Symmetry

In this study, a target-network update of deep reinforcement learning (DRL) based on mutual information (MI) and rewards is proposed. In DRL, updating the target network from the Q network was used to reduce training diversity and contribute to the stability of learning. If it is not properly updated, the overall update rate is reduced to mitigate this problem. Simply slowing down is not recommended because it reduces the speed of the decaying learning rate. Some studies have been conducted to improve the issues with the t-soft update based on the Student’s-t distribution or a method that does not use the target-network. However, there are certain situations in which using the Student’s-t distribution might fail or force it to use more hyperparameters. A few studies have used MI in deep neural networks to improve the decaying learning rate and directly update the target-network by replaying experiences. Therefore, in this study, the MI and reward provided in the experience replay of DRL are combined to improve both the decaying learning rate and the target-network updating. Utilizing rewards is appropriate for use in environments with intrinsic symmetry. It has been confirmed in various OpenAI gymnasiums that stable learning is possible while maintaining an improvement in the decaying learning rate. Full article

We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a scalar product that we put forward which is invariant under the ten-parameter conformal group in three-dimensional Euclidean space. This group is obtained as the static restriction (frequency $\omega =0$) of the symmetry group of Maxwell equations: The fifteen-parameter conformal group in 3+1 Minkowski spacetime. In an exemplary application, we compute the helicity and angular momentum squared stored in a magnetic Hopfion. Full article

We consider the Banach space $C[0,1]$, which is a symmetric Banach space, and prove the existence and approximation of numerical solutions for a broad class of third-order BVPs. Our approach is based on an integral operator that is constructed using Green’s function. The Banach contraction principle (BCP) is applied to guarantee a unique solution to our problem. Moreover, in order to find the value of the numerical solution, this new operator is embedded within the three-step Noor iterative scheme; we named this new iterative scheme the Noor–Green iterative scheme. We provide a convergence theorem for the proposed scheme by employing suitable restrictions on the parameters involved in the problem and in the scheme. The results of the stability of our scheme are also reported. It is worth mentioning that unlike the concept of stability in the classical sense, our result for stability is based on the concept of weak $w^2$ stability. In order to support our findings, we carried out various numerical experiments using different third-order BVPs. Finally, we report on the application of our iterative scheme to solve a class of fractional BVPs in the same symmetric Banach space. Our results are essentially new in the present literature and extend several of the results found in the current literature. Full article

The basic aspect of the research on coefficient problems for numerous families of univalent functions is to describe the coefficients of functions in a specific family by the coefficients of the Carathéodory functions. Thus, in utilizing the inequalities that are known for the class of Carathéodory functions, coefficient functionals may be examined. Several coefficient problems will be addressed in this study by utilizing the methodology for the abovementioned functions’ family. The family of starlike functions with respect to symmetric points connected to a three-leaf-shaped image domain is the topic of our investigation. Full article

Traditional methods for detecting damage in engineering structures often use offline static damage detection. To enable the real-time and precise identification of dynamic damage while maintaining symmetry in engineering structures, this study primarily concentrates on isotropic plate structures widely employed in engineering. Moreover, fiberglass board composite plates were opted as a specific research object. By utilizing the weak S₀ mode signals generated by low-frequency ultrasonic Lamb waves, the non-stationary A₀ wave signals in the composite symmetry plate structure are collected using the non-contact SLDV (Scanning Laser Doppler Vibrometer) technique. The frequency characteristic parameters in the vibration signals are obtained through HHT (Hilbert–Huang Transform) analysis, followed by filtering and noise reduction. Finally, the circular trajectory intersection method is employed to accurately locate dynamic damage sources in plate structures with different material properties, thereby validating the positioning effect of contact sensors in detecting impacts caused by random impulses. Full article

