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We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

(1) Background: In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. (2) Methods: We use standard physical theories such as Maxwell electrodynamics and quantum mechanics, supplemented by tools from vector analysis and numerics. (3) Results: We show that a hydrogen atom either in the ground state or excited state will not produce a relativistic engine effect, but by breaking the symmetry or putting the electron in a wave packet state may produce relativistic motor effect. (4) Conclusions: A highly localized wave packet will produce a strong relativistic motor effect. The preliminary analysis of the current paper suggests new promising directions of research both theoretical and experimental.

Most existing Siamese trackers mainly use a pre-trained convolutional neural network to extract target features. However, due to the weak discrimination of the target and background information of pre-trained depth features, the performance of the Siamese tracker can be significantly degraded when facing similar targets or changes in target appearance. This paper proposes a multi-channel-aware and adaptive hierarchical deep features module to enhance the discriminative ability of the tracker. Firstly, through the multi-channel-aware deep features module, the importance values of feature channels are obtained from both the target details and overall information, to identify more important feature channels. Secondly, by introducing the adaptive hierarchical deep features module, the importance of each feature layer can be determined according to the response value of each frame, so that the hierarchical features can be integrated to represent the target, which can better adapt to changes in the appearance of the target. Finally, the proposed two modules are integrated into the Siamese framework for target tracking. The Siamese network used in this paper is a two-input branch symmetric neural network with two input branches, and they share the same weights, which are widely used in the field of target tracking. Experiments on some Benchmarks show that the proposed Siamese tracker has several points of improvement compared to the baseline tracker.

Automatic segmentation of intracranial brain tumors in three-dimensional (3D) image series is critical in screening and diagnosing related diseases. However, there are various challenges in intracranial brain tumor images: (1) Multiple brain tumor categories hold particular pathological features. (2) It is a thorny issue to locate and discern brain tumors from other non-brain regions due to their complicated structure. (3) Traditional segmentation requires a noticeable difference in the brightness of the interest target relative to the background. (4) Brain tumor magnetic resonance images (MRI) have blurred boundaries, similar gray values, and low image contrast. (5) Image information details would be dropped while suppressing noise. Existing methods and algorithms do not perform satisfactorily in overcoming these obstacles mentioned above. Most of them share an inadequate accuracy in brain tumor segmentation. Considering that the image segmentation task is a symmetric process in which downsampling and upsampling are performed sequentially, this paper proposes a segmentation algorithm based on U-Net++, aiming to address the aforementioned problems. This paper uses the BraTS 2018 dataset, which contains MR images of 245 patients. We suggest the generative mask sub-network, which can generate feature maps. This paper also uses the BiCubic interpolation method for upsampling to obtain segmentation results different from U-Net++. Subsequently, pixel-weighted fusion is adopted to fuse the two segmentation results, thereby, improving the robustness and segmentation performance of the model. At the same time, we propose an auto pruning mechanism in terms of the architectural features of U-Net++ itself. This mechanism deactivates the sub-network by zeroing the input. It also automatically prunes GenU-Net++ during the inference process, increasing the inference speed and improving the network performance by preventing overfitting. Our algorithm’s PA, MIoU, P, and R are tested on the validation dataset, reaching 0.9737, 0.9745, 0.9646, and 0.9527, respectively. The experimental results demonstrate that the proposed model outperformed the contrast models. Additionally, we encapsulate the model and develop a corresponding application based on the MacOS platform to make the model further applicable.

Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means, using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. We explore certain convex or concave functions, which are symmetric functions on the axis t=1/2.

