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Community detection can help analyze the structural features and functions of complex networks, and plays important roles in many aspects such as project recommendation and network evolution analysis. Therefore, community detection has always been a hot topic in the field of complex networks. Although various community-detection methods have been proposed, how to improve their accuracy and efficiency is still an ambition pursued by researchers. In view of this, this paper proposes a community-detection method for complex networks based on node influence analysis. First, the influence of nodes is represented as a vector composed by neighborhood degree centrality, betweennes centrality and clustering coefficient. Then, Pareto dominance is used to rank the influence of nodes. After that, the community centers are selected by comprehensively considering the node influence and crowding degree. Finally, the remaining nodes are allocated to different communities using a labeling algorithm. The proposed method in this paper is applied to several actual networks. The comparison results with other methods demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The first part of this work provides explicit solutions for two integral equations; both are solved by means of Fourier transform. In the second part of this paper, sufficient conditions for the existence and uniqueness of the solutions satisfying sandwich constraints for two types of full moment problems are provided. The only given data are the moments of all positive integer orders of the solution and two other linear, not necessarily positive, constraints on it. Under natural assumptions, all the linear solutions are continuous. With their value in the subspace of polynomials being given by the moment conditions, the uniqueness follows. When the involved linear solutions and constraints are positive, the sufficient conditions mentioned above are also necessary. This is achieved in the third part of the paper. All these conditions are written in terms of quadratic expressions. [ABSTRACT FROM AUTHOR]

With the ongoing advancements in material technology, the domain of soft robotics has garnered increasing attention. Soft robots, in contrast to their rigid counterparts, offer superior adaptability to the environment, enhanced flexibility, and improved safety, rendering them highly suitable for complex application scenarios such as rescue operations and medical interventions. In this paper, a new type of pneumatic software actuator is proposed. The actuator adopts a combination of a soft structure and pneumatic control, which is highly flexible and versatile. By using the flow of gas inside the soft structure, high-precision and flexible motion control is realized. In the design process, the extensibility and adaptability of the structure are considered, so that the actuator can adapt to different working environments and task requirements. The experimental results show that the pneumatic soft actuator exhibits excellent performance in terms of accuracy, response speed, and controllability. This research provides new ideas and methods for the development of the field of pneumatic actuators and has wide application prospects. The main research content of this paper is as follows: first, the soft pneumatic actuator is modeled and simulated, the structure is optimized on the basis of simulation, and finally, the performance of the actuator is tested. [ABSTRACT FROM AUTHOR]

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from φ -contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of α -fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. [ABSTRACT FROM AUTHOR]

Target detection algorithms can greatly improve the efficiency of tomato leaf disease detection and play an important technical role in intelligent tomato cultivation. However, there are some challenges in the detection process, such as the diversity of complex backgrounds and the loss of leaf symmetry due to leaf shadowing, and existing disease detection methods have some disadvantages in terms of deteriorating generalization ability and insufficient accuracy. Aiming at the above issues, a target detection model for tomato leaf disease based on deep learning with a global attention mechanism, TDGA, is proposed in this paper. The main idea of TDGA includes three aspects. Firstly, TDGA adds a global attention mechanism (GAM) after up-sampling and down-sampling, as well as in the SPPF module, to improve the feature extraction ability of the target object, effectively reducing the interference of invalid targets. Secondly, TDGA uses a switchable atrous convolution (SAConv) in the C3 module to improve the model's ability to detect. Thirdly, TDGA adopts the efficient IoU loss (EIoU) instead of complete IoU loss (CIoU) to solve the ambiguous definition of aspect ratio and sample imbalance. In addition, the influences of different environmental factors such as single leaf, multiple leaves, and shadows on the performance of tomato disease detection are extensively experimented with and analyzed in this paper, which also verified the robustness of TDGA. The experimental results show that the average accuracy of TDGA reaches 91.40%, which is 2.93% higher than that of the original YOLOv5 network, which is higher than YOLOv5, YOLOv7, YOLOHC, YOLOv8, SSD, Faster R-CNN, RetinaNet and other target detection networks, so that TDGA can be utilized for the detection of tomato leaf disease more efficiently and accurately, even in complex environments. [ABSTRACT FROM AUTHOR]

The modular robotic arms can achieve desired performances in different scenarios through the combination of various modules, and concurrently hold the potential to exhibit geometric symmetry and uniform mass symmetry. Therefore, selecting the appropriate combination of modules is crucial for realizing the functions of the robotic arm and ensuring the elegance of the system. To this end, this paper proposes a double deep Q-network (DDQN)-based configuration design algorithm for modular robotic arms, which aims to find the optimal configuration under different tasks. First, a library of small modules of collaborative robotic arms consisting of multiple tandem robotic arms is constructed. These modules are described in a standard format that can be directly imported into the software for simulation, providing greater convenience and flexibility in the development of modular robotic arms. Subsequently, the DDQN design framework for module selection is established to obtain the optimal robotic arm configuration. The proposed method could deal with the overestimation problem in the traditional deep Q-network (DQN) method and improve the estimation accuracy of the value function for each module. In addition, the experience replay mechanism is improved based on the SumTree technique, which enables the algorithm to make effective use of historical experience and prevents the algorithm from falling into local optimal solutions. Finally, comparative experiments are carried out on the PyBullet simulation platform to verify the effectiveness and superiority of the configuration design method developed in the paper. The simulation results show that the proposed DDQN-based method with experience replay mechanism has higher search efficiency and accuracy compared to the traditional DQN scheme. [ABSTRACT FROM AUTHOR]

Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer's supply, and distributor's demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

To ensure precise positioning of the macro–micro platform with a symmetrical structure, it is crucial to mitigate the impact of various perturbations, including disturbances, as well as complex factors such as external loads, electrical noise, and model parameter variations. This paper proposes a novel macro–micro master–slave control structure that incorporates adaptive fuzzy linear active disturbance rejection control (AFLADRC). The Kp and Kd parameters of the linear state error feedback (LSEF) are dynamically tuned and adjusted using fuzzy reasoning. This approach enhances the robustness of the system and simplifies the tuning process. In addition, this paper also analyzes the symmetry of the coupling effect between macro and micro, as the coupling will affect the motor force and the reaction potential of the motor. The macro–micro platform adopts a symmetric design; the macro stage is driven by a permanent magnet synchronous linear motor (PMLSM), and the micro stage is driven by a voice coil motor. Finally, we built the macro–micro linear motion experimental platform to verify the control effect of the proposed method by conducting trajectory tracking experiments and comparison experiments. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

This paper considers a nonlinear fractional-order boundary value problem   H D a , g α 1 , β , μ x (t) + f (t , x (t) , H D a , g α 2 , β , μ x (t)) = 0 , for t ∈ [ a , b ] , α 1 ∈ (1 , 2 ] , α 2 ∈ (0 , 1 ] , β ∈ [ 0 , 1 ] with appropriate integral boundary conditions on the Hölder spaces. Here, f is a real-valued function that satisfies the Hölder condition, and   H D a , g α , β , μ represents the tempered-Hilfer fractional derivative of order α > 0 with parameter μ ∈ R + and type β ∈ [ 0 , 1 ] . The corresponding integral problem is introduced in the study of this issue. This paper addresses a fundamental issue in the field, namely the circumstances under which differential and integral problems are equivalent. This approach enables the study of differential problems using integral operators. In order to achieve this, tempered fractional calculus and the equivalence problem of the studied problems are introduced and studied. The selection of an appropriate function space is of fundamental importance. This paper investigates the applicability of these operators on Hölder spaces and provides a comprehensive rationale for this choice. [ABSTRACT FROM AUTHOR]

One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators. [ABSTRACT FROM AUTHOR]

In this paper, we consider the influence of a nonlinear contact rate caused by multiple contacts in classical SIR model. In this paper, we unversal unfolding a nilpotent cusp singularity in such systems through normal form theory, we reveal that the system undergoes a Bogdanov-Takens bifurcation with codimension 2. During the bifurcation process, numerous lower codimension bifurcations may emerge simultaneously, such as saddle-node and Hopf bifurcations with codimension 1. Finally, employing the Matcont and Phase Plane software, we construct bifurcation diagrams and topological phase portraits. Additionally, we emphasize the role of symmetry in our analysis. By considering the inherent symmetries in the system, we provide a more comprehensive understanding of the dynamical behavior. Our findings suggest that if this occurrence rate is applied to the SIR model, it would yield different dynamical phenomena compared to those obtained by reducing a 3-dimensional dynamical model to a planar system by neglecting the disease mortality rate, which results in a stable nilpotent cusp singularity with codimension 2. We found that in SIR models with the same occurrence rate, both stable and unstable Bogdanov-Takens bifurcations occur, meaning both stable and unstable limit cycles appear in this system. [ABSTRACT FROM AUTHOR]

The operational stability of a power transformer exerts an extremely important impact on the power symmetry, balance, and security of power systems. When the grid load fluctuates greatly, if the load factor of the transformer cannot be maintained within a reasonable range, it leads to increased instability in grid operation. Adjusting the transformer capacity based on load changes is of great significance. The existing control methods for on-load capacity-regulating (OLCR) transformers have low timeliness, and the daily switching frequency of the capacity-regulating switch is not controlled. To ensure the safe and stable operation of transformers, this paper proposes a control method for OLCR transformers based on load prediction and fuzzy control. Firstly, the operating principle of OLCR transformers is analyzed, and a multi-strategy enhanced dung beetle optimizer (MSDBO) combined with a CNN−LSTM model is proposed for load forecasting. On this basis, the daily switching frequency of the capacity-regulating transformer is introduced, and hesitant fuzzy control is used to select the optimal capacity-regulating strategy relying on three factors: loss, economy, and switching frequency. Finally, simulation models are constructed using the MATLAB/SIMULINK platform and simulation analysis is conducted to verify the effectiveness and superiority of the proposed control method. For the three scenarios in this paper, the method reduces daily power loss by 28.5% to 56.3% and daily operating costs by 25.4% to 50.8%. The method used in this paper can sacrifice 3.5% to 9.2% of the loss reduction capability in exchange for reducing the number of switch operations by 28.6% to 57.1%, significantly extending the lifespan of the switches and thereby increasing the operational lifespan of the transformer. [ABSTRACT FROM AUTHOR]

