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Highlights: 3D hydraulic fractures were extracted from X-ray computed tomography images by manual selection and surface interpolation. Joint roughness was measured for hydraulic fractures induced along different cleavage planes in granite. The cleavage plane and pressurization rate have an effect on the roughness of hydraulically induced fractures. [ABSTRACT FROM AUTHOR]

A 2D topology optimization algorithm is proposed, which integrates the control of hole shape, hole number, and the minimum scale between holes through the utilization of an appearance target image. The distance between the structure and the appearance target image is defined as the hole appearance constraint. The appearance constraint is organized as inequality constraints to control the performance of the structure in an iterative optimization. Specifically, hole shapes are controlled by matching adaptable equivalent shape templates, the minimum scales between holes are controlled by a hole shrinkage strategy, and the hole number is controlled by a hole number calculation and filling method. Based on the SIMP interpolation topology optimization model, the effectiveness of the proposed method is verified through numerical examples. [ABSTRACT FROM AUTHOR]

A fundamental aspect in the evolution of Time-to-Digital Converters (TDCs) implemented within Field-Programmable Gate Arrays (FPGAs), given the increasing demand for detection channels, is the optimization of resource utilization. This study reviews the principal methodologies employed for implementing low-resource TDCs in FPGAs. It outlines the foundational architectures and interpolation techniques utilized to bolster TDC performances without unduly burdening resource consumption. Low-resource Tapped Delay Line, Vernier Ring Oscillator, and Multi-Phase Shift Counter TDCs, including the use of SerDes, are reviewed. Additionally, novel low-resource architectures are scrutinized, including Counter Gray Oscillator TDCs and interpolation expansions using Process–Voltage–Temperature stable IODELAYs. Furthermore, the advantages and limitations of each approach are critically assessed, with particular emphasis on resolution, precision, non-linearities, and especially resource utilization. A comprehensive summary table encapsulating existing works on low-resource TDCs is provided, offering a comprehensive overview of the advancements in the field. [ABSTRACT FROM AUTHOR]

Face morphing attacks disrupt the essential correlation between a face image and its identity information, posing a significant challenge to face recognition systems. Despite advancements in face morphing attack detection methods, these techniques cannot reconstruct the face images of accomplices. Existing deep learning-based face de-morphing techniques have mainly focused on identity disentanglement, overlooking the morphing factors inherent in the morphed images. This paper introduces a novel face de-morphing method to restore the identity information of accomplices by predicting the corresponding de-morphing factor. To obtain reasonable de-morphing factors, a channel-wise attention mechanism is employed to perform feature interaction, and the correlation between the morphed image and the real-time captured reference image is integrated to promote the prediction of the de-morphing factor. Furthermore, the identity information of the accomplice is restored by mapping the morphed and reference images into the StyleGAN latent space and performing inverse linear interpolation using the predicted de-morphing factor. Experimental results demonstrate the superiority of this method in restoring accomplice facial images, achieving improved restoration accuracy and image quality compared to existing techniques. [ABSTRACT FROM AUTHOR]

Satellite imagery has become a widespread resource for modeling variability in lake surfaces. However, the extended monitoring of a lake's perimeter faces significant challenges due to atmospheric obstacles that cannot be rectified. Due to the atmosphere's everchanging opacity, only half of the acquired satellite images have reliable qualitative accuracy making it possible to identify a lake's contour. Consequently, approximately 50% of the monthly lake outline values can be determined using remote sensing methods, leaving the remaining 50% unknown. This situation is applicable to three lakes in Morocco (Abakhan, Ouiouan, and Tiglmanine), the subjects of the current research for the period between 1984 and 2022. What can we do if, during a period of time in which we monitored the evolution of the surface of a lake by satellite means, we obtain only about 50% of the possible images? Shall we just settle for this and stop the analysis? Although it may be challenging to believe, the present study introduces two statistical methods for interpolating and validating the monthly values of the lake outline: the iterative ratio method based on the autocorrelation of the monthly water balance and the Kalman filter. We estimated the reconstruction errors of the missing values and validated the methodology using an inverse philosophy, reconstructing the initial data from the table of the simulation results. Given that the difference between the initial values and the reconstructed initial values resembles white noise or an AR (1) process with a low coefficient, we deemed the methodological approach acceptable. Several comparison criteria between the two interpolation methods were employed, yet determining the more appropriate one remains challenging. Based on our surface reconstruction method, Lake Abakhan, with an average area of 22 hectares, experienced significant fluctuations, ranging from a maximum of 34 hectares in 2010 to a minimum of 0.8 hectares in 2022. Lake Ouiouan, with an average area of 14 hectares, displayed much lower variation, with a maximum of 17 hectares in 2020 and a minimum of 6.5 hectares in 1988. Lake Tiglmanine showed a pattern similar to that of Lake Abakhan but with less pronounced fluctuations. With an average area of 6.1 hectares, its maximum was 9.2 hectares in 2011 and its minimum was 4.1 hectares in 1984. [ABSTRACT FROM AUTHOR]