This paper investigates a relativistic Toda lattice system with an arbitrary parameter that is a very remarkable generalization of the usual Toda lattice system, which may describe the motions of particles in lattices. Firstly, we study some integrable properties for this system such as Hamiltonian structures, Liouville integrability and conservation laws. Secondly, we construct a discrete generalized (m,2N−m)-fold Darboux transformation based on its known Lax pair. Thirdly, we obtain some exact solutions including soliton, rational and semi-rational solutions with arbitrary controllable parameters and hybrid solutions by using the resulting Darboux transformation. Finally, in order to understand the properties of such solutions, we investigate the limit states of the diverse exact solutions by using graphic and asymptotic analysis. In particular, we discuss the asymptotic states of rational solutions and exponential-and-rational hybrid solutions graphically for the first time, which might be useful for understanding the motions of particles in lattices. Numerical simulations are used to discuss the dynamics of some soliton solutions. The results and properties provided in this paper may enrich the understanding of nonlinear lattice dynamics.

A cable-stayed bridge is a typical symmetrical structure, and symmetry affects the deformation characteristics of such bridges. The main girder of a cable-stayed bridge will produce obvious deflection under the inducement of temperature. The regression model of temperature-induced deflection is hoped to provide a comparison value for bridge evaluation. Based on the temperature and deflection data obtained by the health monitoring system of a bridge, establishing the correlation model between temperature and temperature-induced deflection is meaningful. It is difficult to complete a high-quality model only by the girder temperature. The temperature features based on prior knowledge from the mechanical mechanism are used as the input information in this paper. At the same time, to strengthen the nonlinear ability of the model, this paper selects an independent recurrent neural network (IndRNN) for modeling. The deep learning neural network is compared with machine learning neural networks to prove the advancement of deep learning. When only the average temperature of the main girder is input, the calculation accuracy is not high regardless of whether the deep learning network or the machine learning network is used. When the temperature information extracted by the prior knowledge is input, the average error of IndRNN model is only 2.53%, less than those of BPNN model and traditional RNN. Combining knowledge with deep learning is undoubtedly the best modeling scheme. The deep learning model can provide a comparison value of bridge deformation for bridge management.

The paper aims to analyze the vibrations of a summing box, used in heavy vehicles. An experimental setup is proposed and used for the analysis of these vibrations transmitted by the box housing, based on the measurement of the mechanical impedance. It is then shown that a simpler measurement, namely that of the generated noise spectrum, can provide equally useful results, with less effort and in a shorter time. The experimental setup is much simpler, involving a sonometer arranged in the experimental assembly. The symmetry of the box allows us to facilitate the execution of the experimental assembly, and the use of the symmetrical structure to facilitate the calculation of vibrations. The results obtained using this method in the case of a redesigned adder box are presented in the paper.

Most of the papers published so far in literature have focused on the theoretical phenomena underlying the formation of chaos, rather than on the investigation of potential applications of chaos to the real world. This paper aims to bridge the gap between chaos theory and chaos applications by presenting a survey of very recent applications of chaos. In particular, the manuscript covers the last three years by describing different applications of chaos as reported in the literature published during the years 2018 to 2020, including the matter related to the symmetry properties of chaotic systems. The topics covered herein include applications of chaos to communications, to distributed sensing, to robotic motion, to bio-impedance modelling, to hardware implementation of encryption systems, to computing and to random number generation.

Increasingly, cities worldwide are striving for green travel and slow traffic, and vigorously developing people-oriented urban pedestrian traffic with sustainability has become a fixture in recent discourse. This paper comprehensively considers the sidewalk’s facilities environment and the status of pedestrian traffic flow; divides the urban pedestrian road system (UPRS) into five subsystems around the underpass, overpass, crosswalk, sidewalk, and road crosswalk; and introduces the basic structure as well as the function of each system. Then, the indicators are classified into two types of crosswalk facilities and sidewalk facilities, and a comprehensive pedestrian road indicator system with the combination of subjective and objective is established. Consequently, the integration of the fuzzy AHP and DEA-based symmetrical technique for the subjective evaluation indicator combined with pedestrian traffic characteristics is developed. A nine-step semantics scale of relative importance was used so that the symmetry of the response of pedestrian satisfaction was maintained. Fuzzy evaluation based on AHP is further modeled, and the DEA is employed to achieve an overall evaluation of the quality of service (QoS) for UPRS. The applicability of the established evaluation system is finally verified through a real case study in Harbin, China. The serviceability assessment method in this paper provides a new idea for planners to conduct sustainability evaluation for UPRS in future urban renewal development.