The pointing accuracy of large radio telescopes is affected by antenna structure errors, installation errors, servo errors, gravity, and varying environmental factors. Although an on-line pointing model had been developed in the past for several large radio telescopes to correct these effects, it is also valuable to explore new ways to correct these effects. Therefore, in order to estimate the dynamic pointing error of large radio telescopes under solar radiation, a new way based on digital twin (DT) is used in this paper. Digital models of the Wuqing 70-m radio telescope (WRT70) are created based on the DT operational framework. Finally, the reliability of the WRT70's DT system is verified, and the dynamic pointing error of WRT70 (staying at the position of the elevation angle of 90° and the azimuth angle of 180°) on two sunny days in different seasons is estimated by the created DT system. The research results show that the pointing error of large radio telescopes under solar radiation fluctuates greatly and the seasonal differences are very striking. The maximum elevation pointing error of WRT70 under solar radiation around the winter solstice is over 40 arcsec, which is equal to 4/11 of the beam width for WRT70 operating at 8 GHz. In this paper, it is feasible to estimate the time-varying pointing errors of large radio telescopes at rest under solar radiation by constructing a DT system, but it is not effective to estimate the dynamic pointing errors of large radio telescopes in operation. It is expected to establish a dynamic pointing error model and calibrate the dynamic pointing errors of large radio telescopes in operation by DT technology in the future. [ABSTRACT FROM AUTHOR]

This paper presents the numerical solution of the heat conduction model with a fractional derivative of the Riemann–Liouville type with respect to the spatial variable. The considered mathematical model assumes the dependence on temperature of the material parameters (such as specific heat, density, and thermal conductivity) of the model. In the paper, the boundary conditions of the first and second types are considered. If the heat flux equal to zero is assumed on the left boundary, then the thermal symmetry is obtained, which results in a simplification of the problem and the possibility of considering only half the area. The numerical examples presented in the paper illustrate the effectiveness and convergence of the discussed computational method. [ABSTRACT FROM AUTHOR]

Network traffic classification is crucial for identifying network applications and defending against network threats. Traditional traffic classification approaches struggle to extract structural features and suffer from poor interpretability of feature representations. The high symmetry between network traffic classification and its interpretable feature representation is vital for network traffic analysis. To address these issues, this paper proposes a traffic classification and feature representation model named the attention mechanism autoencoder (AMAE). The AMAE model extracts the global spatial structural features of network traffic through attention mechanisms and employs an autoencoder to extract local structural features and perform dimensionality reduction. This process maps different network traffic features into one-dimensional coordinate systems in the form of spectra, termed FlowSpectrum. The spectra of different network traffic represent different intervals in the coordinate system. This paper tests the interpretability and classification performance of network traffic features of the AMAE model using the ISCX-VPN2016 dataset. Experimental results demonstrate that by analyzing the overall distribution of attention weights and local weight values of network traffic, the model effectively explains the differences in the spectral representation intervals of different types of network traffic. Furthermore, our approach achieves the highest classification accuracy of up to 100% for non-VPN-encrypted traffic and 99.69% for VPN-encrypted traffic, surpassing existing traffic classification schemes. [ABSTRACT FROM AUTHOR]

One of the limitations of the dung beetle optimization (DBO) is its susceptibility to local optima and its relatively low search accuracy. Several strategies have been utilized to improve the diversity, search precision, and outcomes of the DBO. However, the equilibrium between exploration and exploitation has not been achieved optimally. This paper presents a novel algorithm called the ODBO, which incorporates cat map and an opposition-based learning strategy, which is based on symmetry theory. In addition, in order to enhance the performance of the dung ball rolling phase, this paper combines the global search strategy of the osprey optimization algorithm with the position update strategy of the DBO. Additionally, we enhance the population's diversity during the foraging phase of the DBO by incorporating vertical and horizontal crossover of individuals. This introduction of asymmetry in the crossover operation increases the exploration capability of the algorithm, allowing it to effectively escape local optima and facilitate global search. [ABSTRACT FROM AUTHOR]

This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements. [ABSTRACT FROM AUTHOR]

With the continuous development and progress of wireless self-organizing network communication technology, how to carry out long-distance cooperative control of multiple intelligences under the framework of an air–ground integrated wireless high-mobility self-organizing network has become a hot and difficult topic that needs to be solved urgently. This paper takes the air–ground integrated wireless high-mobility self-organizing network system as the basic framework and focuses on solving the long-distance cooperative fault-tolerant control of multi-intelligent bodies and the topological stability of a wireless mobile self-organizing network. To solve the above problems, a direct neural network with a robust adaptive fault-tolerant controller is designed in this paper. By constructing a symmetric population neural network model and combining it with the Lyapunov stabilization criterion, the system feedback matrix K has the ability of autonomous adaptive learning, and symmetrically distorts, rotates, or scales the training data to instantly adjust the system's fault-tolerant corrections and adaptive adjusting factors to resist the unknown disturbances and faults, to achieve the goals of multi-intelligent body stable control and the stable operation of a wireless high-mobility self-organizing network topology. Simulation results show that with the feedback adjustment of the multi-system under the designed controller, the multi-system as a whole has good fault-tolerant performance and autonomous learning approximation performance, and the tracking error asymptotically converges to zero. The experimental results show that the multi-flight subsystems fly stably, the air–ground integrated wireless high-mobility self-organizing network topology has good stability performance, and the maximum relative improvement of the topology stability performance is 50%. [ABSTRACT FROM AUTHOR]

