Symbolic regression, a type of machine learning technique, can efficiently disregard variables that are not significant to the final output, even if they were initially preselected as inputs. Various input parameters are tested in the three examples presented here, where the outputs are modeled using symbolic regression: estimating the middle plasma torch temperature used for waste gasification, the active energy of a solar power plant, and the diameter of a pipe with a known flow and pressure drop through it. Final highly accurate formulas are produced after numerous attempts with lower performances. The process for rejecting the parameters without or with limited influence is automatic and can be performed without human intervention and supervision. The results obtained using symbolic regression are easily interpretable by human experts. This approach shows how to use machine learning-based modeling as an additional tool for sensitivity analysis.

In this work, a new spectral Galerkin approach to solving the time-fractional diffusion-wave equation (TFDWE) with non-homogeneous initial and boundary conditions is presented. A suitable transformation is used to convert the TFDWE governed by non-homogeneous conditions into a modified one governed by homogeneous conditions. New basis functions in terms of specific shifted Horadam polynomials are used. Some new definite integral formulas that are crucial to the numerical implementation are developed, and the Galerkin scheme is analyzed in detail to obtain the approximate solutions. A thorough convergence and error analysis of the proposed expansion is established. A number of numerical experiments are carried out to show the scheme’s applicability and accuracy when compared to other methods.

Researchers have reported on prescribed-time stability (PTS) for delay systems, but they do not take into account the significant impulses phenomenon and focus on only single delay. To tackle these two aspects, we aimed to investigate PTS issues for nonlinear impulsive systems with multiple time-varying delays and uncertainties. By the Lyapunov-Krasovskii functional method, PTS criteria were established for multi-delay systems. Specifically speaking, an adaptive control strategy was proposed for multi-delay systems to achieve PTS through the integrated design of time-varying delay compensation and uncertainty handling, which could ensure system states and control inputs to precisely converge to the origin within the prescribed time frame. Furthermore, the proposed method significantly enhanced the system’s robustness against time-varying delays and uncertainties, thus overcoming the limitations of traditional methods in terms of convergence time and disturbance rejection capability. Finally, a simulation result was given to verify the feasibility and effectiveness of the proposed method.

In this study, a three-dimensional numerical model was developed to investigate the influence of obstacles on the hydrodynamic behavior of a serpentine flow field. Various obstacle geometries (rectangular, trapezoidal, triangular, and cylindrical), quantities (1–3 blocks), and positions (straight vs. curved channel sections) were systematically analyzed. Results show that rectangular obstacles enhance mean velocity but significantly increase pressure drop and reduce flow uniformity. In contrast, trapezoidal and cylindrical shapes offer a more balanced tradeoff, achieving improved uniformity and flow enhancement with moderate hydraulic penalties. Increasing obstacle number improves electrolyte velocity uniformity across all cases, though diminishing returns are observed beyond two blocks. Importantly, placing obstacles in curved sections of the serpentine field yields up to 9% higher uniformity compared to straight placements, without increasing pressure loss- leveraging pre-existing low-velocity regions to enhance distribution. These findings align with previous literature and highlight that optimized obstacle shape, number, and positioning can significantly improve mass transport and flow distribution in vanadium redox flow batteries (VRFBs). To complement the computational fluid dynamics (CFD) analysis, an artificial neural network (ANN) was trained to predict pressure drop using key geometric and flow features as inputs. The ANN demonstrated excellent agreement with numerical results and reduced the computational time required to obtain the results by 6 orders of magnitude.

We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, expressing them as the sums of powers of independent linear forms. It is based on Harrison’s center theory and consists of a criterion and a diagonalization algorithm. Detailed formulations and the computational complexity of each component of the technique are given. The complexity analysis focuses on the impacts of the number of variables and the degree of given polynomials. We show that this criterion runs in polynomial time, and the diagonalization process performs efficiently in numerical experiments. Other diagonalization techniques are reviewed and compared in terms of complexity.

