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The free metaplectic transformation (FMT) is an n$$ n $$‐dimensional linear canonical transform. This transform is much useful, especially in multidimensional signal processing and applications. In this paper, our aim is to achieve an efficient time‐frequency representation of higher‐dimensional nonstationary signals by introducing the novel free metaplectic wave packet transform (FM‐WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$, based on the elegant convolution structure associated with the free metaplectic transforms. The FM‐WPT preserves the properties of classical wave packet transform (WPT) in L2(ℝn)$$ {L}^2\left({\mathrm{\mathbb{R}}}^n\right) $$ and has better mathematical properties. Further, the validity of the proposed transform is demonstrated via a lucid example. The preliminary analysis encompasses the derivation of fundamental properties of the novel FM‐WPT, including boundedness, reconstruction formula, Moyal's formula, and the reproducing kernel. To extend the scope of the study, we formulate several uncertainty inequalities, including Lieb's inequality, Pitt's inequality, logarithmic inequality, Heisenberg's uncertainty inequality, and Nazarov's uncertainty inequality for the proposed transform. [ABSTRACT FROM AUTHOR]

Summary: In this study, we propose an inverse design approach based on a neural network for a novel multiport power divider (MP‐PD) with complex geometry. The inverse design approach is obtaining geometry from the desired physical performance to address the challenge of conventional methods. We develop a hybrid neural network model for this inverse design. The backbone architecture incorporates a bidirectional long short‐term memory module, a multihead self‐attention module, and convolutional modules. This hybrid neural network is employed to capture the feature of physical performance and learn the relationship between the geometric structure of the proposed MP‐PD and its corresponding physical performance. Consider the design of the power divider as an end‐to‐end methodology that directly maps design requirements to optimal geometric parameters. The neural network transfers the designed process into multiple‐input‐multiple‐output. We adopt the network model to successfully predict 20 geometric parameters of MP‐PDs for two distinct operating frequencies. The two operating frequencies are those utilized in real engineering applications, which are 3.5 GHz in the 5G band and 2.45 GHz in the trackside communication band. The predicted MP‐PD improves the return loss and bandwidth by 8.05 dB and 0.25 GHz, respectively, over the desired performance. The experiments and comparisons demonstrate the effectiveness and accuracy of our inverse design approach. The efficiency and flexibility of design are also significantly improved by the hybrid neural network model. [ABSTRACT FROM AUTHOR]

Agriculture is important for the economy of any country, and India is considered to be an agricultural country. One of the primary goals of agriculture is to produce disease-free crops. Since ancient times, farmers and other planting specialists have had to contend with a variety of problems and current agricultural constraints, such as widespread cotton diseases. There is a great need for a rapid, efficient, economical, and reliable approach to diagnosing cotton infection in the agri-informatics area, as severe cotton disease may result in the loss of grain crops. This paper presents an advanced method that automates the detection and classification of diseased cotton leaves and plants through deep learning techniques applied to images. To address the challenge of supervised image classification, we employ a bagging ensemble technique consisting of five transfer learning models: InceptionV3, InceptionResNetV2, VGG16, MobileNet, and Xception. This ensemble approach was adopted to significantly improve the performance of each individual mode. The ETL-NET framework we introduced was thoroughly evaluated using two publicly accessible datasets. Specifically, it achieved an impressive accuracy rate of 99.48% and a sensitivity rate of 99% when applied to binary datasets. Additionally, on the multi-class dataset, the framework achieved an accuracy rate of 98.52% and a sensitivity rate of 99%. Our method outperformed the state-of-the-art techniques and displayed comparatively better results. Remarkably, our approach demonstrated even higher performance than widely used ensemble techniques, generally considered benchmarks in the field. [ABSTRACT FROM AUTHOR]

A novel approach to the construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of positive random variables, such as the exponential, Lindley, and gamma. Some existing distributions, like the uniform, the beta, and the Kummer-beta, are formulated with this method. Several new structures of density functions having potential for future applications in real-life problems are also provided. One of the new distributions, namely the LCG, is considered for detailed study along with a related distribution, namely the GCL. The moments, hazard rate, cumulative distribution function, stress-strength reliability, random sample generation using the quantile function, method of moments along with maximum likelihood estimation, and regression modeling are discussed for both the distributions. Real-life applications of the proposed models and the corresponding regression models show promising results. [ABSTRACT FROM AUTHOR]