The algorithms for determining the active space object maneuver parameters in the conditions of near-circular orbits are presented in the paper. The right ascension and declination angles are used to determine the parameters of a single maneuver with transversal and lateral components (the application moment and the velocity impulse magnitude). Two pairs of angles are used to determine the parameters of the maneuver with only a lateral component. Two pairs of angles are needed for the determination of the parameters of the long-duration maneuver performed by a low-thrust engine (moments of the maneuver start and finish, and components of the acceleration delivered by the engine). The essential detail that makes it possible to determine the parameters of long-duration maneuvers is their symmetry relative to the center of the engine operating interval. Considerable perturbing accelerations, which are not accounted for by traditional perturbing models, affect passive objects, especially membranous objects with a big and variable area-to-mass ratio. This decreases dramatically the accuracy of these objects' motion propagation. In this paper, the magnitude of perturbing acceleration is determined with the assumption that it is constant and is active throughout the whole time interval from the moment of the last orbit determination to the moment of the new measurement used. Examples of the assessment of maneuvers performed by an object in the geostationary orbit are presented. [ABSTRACT FROM AUTHOR]

This paper focuses on addressing the adaptive fuzzy fixed-time issue for a class of nonlinear systems with uncertainty functions and mismatched disturbances. Fuzzy logical systems are utilized for identifying unknown functions. Additionally, to tackle challenges posed by mismatched disturbances, disturbance observers are constructed based on the backstepping method. Utilizing the adding one power integrator approach and the fixed-time control method, this paper introduces a fixed-time adaptive fuzzy control algorithm. Notably, this algorithm accommodates the presence of unknown mismatched disturbances and nonlinear functions. The paper establishes, through the application of the Lyapunov stability theory, that the designed adaptive fixed-time fuzzy control algorithm ensures practical fixed-time stability for the resulting closed-loop systems. Finally, the effectiveness of the derived strategy is demonstrated through an illustrative example involving two cases. [ABSTRACT FROM AUTHOR]

The interactions between topology and algebraic geometry expose various interesting properties. This paper proposes the deformations of topological n-manifolds over the automorphic polynomial ring maps and associated isomorphic imbedding of locally flat submanifolds within the n-manifolds. The manifold deformations include topologically homeomorphic bending of submanifolds at multiple directions under algebraic operations. This paper introduces the concept of a topological equivalence class of manifolds and the associated equivalent class of polynomials in a real ring. The concepts of algebraic compositions in a real polynomial ring and the resulting topological properties (homeomorphism, isomorphism and deformation) of manifolds under algebraic compositions are introduced. It is shown that a set of ideals in a polynomial ring generates manifolds retaining topological isomorphism under algebraic compositions. The numerical simulations are presented in this paper to illustrate the interplay of topological properties and the respective real algebraic sets generated by polynomials in a ring within affine 3-spaces. It is shown that the coefficients of polynomials generated by a periodic smooth function can induce mirror symmetry in manifolds. The proposed formulations do not consider the simplectic class of manifolds and associated quantizable deformations. However, the proposed formulations preserve the properties of Nash representations of real algebraic manifolds including Nash isomorphism. [ABSTRACT FROM AUTHOR]

Cavitation bubbles near narrow gaps widely exist within microfluidic control devices. In the present paper, a laser-induced cavitation bubble is arranged in a narrow gap composed of two parallel plates. The inception position of the bubble is set to be at the same distance from the two plates so that the dynamic behaviors of the bubble are symmetrical. The collapse and rebound dynamics of the bubble near the boundary of a narrow gap are investigated through high-speed photography. The bubble behaviors (e.g., shape deformation, translational movement, and jet characteristics) are analyzed while considering the influence of the dimensionless distance between the bubble and the boundary and the dimensionless gap width. The principal findings include the following: (1) When the dimensionless distance is small, a violent jet towards the gap is generated during the bubble collapse stage, along with a weak counter-jet towards the boundary appearing during the rebound stage. (2) As the dimensionless distance increases, the translational distance of the bubble during the collapse stage initially decreases, then increases, and finally decreases to zero. (3) Within the parameter range considered in this paper, the dimensionless width mainly affects the expansion degree and movement direction of the bubble cloud during its rebound and subsequent stages. The above research findings can provide experimental support for bubble-driven flow control, pumping, and liquid mixing in microfluidic channels. [ABSTRACT FROM AUTHOR]

This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation. [ABSTRACT FROM AUTHOR]