The bursting and subthreshold resonance of mesencephalic trigeminal nucleus neurons play a critical role in bite force control and orofacial pain processing, yet their underlying dynamical mechanisms remain poorly understood. The nonlinear and ionic mechanisms are presented in the present paper. First, bifurcations from the resting state to bursting, modulated by persistent sodium current (I_NaP) and applied current (I_app), are obtained, including a Hopf bifurcation. Second, three typical bursting patterns are distinguished via codimension-2 bifurcations, and coexisting behaviors are acquired through fast/slow analysis. Modulated by I_NaP, the most common bursting pattern, similar to experimental observations, exhibits bursts interrupted by long quiescent states. In the fast subsystem, the limit cycle for the burst is far from the coexisting equilibrium for the quiescent state. Then, stochastic transitions between the two behaviors cannot be evoked, resulting in robustness to noise. Two other bursting patterns manifest transitions between bursts for a large limit cycle and subthreshold oscillation for a small limit cycle. Proximity between the two limit cycles allows noise to drive stochastic transitions, leading to noise-sensitive dynamics. The sensitivity is determined by the distance between the two cycles. Finally, subthreshold resonance evoked from the resting state is reproduced, which is mediated by potassium current. Enhanced I_NaP and I_app amplify the resonance amplitude and frequency by driving the resting state toward the Hopf bifurcation. The dynamics of bursting and resonance advance the understanding of sensorimotor processing and present potential targets for treating orofacial motor disorders.

Intelligent bearing fault diagnosis based on deep learning has immense potential. However, improving the noise immunity, generality, and accuracy of fault diagnosis methods is still challenging. This paper proposes a novel adaptive hybrid attention mechanism deep residual threshold network (AHA-RTN) for bearing fault diagnosis under various noise conditions. First, channel-wise and spatial attention were both integrated into residual blocks to capture multiscale information. Hybrid attention was obtained using the proposed adaptive attention module, which computes adjustment coefficients of each attentional mechanism. Next, a novel noise reduction activation function based on soft thresholding was incorporated to suppress noise. Finally, the method was validated on two distinct bearing datasets under various noise conditions. The results show that the proposed AHA-RTN has better noise immunity and accuracy than the other advanced multiscale convolutional neural networks.

Quantitative analysis of internet memes-digital cultural phenomena that propagate through online networks-remains an understudied domain in computational social science. Building upon established research that modeled meme popularity through ordinary differential equations, this study presents a novel machine learning approach to classify and predict meme popularity trajectories. Previous work identified four distinct post-peak patterns: smooth decay, oscillatory decay, plateau, and sustained growth. We significantly expanded the empirical foundation by constructing a comprehensive dataset of 2000+ memes, leveraging Google Trends time-series data. Our methodological framework employed a two-stage machine learning pipeline: first, implementing k-means clustering (k = 4) for unsupervised pattern discovery, followed by support vector classification for supervised learning. This approach enabled both validation of previously identified trajectory patterns and development of a predictive model for meme popularity evolution. Additionally, we conducted a systematic analysis of the relationship between meme taxonomic categories (e.g., catchphrases, viral videos) and their temporal popularity patterns. Our findings contribute to the emerging field of computational memetics and offer insights into the quantitative dynamics of online cultural transmission. The resulting classification model demonstrates robust predictive capabilities, with implications for understanding viral content dynamics in digital ecosystems.

We relate various characterizations of sandpile dynamics arising in the literature referred to as “Abelian sandpile models”, and we rigorously establish the sense in which they are commutative and associative as algebraic structures. In particular, associativity is approached from different perspectives: directly for the addition of configurations followed by stabilization; as a property of homomorphic images of semigroups; via the composition of operators on configurations; and, more generally, from an asynchronous perspective. We show how the existing formulations all arise within a common framework as substructures or homomorphic images of a non-commutative semigroup of operators. The appendix gives results on the algebraic complexity of sandpile semigroups, with 1) two different proofs determining the Krohn–Rhodes complexity of the finite Abelian sandpile models and all finite Abelian semigroups, 2) exact values of the aperiodic complexity measure for directed non- Abelian sandpile semigroups, and 3) exhibits new kinds of non-Abelian sandpile semigroups of higher Krohn–Rhodes complexity.

Colorization of grayscale images has found widespread applications across artistic, historical, scientific, medical, and industrial domains. Traditional manual colorization methods, however, are labor-intensive, time-consuming, and prone to subjective interpretation. In recent years, various deep learning (DL) approaches have been explored to automate the colorization process. Despite this progress, the efficacy and accuracy of these DL methods remain largely unexamined. One of the primary challenges is the accurate handling of color boundaries, which significantly affects the realism and visual clarity of the colorized output. In this study, we investigated the impact of different DL algorithms and training epochs on the quality of colorized images, comparing them to their corresponding ground truths. To explore these effects, a semantic-guided adversarial generative framework was employed, and five commonly used DL algorithms were compared.