In response to the inadequate utilization of prior information in current mural inpainting processes, leading to issues such as semantically unreliable inpaintings and the presence of artifacts in the inpainting area, a Dunhuang mural inpainting method based on reference guidance and multi‐scale feature fusion is proposed. First, the simulated broken mural, the mask image, and the reference mural are input into the model to complete the multi‐level embedding of patches and align the multi‐scale fine‐grained features of damaged murals and reference murals. Following the patch embedding module, a hybrid residual module is added based on hybrid attention to fully extract mural features. In addition, by continuing the residual concatenation of outputs of the hierarchical embedding module improves the ability of the model to represent deeper features, and improves the robustness and generalisation of the model. Second, the encoded features are fed into the decoder to generate decoded features. Finally, the convolutional tail is employed to propagate them and complete the mural painting. Experimental validation on the Dunhuang mural dataset demonstrates that, compared to other algorithms, this model exhibits higher evaluation metrics in the inpainting of extensively damaged murals and demonstrates overall robustness. In terms of visual effects, the results of this model in the inpainting process exhibit finer textures, richer semantic information, more coherent edge structures, and a closer resemblance to authentic murals. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) have shown great performance in computer vision tasks, from image classification to pattern recognition. However, CNNs′${\rm CNNs}^{\prime }$ superior performance arises at the expense of high computational costs, which restricts their employment in real‐time decision‐making applications. Computationally intensive convolutions can be offloaded to optical metasurfaces, enabling sub‐picosecond latency and nearly zero energy consumption, but the currently reported approaches require additional bulk optics and can only process polarized light, which limits their practical usages in integrated lightweight systems. To solve these challenges, a novel design of the metasurface‐based optical convolutional accelerator is experimentally demonstrated, offering an ultra‐compact volume of 0.016 mm3${\rm mm}^{3}$, a low cross‐talk of ‐20 dB, polarization insensitivity, and is capable of implementing multiple convolution operations and extracting simultaneously various features from light‐encoded images. The ultra‐compact metasurface‐based optical accelerator can be compactly integrated with a digital imaging system to constitute an optical‐electronic hybrid CNN, which experimentally achieves a consistent accuracy of 96 % in arbitrarily polarized MNIST digits classification. The proposed ultra‐compact metasurface‐based optical convolutional accelerator paves the way for power‐efficient edge‐computing platforms for a range of machine vision applications. [ABSTRACT FROM AUTHOR]

A bounded linear operator T on a Banach space X is called a convex-cyclic operator if there exists a vector $ x \in X $ x ∈ X such that the convex hull of $ Orb(T, x) $ O r b (T , x) is dense in X. In this paper, for given an aperiodic element g in a locally compact group G, we give some sufficient conditions for a weighted translation operator $ T_{g,w}: f \mapsto w\cdot f*\delta _g $ T g , w : f ↦ w ⋅ f ∗ δ g on $ \mathfrak {L}^{p}(G) $ L p (G) to be convex-cyclic. A necessary condition is also studied. At the end, to explain the obtained results, some examples are given. [ABSTRACT FROM AUTHOR]

Let G be a locally compact Hausdorff group, and let P(G) denote the class of all regular probability measures on G. It is well known that P(G) forms a semigroup under the convolution of measures. In this paper, we prove that P(G) is not algebraically regular in the sense that not every element has a generalized inverse. Additionally, we attempt to identify algebraically regular elements in some exceptional cases. Several supporting examples are provided to justify these assumptions. [ABSTRACT FROM AUTHOR]

Illusions are like holes in our effortless visual mechanism through which we can peep into the internal mechanisms of the brain. Scientists attempted to explain underlying physiological, physical, and cognitive mechanisms of illusions by the receptive field hierarchical organizations, information sampling, filtering, etc. Some antagonistic illusions cannot be explained by them and for this, deep learning networks were used recently as a model for illusion perception. To further broaden the scope of the perceptual functionality in the brightness contrast genre, handle the background removal effects on some illusions that reduce the illusory effects, and replicate the antagonistic illusions with the same parameter setup, we have used Convolutional Neural Network, Autoencoder, U-Net, and U-Net++ models for replicating the visual illusions. The networks are specialized in low-level vision tasks like De-noising, De-blurring, and a combination of both. A high number of brightness contrast visual illusions are tested on all the networks and most of the outcomes significantly matched human perceptions. Overall, our method will guide the development of neurobiological frameworks which might enrich the computational neuroscience study by distilling some biological principles. On the other hand, the machine learning community will benefit from knowing the inherent flaws of the networks so that the true image of reality can be taken into consideration, especially in imaging situations where experts too can be deceived. [ABSTRACT FROM AUTHOR]