This paper will be devoted to the study of weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will be defined in a sense by the sum of weighted (deformed) free creation, annihilation, scalar, and intermediate operators with certain parameters on a weighted (deformed) free Fock space together with the vacuum expectation. We shall provide a combinatorial moment formula of non-commutative Poisson random variables. This formula gives us a very nice combinatorial interpretation to two parameters of weights. One can see that the deformation treated in this paper interpolates free and boolean Poisson random variables, their distributions and moments, and yields some conditionally free Poisson distribution by taking limit of the parameter. [ABSTRACT FROM AUTHOR]

Purpose: The objective of this work is to analyze the necessary conditions for chaotic behavior with fractional order and fractal dimension values of the fractal-fractional operator. Design/methodology/approach: The numerical technique based on the fractal-fractional derivative is implemented over the fractional model and analyzes the condition at the distinct values of fractional order and fractal dimension. Findings: The obtained numerical solution from the numerical technique is analyzed at distinct fractional order and fractal dimension values, and it has been figured out that the behavior of the solution either chaotic or non-chaotic agrees with the condition. Originality/value: The necessary condition is associated with the fractional order only. So, our work not only studies the condition with fractional order but also examines the model by simultaneously adjusting fractal dimension values. It is found that the model still has chaotic or non-chaotic behavior at certain fractal dimension values and fractional order values corresponding to the condition. [ABSTRACT FROM AUTHOR]

Three-dimensional elastoplastic buckling characteristics of porous functionally graded (FG) plates are studied by a novel meshfree method, which exploits the Tchebychev‐radial point interpolation shape function. Tchebychev polynomials and radial basis functions are combined to achieve superior convergence and numerical accuracy in constructing the shape function. The governing equations are derived using the principle of virtual work, with the involvement of 3D full Green–Lagrange nonlinear strains. The incremental plastic deformation is modeled by the Prandtl-Reuss flow rule along the isotropic hardening von Mises criterion. The effective elastoplastic properties of the FG material (FGM) are evaluated using the Tamura–Tomota–Ozawa homogenization model. The results show excellent agreement with those available in the literature. The influence of different porosity parameters, power‐law exponents, thickness ratios, aspect ratios, porosity distributions, boundary conditions, and loading ratios on the elastoplastic buckling behavior of the porous FG plate is evaluated. [ABSTRACT FROM AUTHOR]

Various types of pixel candidates are available in the literature to replace impulse noise after effective detection. However, using them in the correct location and preserving the signal content, structural similarity, and image details is a task that draws attention, especially in a highly corrupted image. Non-linear Diffusion-based restoration is an efficient solution since it can iteratively update corrupted pixels without diffusing the edge. This work assigns the iterative weighted total variation diffusion technique only for the possibly noisy pixels in high noise ratio processing windows where the windows are pre-classified as low or high noise ratio by a custom CNN classifier. The work, called as CNN-based locally adapting filter (CNN-LAF), can achieve a high structural similarity of.9167 by maintaining a PSNR of 24.01 dB at a 0.8 noise ratio. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the superconvergence of nonconforming Rannacher-Turek finite element for elliptic interface problems under unfitted square meshes. In particular, we analyze its superclose property between the gradient of the numerical solution and the gradient of the interpolation of the exact solution. Moreover, we introduce a postprocessing interpolation operator which is applied to numerical solution, and we prove that the postprocessed gradient converges to the exact gradient with a superconvergent rate O (h 3 2 ). Finally, numerical results coincide with our theoretical analysis, and they show that the error estimates do not depend on the ratio of the discontinuous coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical method for the bi-Laplace problems with inhomogeneous coefficients; particularly, we propose finite element schemes on rectangular grids respectively for an inhomogeneous fourth-order elliptic singular perturbation problem and for the Helmholtz transmission eigenvalue problem. The new methods use the reduced rectangle Morley (RRM for short) element space with piecewise quadratic polynomials, which are of the lowest degree possible. For the finite element space, a discrete analogue of an equality by Grisvard is proved for the stability issue and a locally-averaged interpolation operator is constructed for the approximation issue. Optimal convergence rates of the schemes are proved, and numerical experiments are given to verify the theoretical analysis. • A discrete analogue of an equality (1.3) by Grisvard [1] on H 2 functions is proved for the reduced rectangular Morley (RRM for short in the sequel) element functions. This discrete equality makes the RRM space usable for bi-Laplacian problems with inhomogeneous coefficients. • Based on piecewise quadratic polynomials, the RRM scheme is the lowest-degree finite element scheme for the inhomogeneous bi-Laplace problems. Compared to other kinds of methods, it does not need tuning parameter or using indirect differential operators. • As revealed by [3] , the RRM element space does not admit a locally-defined projective interpolator. In this paper, however, a locally-defined stable interpolator (not projective) is carefully constructed for the RRM element space, and an optimal approximation is proved rigorously on both convex and nonconvex domains. [ABSTRACT FROM AUTHOR]

