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This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, reference or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. The authors present an example in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI). [ABSTRACT FROM AUTHOR]

Generative Adversarial Networks (GANs) emerged thanks to the development of deep neural networks. Forgery images generated by various variants of GANs are widely spread on the Internet, which may be damage personal credibility and cause huge property losses. Thus, numerous methods are proposed to detect forgery images, but most of them are designed to detect forgery faces. Therefore, a method to detect forgery images of various scenes is proposed. In this work, central difference convolution and vanilla convolution (CDC‐Mix) are mixed after considering the depth and width features of neural networks and analyzing the influence of attention on network performance. Based on CDC‐Mix, a separable convolution (SeparableCDC‐Mix) is proposed. The proposed method consists of three parts: (1) CDC‐Mix and SeparableCDC‐Mix are used to extract the gradient information and texture features; (2) CDCM is used to extract the multi‐scale information of the image; (3) multi‐scale fusion module (MS‐Fusion) is used to fuse the multi‐scale information from different locations of the network. A large number of experiments have been carried out on several datasets generated by GAN, and the experimental results show that the proposed method has a great improvement compared with the existing advanced methods. [ABSTRACT FROM AUTHOR]

In this paper we consider the Fourier transform of the convolution of a distribution and a function which is an element of the space S0(ℝ). Also, we give an application of the obtained result to the sequences that converge in the same space, and we give their analytic representation. [ABSTRACT FROM AUTHOR]

In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities, including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer. [ABSTRACT FROM AUTHOR]

Extracting more information from feature interactions is essential to improve click-through rate (CTR) prediction accuracy. Although deep learning technology can help capture high-order feature interactions, the combination of features lacks interpretability. In this paper, we propose a multi-semantic feature interaction learning network (MeFiNet), which utilizes convolution operations to map feature interactions to multi-semantic spaces to improve their expressive ability and uses an improved Squeeze & Excitation method based on SENet to learn the importance of these interactions in different semantic spaces. The Squeeze operation helps to obtain the global importance distribution of semantic spaces, and the Excitation operation helps to dynamically re-assign the weights of semantic features so that both semantic diversity and feature diversity are considered in the model. The generated multi-semantic feature interactions are concatenated with the original feature embeddings and input into a deep learning network. Experiments on three public datasets demonstrate the effectiveness of the proposed model. Compared with state-of-the-art methods, the model achieves excellent performance (+ 0.18% in AUC and - 0.34% in LogLoss VS DeepFM; + 0.19% in AUC and - 0.33% in LogLoss VS FiBiNet). [ABSTRACT FROM AUTHOR]

Delayed‐release and extended‐release methylphenidate hydrochloride (JORNAY PM®) is a novel capsule formulation of methylphenidate hydrochloride, used to treat attention deficit hyperactivity disorder in patients 6 years and older. In this paper, we develop a Level A in vitro‐in vivo correlation (IVIVC) model for extended‐release methylphenidate hydrochloride to support post‐approval manufacturing changes by evaluating a point‐to‐point correlation between the fraction of drug dissolved in vitro and the fraction of drug absorbed in vivo. Dissolution data from an in vitro study of three different release formulations: fast, medium, and slow, and pharmacokinetic data from two in vivo studies were used to develop an IVIVC model using a convolution‐based approach. The time‐course of the drug concentration resulting from an arbitrary dose was considered as a function of the in vivo drug absorption and the disposition and elimination processes defined by the unit impulse response function using the convolution integral. An IVIVC was incorporated in the model due to the temporal difference seen in the scatterplots of the estimated fraction of drug absorbed in vivo and the fraction of drug dissolved in vitro and Levy plots. Finally, the IVIVC model was subjected to evaluation of internal predictability. This IVIVC model can be used to predict in vivo profiles for different in vitro profiles of extended‐release methylphenidate hydrochloride. [ABSTRACT FROM AUTHOR]

Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions, and we show the advantages of utilizing these techniques for bootstrapping. The discrete convolutional approach can provide exact numerical solutions for bootstrap quantities, or at least mathematical error bounds. In contrast, Monte Carlo bootstrap methods can only provide confidence intervals which converge slowly. Additionally, for some problems the computation time of the convolutional approach can be dramatically less than that of Monte Carlo resampling. This article provides several examples of bootstrapping using the proposed convolutional technique and compares the results to those of the Monte Carlo bootstrap, and to those of the competing saddlepoint method. [ABSTRACT FROM AUTHOR]