AbstractThe SARS-CoV-2 virus reportedly originated in Wuhan in 2019, causing the coronavirus outbreak (COVID-19), which was technically designated as a global epidemic. Numerous studies have been carried out to diagnose and treat COVID-19 throughout the midst of the disease’s spread. However, the genetic similarity between COVID-19 and other types of coronaviruses makes it challenging to differentiate between them. Therefore it’s essential to swiftly identify if an epidemic is brought on by a brand-new virus or a well-known disease. In the present article, the DeepCoV deep-learning (DL) approach utilizes layered convolutional neural networks (CNNs) to classify viral serious acute respiratory syndrome coronavirus 2 (SARS-CoV-2) besides other viral diseases. Additionally, various motifs linked with SARS-CoV-2 can be located by examining the computational filter processes. In identifying these important motifs, DeepCoV reveals the transparency of CNNs. Experiments were conducted using the 2019nCoVR datasets, and the results indicate that DeepCoV performed more accurately than several benchmark ML models. Additionally, DeepCoV scored its maximum area under the precision-recall curve (AUCPR) and receiver operating characteristic curve (AUC-ROC) at 98.62% and 98.58%, respectively. Overall, these investigations provide strong knowledge of the employment of deep learning (DL) algorithms as a crucial alternative to identifying SARS-CoV-2 and identifying patterns of disease in the SARS-CoV-2 genes. [ABSTRACT FROM AUTHOR]

Traditional electronic processors often struggle with bandwidth limitations and high power consumption when executing extensive linear operations for deep learning tasks. Optical computing has emerged as a promising alternative, offering parallel and energy‐efficient computation capabilities. Yet, the development of high‐density optical computing architectures on integrated photonic platforms remains limited, hindered by constraints in neuron scalability and control engineering complexities. Addressing these challenges, this work presents a diffraction‐driven multi‐kernel optical convolution unit (MOCU) that enables on‐chip parallel convolution processing. By utilizing cascaded silica 1D metalines as pre‐trained large‐scale weights and employing spatial multiplexing at the output, MOCU allows simultaneous passive computation of diverse convolutions within a single unit. This architecture facilitates the construction of optical convolutional neural networks (OCNNs), enabling efficient machine vision processing with a streamlined design. To mitigate errors in MOCU‐embedded OCNNs, a lightweight electronic neural network operates concurrently to calibrate systematic deviations via a low‐rank adaptation (LoRA) algorithm, with minimal overhead. The fabricated MOCU chip demonstrates the highest independent 8‐kernel convolutions in parallel, each with a 3×3$3\times 3$ kernel size and occupying just 0.06 mm2${\rm mm}^2$. This architecture effectively merges photonic and electronic technologies, offering a scalable design pathway for energy‐efficient, high‐density deep learning hardware. [ABSTRACT FROM AUTHOR]

Human action recognition based on graph convolutional networks (GCNs) is one of the hotspots in computer vision. However, previous methods generally rely on handcrafted graph, which limits the effectiveness of the model in characterising the connections between indirectly connected joints. The limitation leads to weakened connections when joints are separated by long distances. To address the above issue, the authors propose a skeleton simplification method which aims to reduce the number of joints and the distance between joints by merging adjacent joints into simplified joints. Group convolutional block is devised to extract the internal features of the simplified joints. Additionally, the authors enhance the method by introducing multi‐scale modelling, which maps inputs into sequences across various levels of simplification. Combining with spatial temporal graph convolution, a multi‐scale skeleton simplification GCN for skeleton‐based action recognition (M3S‐GCN) is proposed for fusing multi‐scale skeleton sequences and modelling the connections between joints. Finally, M3S‐GCN is evaluated on five benchmarks of NTU RGB+D 60 (C‐Sub, C‐View), NTU RGB+D 120 (X‐Sub, X‐Set) and NW‐UCLA datasets. Experimental results show that the authors' M3S‐GCN achieves state‐of‐the‐art performance with the accuracies of 93.0%, 97.0% and 91.2% on C‐Sub, C‐View and X‐Set benchmarks, which validates the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Fractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as -convolution operators with power law kernels are found to have the largest domains of definition. As a result, extending domains from functions to distributions via convolution operators contributes to far reaching unifications of many previously existing definitions of fractional integrals and derivatives. Weyl fractional operators are thereby extended to distributions using the method of adjoints. In addition, discretized fractional calculus and fractional calculus of periodic distributions can both be formulated and understood in terms of -convolution. [ABSTRACT FROM AUTHOR]

This paper considers a chief interface between mathematical programming and economics, namely: money-based trade of perfectly divisible and transferable goods. Three important and related features are singled out here: first, convexity enters via acceptable payments, second, convolution of monetary criteria secures Pareto efficiency, and third, competitive equilibrium obtains when agents' subdifferentials intersect. [ABSTRACT FROM AUTHOR]