In this work, an efficient scheme is proposed for the 2D damped sine-Gordon equation. The new scheme utilizes the unified weak Galerkin finite element method with or without stabilizer (UWG) in the spatial direction and the second-order explicit differentiation formula in the temporal direction. Both semi discrete schemes and fully discrete schemes are analyzed. First, we demonstrate the stability of the schemes. Subsequently, optimal error estimates are derived in the energy norm and the L² norm. Furthermore, by combining the proper orthogonal decomposition (POD) technique with the WG method, we develop a reduced-order algorithm, significantly improving computational efficiency. Finally, the theoretical results are validated by numerical experiments.

In this study, we explored a diffusive vegetation-sand model with Neumann boundary conditions, investigating the role of Turing instability in vegetation pattern formation. A priori estimates for steady-state solutions were established using the maximum principle and Poincaré inequality. Bifurcation analysis was performed for simple and double eigenvalue cases. By employing bifurcation theory, a local bifurcation was extended globally, and the direction of bifurcation was characterized. Double eigenvalue cases were analyzed through spatial decomposition and the implicit function theorem. Finally, numerical simulations validated and complemented the theoretical results.

In this paper, we find several expressions for the moments of the hyperbolic secant distribution and the moments of the sum of two independent distributions. They are expressed in terms of Euler and Bernoulli numbers, zeta values, an integral representation, and certain infinite series.

The fusion of infrared (IR) and visible (VIS) images aims to synthesize fused images with salient targets and enriched details. However, existing fusion methods face challenges in integrating modality-specific features. Accordingly, we proposed an image fusion method based on a dual-channel fusion strategy, termed DCGAN-Fuse. First, we created a dual-channel fusion strategy and constructed a dual-channel fusion module (DCFM) to integrate shared and complementary information across both modalities. Second, during the feature enhancement phase, we designed an attention-enhanced gradient retention module (AEGRM) to enhance edge feature extraction and enforce spatial consistency. Moreover, we used the multi-scale module (MSM) to capture fused features and avoid information loss from the two source images. We have improved the loss function by introducing the maximum intensity loss function for our proposed method. Experiments on public datasets demonstrated that our method generates fused images with highlighted infrared targets and enriched textures. Both subjective and objective assessments indicated that our DCGAN-Fuse is better than the other thirteen advanced algorithms.

Glaucoma, a leading cause of irreversible blindness, requires early detection to prevent progressive vision loss. Color fundus photography is a non-invasive and widely accessible modality for glaucoma screening; however, traditional manual interpretation is limited by subjectivity, time inefficiency, and inter-observer variability. This study proposes an optic disc (OD)/optic cup (OC)semantic feature pyramid network, a joint OD and OC segmentation model for glaucoma screening. The model extends the Semantic FPN architecture through three key enhancements: (1) a MaxViT backbone that incorporates multi-axis attention to reinforce local-global feature interaction and preserve boundary information during downsampling; (2) inception depthwise convolution modules embedded within MBConv blocks, which enables multi-scale convolution to expand receptive fields without compromising fine-grained details; (3) an optimized semantic FPN structure to improve the cross-scale feature alignment and multi-scale fusion. The proposed OD/OC-Semantic FPN was evaluated on five publicly available fundus image datasets (Drishti-GS, ORIGA, RIM-ONE DL, RIM-ONE-R3, and REFUGE), and its performance was compared against several state-of-the-art segmentation models (U-Net, DeepLabV3+, PSPNet, APCNet, semantic FPN-PoolFormer, and attention U-Net). The results show that the OD/OC-semantic FPN surpasses existing models across several metrics: dice coefficient, Mean Intersection over Union (mIoU), mean pixal accuracy (MPA), and classification accuracy, thus demonstrating superior structural precision for fundus analysis. Collectively, these results indicate that the OD/OC-Semantic FPN is a robust and generalizable tool for intelligent early detection of glaucoma.

