two images is a problem of finding symmetry between two images by matching macro blocks that are symmetrical to each other in two given images. The greater the PSNR value, the greater the symmetry of the two images. In the given two images, the two macro blocks with the minimum matching error values are regarded as symmetrical to each other. The classical method of calculating the matching error function for every pixel in the entire search area and choosing the smallest of them guarantees global convergence but requires a lot of computation, especially for large intensities. For this reason, many sparse search methods have been developed to reduce the amount of computation. In this paper, we introduce a gradient descent vector optimization algorithm with guaranteed global convergence to the image block matching problem by utilizing the conceptual symmetry of the vector optimization problem, which is a continuous variable, and the image block matching problem, which is a discrete variable. By blurring the image, we transform the matching cost function closer to being unimodal so that the descent-type algorithm works well. As a result, although the proposed method is simple, it can reduce the amount of computation remarkably and has more robustness for the large displacement of image blocks compared to existing sparse search methods.

In this study, a facile strategy of regulated self-assembly synthesis of Mn-MIL-100, using sodium acetate (CH3COONa) as a mono-dentate ligand capping agent (CA), was proposed. The as-prepared product is denoted Mn-MIL-100-CA. The coordination modulation of CH3COONa, led by its interference in the connectivity and symmetry of the metal centers and organic nodes, plays a vital role in the synthesis process. The crystallinity, morphology, topology, and properties of such MOF products were improved, since the self-assembly process of Mn-MIL-100-CA was promoted and regulated effectively. The materials were systematically characterized via XRD, SEM, N2 isotherms, XPS, and TGA in terms of crystallization behavior, morphology, topology, chemical composition, and thermal and water stability. The ability of Mn-MIL-100 and Mn-MIL-100-CA to remove methylene blue (MB) from an aqueous solution was investigated using a UV–vis spectrophotometer. The results indicate that with the addition of a molar ratio of 50% CH3COONa, Mn-MIL-100-CA particles developed a regularly symmetrical morphology, i.e., ‘spherical pyramid-like structure’ crystals with a dimension of 2~5 μm. Their specific surface area and pore volume increased by 59.2% and 56.7%, respectively. The increased proportion of Mn3+ implies reduced crystal defects and improved crystal structural order and integrity, and therefore an enhanced water stability. Mn-MIL-100-CA exhibited excellent adsorption performance towards MB from aqueous solution. The equilibrium adsorption value was as high as 1079.9 mg/g, which is 44.7% higher than that of Mn-MIL-100 without the addition of CA. The good adsorption capacity and excellent water stability mean that Mn-MIL-100-CA has great potential for the practical removal of MB dye pollutants from water.

The field of additive manufacturing has experienced a surge in popularity over recent decades, particularly as a viable alternative to traditional metal part production. Directed energy deposition (DED) is one of the most promising additive technologies, characterized by its high deposition rate, with wire arc additive manufacturing (WAAM) being a prominent example. Despite its advantages, DED is known to produce parts with suboptimal surface quality and geometric accuracy, which has been a major obstacle to its widespread adoption. This is due, in part, to a lack of understanding of the complex geometries produced by the additive layer. To address this challenge, researchers have focused on characterizing the geometry of the additive layer, particularly the outer part of the bead. This paper specifically investigates the geometrical characteristics and symmetry of walls produced by comparing two different techniques: an oscillated strategy and overlapping beads.

The stratospheric airship has important value in both commercial and military use. The altitude position control is very crucial for the airship to conduct specific missions, which is also a challenge because of both the severe relative aerodynamic mismatches and the large lag due to the quite low speed of the airship within 15 m/s. In this paper, a coordinated altitude and attitude control method was proposed to realize satisfactory altitude position control while maintaining the attitude stability by properly employing the two actuators, the propeller thrust and the elevator, in a consistent manner. In this process, the references for the vertical speed and the pitch were specified in a straightforward way of proportionating them by considering their physical characteristics and the inherent symmetrical relationship between them, which can be obtained through the kinematics. An extended disturbance observer was used to eliminate the severe aerodynamic uncertainties to symmetrically distribute the two actuator outputs by dynamically decoupling the vertical speed and the pitch angular rate loops into the two independent integrators. As a result, the explicit proportional controllers were sufficient to realize efficient command tracking. Rigorous theoretical investigation was provided to symmetrically prove the quantitative bounded property of the estimation and tracking errors. The simulation results demonstrated the effectiveness of the proposed approach, which can realize a 500-m altitude difference tracking within 200 s with less than 0.5 deg/s pitch angular rate.