Benefiting from self-attention mechanism and convolutional operation, numerous lightweight Transformer-based single image super-resolution (SISR) approaches have made considerable breakthroughs in performance. Nevertheless, higher computational costs of self-attention and parametric overheads of convolution still limit the deployment of these methods on low-budget devices. To tackle the above issues, based on the sequentially cascaded attention and convolution-cooperative blocks (ACCBs), we propose an attention and convolution-cooperative network (ACCNet) for lightweight image super-resolution (SR). Specifically, in each ACCB, to alleviate the computational burden of self-attention mechanism, we propose a multi-group window self-attention (MGWSA), which achieves self-attention calculation on different groups of features via different window sizes. To implement a lightweight convolutional operation that assists self-attention for local feature extraction, we propose a residual blueprint separable convolution (RBSC), which combines the advantages of efficient convolution and residual learning. Additionally, an enhanced multi-layer perceptron (EMLP) is designed to strengthen the representation of features spatially. The contrast-aware channel attention (CCA) is introduced to exploit the beneficial interdependency among channels. Compared to other lightweight state-of-the-art SR methods, the better trade-off between model complexity and performance in our ACCNet is demonstrated by extensive experiments. [ABSTRACT FROM AUTHOR]

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including rotations requires sampling the whole space of rotations, repeating the computation of the correlation each time.This article develops an alternative mathematical theory to handle efficiently, at the same time, rotations and translations. Our proposal has a reduced computational complexity because it does not require to repeatedly sample the space of rotations. To do so, we integrate the information relative to all rotated versions of the template into a unique symmetric tensor template -which is computed only once per template-. Afterward, we demonstrate that the correlation between the image to be processed with the independent tensor components of the tensorial template contains enough information to recover template instance positions and rotations. Our proposed method has the potential to speed up conventional template matching computations by a factor of several magnitude orders for the case of 3D images. [ABSTRACT FROM AUTHOR]

In this paper, we define a new class R t , δ , υ m , n , σ (A , B) of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function G − 1 when G ∈ R t , δ , υ m , n , σ (A , B) . Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions. [ABSTRACT FROM AUTHOR]

In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk E. For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated. [ABSTRACT FROM AUTHOR]

Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples. [ABSTRACT FROM AUTHOR]

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The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell‐wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high‐order and high‐smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points. [ABSTRACT FROM AUTHOR]

Room impulse responses (RIRs) are used in several applications, such as augmented reality and virtual reality. These applications require a large number of RIRs to be convolved with audio, under strict latency constraints. In this paper, we consider the compression of RIRs, in conjunction with fast time-domain convolution. We consider three different methods of RIR approximation for the purpose of RIR compression and compare them to state-of-the-art compression. The methods are evaluated using several standard objective quality measures, both channel-based and signal-based. We also propose a novel low-rank-based algorithm for fast time-domain convolution and show how the convolution can be carried out without the need to decompress the RIR. Numerical simulations are performed using RIRs of different lengths, recorded in three different rooms. It is shown that compression using low-rank approximation is a very compelling option to the state-of-the-art Opus compression, as it performs as well or better than on all but one considered measure, with the added benefit of being amenable to fast time-domain convolution. [ABSTRACT FROM AUTHOR]

In this article, we investigate meromorphic univalent harmonic functions having a simple pole at the origin. First we establish sufficient conditions for the univalence of function f within the broader class of meromorphic harmonic functions. Then, we derive coefficient estimate for some geometric subclasses of meromorphic univalent harmonic functions. Subsequently, we provide several necessary and sufficient conditions for f to be hereditarily λ -spirallike. Finally, we offer a comprehensive characterization of hereditarily meromorphic harmonic Archimedean and hyperbolic spirallike functions. [ABSTRACT FROM AUTHOR]

Skeleton‐based action recognition has received much attention and achieved remarkable achievements in the field of human action recognition. In time series action prediction for different scales, existing methods mainly focus on attention mechanisms to enhance modelling capabilities in spatial dimensions. However, this approach strongly depends on the local information of a single input feature and fails to facilitate the flow of information between channels. To address these issues, the authors propose a novel Temporal Channel Reconfiguration Multi‐Graph Convolution Network (TRMGCN). In the temporal convolution part, the authors designed a module called Temporal Channel Fusion with Guidance (TCFG) to capture important temporal information within channels at different scales and avoid ignoring cross‐spatio‐temporal dependencies among joints. In the graph convolution part, the authors propose Top‐Down Attention Multi‐graph Independent Convolution (TD‐MIG), which uses multi‐graph independent convolution to learn the topological graph feature for different length time series. Top‐down attention is introduced for spatial and channel modulation to facilitate information flow in channels that do not establish topological relationships. Experimental results on the large‐scale datasets NTU‐RGB + D60 and 120, as well as UAV‐Human, demonstrate that TRMGCN exhibits advanced performance and capabilities. Furthermore, experiments on the smaller dataset NW‐UCLA have indicated that the authors' model possesses strong generalisation abilities. [ABSTRACT FROM AUTHOR]