A modified wavelet interpolation Galerkin method (WIGM) with improved flexibility of nodal distribution is formulated and utilized to solve the Bratu's problem. Such a method treats the nonlinear term as an independent function and directly approximates it through the proposed wavelet interpolation, resulting in a low-cost discretization of the Bratu's equation with exponential nonlinearity. An efficient implementation of Newton's method to find the lower and upper branches of solution as well as the turning point is then presented. Numerical results demonstrate that the present WIGM can accurately estimate both two solution branches and turning point for the Bratu's problem. Compared with many other existing methods, the proposed WIGM also offers marked superiority in terms of accuracy when using the same node distribution. Moreover, a convergent solution to the resulting nonlinear discrete system obtained by the WIGM can be observed in a few iterations even when the initial guess significantly deviates from the exact solution. Finally, a highly accurate approximation of both two-branched solutions and the turning point for the two-dimensional Bratu's problem is obtained by the proposed WIGM. [ABSTRACT FROM AUTHOR]

Roundoff errors often disrupt interpolation methods for time-fractional equations, potentially causing suboptimal convergence or even failure. These issues primarily result from catastrophic cancellations. To address this, we introduce a novel framework for computing coefficients in standard and fast interpolation methods on nonuniform meshes. We propose δ -cancellation and associated threshold conditions to prevent such cancellations. If the thresholds aren't met, a Taylor expansion technique can be applied. Numerical experiments demonstrate our method's accuracy, on par with the Gauss–Kronrod quadrature, but significantly more efficient, allowing for extensive simulations with hundreds of thousands of time steps. [ABSTRACT FROM AUTHOR]

This paper proposes a method for obtaining adaptive and high-precision surface meshes directly from Industrial computed tomography (ICT) projection data. Firstly, an adaptive volume octree is recursively constructed from top to bottom using a two-stage geometric error metric function. The CT values and gradient values at the nodes are computed using the Feldkamp–Davis–Kress (FDK) reconstruction algorithm and its derivatives, achieving sub-voxel precision. Next, feature vertices are calculated based on Quadratic error functions (QEFs), and a dual mesh is constructed. Finally, Hermite interpolation is used to determine the iso-surface vertices, and the Convex Contouring lookup table is employed to accurately extract the iso-surface contours, resulting in high-precision and crack-free surface meshes. Experimental results show that the surface meshes generated by the proposed method exhibit superior dimensional accuracy, form and position accuracy, and surface model accuracy compared to traditional methods, and the dimensional accuracy has been enhanced by approximately 10–30%. [ABSTRACT FROM AUTHOR]

This paper considers a new stabilized finite element method (FEM) of the Stokes equations based on Clément interpolation by the constrained quadrilateral nonconforming rotated Q 1 - Q 0 finite element pair. The stabilized term constructed in this method is quite different from those of the existing literature. This method not only has the same attractive computational properties as the conforming stabilized finite element method with local polynomial pressure projection, such as parameter-free, avoiding higher-order derivatives and edge-based date structure, but also guarantees the superclose and superconvergence results for the velocity and pressure. Finally, two numerical examples are supported to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of trend function made from adaptive Fourier decomposition. Through applying a data preprocessing method, we achieve trend functions of the rational function type. The trend functions are divided into different levels to describe the tendency of the signal or time series in question. They are, in particular, smooth, and are free from the Gibbs phenomenon as usually introduced by the Fourier type methods. To justify the role of the trend function concept, an interpolation result is proved. An effective application of trend function in predicting stochastic time series is presented based on real COVID-19 outbreak data of China. The algorithm aspect is fully discussed. [ABSTRACT FROM AUTHOR]

Artifact correction is a great challenge in cardiac imaging. During the correction of coronary tissue with motion‐induced artifacts, the spatial distribution of CT value not only shifts according to the motion vector field (MVF), but also shifts according to the volume change rate of the local voxels. However, the traditional interpolation method does not conserve the CT value during motion compensation. A new sample interpolation algorithm is developed based on the constraint of conservation of CT value before and after image deformation. This algorithm is modified on the existing interpolation algorithms and can be embedded into neural networks with deterministic back propagation. Comparative experimental results illustrate that the method can not only correct motion‐induced artifacts, but also ensure the conservation of CT value in the region of interest (ROI) area, so as to obtain corrected images with clinically recognized CT value. Both effectiveness and efficiency are proved in forward motion correction process and backward training steps in deep learning. Simultaneously, using the network to learn the MVF making this method more interpretable than the existing image‐based end‐to‐end deep learning method. [ABSTRACT FROM AUTHOR]

The periodic sinc function interpolation offers a compelling solution to address the issue of noise in the analysis of thermogravimetric analysis (TGA) data, thereby enhancing the outcomes of differential techniques such as the Friedman isoconversional method. In this study, we introduce a novel approach that leverages the periodic sinc function interpolation to directly obtain smooth reaction rates from TGA data, eliminating the reliance on numerical differentiation methods. The efficacy of this method has been confirmed through its application to noisy experimental data derived from the thermal decomposition of various polymers, showcasing its robustness. Readers are provided with the corresponding code for Gnu Octave, serving as a free alternative to MATLAB. Additionally, the activation energies calculated from the experimental data using both the Friedman method and periodic sinc function interpolation closely align with those determined by the integral Vyazovkin method, emphasizing the validity and reliability of this new approach. [ABSTRACT FROM AUTHOR]