Digital signal processing and image processing applications require the noise free and efficient arithmetic operations. To overcome the noise problem, an efficient expanded operand decomposition (ExOD) based logarithm multiplication is proposed and applied for convolution of Gaussian smoothing filter to minimize the noise. The ExOD approach improves the average error percentage (AEP), mean square error (MSE) and the error rate in comparison of reported operand decomposition (OD) and improved operand decomposition (IOD). The peak signal-to-noise ratio (PSNR), MSE and the AEP of the ExOD logarithm multiplication method are improved as compared to the reported logarithm multiplication to the convolution operation. The ExOD method for logarithmic multiplication gives AEP of 0.276, 0.294 and 0.309%, whereas Mitchell's algorithm gives 2.702, 2.661 and 2.830%, OD-Mitchell's multiplication gives 1.441, 1.449 and 2.170% and IOD-Mitchell's multiplication gives 1.627, 1.678 and 2.064% for 4-, 8-, and 16-bit operations respectively. ExOD-Mitchell's multiplication gives 1.867% MSE, 45.453 db PSNR and 0.293% AEP, whereas Mitchell's algorithm gives 18.688% MSE, 35.449 db PSNR and 2.731% AEP, OD-Mitchell's multiplication gives 9.877% MSE, 38.218 db PSNR and 1.686% AEP and IOD-Mitchell's multiplication gives 10.866% MSE, 37.804 db PSNR and 1.789% AEP. The proposed ExOD based Mitchell algorithm multiplication has useful applications in image processing with efficient accuracy. [ABSTRACT FROM AUTHOR]

In this work we consider the problem of computing the (min , +) -convolution of two sequences a and b of lengths n and m, respectively, where n ≥ m . We assume that a is arbitrary, but b i = f (i) , where f (x) : [ 0 , m) → R is a function with one of the following properties: f is linear, f is monotone, f is convex, f is concave, f is piece-wise linear, f is a polynomial function of a fixed degree. To the best of our knowledge, the concave, piece-wise linear and polynomial cases were not considered in literature before. We develop true sub-quadratic algorithms for them. We apply our results to the knapsack problem with a separable nonlinear objective function, shortest lattice vector, and closest lattice vector problems. [ABSTRACT FROM AUTHOR]

Physiological reports have confirmed that there are differences in speech signals between depressed and healthy individuals. Therefore, as an application in the field of affective computing, automatic depression level prediction through speech signals has received the attention of researchers, which often estimate the depression severity of individuals by the Fourier or Mel spectrograms of speech signals. However, some studies on speech emotion recognition suggest that directly modeling the raw speech signal is more helpful for extracting emotion-related information. Inspired by this fact, we develop a WavDepressionNet to model raw speech signals for the improvement of prediction accuracy. In our method, a representation block is proposed to find a set of basis vectors to construct the optimal transformation space and generate the transformation result (named Depression Feature Map, DFM) of speech signal for facilitating the perception of depression cues. We further propose an assessment block, which cannot only use the designed spatiotemporal self-calibration mechanism to calibrate the DFM and highlight the useful elements, but also aggregates the calibrated DFM across various temporal ranges with the dilated convolution. Experimental results on the AVEC 2013 and AVEC 2014 depression databases demonstrate the effectiveness of our approach over previous works. [ABSTRACT FROM AUTHOR]

The recognition of T‐cell receptor (TCR) on the surface of T cell to specific epitope presented by the major histocompatibility complex is the key to trigger the immune response. Identifying the binding rules of TCR–epitope pair is crucial for developing immunotherapies, including neoantigen vaccine and drugs. Accurate prediction of TCR–epitope binding specificity via deep learning remains challenging, especially in test cases which are unseen in the training set. Here, we propose TEPCAM (TCR–EPitope identification based on Cross‐Attention and Multi‐channel convolution), a deep learning model that incorporates self‐attention, cross‐attention mechanism, and multi‐channel convolution to improve the generalizability and enhance the model interpretability. Experimental results demonstrate that our model outperformed several state‐of‐the‐art models on two challenging tasks including a strictly split dataset and an external dataset. Furthermore, the model can learn some interaction patterns between TCR and epitope by extracting the interpretable matrix from cross‐attention layer and mapping them to the three‐dimensional structures. The source code and data are freely available at https://github.com/Chenjw99/TEPCAM. [ABSTRACT FROM AUTHOR]