This paper presents an improved swarming algorithm that enhances low-illumination images. The algorithm combines a hybrid Harris Eagle algorithm with double gamma (IHHO-BIGA) and incomplete beta (IHHO-NBeta) functions. This paper integrates the concept of symmetry into the improvement steps of the image adaptive enhancement algorithm. The enhanced algorithm integrates chaotic mapping for population initialization, a nonlinear formula for prey energy calculation, spiral motion from the black widow algorithm for global search enhancement, a nonlinear inertia weight factor inspired by particle swarm optimization, and a modified Levy flight strategy to prevent premature convergence to local optima. This paper compares the algorithm's performance with other swarm intelligence algorithms using commonly used test functions. The algorithm's performance is compared against several emerging swarm intelligence algorithms using commonly used test functions, with results demonstrating its superior performance. The improved Harris Eagle algorithm is then applied for image adaptive enhancement, and its effectiveness is evaluated on five low-illumination images from the LOL dataset. The proposed method is compared to three common image enhancement techniques and the IHHO-BIGA and IHHO-NBeta methods. The experimental results reveal that the proposed approach achieves optimal visual perception and enhanced image evaluation metrics, outperforming the existing techniques. Notably, the standard deviation data of the first image show that the IHHO-NBeta method enhances the image by 8.26%, 120.91%, 126.85%, and 164.02% compared with IHHO-BIGA, the single-scale Retinex enhancement method, the homomorphic filtering method, and the limited contrast adaptive histogram equalization method, respectively. The processing time of the improved method is also better than the previous heuristic algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine's notions of generalized closed sets and Maki's  Λ  sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine's generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine's method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of  Λ -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples. [ABSTRACT FROM AUTHOR]

In recent years, with the rapid development of deep learning technology, a large number of excellent convolutional neural networks (CNNs) have been proposed, many of which are based on improvements to classical methods. Based on the Inception family of methods, depthwise separable convolution was applied to Xception to achieve lightweighting, and Inception-ResNet introduces residual connections to accelerate model convergence. However, existing improvements for the Inception module often neglect further enhancement of its receptive field, while increasing the receptive field of CNNs has been widely studied and proven to be effective in improving classification performance. Motivated by this fact, three effective expansion modules are proposed in this paper. The first expansion module, Inception expand (Inception-e) module, is proposed to improve the classification accuracy by concatenating more and deeper convolutional branches. To reduce the number of parameters for Inception e, this paper proposes a second expansion module—Equivalent Inception-e (Eception) module, which is equivalent to Inception-e in terms of feature extraction capability, but which suppresses the growth of the parameter quantity brought by the expansion by effectively reducing the redundant convolutional layers; on the basis of Eception, this paper proposes a third expansion module—Lightweight Eception (Lception) module, which crosses depthwise convolution with ordinary convolution to further effectively reduce the number of parameters. The three proposed modules have been validated on the Cifar10 dataset. The experimental results show that all these extensions are effective in improving the classification accuracy of the models, and the most significant effect is the Lception module, where Lception (rank = 4) on the Cifar10 dataset improves the accuracy by 1.5% compared to the baseline model (Inception module A) by using only 0.15 M more parameters. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the necessary and sufficient conditions for solving a dual split quaternion matrix equation A X B   =   C , and present the general solution expression when the solvability conditions are met. As an application, we delve into the necessary and sufficient conditions for the existence of a Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations A X   =   C and X B   =   C . Finally, we provide a numerical example to demonstrate the findings of this paper. [ABSTRACT FROM AUTHOR]

Occlusion or posture change of the face in natural scenes has typical asymmetry; however, an asymmetric face plays a key part in the lack of information available for facial expression recognition. To solve the problem of low accuracy of asymmetric facial expression recognition, this paper proposes a fusion of channel global features and a spatial local information expression recognition network called the "Channel–Spatial Integration Network" (CSINet). First, to extract the underlying detail information and deepen the network, the attention residual module with a redundant information filtering function is designed, and the backbone feature-extraction network is constituted by module stacking. Second, considering the loss of information in the local key area of face occlusion, the channel–spatial fusion structure is constructed, and the channel features and spatial features are combined to enhance the accuracy of occluded facial recognition. Finally, before the full connection layer, more local spatial information is embedded into the global channel information to capture the relationship between different channel–spatial targets, which improves the accuracy of feature expression. Experimental results on the natural scene facial expression data sets RAF-DB and FERPlus show that the recognition accuracies of the modeling approach proposed in this paper are 89.67% and 90.83%, which are 13.24% and 11.52% higher than that of the baseline network ResNet50, respectively. Compared with the latest facial expression recognition methods such as CVT, PACVT, etc., the method in this paper obtains better evaluation results of masked facial expression recognition, which provides certain theoretical and technical references for daily facial emotion analysis and human–computer interaction applications. [ABSTRACT FROM AUTHOR]