We propose an efficient method with energy constraints for constructing a Catmull–Clark surface that interpolates a given mesh. We approximate the surface energy of Catmull–Clark surfaces near extraordinary points by summing their finite subpatches and then represent the energy of the subpatches as linear combinations of the vertices of control mesh. By minimizing the surface energy as a constraint, we generate a new control mesh whose limit surfaces interpolate a given mesh. Numerous examples and comparisons demonstrate that our method has the following characteristics: (1) The limit surfaces are fairer, reducing unnecessary undulations and having minimal surface energy, and (2) the approximation process is simple and intuitive, requiring only a small number of computational steps and avoiding complex parameterization processes. [ABSTRACT FROM AUTHOR]

The main concern is the uncertainty in the real-world solid transportation problem. This study examines a supply, demand, and conveyance capacity-based multi-choice solid stochastic multi-objective transportation problem (MCSS-MOTP). Due to uncertainty, the concrete objective function coefficients of the proposed model are of multivariate type. Furthermore, the parameters of the constraints are treated as independent multivariate random variables with normal distribution. First, a Newton divided difference method-based interpolation polynomial is described that extends an interpolation polynomial using practical properties at non-negative integer nodes to deal with any multiple-choice parameter. Second, the probabilistic constraints are converted into precise ones utilizing a stochastic programming approach. In the end, ranking procedure was used to compare the existing approach with the old models. The proposed model’s applicability was confirmed using a numerical example. [ABSTRACT FROM AUTHOR]

The construction of an accurate and high‐resolution reservoir parameter model is crucial for reservoir characterization. However, due to the band‐limited characteristics of seismic data, the inversion results heavily rely on the accuracy of the initial model. Most existing techniques for constructing an initial model interpolate well logging data within the stratigraphic framework, neglecting the effect of the stratigraphic sequence, which compromises the reliability of the initial model. The stratigraphic sequence is essential for dividing stratigraphic evolution stages and defining a geological relationship between reservoirs within the stratigraphic framework. Therefore, an initial model construction method constrained by stratigraphic sequence representation is proposed for pre‐stack seismic inversion. The process begins with establishing the stratigraphic framework using horizon and fault data. Subsequently, the collaborative sparse representation algorithm is used to learn a joint dictionary that captures the relationship of structural features between seismic data and stratigraphic sequence from the well logging data. In the process of seismic data representation, the stratigraphic sequence is accurately represented in three‐dimensional space by sharing sparse coefficients in the joint dictionary. Finally, the elastic parameter model is constructed by integrating the stratigraphic framework, stratigraphic sequence and well logging data, providing a reliable initial model for pre‐stack seismic inversion. The main innovation of the proposed method is the three‐dimensional representation of the stratigraphic sequence. A synthetic example demonstrates that the proposed method produces a more accurate initial model than conventional interpolation methods. Additionally, when applied to field data, it yields satisfactory results even without complete S‐wave velocity well logging data. [ABSTRACT FROM AUTHOR]

The article focuses on enhancing contextual ranking models by proposing data augmentation methods to improve ranking performance effectively and robustly. It mentions by utilizing supervised and unsupervised augmentation schemes, along with contrastive losses adapted for ranking tasks, the study demonstrates significant performance improvements, particularly in sample efficiency and robustness across in-domain and out-of-domain benchmarks.

This paper presents a comparison of numerical properties of the fixed-grid method of characteristics resulting from space and time linear interpolation used for the solution of transient flow in pipe equations. Modified equation analysis method is applied, in which the modified equations derived for the simplified linear version of the transient pipe flow equations provide explicitly the coefficients of numerical diffusion and dispersion generated by the method of characteristics. Through this approach the value of the numerical diffusion coefficient generated in the solution can be precisely estimated. Consequently, the effects resulting from the interpolation in time and space can be compared. The conclusions presented were confirmed by the results of numerical calculations. Practical Applications: If a valve is suddenly closed at the end of a pipeline in which water flows, a pressure wave will appear in it. This phenomenon, known as the water hammer, commonly occurs in water supply networks and in various industrial installations. The wave propagation process is described by a system of differential equations, which are solved using numerical methods. Numerical methods are approximate; they allow to solve the mathematical problems in which both the data and the results of calculations are given in the form of numbers. Numerical methods enable the calculation of approximate pressure and velocity values at selected cross-sections of the pipeline and at selected moments of time. The calculated values contain an error that depends on the solution method. This error determines the quality of the water hammer simulation results. There are a number of methods for numerical solution of water hammer equations. In this paper, the method of characteristics is used, which requires interpolating pressure and velocity values between selected points. The article shows that the generated numerical error depends on the applied technique of interpolation. Two techniques, interpolation in space and interpolation in time, are considered. [ABSTRACT FROM AUTHOR]