A review of experimental studies carried out at the NRC “Kurchatov Institute” on plasma-facing thermonuclear fusion reactor materials is presented in the paper. An experimental method was developed to produce high-level radiation damage in materials simulating the neutron effect by surrogate irradiation with high-energy ions. Plasma-surface interaction is investigated on materials irradiated to high levels of radiation damage in high-flux deuterium plasma. The total fluence of accelerated ions (3–30 MeV, 4He2+, 12C3+, 14N3+, protons) on the samples was 1021–1023 m−2. Experiments were carried out on graphite materials, tungsten, and silicon carbide. Samples have been obtained with a primary defect concentration from 0.1 to 100 displacements per atom, which covers the predicted damage for the ITER and DEMO projects. Erosion dynamics of the irradiated materials in steady-state deuterium plasma, changes of the surface microstructure, and deuterium retention were studied using SEM, TEM, ERDA, TDS, and nuclear backscattering techniques. The surface layer of the materials (3 to hundreds µm) was investigated, and it was shown that the changes in the crystal structure, the loss of their symmetry, and diffusion of defects to grain boundaries play an important role. The most significant results are presented in the paper as an overview of our previous work for many years (carbon and tungsten materials) as well as the relatively recent results (silicon carbide).

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.

In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings.

This paper studies the multi-depot joint distribution vehicle routing problem considering energy consumption with time-dependent networks (MDJDVRP-TDN). Aiming at the multi-depot joint distribution vehicle routing problem where the vehicle travel time depends on the variation characteristics of the road network speed in the distribution area, considering the influence of the road network on the vehicle speed and the relationship between vehicle load and fuel consumption, a multi-depot joint distribution vehicle routing optimization model is established to minimize the sum of vehicle fixed cost, fuel consumption cost and time window penalty cost. Traditional vehicle routing problems are modeled based on symmetric graphs. In this paper, considering the influence of time-dependent networks on routes optimization, modeling is based on asymmetric graphs, which increases the complexity of the problem. A hybrid genetic algorithm with variable neighborhood search (HGAVNS) is designed to solve the model, in which the nearest neighbor insertion method and Logistic mapping equation are used to generate the initial solution firstly, and then five neighborhood structures are designed to improve the algorithm. An adaptive neighborhood search times strategy is used to balance the diversification and depth search of the population. The effectiveness of the designed algorithm is verified through several groups of numerical instances with different scales. The research can enrich the relevant theoretical research of multi-depot vehicle routing problems and provide the theoretical basis for transportation enterprises to formulate reasonable distribution schemes.

In this paper, we consider convex multiobjective optimization problems with equality and inequality constraints in real Banach space. We establish saddle point necessary and sufficient Pareto optimality conditions for considered problems under some constraint qualifications. These results are motivated by the symmetric results obtained in the recent article by Cobos Sánchez et al. in 2021 on Pareto optimality for multiobjective optimization problems of continuous linear operators. The discussions in this paper are also related to second order symmetric duality for nonlinear multiobjective mixed integer programs for arbitrary cones due to Mishra and Wang in 2005. Further, we establish Karush–Kuhn–Tucker optimality conditions using saddle point optimality conditions for the differentiable cases and present some examples to illustrate our results. The study in this article can also be seen and extended as symmetric results of necessary and sufficient optimality conditions for vector equilibrium problems on Hadamard manifolds by Ruiz-Garzón et al. in 2019.