Since plant diseases occurring during the growth process are a significant factor leading to the decline in both yield and quality, the classification and detection of plant leaf diseases, followed by timely prevention and control measures, are crucial for safeguarding plant productivity and quality. As the traditional convolutional neural network structure cannot effectively recognize similar plant leaf diseases, in order to more accurately identify the diseases on plant leaves, this paper proposes an effective plant disease image recognition method aECA-ResNet34. This method is based on ResNet34, and in the first and the last layers of this network, respectively, we add this paper's improved aECAnet with the symmetric structure. aECA-ResNet34 is compared with different plant disease classification models on the peanut dataset constructed in this paper and the open-source PlantVillage dataset. The experimental results show that the aECA-ResNet34 model proposed in this paper has higher accuracy, better performance, and better robustness. The results show that the aECA-ResNet34 model proposed in this paper is able to recognize diseases of multiple plant leaves very accurately. [ABSTRACT FROM AUTHOR]

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient. [ABSTRACT FROM AUTHOR]

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies' green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]

With the development of autonomous driving, consensus is gradually forming around vehicle–infrastructure cooperative (VIC) autonomous driving. The VIC environment-sensing system uses roadside sensors in collaboration with automotive sensors to capture traffic target information symmetrically from both the roadside and the vehicle, thus extending the perception capabilities of autonomous driving vehicles. However, the current target detection accuracy for feature fusion based on roadside LiDAR and automotive LiDAR is relatively low, making it difficult to satisfy the sensing requirements of autonomous vehicles. This paper proposes PAFNet, a VIC pillar attention fusion network for target detection, aimed at improving LiDAR target detection accuracy under feature fusion. The proposed spatial and temporal cooperative fusion preprocessing method ensures the accuracy of the fused features through frame matching and coordinate transformation of the point cloud. In addition, this paper introduces the first anchor-free method for 3D target detection for VIC feature fusion, using a centroid-based approach for target detection. In the feature fusion stage, we propose the grid attention feature fusion method. This method uses the spatial feature attention mechanism to fuse the roadside and vehicle-side features. The experiment on the DAIR-V2X-C dataset shows that PAFNet achieved a 6.92% higher detection accuracy in 3D target detection than FFNet in urban scenes. [ABSTRACT FROM AUTHOR]

Disk galaxies have a typical dimension of a few tens of kiloparsecs. It follows from the theory of general relativity that any signal originating from the galactic center will be noticed at the outskirts of the galaxy only tens of thousands of years later. This retardation effect, however, is absent in modelling used to calculate rotation curves throughout entire galaxies and their external gas. The considerable differences between Newtonian predictions and observed velocities are currently removed either by assuming dark matter or by suggesting various modifications to the laws of gravity, MOND being a long standing alternative to Newtonian gravity. In previous papers we have shown that by applying general relativity in a rigorous fashion, without neglecting retardation, one can explain the rotational velocities of galactic matter without modifying gravity or adding dark matter. Moreover, it was shown that dark matter effects, as they appear in gravitational lensing, the Tully-Fisher relation, and mass estimations based on the virial theorem could also be explained as retarded-gravity effects. It must be noted, however, that the proposed theory relies on the existence of a mass flow (of a changing rate) into the galaxy; a requirement that was not directly observed. In the original paper on the subject only one galaxy (M33) was analysed in detail. This was later amended with a published study of eleven galaxies. Here we give a more comprehensive retardation analysis of 143 galaxies of different types from the SPARC Galaxy collection. We show that in most cases we obtain very accurate fits to the data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples. [ABSTRACT FROM AUTHOR]

The aero-engine serves as the "heart" of an aircraft and is a primary factor determining the aircraft's performance. Among the crucial components in the core of aero-engines, aero-engine compressor blades stand out as extremely important. They are not only numerous but also characterized by a multitude of parameters, making them the most complex parts in an aero-engine. This paper aims to address the trade-off between accuracy and efficiency in the existing measurement methods for asymmetric blades. Non-contact measurements were conducted using a structured light system composed of a stereo camera and a DLC projector. The point cloud data of the blades are processed using methods such as the PCA (Principal Component Analysis) algorithm, binary search, and least squares fitting. This paper established a fringe-projection profilometry light sensor system for the multi-view measurement of the blades. High-precision rotary tables are utilized to rotate and extract complete spatial point cloud data of aviation blades. Finally, measurements and comparative experiments on the blade body are conducted. The obtained blade point cloud data undergo sorting and denoising processes, resulting in improved measurement accuracy. The measurement error of the blade chord length is 0.001%, the measurement error of blade maximum thickness is 0.895%, compared to CMM (Coordinate Measuring Machine), where the measurement error of chord is 0.06%. [ABSTRACT FROM AUTHOR]

This paper investigates various aspects of the distribution of roots and critical points of a complex polynomial, including their variance and the relationships between their moduli using an inequality due to de Bruijn. Making use of two other inequalities-again due to de Bruijn-we derive two probabilistic results concerning upper bounds for the average moduli of the imaginary parts of zeros and those of critical points, assuming uniform distribution of the zeros over a unit disc and employing the Markov inequality. The paper also provides an explicit formula for the variance of the roots of a complex polynomial for the case when all the zeros are real. In addition, for polynomials with uniform distribution of roots over the unit disc, the expected variance of the zeros is computed. Furthermore, a bound on the variance of the critical points in terms of the variance of the zeros of a general polynomial is derived, whereby it is established that the variance of the critical points of a polynomial cannot exceed the variance of its roots. Finally, we conjecture a relation between the real parts of the zeros and the critical points of a polynomial. [ABSTRACT FROM AUTHOR]