The present analysis deals with the study of the $f(Q,T)$ theory of gravity, which was recently considered by many cosmologists. In this theory of gravity, the action is taken as an arbitrary function $f(Q,T)$, where Q is non-metricity and T is the trace of the energy–momentum tensor for matter fluid. In this study, we took two different forms of the function $f(Q,T)$ as $f(Q,T)=a_{1}Q+a_{2}T$ and $f(Q,T)=a_3{Q}^2+a_{4}T$, and discussed the physical properties of the models. Also, we obtained the various cosmological parameters for the Friedmann–Lemaître–Robertson–Walker (FLRW) universe by defining the transit form of a scale factor that yielded the Hubble parameter in redshift form, as $H\left(z\right)=\frac{H_0}{(\lambda +1)}\left(\lambda +{(1+z)}^{\delta }\right)$. We obtained the best-fit values of model parameters using the least squares method for observational constraints on available datasets, like Hubble $H\left(z\right)$, Supernova SNe-Ia, etc., by applying the root mean squared error formula (RMSE). For the obtained approximate best-fit values of model parameters, we observed that the deceleration parameter $q\left(z\right)$ shows a signature-flipping (transition) point within the range of $0.623\le z_0\le 1.668$. Thus, it shows the decelerated expansion transiting into the accelerated universe expansion with $\omega \to -1$ as $z\to -1$ in the extreme future. Full article

Medical imaging plays an indispensable role in evaluating, predicting, and monitoring a range of medical conditions. Radiomics, a specialized branch of medical imaging, utilizes quantitative features extracted from medical images to describe underlying pathologies, genetic information, and prognostic indicators. The integration of radiomics with artificial intelligence presents innovative avenues for cancer diagnosis, prognosis evaluation, and therapeutic choices. In the context of oncology, radiomics offers significant potential. Feature selection emerges as a pivotal step, enhancing the clinical utility and precision of radiomics. It achieves this by purging superfluous and unrelated features, thereby augmenting model performance and generalizability. The goal of this review is to assess the fundamental radiomics process and the progress of feature selection methods, explore their applications and challenges in cancer research, and provide theoretical and methodological support for future investigations. Through an extensive literature survey, articles pertinent to radiomics and feature selection were garnered, synthesized, and appraised. The paper provides detailed descriptions of how radiomics is applied and challenged in different cancer types and their various stages. The review also offers comparative insights into various feature selection strategies, including filtering, packing, and embedding methodologies. Conclusively, the paper broaches the limitations and prospective trajectories of radiomics. Full article

In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation–extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method. Full article

Images taken in various real-world scenarios meet the symmetrical goal of simultaneously removing foreground rain-induced occlusions and restoring the background details. This inspires us to remember the principle of symmetry; real-world rain is a mixture of rain streaks and rainy haze and degrades the visual quality of the background. Current efforts formulate image rain streak removal and rainy haze removal as separate models, which disrupts the symmetrical characteristics of real-world rain and background, leading to significant performance degradation. To achieve this symmetrical balance, we propose a novel semisupervised coarse-to-fine guided generative adversarial network (Semi-RainGAN) for the mixture of rain removal. Beyond existing wisdom, Semi-RainGAN is a joint learning paradigm of the mixture of rain removal and attention and depth estimation. Additionally, it introduces a coarse-to-fine guidance mechanism that effectively fuses estimated image, attention, and depth features. This mechanism enables us to achieve symmetrically high-quality rain removal while preserving fine-grained details. To bridge the gap between synthetic and real-world rain, Semi-RainGAN makes full use of unpaired real-world rainy and clean images, enhancing its generalization to real-world scenarios. Extensive experiments on both synthetic and real-world rain datasets demonstrate clear visual and numerical improvements of Semi-RainGAN over sixteen state-of-the-art models. Full article

In this manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar $\mathfrak{b}$-metric space as a generalized version and expansion of the well-known results. We also provide some examples and applications of the integral equation to the solution for our main results. Full article

Developing low-cost and stable materials for converting solar energy into electricity is vital in meeting the world’s energy demand. Metal-organic frameworks (MOFs) have gained attention for solar cells due to their natural porous architectures and tunable chemical structures. They are built by high-symmetry metal clusters as secondary building units and organic carboxylate/azolate ligands as linkers. This review commences with an exploration of the synthetic methods of MOFs. Moreover, we discuss the various roles of MOFs, including photoanodes and counter electrodes in dye-sensitized solar cells and interfacial layers and charge carriers in perovskite solar cells. Additionally, studies involving the application of MOFs for OSC were additionally presented. Ultimately, burdensome tasks and possible directions for advancing MOFs-based nanomaterials are provided for solar cells. Full article