In order to play the important role of electric vehicles to promote the realization of the 3060 double carbon target, electric vehicles have seen explosive growth. However, due to the tight symmetry between the number and distribution of electric vehicles and their corresponding charging facilities, the layout of charging facilities has higher requirements. This paper collects travel data in the form of a traffic travel questionnaire for electric vehicle users. Based on the vehicle parking demand model of the queuing theory and Monte Carlo simulation, the paper gives the number of stopping vehicles and the time of vehicles stopping in different places such as residential areas, workplaces, supermarket parking and roadside. In addition, based on the Bass prediction model, the main parameters are modeled in the model, and the price correction coefficient is introduced. The improved Bass model is used to predict the growth trend of electric vehicles in different regions in different years and in different incentive sites. By predicting the ownership of urban electric vehicles and accurately grasping the distribution and operation of electric vehicles, this paper can provide guidance and suggestions for the planning and construction of charging facilities in different regions, effectively reduce the investment cost of charging facilities and guide local governments to formulate reasonable planning schemes.

Based on the current background of airport management and flight-gate scheduling in China, this paper takes Shanghai Pudong International Airport’s flight number of the rising and landing aircraft in a certain day as the research object, and it establishes an uncertain FGAP (Flight-Gate Assignment Problem) multi-objective programming model under the framework of uncertainty theory. Using genetic algorithm to solve the model, the specific flight-gate assignment scheduling plan is given. The research results show that the model in this paper can effectively alleviate the problems, such as unbalanced flight-gate allocation and excessive operating pressure of a single gate, in the conventional model, and make the allocation and scheduling more reasonable and efficient. Finally, we give the future application of uncertainty theory in finance and management, as well as the prospect of combining it with symmetry in physics.

In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of Hermite–Hadamard type via Hölder’s inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact.

The implications of the end effect for flux linkage and thrust ripple in a slot-less long-stator permanent magnet linear synchronous motor (LSPMLSM), are analyzed in this paper. Since it is affected by the end effect, the air-gap magnetic field density under the end permanent magnet is different from that under the non-end permanent magnet, leading to asymmetry in the thrust ripple. For this reason, we establish a dynamic permanent magnet flux linkage model, which proves that the end effect leads to sub-harmonics in the permanent magnet flux linkage. The motor’s magnetic field distribution in the left and right parts is symmetrical. A thrust model taking into account the flux linkage sub-harmonics is established, from which the amplitude and period of the thrust ripple caused by the end effect can be calculated. There is no detent force for the slot-less LSPMLSM, and the end effect is the primary origin of the motor thrust ripple. In order to suppress the end effect, a method of increasing the end iron length is proposed, as a result of which the sub-harmonics in the flux linkage and the motor thrust ripple are effectively suppressed. Experimental and simulation results verify the results of this paper.

The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring. The notion of ordered semihyperrings is a generalization of ordered semirings and a generalization of semihyperrings. In this paper, the Galois connection between ordered semihyperrings are studied in detail and various interesting results are obtained. A construction of an ordered semihyperring via a regular relation is given. Furthermore, we present the Galois connection between homomorphisms and derivations on an ordered semihyperring.

Class imbalance, as a phenomenon of asymmetry, has an adverse effect on the performance of most machine learning and overlap is another important factor that affects the classification performance of machine learning algorithms. This paper deals with the two factors simultaneously, addressing the class overlap under imbalanced distribution. In this paper, a theoretical analysis is firstly conducted on the existing class overlap metrics. Then, an improved method and the corresponding metrics to evaluate the class overlap under imbalance distributions are proposed based on the theoretical analysis. A well-known collection of the imbalanced datasets is used to compare the performance of different metrics and the performance is evaluated based on the Pearson correlation coefficient and the ξ correlation coefficient. The experimental results demonstrate that the proposed class overlap metrics outperform other compared metrics for the imbalanced datasets and the Pearson correlation coefficient with the AUC metric of eight algorithms can be improved by 34.7488% in average.