Producing spatial transformations that are diffeomorphic is a key goal in deformable image registration. As a diffeomorphic transformation should have positive Jacobian determinant | J | everywhere, the number of pixels (2D) or voxels (3D) with | J | < 0 has been used to test for diffeomorphism and also to measure the irregularity of the transformation. For digital transformations, | J | is commonly approximated using a central difference, but this strategy can yield positive | J | 's for transformations that are clearly not diffeomorphic—even at the pixel or voxel resolution level. To show this, we first investigate the geometric meaning of different finite difference approximations of | J | . We show that to determine if a deformation is diffeomorphic for digital images, the use of any individual finite difference approximation of | J | is insufficient. We further demonstrate that for a 2D transformation, four unique finite difference approximations of | J | 's must be positive to ensure that the entire domain is invertible and free of folding at the pixel level. For a 3D transformation, ten unique finite differences approximations of | J | 's are required to be positive. Our proposed digital diffeomorphism criteria solves several errors inherent in the central difference approximation of | J | and accurately detects non-diffeomorphic digital transformations. The source code of this work is available at https://github.com/yihao6/digital_diffeomorphism. [ABSTRACT FROM AUTHOR]

Let {Xυ: υ ∈ ℤd} be i.i.d. random variables. Let S (π) = ∑ υ ∈ π X υ be the weight of a self-avoiding lattice path π. Let M n = max { S (π) : π has length n and starts from origin }. We are interested in the asymptotics of Mn as n → ∞. This model is closely related to the first passage percolation when the weights {Xυ: υ ∈ ℤd} are non-positive and it is closely related to the last passage percolation when the weights {Xυ, υ ∈ ℤd} are non-negative. For general weights, this model could be viewed as an interpolation between first passage models and last passage models. Besides, this model is also closely related to a variant of the position of right-most particles of branching random walks. Under the two assumptions that ∃ α > 0 , E (X 0 +) d (log + X 0 +) d + α < + ∞ and that E [ X 0 − ] < + ∞ , we prove that there exists a finite real number M such that Mn/n converges to a deterministic constant M in L1 as n tends to infinity. And under the stronger assumptions that ∃ α > 0 , E (X 0 +) d (log + X 0 +) d + α < + ∞ and that E [ (X 0 −) 4 ] < + ∞ , we prove that Mn/n converges to the same constant M almost surely as n tends to infinity. [ABSTRACT FROM AUTHOR]

Many research methodologies aim to calculate forest resource and firewood consumption on the village, community, municipality, regional, and national levels. This parameter is vital for decision-makers in a number of areas, such as environmental protection, forest governance, energy, the economy, and disaster risk management and prevention. As a number of studies show, there is no alternative to heating with firewood in Georgian villages. This model uses a dataset for Georgia to facilitate the calculation of the aforementioned parameter for populated areas via PostGIS spatial analysis and statistical analysis of existing data. Elevations, degree-days, and firewood consumption rates were measured per capita and household for populated areas. The model determines the volume of firewood required for heating in rural settlements. The demand for firewood in each village can be calculated by the number of inhabitants. Settlements represent minor administrative units according to which firewood consumption on any administrative level, whether it be on regional or municipal levels, is defined. [ABSTRACT FROM AUTHOR]

This paper deals with the methods of construction of trigonometrical tables and interpolation techniques used by ancient Indian mathematicians to calculate intermediate functional values by taking different values of Sinus Totus. The primary purpose for the development of these techniques is to know the correct positions of stars, planets, and other celestial bodies. Some instances have been given for interpolating sine, and charts comparing the values obtained through these techniques to contemporary values have been presented. [ABSTRACT FROM AUTHOR]

This paper proposes a Fourier-Legendre spectral method to find the minimizers of a variational problem, called \sigma _{2,p}-energy, in polar coordinates. Let {\mathbb {X}}\subset \mathbb {R}^n be a bounded Lipschitz domain and consider the energy functional (1.1) whose integrand is defined by {\mathbf {W}}(\nabla u(x))≔(\sigma _2(u))^{\frac {p}{2}}+\Phi (\det \nabla u) over an appropriate space of admissible maps, \mathcal {A}_p({\mathbb {X}}). Using Fourier and Legendre interpolation errors, we obtain an error estimate for the energy functional and prove a convergence theorem for the proposed method. Furthermore, we apply the gradient descent method to solve a nonlinear algebraic system which is obtained by discretizing the Euler-Lagrange equations. The numerical experiments are performed to demonstrate the accuracy and effectiveness of our method. [ABSTRACT FROM AUTHOR]

This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime. • A global LPV model of the BSD is built by interpolation modeling. • A modal-based LPV pole placement control is proposed to achieve modal control. • The proposed modeling and control achieve precise tracking and excellent robustness. [ABSTRACT FROM AUTHOR]

Fast Leja points on an interval are points constructed using a discrete modification of the algorithm for constructing Leja points. Not much about fast Leja points has been proven theoretically. We present an asymptotic property of a triangular interpolation array, and under the assumption that fast Leja points satisfy this property, we prove that they are good for Lagrange interpolation. [ABSTRACT FROM AUTHOR]