In this paper, we investigate the solution to a class of symmetric non-homogeneous two-dimensional fractional integro-differential equations using both analytical and numerical methods. We first show the differences between the Caputo derivative and the symmetric sequential fractional derivative and how they help facilitate the implementation of numerical and analytical approaches. Then, we propose a numerical approach based on the operational matrix method, which involves deriving operational matrices for the differential and integral terms of the equation and combining them to generate a single algebraic system. This method allows for the efficient and accurate approximation of the solution without the need for projection. Our findings demonstrate the effectiveness of the operational matrix method for solving non-homogeneous fractional integro-differential equations. We then provide examples to test our numerical method. The results demonstrate the accuracy and efficiency of the approach, with the graph of exact and approximate solutions showing almost complete overlap, and the approximate solution to the fractional problem converges to the solution of the integer problem as the order of the fractional derivative approaches one. We use various methods to measure the error in the approximation, such as absolute and L2 errors. Additionally, we explore the effect of the derivative order. The results show that the absolute error is on the order of 10−14, while the L2 error is on the order of 10−13. Next, we apply the Laplace transform to find an analytical solution to a class of fractional integro-differential equations and extend the approach to the two-dimensional case. We consider all homogeneous cases. Through our examples, we achieve two purposes. First, we show how the obtained results are implemented, especially the exact solution for some 1D and 2D classes. We then demonstrate that the exact fractional solution converges to the exact solution of the ordinary derivative as the order of the fractional derivative approaches one.

In graph-structured data, the node content contains rich information. Therefore, how to effectively utilize the content is crucial to improve the performance of graph convolutional networks (GCNs) on various analytical tasks. However, current GCNs do not fully utilize the content, especially multi-order content. For example, graph attention networks (GATs) only focus on low-order content, while high-order content is completely ignored. To address this issue, we propose a novel graph attention network with adaptability that could fully utilize the features of multi-order content. Its core idea has the following novelties: First, we constructed a high-order content attention mechanism that could focus on high-order content to evaluate attention weights. Second, we propose a multi-order content attention mechanism that can fully utilize multi-order content, i.e., it combines the attention mechanisms of high- and low-order content. Furthermore, the mechanism has adaptability, i.e., it can perform a good trade-off between high- and low-order content according to the task requirements. Lastly, we applied this mechanism to constructing a graph attention network with structural symmetry. This mechanism could more reasonably evaluate the attention weights between nodes, thereby improving the convergence of the network. In addition, we conducted experiments on multiple datasets and compared the proposed model with state-of-the-art models in multiple dimensions. The results validate the feasibility and effectiveness of the proposed model.

In the current research, the elastoplastic behaviour of symmetrical and asymmetrical reinforced concrete buildings is explored by dynamic analysis. The used ground excitations are of sequential type, which is found in the literature to possibly strongly affect the dynamic structural behaviour. The contemporary seismic codes neglect the impact of sequential earthquakes on the seismic response, highlighting a scientific gap necessary to be studied. Within the scope of this study, ordinary 3D reinforced concrete low-rise building frames are forced to sequential ground excitations, as well as to a respective single-occurrence corresponding ground excitation, for comparability reasons. In the present dynamic analyses, the two horizontal directions of the excitations, along with the vertical one, are included in the analysis input. The nonlinear behaviour of reinforced concrete sections under strong strain is considered in the present analyses. The geometrical in-plan asymmetry of the 3D models is expressed by a simply defined ratio. Selected unitless resulting plots of the current dynamic analyses are presented and appropriately discussed given the relative geometrical asymmetry. The role of sequential ground excitations on the dynamic response is recognized, along with the role of simple geometrical symmetry or asymmetry, in the resulting response plots. Thus, useful conclusions are acquired, pointing to remarks on the geometrical structural design helpful for the development of recommendations of seismic provisions.