Conjectures on permanents are well-known unsettled conjectures in linear algebra. Let A be an n×n matrix and Sn be the symmetric group on n element set. The permanent of A is defined as perA=∑σ∈Sn∏i=1naiσ(i). The Merris conjectured that for all n×n doubly stochastic matrices (denoted by Ωn), nperA≥min1≤i≤n∑j=1nperA(j|i), where A(j|i) denotes the matrix obtained from A by deleting the jth row and ith column. Foregger raised a question whether per(tJn+(1−t)A)≤perA for 0≤t≤nn−1 and for all A∈Ωn, where Jn is a doubly stochastic matrix with each entry 1n. The Merris conjecture is one of the well-known conjectures on permanents. This conjecture is still open for n≥4. In this paper, we prove the Merris inequality for some classes of matrices. We use the sub permanent inequalities to prove our results. Foregger’s inequality is also one of the well-known inequalities on permanents, and it is not yet proved for n≥5. Using the concepts of elementary symmetric function and subpermanents, we prove the Foregger’s inequality for n=5 in [0.25, 0.6248]. Let σk(A) be the sum of all subpermanents of order k. Holens and Dokovic proposed a conjecture (Holen–Dokovic conjecture), which states that if A∈Ωn,A≠Jn and k is an integer, 1≤k≤n, then σk(A)≥(n−k+1)2nkσk−1(A). In this paper, we disprove the conjecture for n=k=4.

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups are vanishing, and M3 is homotopic to the Euclidean sphere S3 under various extrinsic restrictions, involving the eigenvalue of the warped function, integral Ricci curvature, and the Hessian tensor. The results in this paper can be considered an extension of Xin’s work in the framework of a compact warped product submanifold, when the base manifold is minimal in ambient manifolds.

In this paper, the dynamic characteristics of sandwich plates with external rigid layers and an upper layer with magnetorheological properties (MR) are investigated. An analysis of the effect of the magnetic field on frequency and loss factor is presented. Vibration can be controlled by a magnetic-rheological viscoelastomer (MRVE), when used in sandwich plates. During vibration, MRVE exhibits an inhomogeneous complex module, which is controlled by an applied magnetic field and depends on the oscillation frequency. Using the dynamic equilibrium conditions, physical and kinematic relationships, and the partial differential equations for the conjugate transverse and longitudinal oscillations of a sandwich plate, are derived. This paper presents a new method for stress analysis that provides accurate stress distributions for multilayer plates subject to cylindrical bending. It uses an adaptive method that does not make strict assumptions about the plate model. Based on the depicted theoretical model, the deformations of each layer of the plate are accounted for, including both transverse shear deformations and transverse normal deformations where the thickness is concerned, and nonlinear displacement changes. The magnetorheological (MR) identification of an inner layer is carried out using refined plate theory and sandwich bending tests. Using combined methods, the possibility of determining the MRVE parameters robustly, is examined.

In the years 1917–1919 Tullio Levi-Civita published a number of papers presenting new solutions to Einstein’s equations. This work, while partially translated, remains largely inaccessible to English speaking researchers. In this paper we review these solutions, and present them in a modern readable manner. We will also compute both Cartan–Karlhede and Carminati–Mclenaghan invariants such that these solutions are invariantly characterized by two distinct methods. These methods will allow for these solutions to be totally and invariantly characterized. Because of the variety of solutions considered here, this paper will also be a useful reference for those seeking to learn to apply the Cartan–Karlhede algorithm in practice.

Recent years have seen a growing call for use of big data analytics techniques to support the realisation of symmetries and simulations in digital twins and smart factories, in which data quality plays an important role in determining the quality of big data analytics products. Although data quality affecting big data analytics has received attention in the smart factory research field, to date a systematic review of the topic of interest for understanding the present state of the art is not available, which could help reveal the trends and gaps in this area. This paper therefore presents a systematic literature review of research articles about data quality affecting big data analytics in smart factories that have been published up to 2020. We examined 31 empirical studies from our selection of papers to identify the research themes in this field. The analysis of these studies links data quality issues toward big data analytics with data quality dimensions and methods used to address these issues in the smart factory context. The findings of this systematic review also provide implications for practitioners in addressing data quality issues to better use big data analytics products to support digital symmetry in the context of smart factory.