We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be cast within a modified weighted pluripotential theoretic framework. Indeed, in the proposed modification a vector valued weight is considered, allowing to partially extend the main asymptotic results holding for interpolation of scalar valued functions to the case of vector valued ones. As motivating example and main application we specialize our results to interpolation of differential forms by differential forms with polynomial coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we compare two novel approaches for effectively determining the optimal value of the shape parameter in Radial Basis Function (RBF) interpolation, a crucial factor for numerical method accuracy. We analyze the results of applying the deterministic Leave-One-Out Cross Validation (LOOCV) method in combination with Lipschitz Global Optimization with Pessimistic Improvement (GOPI) and Optimistic Improvement (GOOI), contrasting them with the statistical Bayesian Optimization (BO). Both techniques yield similar validation errors, underlining their effectiveness in shape parameter search. However, the deciding factor in technique selection lies in computational time, which is contingent upon the cardinality of the interpolation set. [ABSTRACT FROM AUTHOR]

This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this, we develop some aspects of the theory of such polynomials. We then give a number of related multivariate polynomial interpolation schemes for R4 and C2 with good geometric properties, and some aspects of least interpolation and of Kergin interpolation. [ABSTRACT FROM AUTHOR]

Surface defect detection on wafers is crucial for quality control in semiconductor manufacturing. However, the complexity of defect spatial features, including mixed defect types, large scale differences, and overlapping, results in low detection accuracy. In this paper, we propose a CC-De-YOLO model, which is based on the YOLOv7 backbone network. Firstly, the coordinate attention is inserted into the main feature extraction network. Coordinate attention decomposes channel attention into two one-dimensional feature coding processes, which are aggregated along both horizontal and vertical spatial directions to enhance the network's sensitivity to orientation and position. Then, the nearest neighbor interpolation in the upsampling part is replaced by the CAR-EVC module, which predicts the upsampling kernel from the previous feature map and integrates semantic information into the feature map. Two residual structures are used to capture long-range semantic dependencies and improve feature representation capability. Finally, an efficient decoupled detection head is used to separate classification and regression tasks for better defect classification. To evaluate our model's performance, we established a wafer surface defect dataset containing six typical defect categories. The experimental results show that the CCDe-YOLO model achieves 91.0% mAP@0.5 and 46.2% mAP@0.5:0.95, with precision of 89.5% and recall of 83.2%. Compared with the original YOLOv7 model and other object detection models, CC-De-YOLO performs better. Therefore, our proposed method meets the accuracy requirements for wafer surface defect detection and has broad application prospects. The dataset containing surface defect data on wafers is currently publicly available on GitHub (https://github.com/ztao3243/Wafer-Datas.git). [ABSTRACT FROM AUTHOR]

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Aiming at the interpolation and prediction problems in pit monitoring data processing, this paper introduced the interpolation model and extrapolation model of the generalised extended approximation method. Firstly, the formula of the generalised extended approximation method was derived, and then the 10-month monitoring data of the vertical displacement monitoring point of the pile top of a foundation pit was used for denoising pre-processing before calculation and analysis. The interpolation analysis was carried out based on the generalised extended approximation method, and the sliding algorithm was adopted to study the relationship between the combination of different unit domain nodes r, extended domain nodes s and approximation function terms t and the interpolation accuracy. The results of the data calculations show that the accuracy is relatively stable when s is larger, r and t are relatively small and closer, and the interpolation accuracy of the combination r = 2, t = 3 and s = 4 reaches the highest. The extrapolation accuracy of the generalised extended approximation method is investigated, and the data analysis shows that there is a positive relationship between the number of known nodes and the interpolation accuracy. The study concludes that the interpolation model and extrapolation model of the generalised extended approximation method have high computational accuracy, which can reach the sub-millimetre level, and are suitable for pit monitoring data processing, with good engineering value and application prospects. [ABSTRACT FROM AUTHOR]

We propose new methods to obtain simultaneous false discovery proportion bounds for knockoff-based approaches. We first investigate an approach based on Janson and Su's k -familywise error rate control method and interpolation. We then generalize it by considering a collection of k values, and show that the bound of Katsevich and Ramdas is a special case of this method and can be uniformly improved. Next, we further generalize the method by using closed testing with a multi-weighted-sum local test statistic. This allows us to obtain a further uniform improvement and other generalizations over previous methods. We also develop an efficient shortcut for its implementation. We compare the performance of our proposed methods in simulations and apply them to a data set from the UK Biobank. [ABSTRACT FROM AUTHOR]

It has been proven that Graph Neural Networks focus more on the majority class instances and ignore minority class instances when the class distribution is imbalanced. To address the class imbalance problems on graphs, most of the existing approaches rely on the availability of minority nodes in the training set, which may be scarce in extremely imbalanced situations and lead to overfitting. To tackle this issue, this paper proposes a novel oversampling-based Neighbor imbalanced-aware Graph Neural Networks, abbreviated as Nia-GNNs. Specifically, we propose a novel interpolation method that selects interpolated minority nodes from the entire dataset according to their predicted labels and similarity. Meanwhile, a class-wise interpolation ratio is applied to prevent the generation of out-of-domain nodes. Additionally, the generated minority nodes are inserted into the neighbor of minority nodes according to their neighbor distribution to balance the graph both neighborly and globally. Numerous experiments on different imbalanced datasets demonstrate the superiority of our method in classifying imbalanced nodes. [ABSTRACT FROM AUTHOR]

We derive a family of interpolation estimates which improve Hardy's inequality and cover the Sobolev critical exponent. We also determine all optimizers among radial functions in the endpoint case and discuss open questions on nonrestricted optimizers. [ABSTRACT FROM AUTHOR]