Quite often (e.g., using numerical methods), we are only able to find approximate solutions of some equations, and it is necessary to know the size of the difference between such approximate solutions and the mappings that satisfy the equation exactly. This issue is the main subject of the theory of Ulam stability, and it is related to other areas of research such as, e.g., shadowing, optimization, and approximation theory. In this expository paper, we present several selected outcomes on Ulam stability of difference equations, show possible extensions of them and indicate further directions for research. We also present and discuss some simple methods that allow improvement of several already known results concerning Ulam stability of some difference equations in normed or metric spaces and extend them to b-metric and 2-normed spaces. Our results show that the noticeable symmetry exists between the outcomes of this type in normed and metric spaces and those obtained by us for other spaces. In particular, we extend the result of Pólya and Szegö concerning the stability of equation $x_{n+m}=x_n+x_m$ for $m,n\in T$, where T means either the set of integers $\mathbb{Z}$ or the set of positive integers $\mathbb{N}$. We also consider the stability of equation $x_{n+p}+a_1{x}_{n+p-1}+\dots +a_p{x}_n+b_n=0$ (with a fixed positive integer p) and of two more general difference equations. Full article

A continuum mechanical theory with foundations in generalized Finsler geometry describes the complex anisotropic behavior of skin. A fiber bundle approach, encompassing total spaces with assigned linear and nonlinear connections, geometrically characterizes evolving configurations of a deformable body with the microstructure. An internal state vector is introduced on each configuration, describing subscale physics. A generalized Finsler metric depends on the position and the state vector, where the latter dependence allows for both the direction (i.e., as in Finsler geometry) and magnitude. Equilibrium equations are derived using a variational method, extending concepts of finite-strain hyperelasticity coupled to phase-field mechanics to generalized Finsler space. For application to skin tearing, state vector components represent microscopic damage processes (e.g., fiber rearrangements and ruptures) in different directions with respect to intrinsic orientations (e.g., parallel or perpendicular to Langer’s lines). Nonlinear potentials, motivated from soft-tissue mechanics and phase-field fracture theories, are assigned with orthotropic material symmetry pertinent to properties of skin. Governing equations are derived for one- and two-dimensional base manifolds. Analytical solutions capture experimental force-stretch data, toughness, and observations on evolving microstructure, in a more geometrically and physically descriptive way than prior phenomenological models. Full article

In recent years, researchers have looked at how tube-like nanostructures respond to moving loads and masses. However, no one has explored the scenario of a nanostructure embedded in a vibrating medium used for moving nano-objects. In this study, the governing equations of the problem are methodically derived using the nonlocal elasticity of Eringen as well as the Rayleigh and Reddy–Bickford beam theories. Analytical and numerical solutions are developed for capturing the nonlocal dynamic deflection of the nanostructure based on the moving nanoforce approach (excluding the inertia effect) and the moving nanomass approach (including the inertia effect), respectively. The results predicted by the established models are successfully verified with those of other researchers in some special cases. The results reveal that for low velocities of the moving nano-object in the absence of the medium excitation, the midspan deflection of the simply supported nanotube exhibits an almost symmetric time-history curve; however, by increasing the nano-object velocity or the medium excitation amplitude, such symmetry is violated, mainly due to the lateral inertia of the moving nano-object, as displayed by the corresponding three-dimensional plots. The study addresses the effects of the mass and velocity of the moving nano-object, amplitude, and frequency of the medium excitation, and the lateral and rotational stiffness of the nearby medium in contact with the nanostructure on the maximum dynamic deflection. The achieved results underscore the significance of considering both the inertial effect of the moving nano-object and the shear effect of stocky nanotubes embedded in vibrating media. This research can serve as a strong basis for conducting further investigations into the vibrational properties of more intricate tube-shaped nanosystems that are embedded in a vibrating medium, with the aim of delivering nano-objects. Full article