The Geometric Theory of Analytic Functions was initially developed for the space of functions that are analytic in the unit disk. The convexity and starlikeness of functions are the first geometric ideas considered in this theory. We can notice a symmetry between the subjects considered in the space of analytic functions and those in the space of harmonic functions. In the presented paper, we consider the starlikeness of functions in the space of meromorphic harmonic functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove explicit asymptotic formulae for some functions used in sieve methods and show that there exists no odd multiperfect number of abundancy four whose squared part is cubefree. [ABSTRACT FROM AUTHOR]

We study in this paper the monotonicity properties of the numerical solutions to Volterra integral equations with nonincreasing completely positive kernels on nonuniform meshes. There is a duality between the complete positivity and the properties of the complementary kernel being nonnegative and nonincreasing. Based on this, we propose the “complementary monotonicity” to describe the nonincreasing completely positive kernels, and the “right complementary monotone” (R-CMM) kernels as the analogue for nonuniform meshes. We then establish the monotonicity properties of the numerical solutions inherited from the continuous equation if the discretization has the R-CMM property. Such a property seems weaker than log-convexity and there is no restriction on the step size ratio of the discretization for the R-CMM property to hold. [ABSTRACT FROM AUTHOR]

In this article, we make use of convex analytic functions Ha(z) = [1/(1 - a)] log[(1 - az)/(1 - z)], a - ℝ, |a| ≤ 1, a ≠ 1 and starlike analytic functions Lb(z) = z/[(1 - bz)(1 - z)], b - ℝ, |b| ≤ 1, to construct univalent harmonic functions by means of a transformation on some normalized univalent analytic functions. Besides exploring mapping properties of harmonic functions so constructed, we establish sufficient conditions for their harmonic convolutions or Hadamard products to be locally univalent and sense preserving, univalent and convex in some direction. [ABSTRACT FROM AUTHOR]

In this work, we define the composition of wavelet transforms and obtain its Parsevals's identity. Furthermore, we discuss the convolution operator and continuous Dunkl wavelet transform as time-invariant filters. The physical interpretation and potential application of time-invariant filter involving Fredholm type integral are obtained. [ABSTRACT FROM AUTHOR]

The main objective of this work is to introduce the generalized convolution with trigonometric weighted $ \gamma =\sin y $ γ = sin ⁡ y involving the Fourier cosine–sine and Kontorovich–Lebedev transforms, and to study its fundamental results. We establish the boundedness properties in a two-parametric family of Lebesgue spaces for this convolution operator. Norm estimation in the weighted $ L_p $ L p space is obtained and applications of the corresponding class of convolution integro-differential equations are discussed. The conditions for the solvability of these equations in $ L_1 $ L 1 space are also founded. [ABSTRACT FROM AUTHOR]

This paper gives new expansions of characteristic functions of convolution of symmetric probability distributions with an explicit estimate of the remainder. [ABSTRACT FROM AUTHOR]

In response to the challenges of small-size defects and low recognition rates in Printed Circuit Boards (PCBs), as well as the need for lightweight detection models that can be embedded in portable devices, this paper proposes an improved defect detection method based on a lightweight shared convolutional head using YOLOv8n. Firstly, the Spatial and Channel reconstruction Convolution (SCConv) is embedded into the Cross Stage Partial with Convolutional Layer Fusion (C2f) structure of the backbone network, which reduces redundant computations and enhances the model's learning capacity. Secondly, an adaptive feature selection module is integrated to improve the network's ability to recognize small targets. Subsequently, a Shared Lightweight Convolutional Detection (SLCD) Head replaces the original Decoupled Head, reducing the model's computational complexity while increasing detection accuracy. Finally, the Weighted Intersection over Union (WIoU) loss function is introduced to provide more precise evaluation results and improve generalization capability. Comparative experiments conducted on a public PCB dataset demonstrate that the improved algorithm achieves a mean Average Precision (mAP) of 98.6% and an accuracy of 99.8%, representing improvements of 3.8% and 3.1%, respectively, over the original model. The model size is 4.1 M, and its FPS is 144.1, meeting the requirements for real-time and lightweight portable deployment. [ABSTRACT FROM AUTHOR]

Abstract In response to the inadequate utilization of prior information in current mural inpainting processes, leading to issues such as semantically unreliable inpaintings and the presence of artifacts in the inpainting area, a Dunhuang mural inpainting method based on reference guidance and multi‐scale feature fusion is proposed. First, the simulated broken mural, the mask image, and the reference mural are input into the model to complete the multi‐level embedding of patches and align the multi‐scale fine‐grained features of damaged murals and reference murals. Following the patch embedding module, a hybrid residual module is added based on hybrid attention to fully extract mural features. In addition, by continuing the residual concatenation of outputs of the hierarchical embedding module improves the ability of the model to represent deeper features, and improves the robustness and generalisation of the model. Second, the encoded features are fed into the decoder to generate decoded features. Finally, the convolutional tail is employed to propagate them and complete the mural painting. Experimental validation on the Dunhuang mural dataset demonstrates that, compared to other algorithms, this model exhibits higher evaluation metrics in the inpainting of extensively damaged murals and demonstrates overall robustness. In terms of visual effects, the results of this model in the inpainting process exhibit finer textures, richer semantic information, more coherent edge structures, and a closer resemblance to authentic murals.