The aim of this paper is to study and investigate generating-type functions, which have been recently constructed by the author, with the aid of the Euler’s identity, combinatorial sums, and p-adic integrals. Using these generating functions with their functional equation, we derive various interesting combinatorial sums and identities including new families of numbers and polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Daehee numbers, the Changhee numbers, and other numbers and polynomials. Moreover, we present some revealing remarks and comments on the results of this paper.

To beat competition and obtain valuable information, decision-makers must conduct in-depth machine learning or data mining for data analytics. Traditionally, clustering and classification are two common methods used in machine mining. For clustering, data are divided into various groups according to the similarity or common features. On the other hand, classification refers to building a model by given training data, where the target class or label is predicted for the test data. In recent years, many researchers focus on the hybrid of clustering and classification. These techniques have admirable achievements, but there is still room to ameliorate performances, such as distributed process. Therefore, we propose clustering and classification based on distributed automatic feature engineering (AFE) for customer segmentation in this paper. In the proposed algorithm, AFE uses artificial bee colony (ABC) to select valuable features of input data, and then RFM provides the basic data analytics. In AFE, it first initializes the number of cluster k. Moreover, the clustering methods of k-means, Wald method, and fuzzy c-means (FCM) are processed to cluster the examples in variant groups. Finally, the classification method of an improved fuzzy decision tree classifies the target data and generates decision rules for explaining the detail situations. AFE also determines the value of the split number in the improved fuzzy decision tree to increase classification accuracy. The proposed clustering and classification based on automatic feature engineering is distributed, performed in Apache Spark platform. The topic of this paper is about solving the problem of clustering and classification for machine learning. From the results, the corresponding classification accuracy outperforms other approaches. Moreover, we also provide useful strategies and decision rules from data analytics for decision-makers.

Logistics plays an important role in the field of global economy, and the storage and retrieval of tasks in a warehouse which has symmetry is the most important part of logistics. Generally, the shelves of a warehouse have a certain degree of symmetry and similarity in their structure. The storage and retrieval efficiency directly affects the efficiency of logistics. The efficiency of the traditional storage and retrieval mode has become increasingly inconsistent with the needs of the industry. In order to solve this problem, this paper proposes a greedy algorithm based on cost matrix to solve the path planning problem of the automatic storage and retrieval system (AS/RS). Firstly, aiming at the path planning mathematical model of AS/RS, this paper proposes the concept of cost matrix, which transforms the traditional storage and retrieval problem into the element combination problem of cost matrix. Then, a more efficient backtracking algorithm is proposed based on the exhaustive method. After analyzing the performance of the backtracking algorithm, combined with some rules, a greedy algorithm which can further improve efficiency is proposed; the convergence of the improved greedy algorithm is also proven. Finally, through simulation, the time consumption of the greedy algorithm is only 0.59% of the exhaustive method, and compared with the traditional genetic algorithm, the time consumption of the greedy algorithm is about 50% of the genetic algorithm, and it can still maintain its advantage in time consumption, which proves that the greedy algorithm based on cost matrix has a certain feasibility and practicability in solving the path planning of the automatic storage and retrieval system.

This paper presents a computational tool for estimating energy generated by low-power photovoltaic systems based on the specific conditions of the study region since the characteristic energy equation can be obtained considering the main climatological factors affecting these systems in terms of the symmetry or skewness of the random distribution of the generated energy. Furthermore, this paper is aimed at determining any correlation that exists between meteorological variables with respect to the energy generated by 5-kW solar systems in the specific climatic conditions of the Republic of Cuba. The paper also presents the results of the influence of each climate factor on the distribution symmetry of the generated energy of the solar system. Studying symmetry in statistical models is important because they allow us to establish the degree of symmetry (or skewness), which is the probability distribution of a random variable, without having to make a graphical representation of it. Statistical skewness reports the degree to which observations are distributed evenly and proportionally above and below the center (highest) point of the distribution. In the case when the mentioned distribution is balanced, it is called symmetric.