In the present paper, we study the operator I (w, zw′; 2) = wγ {a+b/w+ cw + dzw/w′}; w ∈ D = C\{0}, z ∈ E, where E = {z; |z |<1} and a, b, c, d, β, γ be complex numbers such that d≠0, β≠ 0, to obtain superordination theorems which generalise and unify various well known results. In what follows, all the powers taken are the principle ones. [ABSTRACT FROM AUTHOR]

In the detection of building changes in high spatial-resolution remote sensing images, both the distribution position and surface characteristics of the same objects are probably different under different imaging phases, which potentially causes high false positives. In order to improve the detection accuracy of building changes, an integration network, named R&D net is proposed in this article, which comprises a registration network (R-net) followed by a change detection network (D-net). In R-net, two different phase images are accepted as inputs, corner points and their descriptors are generated to spatially align those images. After that, the spatially aligned images are fed into the D-net, and building images are detected accordingly. In this article, a multiview automatic labeling method is proposed to obtain labeling corner points. A new dataset containing 5104 image pairs is established. Experimental results demonstrate that the R-net can extract robust invariant features, and then improve registration accuracy under circumstances with obvious changes of surface feature, which is a base of D-net. Uniting pyramid pooling structure with a focal loss function in D-net, both leaky and wrong segmentations can be dramatically improved under complex scenes with many interferences. When compared with baseline methods on different high-resolution remote sensing scenes, the proposed method achieves better performance and more accurate detection results of building changes. [ABSTRACT FROM AUTHOR]

Due to their spatial and spectral information, hyperspectral images are frequently used in various scientific and industrial fields. Recent developments in hyperspectral image classification have revolved around the use of convolutional neural networks and transformers, which are capable of modeling local and global data. However, most of the backbone networks of existing methods are based on 3-D convolution, which has high complexity in network structure. Moreover, local information and global information are extracted through different modules, and the coupling relationship between the two types of information is weak. To address the above-mentioned issues, we propose a method named main–sub transformer network with spectral–spatial separable convolution method (MST-SSSNet), which includes two key modules: the spectral–spatial separable convolution (SSSC) module and the main–sub transformer encoder (MST) module. The SSSC module uses the proposed spectral–spatial separable convolution, reducing network parameters and efficiently extracting local features. The MST module adds the designed subtransformer in front of the conventional transformer encoder (main transformer). It assists the main-transformer encoder to establish global correlation by learning local information. The WHU-Hi dataset can be used as a benchmark dataset for precise crop classification and hyperspectral image classification research. MST-SSSNet is shown to deliver better classification performance than current state-of-the-art methods on the datasets. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing is to decompose the mixed pixel into the spectral signatures (endmembers) with their corresponding abundances. However, the ignorance of endmember variability in hyperspectral unmixing results in low performance. To solve this problem, a multi-scale convolution attention network containing endmember unmixing network (EU-Net) and abundance unmixing network, which was called as-the hyperspectral unmixing with multi-scale convolution attention network (HUMSCAN) was proposed in this article. The EU-Net is composed of the variational autoencoder and the multi-scale effective convolution block attention module (MSECBAM), which is combined with the S-VCA pretraining to adaptively extract endmembers at the pixel and subpixel levels. The AU-Net is based on the MSECBAM frame jointed the spectral and spatial attention features. The proposed HUMSCAN method can simultaneously and unsupervisedly extract endmembers and their corresponding abundances, which can improve the accuracy and efficiency of spectral unmixing. The performance of the proposed method is evaluated both on synthetic and real datasets. Experimental results show its superiority in comparison with other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The detection of objects with larger aspect ratios (OLARs) is a challenging problem in a special application scenario, such as remote-sensing object recognition and scene text detection. However, current object detectors perform poorly in OLAR feature extraction because they are incapable of adaptively responding to object shapes, which leads to severe misalignment between impure feature representations and region proposals. In this letter, we aim to solve this problem by proposing our shape-sensitive convolution network (SSC-Net). SSC-Net is carefully embedded with a feature enhancement module (SSC module) specifically suitable for OLAR. This module can use fewer sampling points to achieve more intelligent feature sampling area transformation, thus achieving the goal of enhancing OLAR feature representation. Extensive experiments on benchmark datasets that are rich in OLARs have proved the superiority of our method. Besides, we further verified the plug-and-play performance of the SSC module, and the experimental results show that it can significantly improve the detection performance of the detector for OLAR. [ABSTRACT FROM AUTHOR]