The time-fractional Cable (TFC) equation constitutes a significant advancement of the classical Cable equation within the context of fractional calculus. In contrast to conventional numerical techniques such as finite difference and finite element methods, the barycentric interpolation method exhibits superior capability in handling the nonlocal properties inherent in fractional operators. This study thoroughly examines the principles and attributes of the barycentric interpolation method, integrating them with the unique aspects of the TFC equation to develop an appropriate matrix formulation. This transformation facilitates the conversion of the TFC equation into a solvable algebraic system. The proposed algorithm’s accuracy and convergence rate are meticulously evaluated. Numerical experiments are performed to underscore the benefits of this approach in solving the TFC equation, thereby confirming the efficacy of the error analysis and convergence assessment.

High-dimensional optimization problems face challenges from exponentially expanding search spaces and deceptive local optima resisting metaheuristics. In order to address these issues, a reinforcement learning-guided Animated Oat Optimization Algorithm with a dynamic niching strategy, called RLDN-AOO, is proposed in this research. RLDN-AOO offers the following major novelties: i) a mathematically formulated three-state dynamic niching mechanism that adaptively partitions the population, preserves diversity, and enhances the algorithm’s ability to escape local optima, and ii) a reinforcement learning strategy selection mechanism is proposed to address the issue of the algorithm’s inadequate dynamic adaptability. We compared it with state-of-the-art algorithms (CEC2017, Dim = 50, 100, 200, 500), including LSHADE-SPACMA, CMA-ES variants, and RL-based optimizers. In addition, we applied it in the optimization of BP neural networks. Experimental results showed that RLDN-AOO achieves competitive performance across most benchmarks and, in some cases, performs comparably to LSHADE-SPACMA variants. The source code of RLDN-AOO is openly accessible via https://github.com/robingit77/RLDN-AOO.

With the increasing prominence of autonomous vehicles in recent years, rapid and accurate environmental perception has become crucial for the operational safety and decision-making capabilities. To address the challenge of achieving an optimal balance between accuracy and real-time performance under in-vehicle computational constraints, this paper presented an efficient object detection algorithm for self-driving cars, which extracted the hierarchical cross-scale features based on a shifted-window attention mechanism. By integrating this improved feature representation with the more efficient feature fusion neck and detection head based on depth-wise separable convolution, the proposed approach significantly reduced model complexity and improves detection speed while maintaining near-identical detection accuracy. Experimental results demonstrate that this method simultaneously enhances processing speed and reduced model complexity while maintaining high detection precision, with floating-point operations reduced from 21.5 G to 6.0 G, a decrease of 15.5 G and an increase of 139 frames per second compared to YOLOv11s. This combination of efficiency and accuracy made the proposed algorithm particularly adaptable for resource-constraint self-driving systems.

In this paper, we first introduced the Riemann integral for an abstract-valued function from a finite closed real interval to a sequentially complete random Saks space and gave the fundamental theorem of calculus for an L⁰-Lipschitz function. Then we investigated some important properties peculiar to bi-continuous semigroups on a sequentially complete random Saks space. Finally, based on the above work, we established the Hille-Yosida generation theorem for such bi-continuous semigroups, which extends and improves several known results.

Ship imaging has an impact on the visual judgment of the steersman and influences ship navigation safety. Traditional image enhancement methods struggle under adverse conditions and fail to account for the physiological mechanisms of human visual perception. Therefore, a novel method was proposed to enhance ship imaging by combining a visual neural signal encoding mechanism (accomplished by multi-scale spiking neural networks) with a multi-scale frequency-domain stochastic resonance model. First, the noisy image is encoded by mapping the neuron pulse count per unit time, and then the encoded signal is directionally filtered by constructing a spatial dot-matrix dual-view perception receptive field model to achieve preliminary low-level noise reduction. Second, a stochastic resonance system is constructed and applied in series to enhance the decomposed multi-scale wavelet coefficients. Finally, considering the brightness characteristics of the visual system, the processed wavelet coefficients of each scale are inversely transformed and reconstructed. The reconstructed image is then fused with the image obtained by directional filtering of the spatial dot-matrix dual-view pathway receptive field model to produce the final enhanced image. According to the experimental results, compared with the original noisy image, the peak signal-to-noise ratio (PSNR) and visual information fidelity (VIF) improve by 27% and 30%, respectively. These findings indicate that the proposed method can effectively enhance ship images in a manner more consistent with the physiological characteristics of human visual imaging and signal processing.