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Summary: Weighted compact nonlinear schemes (WCNSs) are a popular family of high‐resolution shock‐capturing schemes for simulating compressible flows, of which the nonlinear interpolation procedure is dominant for the performance. In this work, a simplified weighting strategy is introduced for the nonlinear interpolation procedure. Firstly, an equivalent weighting formulation of WCNS is presented by explicitly including the whole‐point stencil into the set of candidate stencils. Secondly, motivated by the reorganization of WCNS, the WCNS‐CU6 scheme is achieved in a more straightforward way. Thirdly, by introducing a TENO selection procedure in the framework of WCNS‐CU6‐Simplified, a TCNS6‐Simplified scheme is proposed, the resolution of which is comparable with the excellent TENO6 scheme, while the computational cost is much lower. The simplified schemes exhibit more outstanding, at least comparable, fidelity than the original schemes, however, with superior characteristics in terms of efficiency and simplicity. A variety of benchmark test problems are studied to demonstrate the behaviour of the simplified weighting strategy. [ABSTRACT FROM AUTHOR]

Space-time video super-resolution (ST-VSR) aims to simultaneously expand a given source video to a higher frame rate and resolution. However, most existing schemes either consider fixed intermediate time and scale or fail to exploit long-range temporal information due to model design or inefficient motion estimation and compensation. To address these problems, we propose a continuous ST-VSR method to convert the given video to any frame rate and spatial resolution with Multi-stage Motion information reorganization (MsMr). To achieve time-arbitrary interpolation, we propose a forward warping guided frame synthesis module and an optical flow-guided context consistency loss to better approximate extreme motion and preserve similar structures among input and prediction frames. To realize continuous spatial upsampling, we design a memory-friendly cascading depth-to-space module. Meanwhile, with the sophisticated reorganization of optical flow, MsMr realizes more efficient motion estimation and motion compensation, making it possible to propagate information from long-range neighboring frames and achieve better reconstruction quality. Extensive experiments show that the proposed algorithm is flexible and performs better on various datasets than the state-of-the-art methods. The code will be available at https://github.com/hahazh/LD-STVSR. [ABSTRACT FROM AUTHOR]

Particulate matter 2.5 µm (PM2.5) or less in diameter is one of the most important air pollutants owing to its harmful effects on health. However, the measured data of PM2.5 in air quality monitoring networks may have large missing values owing to equipment failure. We conducted a comparative study of imputation techniques for missing value estimation in PM2.5, which was regularly measured in the air quality monitoring network in Lima City, Peru. Lima is the second most polluted city in South America. In this regard, various imputation techniques were implemented, among them, moving averages-based approaches (e.g., Autoregressive Integrated Moving Average ARIMA, Exponentially Weighted Moving Average EWMA, Linear Weighted Moving Average LWMA, and Local Average of Nearest Neighbors LANN), interpolation-based models (e.g., spline), and deep learning-based methods (e.g., Long Short-Term Memory LSTM, Bidirectional LSTM, Gated Recurrent Unit GRU, and Bidirectional GRU) to estimate missing values in PM2.5 time series. For experimentation, a dataset of 11822 h was used, considering 80% for training and the remaining 20% for testing. The results in terms of RMSE, MAPE, and R2 demonstrated that for different configurations of short-gaps of missing values, the techniques based on moving averages yielded better results than those based on deep learning. Among the moving average-based techniques, ARIMA was the best model for estimating missing values in PM2.5 time series, and the MAPE values ranged from 0.0005% to 11.6522%. [ABSTRACT FROM AUTHOR]

This article explores various techniques for generating fractal-like Bézier curves in both 2D and 3D environments. It delves into methods such as subdivision schemes, Iterated Function System (IFS) theory, perturbation of Bézier curves, and perturbation of Bézier basis functions. The article outlines conditions on subdivision matrices necessary for convergence and demonstrates their use in creating an IFS with an attractor aligned to the convergent point of the subdivision scheme based on specified initial data. Additionally, it discusses conditions for obtaining a one-sided approximation of a given Bézier curve through perturbation. The article also addresses considerations for perturbed Bézier basis functions to construct fractal-like Bézier curves that remain within the convex hull polygon/polyhedron defined by control points. These methods find applications in various fields, including computer graphics, art, and design. [ABSTRACT FROM AUTHOR]