Deep-learning (DL)-based methods have been increasingly used in hyperspectral unmixing (HU), especially the recent trend of unsupervised autoencoder (AE) networks, which have achieved excellent performances. Although some existing unmixing methods take spatial information into account, the utilization of spatial structure is not sufficient and effective. In this letter, we present a deep attention-guided spatial–spectral network for hyperspectral image (HSI) unmixing called DASS-Net, which adopts a parallel dual-stream structure. We design a neighborhood spatial attention (NSA) module, where the abundance features of the central pixel are dynamically weighted by the coarse-grained features of the neighborhood pixels. In addition, a dual-gated mechanism is introduced to further integrate and express the spatial and spectral information. Experimental results show that the proposed DASS-Net performs particularly well in endmember extraction and outperforms all compared methods. [ABSTRACT FROM AUTHOR]

Few-shot remote-sensing scene classification (FSRSSC) is the task of categorizing remote-sensing images (RSIs) with insufficient labeled samples. This task becomes particularly challenging due to low intraclass similarity and high interclass similarity in RSIs. To overcome these challenges, we introduce a novel masked second-order pooling (MSoP) module to exploit the masked second-order features, enhancing feature representation and classification performance for FSRSSC. The MSoP module comprises two key components: a learnable DropBlock (LDB) and a compressed second-order pooling (CSoP). The LDB selectively masks discriminative regions in feature maps, effectively alleviating the low intraclass similarity problem. On the other hand, the CSoP enhances second-order statistics by computing and aggregating channel-wise similarity, thereby reducing the impact of interclass similarity. We construct an MSoP-Net based on the proposed MSoP module. Experimental results demonstrate its superior performance on two widely used datasets, that is, NWPU-RESISC45 and UCM. [ABSTRACT FROM AUTHOR]

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Computer vision obtains object and environment information by simulating human visual senses and borrowing human sensory activity. As one of the main tasks of computer vision, image classification can be used not only for face recognition, traffic scene recognition, image retrieval, and automatic photo categorization but also as a theoretical basis for target detection and image segmentation. In this paper, we use the existing CNN architecture network-ConvNeXt. By adapting and modifying the residual connectivity and convolutional structure of the network, we achieve a balance between classification accuracy and inference speed. These modifications are able to reduce both computation and memory consumption while keeping accuracy largely unchanged, thus better facilitating network lightweighting. [ABSTRACT FROM AUTHOR]

Remote sensing image scene classification is a fundamental task in intelligent interpretation of remote sensing images. Although Transformers possess a powerful attention mechanism, they require lengthy training procedures to achieve good performance levels. To address this issue, this paper proposes a novel deep learning network model by combining CNN and Swin Transformer named SwinHCST. Firstly, the model uses Weighted Normalized CNN to quickly extract low-level features of the image. Secondly, the Receptive Field Block module facilitates multi-scale information fusion, Thirdly, the Information Fusion Transformer further excavates the deep-level features of the image. Furthermore, this paper has designed a plug-and-play Cross Spatial Information Fusion Block, which is used to encodes dimensional information and extracts global information to enhance information exchange. The scene classification experiments show that the proposed model outperforms other methods on the three selected datasets and can achieve excellent performance without requiring large amounts of data and training. Specifically, the classification accuracy of the proposed method on the three datasets is 93.76%, 93.60%, and 98.10%, which is 1.7% to 3.71% higher than ResNet50 and 3.7% to 5.7% higher than Swin Transformer. [ABSTRACT FROM AUTHOR]