In this article, we study a second-order numerical scheme for the Ericksen-Leslie system. A modified Crank-Nicolson temporal discretization is adopted, and the pressure projection approach is used to decouple the Stokes solver. The second-order convex-concave decomposition is applied to the chemical potential vector, in which the convex nonlinear term is updated by a modified Crank-Nicolson approximation, the expansive concave term is computed by an explicit Adams-Bashforth extrapolation, and the surface diffusion part is discretized by the standard Crank-Nicolson interpolation. Meanwhile, semi-implicit second-order approximations are taken for the convection terms, in both the momentum equation and the orientation vector evolutionary equation, as well as the coupled elastic stress terms. In fact, these semi-implicit terms could be represented as a monotone, linear operator of a vector potential, and its combination with the second order convex splitting approximation to the chemical potential yields a closed nonlinear system of equations for the orientation vector function. The unique solvability analysis of the numerical system is established with the help of the Browder-Minty lemma. A combination of the second order convex splitting approximation to chemical potential vector and the semi-implicit discretization for the coupled terms leads to the total energy stability estimate, composed of kinematic energy and internal elastic free energy. Moreover, an optimal rate convergence analysis and error estimate are provided, with second-order accuracy in both time and space. Some numerical simulation results of liquid crystals’ molecular dynamics are presented to study the scientific issue of defect annihilation. These results are consistent with the existing literature, and the energy evolution in the defect annihilation process is in agreement with the expectations. In addition, the influence of different parameters on the defect annihilation time instant is tested, and the results also agree with the physical laws.

This paper aims to investigate the initial boundary value problem for a class of Kirchhoff-type wave equations modified by Woinowsky-Krieger models, which can be used to describe the nonlinear extensible beam. Using the concave property of the function and a differential inequality, we estimate the upper bounds of the blowup time of the blowup solution at subcritical, critical, and high initial energy levels.

In this study, an inverse problem including the identification of a source function in a time- fractional diffusion equation with initial and mixed boundary conditions is investigated by employing the Laplace transform and the Daftardar-Gejji and Jafari method (DJM). Two kinds of inverse problems are considered, where the source function depends either on the temporal variable or the spatial variable. Initially, the Laplace and inverse Laplace transforms are applied to transform the fractional differential equation into an algebraic form. Subsequently, DJM is utilized to establish the solution of the converted problem by using the initial condition. Then, under the mixed boundary conditions, the unknown source function is explicitly determined. The suggested method’s ability to obtain the source function under no need for extra conditions and overmeasured data is one of its noteworthy features. The Banach fixed-point theorem and the energy estimate for fractional partial differential equations are also used to theoretically support the existence, uniqueness, and stability of the solution.

A stability analysis of a finite difference scheme was presented for the surface Allen–Cahn (AC) equation on curved surfaces. The surface was discretized by a triangular mesh, which accurately represented geometric features and enabled subsequent computational analysis. A discrete Laplace–Beltrami operator was used on this mesh, and it produced a simple and efficient discrete equation. The explicit time-stepping method, although straightforward, requires a moderate restriction on the time step. For practical applications, it is essential to determine the maximum value of this restriction. We derived the theoretical maximum value of the admissible time step that guarantees the discrete maximum principle and analyzed the stability of the explicit scheme under this condition. Numerical tests were performed to verify the theoretical prediction. The computational results confirmed that the proposed scheme maintains stability and reproduces expected interfacial dynamics on curved geometries. The analysis provides rigorous guidance for selecting stable time steps and demonstrates that the fully explicit scheme can be used as a reliable tool for simulating curvature-driven phase transitions and interfacial motion. This work provides a solid theoretical foundation for explicit numerical methods applied to the surface AC equation and contributes to the improvement of both efficiency and accuracy in computational studies involving complex geometries.

The Chermak-Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we determine finite groups with at most six subgroups not in the Chermak-Delgado lattice.