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry developmental stages. This paper introduces a Taylor monomial falling function and presents some properties of this function in a delta fractional model with Green's function kernel. In the deterministic case, Green's function will be non-negative, and this shows that the function has an upper bound for its maximum point. More precisely, in this paper, based on the properties of the Taylor monomial falling function, we investigate Lyapunov-type inequalities for a delta fractional boundary value problem of Riemann–Liouville type. [ABSTRACT FROM AUTHOR]

In this paper, we explore a model of an N-player, non-cooperative stochastic game, drawing inspiration from the discrete formulation of the red-and-black gambling problem, as initially introduced by Dubins and Savage in 1965. We extend upon the work of Pontiggia from 2007, presenting a main theorem that broadens the conditions under which bold strategies by all players can achieve a Nash equilibrium. This is obtained through the introduction of a novel functional inequality, which serves as a key analytical tool in our study. This inequality enables us to circumvent the restrictive conditions of super-multiplicativity and super-additivity prevalent in the works of Pontiggia and others. We conclude this paper with a series of illustrative examples that demonstrate the efficacy of our approach, notably highlighting its ability to accommodate a broader spectrum of probability functions than previously recognized in the existing literature. [ABSTRACT FROM AUTHOR]

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation A X B = C has been extensively studied. However, there is currently limited information on matrix equation A X B = C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation A X B = C , and present the expression for the general solution when it is solvable. As an application, we derive the ϕ -Hermitian solutions for dual quaternion matrix equation A X A ϕ = C , where the ϕ -Hermitian extends the concepts of Hermiticity and η -Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper. [ABSTRACT FROM AUTHOR]

For wireless sensor network (WSN) coverage problems, since the sensing range of sensor nodes is a circular area with symmetry, taking symmetry into account when deploying nodes will help simplify problem solving. In addition, in view of two specific problems of high node deployment costs and insufficient effective coverage in WSNs, this paper proposes a WSN coverage optimization method based on the improved grey wolf optimizer with multi-strategies (IGWO-MS). As far as IGWO-MS is concerned, first of all, it uses Sobol sequences to initialize the population so that the initial values of the population are evenly distributed in the search space, ensuring high ergodicity and diversity. Secondly, it introduces a search space strategy to increase the search range of the population, avoid premature convergence, and improve search accuracy. And then, it combines reverse learning and mirror mapping to expand the population richness. Finally, it adds Levy flight to increase the disturbance and improve the probability of the algorithm jumping out of the local optimum. To verify the performance of IGWO-MS in WSN coverage optimization, this paper rasterizes the coverage area of the WSN into multiple grids of the same size and symmetry with each other, thereby transforming the node coverage problem into a single-objective optimization problem. In the simulation experiment, not only was IGWO-MS selected, but four other algorithms were also selected for comparison, namely particle swarm optimization (PSO), grey wolf optimizer (GWO), grey wolf optimization based on drunk walk (DGWO), and grey wolf optimization led by two-headed wolves (GWO-THW). The experimental results demonstrate that when the number of nodes for WSN coverage optimization is 20 and 30, the optimal coverage rate and average coverage rate using IGWO-MS are both improved compared to the other four comparison algorithms. To make this clear, in the case of 20 nodes, the optimal coverage rate of IGWO-MS is increased by 13.19%, 1.68%, 4.92%, and 3.62%, respectively, compared with PSO, GWO, DGWO, and GWO-THW; while IGWO-MS performs even better in terms of average coverage rate, which is 16.45%, 3.13%, 11.25%, and 6.19% higher than that of PSO, GWO, DGWO, and GWO-THW, respectively. Similarly, in the case of 30 nodes, compared with PSO, GWO, DGWO, and GWO-THW, the optimal coverage rate of the IGWO-MS is increased by 15.23%, 1.36%, 5.55%, and 3.66%; the average coverage rate is increased by 16.78%, 1.56%, 10.91%, and 8.55%. Therefore, it can be concluded that IGWO-MS has certain advantages in solving WSN coverage problems, which is reflected in that not only can it effectively improve the coverage quality of network nodes, but it also has good stability. [ABSTRACT FROM AUTHOR]