In various industrial domains, machinery plays a pivotal role, with bearing failure standing out as the most prevalent cause of malfunction, contributing to approximately 41% to 44% of all operational breakdowns. To address this issue, this research employs a lightweight neural network, boasting a mere 8.69 K parameters, tailored for implementation on an FPGA (field-programmable gate array). By integrating an incremental network quantization approach and fixed-point operation techniques, substantial memory savings amounting to 63.49% are realized compared to conventional 32-bit floating-point operations. Moreover, when executed on an FPGA, this work facilitates real-time bearing condition detection at an impressive rate of 48,000 samples per second while operating on a minimal power budget of just 342 mW. Remarkably, this system achieves an accuracy level of 95.12%, showcasing its effectiveness in predictive maintenance and the prevention of costly machinery failures. [ABSTRACT FROM AUTHOR]

Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken as an investigated domain. The reinforcement is considered and dealt as scattered within the beam. Material characteristics are determined in line with the theory of the reinforcement. Sinusoidal load is taken as the action, stress reaction function is observed. By exploitation of the Fourier transform within the stress-strain relation analysis, both time and frequency interpretation of the constitutive relation can be performed. [ABSTRACT FROM AUTHOR]

In this article, we discuss a bivariate geometric distribution whose conditionals are geometric distributions and the marginals are not geometric and exhibits negative correlation. Several useful structural properties of the bivariate geometric distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of negative correlation, marginal over-dispersion, distribution of sum, and distribution of the conditional given the sum are also derived. The distribution is shown to be a member of the multi-parameter exponential family and some natural but useful consequences are also outlined. A characterization via conditional failure rates is provided. An extensive simulation study is also carried out to explore the flexibility of the bivariate geometric distribution with various choices of the model parameters. Finally, the distribution is fitted to one bivariate count data set with an inherent negative correlation to illustrate its suitability [ABSTRACT FROM AUTHOR]

Over the past ten years, analytical functions' reputation in the literature and their application have grown. We study some practical issues pertaining to multivalent functions with bounded boundary rotation that associate with the combination of confluent hypergeometric functions and binomial series in this research. A novel subset of multivalent functions is established through the use of convolution products and specific inclusion properties are examined through the application of second order differential inequalities in the complex plane. Furthermore, for multivalent functions, we examined inclusion findings using Bernardi integral operators. Moreover, we will demonstrate how the class proposed in this study, in conjunction with the acquired results, generalizes other well-known (or recently discovered) works that are called out as exceptions in the literature. [ABSTRACT FROM AUTHOR]

The aim of this work is to discuss some conditions for Touchard polynomials to be in the classes  TB b (ρ , σ)  and  TK b (ρ , σ) . Also, we obtain some connection between  R η (D , E)  and  TK b (ρ , σ) . Also, we investigate several mapping properties involving these subclasses. Further, we discuss the geometric properties of an integral operator related to the Touchard polynomial. Additionally, briefly mentioned are specific instances of our primary results. Also, several particular examples are presented. [ABSTRACT FROM AUTHOR]

We utilize quasi-subordination to analyze and introduce several new classes, and we construct a new operator by combining the error function and q-convolution. Additionally, we obtain estimates for the Fekete Szego functional and the Taylor–Maclaurin coefficients for functions in c 2 and c 3 new classes. Moreover, we discuss some applications of the operator. [ABSTRACT FROM AUTHOR]

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects such as coefficient bounds, convolution conservation, and convexity constraints. Next, using sufficiency criteria, we calculate the sharp bounds of the real parts of the ratios of harmonic functions to their sequences of partial sums. In addition, for the first time some of the interesting implications of the q-Srivastava–Attiya operator in harmonic functions are also included. [ABSTRACT FROM AUTHOR]

In this study, we describe a linear space AW,V a,p (Rd) of functions (Rd) whose fractional Fourier transforms belong to AW,V a,p(Rd) for. We show that (Rd) (Rd) becomes a Banach algebra with the sum norm ||f||AW,Va,p=||f||1,W and under (fractional convolution) convolution operation. Besides, we indicate that the space AW,Va,p(Rd) is an abstract Segal algebra, where is weight function of regular growth. Moreover, we find an approximate identity for AW,Va,p(Rd). We also discuss some other properties of AW,Va,p (Rd). Finally, we investigate some inclusions of this space. [ABSTRACT FROM AUTHOR]