In this work, we propose an efficient and accurate numerical scheme for computing both the ground and first excited states of the nonlinear fractional Schrödinger eigenvalue problem. The method is based on a fractional gradient flow with discrete normalization, reformulated via the invariant energy quadratization (IEQ) approach to handle the nonlinear term in a linear way. Temporal discretization is performed using a second-order Crank-Nicolson scheme, while spatial discretization employs a Jacobi-Galerkin spectral method, yielding spectral convergence in space. We rigorously prove the discrete energy-decay property with respect to a modified energy functional. The resulting fully discrete scheme can compute different states simply by varying the initial condition, without altering the algorithmic framework. Numerical experiments confirm its high accuracy, efficiency, and robustness, and demonstrate its capability to capture intricate solution structures across a wide range of fractional orders and nonlinear interaction strengths.

Brain images are often disturbed by noise during acquisition, compromising subsequent medical analysis and reducing diagnostic accuracy. Effective denoising that preserves the structural details is therefore essential. This essay proposes a multi-branch convolutional neural network for brain image denoising, integrating a U-shaped network, dynamic convolution, and multi-scale feature extraction. The model includes an attention-enhanced encoder–decoder to improve feature representation, dynamic convolution with a sparse mechanism for adaptive global modeling, multi-scale dense residual blocks with depth-separable convolution to capture local details efficiently, and a multi-branch fusion strategy to process features at different scales in parallel and refine them. Experiments on brain image datasets demonstrate that the proposed method achieves superior denoising performance, effectively suppressing noise while retaining fine structural details. In conclusion, the network significantly enhances the quality of brain images and shows potential for improving the accuracy of subsequent medical image analysis and diagnosis.

The paper studies the existence of at least two positive solutions for a nonlinear differential equation with a fractional Riemann-Liouville derivative of variable order and nonlocal boundary conditions. To transform the original equation into an integral equation, the Green function is constructed and boundedness conditions for the Green function are obtained. A theorem on the existence of at least two positive solutions to the problem is proven. An example is given that shows the existence of two positive solutions, and approximation graphs are constructed for clarity.

Backpropagating action potentials (bpAPs) are retrograde electrical signals crucial for modulating synaptic plasticity. They play a pivotal role in regulating neuronal computation and memory formation. In dentate gyrus granule cells, which are key neuronal populations responsible for pattern separation and memory storage, bpAPs-mediated signaling is particularly important for integrating synaptic inputs and fine-tuning network activity. However, this neuronal population has marked structural and functional heterogeneity, including regular granule cells (GCs), semilunar granule cells (SGCs), and hilar ectopic granule cells (HEGCs). The influence of the distinct biophysical properties of these GC subtypes on backpropagation dynamics such as attenuation amplitude, velocity, and spatial spread remains unclear. Here, we utilized multi-compartment models of three types of GCs to systematically investigate the backpropagation efficiency across three metrics: attenuation amplitude, attenuation rate, and propagation distance. We found that higher dendritic K⁺ channel density drove strong attenuation of bpAPs in SGCs (highest rate, shortest propagation), whereas higher dendritic Na⁺ channel density in HEGCs minimized attenuation. Dendritic branching patterns modulated attenuation amplitude secondarily, while passive axial resistance had negligible effects. These findings establish dendritic active properties rather than morphology as the dominant regulator of attenuation intensity and reveal how activity regulation in these neuronal subtypes contributes to pattern separation and memory storage.

In this paper,we proposed an enhanced whale migration algorithm (EWMA) that integrates two novel strategies: Normal cloud model mutation (NCMM) and Fast Random Opposition- Based Learning. NCMM enables adaptive uncertainty management through expectation-entropy- hyperentropy mechanisms to balance exploration and exploitation. FROBL improves population diversity and convergence speed via oscillatory perturbations and nonlinear scaling. EWMA outperformed eight competing algorithms when evaluated on 23 benchmark functions and the CEC 2019, achieving optimal results on 18 of the 23 benchmark functions and all 10 CEC 2019 functions. It ranked first overall, significantly surpassing the other algorithms. Statistical analysis confirmed notable improvements in solution accuracy, convergence speed, and stability, with standard deviations 2–4 orders of magnitude lower than those of competitors. Engineering applications, including pressure vessel design, cantilever beams, and reinforced concrete beams, further demonstrated EWMA’s practical effectiveness, yielding optimal designs with improved constraint handling. EWMA offers a robust optimization tool for complex engineering problems requiring global search capability and precise local refinement.