The plastic modifications in synaptic connectivity is primarily from changes triggered by neuromodulated dopamine signals. These activities are controlled by neuromodulation, which is itself under the control of the brain. The subjective brain’s self-modifying abilities play an essential role in learning and adaptation. The artificial neural networks with neuromodulated plasticity are used to implement transfer learning in the image classification domain. In particular, this has application in image detection, image segmentation, and transfer of learning parameters with significant results. This paper proposes a novel approach to enhance transfer learning accuracy in a heterogeneous source and target, using the neuromodulation of the Hebbian learning principle, called NDHTL (Neuromodulated Dopamine Hebbian Transfer Learning). Neuromodulation of plasticity offers a powerful new technique with applications in training neural networks implementing asymmetric backpropagation using Hebbian principles in transfer learning motivated CNNs (Convolutional neural networks). Biologically motivated concomitant learning, where connected brain cells activate positively, enhances the synaptic connection strength between the network neurons. Using the NDHTL algorithm, the percentage of change of the plasticity between the neurons of the CNN layer is directly managed by the dopamine signal’s value. The discriminative nature of transfer learning fits well with the technique. The learned model’s connection weights must adapt to unseen target datasets with the least cost and effort in transfer learning. Using distinctive learning principles such as dopamine Hebbian learning in transfer learning for asymmetric gradient weights update is a novel approach. The paper emphasizes the NDHTL algorithmic technique as synaptic plasticity controlled by dopamine signals in transfer learning to classify images using source-target datasets. The standard transfer learning using gradient backpropagation is a symmetric framework. Experimental results using CIFAR-10 and CIFAR-100 datasets show that the proposed NDHTL algorithm can enhance transfer learning efficiency compared to existing methods.

Canonical correlation analysis (CCA) is the default method for investigating the linear dependence structure between two random vectors, but it might not detect nonlinear dependencies. This paper models the nonlinear dependencies between two random vectors by the perturbed independence distribution, a multivariate semiparametric model where CCA provides an insight into their nonlinear dependence structure. The paper also investigates some of its probabilistic and inferential properties, including marginal and conditional distributions, nonlinear transformations, maximum likelihood estimation and independence testing. Perturbed independence distributions are closely related to skew-symmetric ones.

In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite-Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. WOS:000677046700001 2-s2.0-85110868353

This Special Issue covers symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multi-criteria decision-making problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the Special Issue.

This paper focuses on preventing forms of social dysfunction such as invasions of privacy and stalking by understanding the diversified situation of the rapidly increasing number of social media users who use social media services, which are various types of social networking services. To prevent these problems, we aim to identify mutual relationships by layering the relationships between social media users. In other words, in social media that has a relationship with the subject, the subject user is yet another object, so the appearance of the object viewed by the subject user and the correlation between the subjects and objects must be visualized. At this time, because the subject is an object that has changed over time, it is necessary to perform symmetrical and mutual correlation analysis based on relationship through objective layering viewed from a computer. In this paper, the mutual relationship between the subject user and the object user was defined and visualized to apply it to the deep learning model through a software program. Among various types of social media that are mainly used, user information data is gathered through the popular social media site called Instagram and our target community platforms. Consequently, it was processed again to represent user interactions among other users. Finally, three stages of mutual relationship visualization were represented through simulation and tests, and 120,000 data sets were processed, classified, and proved through the simulation results.