Lipschitz mapping appears inevitably in many branches of mathematics, especially in functional analysis, and leads to the study of new results in metric fixed point theory. Goebel and Sims (resp. Goebel and Japon-Pineda) introduced a class of the Lipschitz mappings termed as $(\alpha ,p)$-Liptschitz mappings and studied not only the modified form of the Lipschitz condition, but also the behavior of a finite number of their iterates. The purpose of this paper is to discuss the various types of $(\alpha ,p)$-contractions with cyclic representation that extend the results due to Banach, Kannan, and Chatterjea. Moreover, based on such types of contractions and the property of symmetry, we obtain some related fixed-point results in the setting of metric spaces. Some examples are studied to illustrate the validity of our obtained results. As an application of our results, we establish the existence of the solution to a class of Fredholm integral equations. Full article

The present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has been shown that the exact integration of the thermal diffusion equations is carried out in the Lin–Sidorov–Aristov class. This class of exact solutions is a generalization of the Ostroumov–Birich family of exact solutions. The use of the class of exact solutions by Lin–Sidorov–Aristov makes it possible to take into account not only the inhomogeneity of the pressure field, the temperature field and the concentration field, but also the inhomogeneous velocity field. The present review shows that there is a class of exact solutions for describing the flows of incompressible fluids, taking into account the Soret and Dufour cross effects. Accurate solutions are important for modeling and simulating natural, technical and technological processes. They make it possible to find new physical mechanisms of momentum transfer for the design of new types of equipment. Full article

We consider an isotropic homogeneous cosmological model with five interacting elements: first, the dynamic aether presented by a unit timelike vector field; second, the pseudoscalar field describing an axionic component of the dark matter; third, the cosmic dark energy, described by a rheologic fluid; fourth, the non-axionic dark matter coupled to the dark energy; and fifth, the gravity field. We show that the early evolution of the Universe described by this model can include two specific epochs: the first one can be characterized as a super-inflation epoch; the second epoch is associated with an oscillatory regime. The dynamic aether carries out a regulatory mission; the rheologic dark fluid provides the specific features of the spacetime evolution. The oscillations of the scale factor and of the Hubble function are shown to switch on the parametric (Floquet-type) mechanism of the axion number growth. Full article

The main purpose of this paper is to derive a new perturbation theory (PT) that has converging series. Such series arise in the nonlocal scalar quantum field theory (QFT) with fractional power potential. We construct a PT for the generating functional (GF) of complete Green functions (including disconnected parts of functions) $\mathcal{Z}\left[j\right]$ as well as for the GF of connected Green functions $\mathcal{G}\left[j\right]=ln\mathcal{Z}\left[j\right]$ in powers of coupling constant g. It has infrared (IR)-finite terms. We prove that the obtained series, which has the form of a grand canonical partition function (GCPF), is dominated by a convergent series—in other words, has majorant, which allows for expansion beyond the weak coupling g limit. Vacuum energy density in second order in g is calculated and researched for different types of Gaussian part $S_0\left[\varphi \right]$ of the action $S\left[\varphi \right]$. Further in the paper, using the polynomial expansion, the general calculable series for $\mathcal{G}\left[j\right]$ is derived. We provide, compare and research simplifications in cases of second-degree polynomial and hard-sphere gas (HSG) approximations. The developed formalism allows us to research the physical properties of the considered system across the entire range of coupling constant g, in particular, the vacuum energy density. Full article

Emotion recognition via electroencephalography (EEG) has been gaining increasing attention in applications such as human–computer interaction, mental health assessment, and affective computing. However, it poses several challenges, primarily stemming from the complex and noisy nature of EEG signals. Commonly adopted strategies involve feature extraction and machine learning techniques, which often struggle to capture intricate emotional nuances and may require extensive handcrafted feature engineering. To address these limitations, we propose a novel approach utilizing convolutional neural networks (CNNs) for EEG emotion recognition. Unlike traditional methods, our CNN-based approach learns discriminative cues directly from raw EEG signals, bypassing the need for intricate feature engineering. This approach not only simplifies the preprocessing pipeline but also allows for the extraction of more informative features. We achieve state-of-the-art performance on benchmark emotion datasets, namely DEAP and SEED datasets, showcasing the superiority of our approach in capturing subtle emotional cues. In particular, accuracies of 96.32% and 92.54% were achieved on SEED and DEAP datasets, respectively. Further, our pipeline is robust against noise and artefact interference, enhancing its applicability in real-world scenarios. Full article