The objective of portfolio diversification is to reduce risk and potentially enhance returns by spreading investments across different asset classes. Existing portfolio diversification models have traditionally been trained on historical financial time series data. However, several issues arise with historical financial time series data, making it challenging to train models effectively to achieve the portfolio diversification objective: an insufficient amount of training data and the uncertainty deficiency problem, wherein the uncertainty that existed in the past is not visible in the present. Insufficient datasets, characterized by small data size, result in information asymmetry and compromise portfolio performance. This limitation underscores the importance of adopting a pattern-centric data augmentation approach, capable of unveiling hidden patterns and structures within the financial time series data. To address these challenges, this paper introduces the financial time series decomposition-based variational encoder-decoder (FED) method to augment financial time series data, overcoming the limitations of insufficient training data and providing a more realistic and dynamic simulation of the financial market environment. By decomposing the data into distinct components, such as trend, dispersion, and residual, FED leverages pattern-centric data augmentation within the financial time series data. In the environment generated using the FED method, this paper proposes a two-class portfolio diversification, called FED2Port. It integrates stochastic elements into the reward function, enabling a reinforcement learning algorithm to learn from a comprehensive spectrum of financial market uncertainties. The experimental results demonstrate that the proposed model significantly enhances portfolio performance. [ABSTRACT FROM AUTHOR]

Industrial control terminals play an important role in industrial control scenarios. Due to the special nature of industrial control networks, industrial control terminal systems are vulnerable to malicious attacks, which can greatly threaten the stability and security of industrial production environments. Traditional security protection methods for industrial control terminals have coarse detection granularity, and are unable to effectively detect and prevent attacks, lacking real-time responsiveness to attack events. Therefore, this paper proposes a real-time dynamic credibility evaluation mechanism based on program behavior, which integrates the matching and symmetry ideas of credibility evaluation. By conducting a real-time dynamic credibility evaluation of function call sequences and system call sequences during program execution, the credibility of industrial control terminal application program behavior can be judged. To solve the problem that the system calls generated during program execution are unstable and difficult to measure, this paper proposes a partition-based dynamic credibility evaluation method, dividing program behavior during runtime into function call behavior and system call behavior within function intervals. For function call behavior, a sliding window-based function call sequence benchmark library construction method is proposed, which matches and evaluates real-time measurement results based on the benchmark library, thereby achieving symmetry between the benchmark library and the measured data. For system call behavior, a maximum entropy system call model is constructed, which is used to evaluate the credibility of system call sequences. Experiment results demonstrate that our method performs better in both detection success rate and detection speed compared to the existing methods. [ABSTRACT FROM AUTHOR]

In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper. [ABSTRACT FROM AUTHOR]

Recently, transfer learning has gained popularity in the machine learning community. Transfer Learning (TL) has emerged as a promising paradigm that leverages knowledge learned from one or more related domains to improve prediction accuracy in a target domain with limited data. However, for time series forecasting (TSF) applications, transfer learning is relatively new. This paper addresses the need for empirical studies as identified in recent reviews advocating the need for practical guidelines for Transfer Learning approaches and method designs for time series forecasting. The main contribution of this paper is the suggestion of a comprehensive framework for Transfer Learning Sensitivity Analysis (SA) for time series forecasting. We achieve this by identifying various parameters seen from various angles of transfer learning applied to time series, aiming to uncover factors and insights that influence the performance of transfer learning in time series forecasting. Undoubtedly, symmetry appears to be a core aspect in the consideration of these factors and insights. A further contribution is the introduction of four TL performance metrics encompassed in our framework. These TL performance metrics provide insight into the extent of the transferability between the source and the target domains. Analyzing whether the benefits of transferred knowledge are equally or unequally accessible and applicable across different domains or tasks speaks to the requirement of symmetry or asymmetry in transfer learning. Moreover, these TL performance metrics inform on the possibility of the occurrence of negative transfers and also provide insight into the possible vulnerability of the network to catastrophic forgetting. Finally, we discuss a sensitivity analysis of an Ensemble TL technique use case (with Multilayer Perceptron models) as a proof of concept to validate the suggested framework. While the results from the experiments offer empirical insights into various parameters that impact the transfer learning gain, they also raise the question of network dimensioning requirements when designing, specifically, a neural network for transfer learning. [ABSTRACT FROM AUTHOR]

This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M , g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other geometrical features of l and (M , g) . It is mainly a review of known material but contains some novelties. For example, the brief discussion of the nature of wave surfaces (when viewed geometrically as wave fronts to a null ray direction) in Wave Surfaces Section is new in the sense that although it appeared in the author's work by the present author, it has not, to the best of his knowledge, appeared in this form anywhere else. Further, the work on conical symmetry and plane waves are, to the best of the author's knowledge, original with him from earlier papers and are reviewed here while the work on complete wave surface (sectional curvature-) symmetry is believed to be entirely new. Geometrical use of the sectional curvature function is employed in many places. The consequences of the various symmetry conditions imposed on the collection of all wave surfaces to a null direction spanned by a null vector l are described in terms of l spanning a principal null direction of the Weyl tensor (if non-zero) at the point concerned (in the sense of Petrov and Bel). [ABSTRACT FROM AUTHOR]

In this article, the symmetric operator L corresponding to the boundary value problem is represented as the difference of two commuting operators A and  B.  The uniqueness of the solution is guaranteed if the spectra of the operators A and B do not intersect and the domain of the operator B is given by non-degenerate boundary conditions. In contrast to the existing papers, the criterion for the uniqueness of the boundary value problem formulated in this paper is satisfied even when the system of root functions of the operator B does not form a basis in the corresponding space. At the same time, only the closedness of the linear operator A is required. [ABSTRACT FROM AUTHOR]