Abstract Accurate segmentation of retinal blood vessels is crucial for enhancing diagnostic efficiency and preventing disease progression. However, the small size and complex structure of retinal blood vessels, coupled with low contrast in corresponding fundus images, pose significant challenges for this task. We propose a novel approach for retinal vessel segmentation, which combines the transformer and convolutional dual-path decoding U-Net (TCDDU-Net). We propose the selective dense connection swin transformer block, which converts the input feature map into patches, introduces MLPs to generate probabilities, and performs selective fusion at different stages. This structure forms a dense connection framework, enabling the capture of long-distance dependencies and effective fusion of features across different stages. The subsequent stage involves the design of the background decoder, which utilizes deformable convolution to learn the background information of retinal vessels by treating them as segmentation objects. This is then combined with the foreground decoder to form a dual-path decoding U-Net. Finally, the foreground segmentation results and the processed background segmentation results are fused to obtain the final retinal vessel segmentation map. To evaluate the effectiveness of our method, we performed experiments on the DRIVE, STARE, and CHASE datasets for retinal vessel segmentation. Experimental results show that the segmentation accuracies of our algorithms are 96.98, 97.40, and 97.23, and the AUC metrics are 98.68, 98.56, and 98.50, respectively.In addition, we evaluated our methods using F1 score, specificity, and sensitivity metrics. Through a comparative analysis, we found that our proposed TCDDU-Net method effectively improves retinal vessel segmentation performance and achieves impressive results on multiple datasets compared to existing methods.

Abstract Human action recognition based on graph convolutional networks (GCNs) is one of the hotspots in computer vision. However, previous methods generally rely on handcrafted graph, which limits the effectiveness of the model in characterising the connections between indirectly connected joints. The limitation leads to weakened connections when joints are separated by long distances. To address the above issue, the authors propose a skeleton simplification method which aims to reduce the number of joints and the distance between joints by merging adjacent joints into simplified joints. Group convolutional block is devised to extract the internal features of the simplified joints. Additionally, the authors enhance the method by introducing multi‐scale modelling, which maps inputs into sequences across various levels of simplification. Combining with spatial temporal graph convolution, a multi‐scale skeleton simplification GCN for skeleton‐based action recognition (M3S‐GCN) is proposed for fusing multi‐scale skeleton sequences and modelling the connections between joints. Finally, M3S‐GCN is evaluated on five benchmarks of NTU RGB+D 60 (C‐Sub, C‐View), NTU RGB+D 120 (X‐Sub, X‐Set) and NW‐UCLA datasets. Experimental results show that the authors’ M3S‐GCN achieves state‐of‐the‐art performance with the accuracies of 93.0%, 97.0% and 91.2% on C‐Sub, C‐View and X‐Set benchmarks, which validates the effectiveness of the method.

In this paper, we define a new class $ \mathcal{R}_{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $ of holomorphic functions in the open unit disk defined connected with the combination binomial series and Babalola operator using the differential subordination with Janowski-type functions. Using the well-known Carathéodory's inequality for function with real positive parts and the Keogh-Merkes and Ma-Minda's in equalities, we determined the upper bound for the first two initial coefficients of the Taylor-Maclaurin power series expansion. Then, we found an upper bound for the Fekete-Szegö functional for the functions in this family. Further, a similar result for the first two coefficients and for the Fekete-Szegő inequality have been done the function $ \mathcal{G}^{-1} $ when $ \mathcal{G}\in \mathcal{R} _{t, \delta, \upsilon }^{m, n, \sigma }\left(\mathcal{A}, \mathcal{B}\right) $. Next, for the functions of these newly defined family we determine coefficient estimates, distortion bounds, radius problems, and the radius of starlikeness and close-to-convexity. The novelty of the results is that we were able to investigate basic properties of these new classes of functions using simple methods and these classes are connected with the new convolution operator and the Janowski functions.