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

This article belongs to the Special Issue Discrete and Fractional Mathematics: Symmetry and Applications. In this paper we introduce a generalized Laplace transform in order to work with a very general fractional derivative, and we obtain the properties of this new transform. We also include the corresponding convolution and inverse formula. In particular, the definition of convolution for this generalized Laplace transform improves previous results. Additionally, we deal with the generalized harmonic oscillator equation, showing that this transform and its properties allow one to solve fractional differential equations. We would like to thank the referees for their comments, which have improved the paper. The research of José M. Rodríguez and José M. Sigarreta was supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).

The dataset distribution of actual logging is asymmetric, as most logging data are unlabeled. With the traditional classification model, it is hard to predict the oil and gas reservoir accurately. Therefore, a novel approach to the oil layer recognition model using the improved whale swarm algorithm (WOA) and semi-supervised support vector machine (S3VM) is proposed in this paper. At first, in order to overcome the shortcomings of the Whale Optimization Algorithm applied in the parameter-optimization of the S3VM model, such as falling into a local optimization and low convergence precision, an improved WOA was proposed according to the adaptive cloud strategy and the catfish effect. Then, the improved WOA was used to optimize the kernel parameters of S3VM for oil layer recognition. In this paper, the improved WOA is used to test 15 benchmark functions of CEC2005 compared with five other algorithms. The IWOA–S3VM model is used to classify the five kinds of UCI datasets compared with the other two algorithms. Finally, the IWOA–S3VM model is used for oil layer recognition. The result shows that (1) the improved WOA has better convergence speed and optimization ability than the other five algorithms, and (2) the IWOA–S3VM model has better recognition precision when the dataset contains a labeled and unlabeled dataset in oil layer recognition.

Cloud based healthcare computing have changed the face of healthcare in many ways. The main advantages of cloud computing in healthcare are scalability of the required service and the provision to upscale or downsize the data storge, collaborating Artificial Intelligence (AI) and machine learning. The current paper examined various research studies to explore the utilization of intelligent techniques in health systems and mainly focused into the security and privacy issues in the current technologies. Despite the various benefits related to cloud-computing applications for healthcare, there are different types of management, technology handling, security measures, and legal issues to be considered and addressed. The key focus of this paper is to address the increased demand for cloud computing and its definition, technologies widely used in healthcare, their problems and possibilities, and the way protection mechanisms are organized and prepared when the company chooses to implement the latest evolving service model. In this paper, we focused on a thorough review of current and existing literature on different approaches and mechanisms used in e-Health to deal with security and privacy issues. Some of these approaches have strengths and weaknesses. After selecting original articles, the literature review was carried out, and we identified several models adopted in their solutions. We arrived at the reviewed articles after comparing the models used.

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories.

The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied.

Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann&ndash, Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann&ndash, Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green&rsquo, s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula ()(1&minus, z2)f&prime, (z)}&gt, 0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated.

This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.

The fundamental groups and homotopy decompositions of algebraic topology have applications in systems involving symmetry breaking with topological excitations. The main aim of this paper is to analyze the properties of homotopy decompositions in quotient topological spaces depending on the connectedness of the space and the fundamental groups. This paper presents constructions and analysis of two varieties of homotopy decompositions depending on the variations in topological connectedness of decomposed subspaces. The proposed homotopy decomposition considers connected fundamental groups, where the homotopy equivalences are relaxed and the homeomorphisms between the fundamental groups are maintained. It is considered that one fundamental group is strictly homotopy equivalent to a set of 1-spheres on a plane and as a result it is homotopy rigid. The other fundamental group is topologically homeomorphic to the first one within the connected space and it is not homotopy rigid. The homotopy decompositions are analyzed in quotient topological spaces, where the base space and the quotient space are separable topological spaces. In specific cases, the decomposed quotient space symmetrically extends Sierpinski space with respect to origin. The connectedness of fundamental groups in the topological space is maintained by open curve embeddings without enforcing the conditions of homotopy classes on it. The extended decomposed quotient topological space preserves the trivial group structure of Sierpinski space.

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov&rsquo, s sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy&ndash, Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam&ndash, Hyers stability of the fixed point problem. An example is also given to sustain the presented results.