The creation of two-dimensional copulas is crucial for the proposal of novel families of two-dimensional distributions and the analysis of original dependence structures between two quantitative variables. Such copulas can be developed in a variety of ways. In this article, we provide theoretical contributions to this subject; we emphasize a new parametric ratio scheme to create copulas of the following form: C(x,y)=(b+1)xy/[b+ϕ(x,y)], where b is a constant and ϕ(x,y) is a two-dimensional function. As a notable feature, this form can operate an original trade-off between the product copula and more versatile copulas (not symmetric, with tail dependence, etc.). Instead of a global study, we examine seven concrete examples of such copulas, which have never been considered before. Most of them are extended versions of existing non-ratio copulas, such as the Celebioglu–Cuadras, Ali-Mikhail-Haq, and Gumbel–Barnett copulas. We discuss their attractive properties, including their symmetry, dominance, dependence, and correlation features. Some graphics and tables are given as complementary works. Our findings expand the horizons of new two-dimensional distributional or dependence modeling.

This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results.

Person re-identification is a challenging task due to the lack of person image information in occluded scenarios. The current methods for person re-identification only take into account global information, neglect local information, and are not responsive to changes in input. Additionally, these methods do not address the issue of inaccurate joint detection caused by occlusion. In this paper, we propose an occluded person re-identification method based on a graph model and deformable method, which is able to simultaneously focus on global and local information and can flexibly adapt to local information and changes in the input, efficiently resolving issues such as occluded or incorrect joint information. Our method consists of three modules: the mutual help denoising module, inter-node aggregation and update module, and graph matching module. The mutual help denoising module acquires global features and person skeleton node features using a CNN backbone network and a pose estimation model, respectively. It uses symmetric deformable graph attention to obtain the local and global features of the joint points in different views, correcting the information of incorrect nodes and extracting favorable human features. The inter-node aggregation and update module employs deformable graph convolution operations to enhance the relations between the nodes in the same view, resulting in higher-order information. The graph matching module uses graph matching methods based on the human topology to obtain a more accurate similarity calculation for masked images. Experimental results on the Occluded-Duck and Occluded-REID datasets show that our proposed method achieves Rank-1 accuracies of 64.8% and 84.5%, respectively, outperforming current mainstream methods such as HOReID. Our method also achieves good results on the MARKET-1501 and DukeMTMC-ReID datasets. These results demonstrate that our proposed method can extract person features well and effectively improve the accuracy of person re-identification tasks.

Most popular graph attention networks treat pixels of a feature map as individual nodes, which makes the feature embedding extracted by the graph convolution lack the integrity of the object. Moreover, matching between a template graph and a search graph using only part-level information usually causes tracking errors, especially in occlusion and similarity situations. To address these problems, we propose a novel end-to-end graph attention tracking framework that has high symmetry, combining traditional cross-correlation operations directly. By utilizing cross-correlation operations, we effectively compensate for the dispersion of graph nodes and enhance the representation of features. Additionally, our graph attention fusion model performs both part-to-part matching and global matching, allowing for more accurate information embedding in the template and search regions. Furthermore, we optimize the information embedding between the template and search branches to achieve better single-object tracking results, particularly in occlusion and similarity scenarios. The flexibility of graph nodes and the comprehensiveness of information embedding have brought significant performance improvements in our framework. Extensive experiments on three challenging public datasets (LaSOT, GOT-10k, and VOT2016) show that our tracker outperforms other state-of-the-art trackers.

Projector theory can serve as a powerful tool to perform the symmetric computation of molecular systems. The work of William Harter has long demonstrated the effectiveness of this theory in molecular spectroscopy; however, it seems its usefulness has not been realized by many in the field. We have described this methodology and have considered the D3 symmetry system and the tetrahedral symmetry of methane molecules as concrete examples where the computed rotation tensors and vibrational wavefunction were derived for some symmetry states.