Abstract Skeleton‐based action recognition has received much attention and achieved remarkable achievements in the field of human action recognition. In time series action prediction for different scales, existing methods mainly focus on attention mechanisms to enhance modelling capabilities in spatial dimensions. However, this approach strongly depends on the local information of a single input feature and fails to facilitate the flow of information between channels. To address these issues, the authors propose a novel Temporal Channel Reconfiguration Multi‐Graph Convolution Network (TRMGCN). In the temporal convolution part, the authors designed a module called Temporal Channel Fusion with Guidance (TCFG) to capture important temporal information within channels at different scales and avoid ignoring cross‐spatio‐temporal dependencies among joints. In the graph convolution part, the authors propose Top‐Down Attention Multi‐graph Independent Convolution (TD‐MIG), which uses multi‐graph independent convolution to learn the topological graph feature for different length time series. Top‐down attention is introduced for spatial and channel modulation to facilitate information flow in channels that do not establish topological relationships. Experimental results on the large‐scale datasets NTU‐RGB + D60 and 120, as well as UAV‐Human, demonstrate that TRMGCN exhibits advanced performance and capabilities. Furthermore, experiments on the smaller dataset NW‐UCLA have indicated that the authors’ model possesses strong generalisation abilities.

In this article, using the Sǎlǎgean operator, we introduced three new subclasses of bi-univalent functions associated with bounded boundary rotation in open unit disk $ \mathbb{E}. $ For these new classes, we first obtain initial Taylor-Maclaurin's coefficient bounds. Furthermore, the famous Fekete-Szegö inequality was also derived for these new subclass functions. Some improved results, when compared with those available in the literature, are also stated.

Our aim was to develop a new class of bi starlike functions by utilizing the concept of subordination, driven by the idea of multiplicative calculus, specifically multiplicative derivatives. Several restrictions were imposed, which were indeed strict constraints, because we have tried to work within the current framework or the design of analytic functions. To make the study more versatile, we redefined our new class of function with Miller-Ross Poisson distribution (MRPD), in order to increase the study's adaptability. We derived the first coefficient estimates and Fekete-Szegő inequalities for functions in this new class. To demonstrate the characteristics, we have provided a few examples.

Abstract Room impulse responses (RIRs) are used in several applications, such as augmented reality and virtual reality. These applications require a large number of RIRs to be convolved with audio, under strict latency constraints. In this paper, we consider the compression of RIRs, in conjunction with fast time-domain convolution. We consider three different methods of RIR approximation for the purpose of RIR compression and compare them to state-of-the-art compression. The methods are evaluated using several standard objective quality measures, both channel-based and signal-based. We also propose a novel low-rank-based algorithm for fast time-domain convolution and show how the convolution can be carried out without the need to decompress the RIR. Numerical simulations are performed using RIRs of different lengths, recorded in three different rooms. It is shown that compression using low-rank approximation is a very compelling option to the state-of-the-art Opus compression, as it performs as well or better than on all but one considered measure, with the added benefit of being amenable to fast time-domain convolution.

Special functions and special polynomials have been used and studied widely in the context of Geometric function theory of Complex Analysis by the many authors. Here, in our present investigations, making use of the convolution, we first introduce a new subclass of Bazilevivč bi-univalent functions involving the Bernoulli Polynomials. We then find the first two Taylor-Maclaurin coefficient [Formula: see text] and [Formula: see text] for our defined functions class. We then calculate the bounds for the Fekete Szegö inequality for the defined function class. Also some known consequences of our main results are highlighted in the form of Corollaries.

Neural networks are widely used in critical environments such as healthcare, autonomous vehicles, or video surveillance. To ensure the safety of the systems that rely on their functionality, it is essential to validate their correct behaviour in the presence of faults. This paper studies the behaviour of state-of-the-art neural network models with fault injection in their weights. For this purpose, we analyse the sensitivity of these models and identify the impact of bit flips on their accuracy. To mitigate the effects of faults, we introduce two mechanisms that leverage bit-level redundancy for protection. The first mechanism, Fixed Protection, safeguards consecutive sets of bits, while the second, Variable Protection, targets non-consecutive bits. Our findings demonstrate that, on average, random bit flip faults cause the accuracy of the original models to drop by 1.3% to over 3%. However, with our protection mechanisms in place, accuracy reductions are significantly minimised, ranging from only 0.0001% to 0.4%. [ABSTRACT FROM AUTHOR]

In this paper, we study some properties of the Mehler–Fock convolution operator. We also analyse the Banach algebraic structure on the space of integrable functions $ L_1(1,\infty) $ L 1 (1 , ∞) with the multiplication being the Mehler–Fock convolution. The Titchmarsh-type theorem for this convolution operator is also obtained. As applications, we apply these properties of the convolution operator to solve some classes of Fredholm integral and integro-differential equations and prove some priori estimations under the given conditions. [ABSTRACT FROM AUTHOR]