Strongly Janowski functions are used to define certain classes of analytic functions which generalize the concepts of close-to-convexity and bounded boundary rotation. Coefficient results, a necessary condition, distortion bounds, Hankel determinant problem and several other interesting properties of these classes are studied. Some significant well known results are derived as special cases. [ABSTRACT FROM AUTHOR]

A new subclass of meromorphic univalent functions by using the qhypergeometric and Hurwitz-Lerch Zeta functions is defined. Also, by applying the generalized Liu-Srivastava operator on meromorphic functions, some geometric properties of the new defined subclass such as coefficient estimates, extreme points, convexity and connected set structure are investigated. [ABSTRACT FROM AUTHOR]

This paper examines a three-component differential equation model with a self-control mechanism in vision as a slight extension of the lateral inhibition model proposed by Peskin (Partial differential equations in biology: Courant Institute of Mathematical Sciences Lecture Notes, New York, 1976). First, we derive a condition under which the exact solution of our differential equation model for time-dependent input I = I (t) is described by the convolution integral with a temporal biphasic function. Second, we analyze the model with the input signal I = I (t , x) depending on time t and position x ∈ R , and we prove that the solution can be represented in convolution integral form and that t 1 > 0 exists such that the spatiotemporal integral kernel K u (t 1 , x) is positive for x ∈ R and t ∈ (0 , t 1) . Moreover, we numerically demonstrate that there exists t 2 (> t 1) such that K u (t 2 , x) includes the Mexican-hat function and a temporal biphasic function under certain parameter conditions. From these mathematical and numerical results, we find that there is a time lag before the Mexican-hat function appears in K u (t , x) , and the shape of K u (t , x) is similar to the receptive field structure observed in experiments in the field of neurophysiology. We conclude that the partial differential equations for visual information processing can be used to analytically determine the shape of the spatiotemporal kernel indicating the self-control mechanism. [ABSTRACT FROM AUTHOR]

Neural fields are evolving towards a general-purpose continuous representation for visual computing. Yet, despite their numerous appealing properties, they are hardly amenable to signal processing. As a remedy, we present a method to perform general continuous convolutions with general continuous signals such as neural fields. Observing that piecewise polynomial kernels reduce to a sparse set of Dirac deltas after repeated differentiation, we leverage convolution identities and train a repeated integral field to efficiently execute large-scale convolutions. We demonstrate our approach on a variety of data modalities and spatially-varying kernels. [ABSTRACT FROM AUTHOR]

The quadratic phase Fourier transform(QPFT) has received my attention in recent years because of its applications in signal processing. At the same time the applications of Wigner-Ville distribution (WVD) and ambiguity function (AF) in signal analysis and image processing can not be excluded. In this paper we investigated the Wigner-Ville Distribution (WVD) and ambiguity function (AF) associated with quadratic phase Fourier transform (WVD-QPFT/AF-QPFT). Firstly, we propose the definition of the WVD-QPFT, and then several important properties of newly defined WVD-QPFT, such as nonlinearity, boundedness, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly, we propose the definition of the AF-QPFT, and its with classical AF, then several important properties of newly defined AF-QPFT, such as non-linearity, the reconstruction formula, the time-delay marginal property, the quadratic-phase marginal property and orthogonal relation are studied. Further, a novel quadratic convolution operator and a related correlation operator for WVD-QPFT are proposed. Based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied. Finally, a novel algorithm for the detection of linear frequency-modulated(LFM) signal is presented by using the proposed WVD-QPFT and AF-QPFT. [ABSTRACT FROM AUTHOR]

Abstract Convolutional neural networks (CNNs) have demonstrated impressive results in additive white Gaussian noise removal due to their strong fitting ability. However, their performance in mixed noise removal remains unsatisfactory, primarily due to their limited receptive field that focuses only on the local features of images and disregards global information. To ameliorate this issue, recent state‐of‐the‐art approaches employ attention mechanism (AM) to capture the global information. However, most AM based methods still suffer from low computational efficiency. In this paper, a novel model named simple dual attention mechanism UNet (SDAUNet) for mixed noise removal is proposed. In SDAUNet, the UNet architecture is used to gradually acquire multi‐scale image features and provide a more comprehensive and accurate representation of the image features than other CNNs. A simple dual attention convolutional block is presented to acquire the global image features that can successfully capture image details with a low burden. The experimental results demonstrate that the SDAUNet model can achieve better measurement metrics and visual performance than other state‐of‐the‐art methods.