There has been a significant increase in the use of the Fractional Fourier transform (FrFT) in recent years due to its numerous applications in signal and image processing, among other fields. At the same time, the applications of Wigner distributions (WD) and ambiguity functions (AF) in signal analysis and image processing cannot be excluded. This paper investigates the convolution-based WD and AF associated with the Fractional Fourier transform (CFrWD/CFrAF). Firstly, we propose the definition of the CFrWD and CFrAF, and then relations with other classical time-frequency representations of the newly defined CFrWD and CFrAF are investigated. Furthermore, some essential properties, including conjugate-symmetry, nonlinearity, shifting, scaling, marginal, Moyal’s formula, and convolution, are also examined in detail. Finally, to demonstrate the benefit of the theory, applications of CFrWD and CFrAF for detecting LFM signals are also carried out with the aid of simulations. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new subclass of normalized analytic and univalent functions in the open unit disk associated with Sigmoid function. Coefficient estimates, convolution conditions, convexity and some other geometric properties for functions in this class are investigated. Also, subordination and inclusion results are obtained.

In recent years, the concept of fuzzy set has been incorporated into the field of geometric function theory, leading to the evolution of the classical concept of differential subordination into that of fuzzy differential subordination. In this study, certain generalized classes of $ p $ -valent analytic functions are defined in the context of fuzzy subordination. It is highlighted that for particular functions used in the definitions of those classes, the classes of fuzzy $ p $-valent convex and starlike functions are obtained, respectively. The new classes are introduced by using a $ \mathfrak{q} $-calculus operator defined in this investigation using the concept of convolution. Some inclusion results are discussed concerning the newly introduced classes based on the means given by the fuzzy differential subordination theory. Furthermore, connections are shown between the important results of this investigation and earlier ones. The second part of the investigation concerns a new generalized $ \mathfrak{q} $-calculus operator, defined here and having the $ (p, \mathfrak{q)} $-Bernardi operator as particular case, applied to the functions belonging to the new classes introduced in this study. Connections between the classes are established through this operator.

Abstract Deep neural networks have seen a surge of successful methods in natural image matting. However, the overlap of foreground and background color distributions in an image is still troubling in matting. It is observed that the three color channels contain different contrast information of an image: some color channels may provide clearer contrast information for separating the foreground from the image, while the foreground and background color distributions in other channels may heavily overlap, resulting in blurred foreground‐background boundaries. Motivated by this observation, the Color Subspace Exploring Network (CSEMat) is proposed to extract the foreground object from an image by exploring high‐contrast appearance information in individual color spaces. Specifically, a 4‐branch encoder is constructed, with one branch for the RGB image and three branches for subdividing the color space. Each color channel is individually processed by a sub‐encoder. Additionally, the trimap‐based color information aggregation module (CIA) is introduced to integrate the feature maps from the independent sub‐encoders, facilitating the transfer of optimized features to the decoder. Extensive experiments demonstrate that the proposed CSEMat achieves favorable performance on publicly available matting datasets.

Abstract Recently, El-Deeb and Cotîrlă (Mathematics 11:11234834, 2023) used the error function together with a q-convolution to introduce a new operator. By means of this operator the following class R α , ϒ λ , q ( δ , η ) $\mathcal{R}_{\alpha ,\Upsilon}^{\lambda ,q}(\delta ,\eta )$ of analytic functions was studied: R α , ϒ λ , q ( δ , η ) : = { F : ℜ ( ( 1 − δ + 2 η ) H ϒ λ , q F ( ζ ) ζ + ( δ − 2 η ) ( H ϒ λ , q F ( ζ ) ) ′ + η ζ ( H ϒ λ , q F ( ζ ) ) ″ ) } > α ( 0 ≦ α < 1 ) . $$\begin{aligned} &\mathcal{R}_{\alpha ,\Upsilon }^{\lambda ,q}(\delta ,\eta ) \\ &\quad := \biggl\{ \mathcal{ F}: {\Re} \biggl( (1-\delta +2\eta ) \frac{\mathcal{H}_{\Upsilon }^{\lambda ,q}\mathcal{F}(\zeta )}{\zeta}+(\delta -2\eta ) \bigl(\mathcal{H} _{\Upsilon}^{\lambda ,q}\mathcal{F}(\zeta ) \bigr) ^{{ \prime}}+\eta \zeta \bigl( \mathcal{H}_{\Upsilon}^{\lambda ,q} \mathcal{F}( \zeta ) \bigr) ^{{{\prime \prime}}} \biggr) \biggr\} \\ &\quad >\alpha \quad (0\leqq \alpha < 1). \end{aligned}$$ For these general analytic functions F ∈ R β , ϒ λ , q ( δ , η ) $\mathcal{F}\in \mathcal{R}_{\beta ,\Upsilon}^{\lambda ,q}(\delta , \eta )$ , we give upper bounds for the Fekete–Szegö functional and for the second and third Hankel determinants.