There are many integral transforms that are widely used to solve numerous real-life, science, and engineering problems. In this article, we present SEE transform for determining the solution of the system of linear Volterra integro-differential equations of the second kind. Some applications have been given and solved by using the SEE transform for illustrating the applicability of the SEE transform. Results of the applications assert that the SEE transform is very effective for obtaining the exact solution of this equation.

This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data.

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.

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.

In this paper, we introduce new classes of functions defined within the open unit disk by integrating the concepts of (λ,γ)-symmetrical functions, generalized Janowski functions, and quantum calculus. We derive a structural formula and a representation theorem for the class Sqλ,γ(x,y,z). Utilizing convolution techniques and quantum calculus, we investigate convolution conditions supported by examples and corollary, establishing sufficient conditions. Additionally, we derive properties related to coefficient estimates, which further elucidate the characteristics of the defined function classes.

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk D. For these new classes, the authors establish initial coefficient bounds of |a2| and |a3|. Furthermore, the famous Fekete–Szegö coefficient inequality is also obtained for these new classes of functions.

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given.

A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor–Maclaurin series of univalent functions. Using Caputo-type fractional derivatives to define the families of Sakaguchi-type starlike functions with respect to symmetric points, this article aims to investigate the first three initial coefficient estimates, the bounds for various problems such as Fekete–Szegő inequality, and the Zalcman inequalities, by subordinating to the function of the three leaves domain. Fekete–Szegő-type inequalities and initial coefficients for functions of the form H−1 and ζH(ζ) and 12logHζζ connected to the three leaves functions are also discussed.

In the present investigation, we introduce a new subclass of univalent functions F(u,λ) and a subclass of bi-univalent function Fo,Σ(u,λ) with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes F(u,λ) are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class Fo,Σ(u,λ) are established.

The topic concerning the introduction and investigation of new classes of analytic functions using subordination techniques for obtaining certain geometric properties alongside coefficient estimates and inclusion relations is enriched by the results of the present investigation. The prolific tools of quantum calculus applied in geometric function theory are employed for the investigation of a new class of analytic functions introduced by applying a previously defined generalized q−integral operator and the concept of subordination. Investigations are conducted on the new class, including coefficient estimates, integral representation for the functions of the class, linear combinations, forms of the weighted and arithmetic means involving functions from the class, and the estimation of the integral means results.

Semantic scene completion is a crucial outdoor scene understanding task that has direct implications for technologies like autonomous driving and robotics. It compensates for unavoidable occlusions and partial measurements in LiDAR scans, which may otherwise cause catastrophic failures. Due to the inherent complexity of this task, existing methods generally rely on complex and computationally demanding scene completion models, which limits their practicality in downstream applications. Addressing this, we propose a novel integrated network that combines the strengths of 3D and 2D semantic scene completion techniques for efficient LiDAR point cloud scene completion. Our network leverages a newly devised lightweight multi-scale convolutional block (MSB) to efficiently aggregate multi-scale features, thereby improving the identification of small and distant objects. It further utilizes a layout-aware semantic block (LSB), developed to grasp the overall layout of the scene to precisely guide the reconstruction and recognition of features. Moreover, we also develop a feature fusion module (FFM) for effective interaction between the data derived from two disparate streams in our network, ensuring a robust and cohesive scene completion process. Extensive experiments with the popular SemanticKITTI dataset demonstrate that our method achieves highly competitive performance, with an mIoU of 35.7 and an IoU of 51.4. Notably, the proposed method achieves an mIoU improvement of 2.6 % compared to previous methods.

Convolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter analysis. Firstly, we propose QLCcT by combining quaternion algebra with linear canonical cosine transform (LCcT), which extends LCcT to Hamiltonian quaternion algebra. Secondly, we introduce weighted convolution and correlation operations for QLCcT, accompanied by their corresponding theorems. We also explore the properties of QLCcT. Thirdly, we utilize these proposed convolution structures to analyze multiplicative filter models that offer lower computational complexity compared to existing methods based on quaternion linear canonical transform (QLCT). Additionally, we discuss the rationale behind studying such transforms using quaternion functions as an illustrative example.

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.