The goal of this investigation is to achieve the numerical solution of a two-dimensional parabolic partial differential equation(PDE). The proposed method of this paper is based on the discrete Legendre Galerkin method and spectral collocation method to simplify the spatial derivatives and time derivatives. The discrete Galerkin method is a very fast technique compared to the classical Galerkin method since a finite sum is needed for determining the interpolation coefficients. The operational matrix of the discrete Legendre polynomials is introduced to discretize the time derivatives. Using these couple of techniques and the collocation method, the aforementioned problem is transformed into a solvable algebraic system. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we explain how to obtain sets of descriptors of the spatial variation, which we call “predictive Moran's eigenvector maps” (pMEM), that can be used to make spatially explicit predictions for any environmental variables, biotic or abiotic. It unites features of a method called “Moran's eigenvector maps” (MEM) and those of spatial interpolation, and produces sets of descriptors that can be used with any other modelling method, such as regressions, support vector machines, regression trees, artificial neural networks and so on. The pMEM are the predictive eigenvectors produced by using a distance‐weighting function (DWF) in the construction of MEM. Seven types of pMEM, each associated with one of seven different DWFs, were defined and studied. We performed a simulation study to determine the power of different types of pMEM eigenfunctions at making accurate predictions for spatially structured variables. We exemplified the application of the method to the prediction of the spatial distribution of 35 Oribatid mites living in a peat moss (Sphagnum) mat on the shore of a Laurentian lake. We also provide an R language package called pMEM to make calculations easily available to end users. The results indicate that anyone of the pMEMs obtained from the different DWFs could be the best suited one to predict spatial variability in a given data set. Their application to the prediction of mite distributions highlights the capability of pMEMs for predicting distributions, and for providing spatially explicit estimates of environmental variables that are useful for predicting distributions.

Groundwater analysis across the Oum Rbia watershed is currently hampered by technical constraints and high costs. This research aims to produce comprehensive groundwater quality maps throughout the basin's aquifers by integrating the Water Quality Index (WQI) and Microbiological Quality Index (MQI) with GIS-Pro for a spatiotemporal assessment of water quality. Twenty physicochemical parameters, including pH, temperature, conductivity, total dissolved solids, permanganate index, ammonium (NH₄⁺), major cations (Na⁺, K⁺, Ca²⁺, Mg²⁺, Mn²⁺), major anions (Cl⁻, HCO₃⁻, NO₂⁻, NO₃⁻, CO₃²⁻, SO₄²⁻), total hardness (TH), total alkalinity (TAC), and total iron (FeT) concentration were analyzed. Additionally, the microbiological parameters such as the fecal streptococci, fecal coliforms, and total coliforms were investigated. Fieldwork spanning twelve campaigns across 2021 and 2022 seasons involved sample collection at fifty four locations distributed throughout the watershed's six aquifers. The comprehensive database facilitated the calculation of both MQI and WQI. Kriging interpolation was utilized to create spatial estimates of these indices beyond the sampling points, enabling the generation of maps that visualize water quality across the study area. The WQI indicated that groundwater in most of the studied basin is of excellent quality, though water quality deteriorates in areas receiving wastewater discharge from urban, industrial, and agricultural activities. The MQI results revealed significant pathogenic germ contamination across a substantial portion of the watershed, intensifying during the summer due to factors such as temperature, river flow, human activities, and seasonal pollution sources. These maps enhance the understanding of water table information for non-experts and aid decision-makers in identifying critical areas and developing effective management strategies. However, complexities in water quality and training data influence the accuracy of ArcGIS-Pro predictions, potentially overlooking key factors if the data is insufficient.

Agricultural insect pests reduce crop productivity, causing a gap between global food demand and production. Early detection and early response can improve pest control efficiency. The study aimed to investigate the spatial correlations between Brown Plant Hopper (BPH) occurrence and affected factors using field data collection in Can Tho City, Vietnam. The data on cultivation practices and meteorological conditions at 120 sites every week during the rice cropping season of 2016–2017 were collected to find the correlation between the occurrence frequency and density of BHP. Besides, GIS and spatial interpolation were applied to assess the current status of harmful situations, predict the impact trends of crop pests or diseases in space and time to serve a community's needs, and forecast plant protection. As a result, in the 2nd rice cropping stage, the population of brown planthoppers were found to be highly significantly influenced by factors: (1) planthopper age, (2) natural enemy density, (3) air temperature, (4) field water level, and (5) number of leaves, which is highly positively correlated with brown hopper density. There is a lower correlation between leaf color code (6) and air humidity (7) and a negative correlation between pesticides used (8). The variables of rice leaf color code (6) and air humidity (7) correlate with the BHP population, although the field water level (4) and leaf count (5) do not correlate for the whole crop. It can be used to predict the changing trend of BHP in rice fields. However, the factors influencing the brown planthopper would determine the prognosis's accuracy.

Extended Abstract Background: The use of groundwater for agricultural, industrial, and drinking purposes is significantly increasing worldwide. These resources are considered an important part of the renewable water ecosystem and have various advantages over surface waters, such as higher quality and less contamination. However, recent intermittent droughts and a noticeable decrease in surface water resources have led to the excessive use of groundwater sources and a decline in their quality. Therefore, understanding the quality of groundwater is crucial for proper planning and management of these resources and requires serious attention and detailed analysis. Additionally, one of the health problems in developing areas is the lack of access to safe drinking water, and human health is at the core of sustainable development in the region. Therefore, ensuring the welfare and health of the community at an acceptable level is not possible without access to clean and standardized drinking water. Water is important from both health and economic perspectives as it serves as a catalyst for industrial growth and the prosperity of the agricultural sector. In this regard, this research aims to evaluate and analyze the quality and spatial changes in groundwater quality based on the GQI assessment index. Methods: This research focuses on evaluating and analyzing spatial changes in groundwater quality within the study areas of Khanmirza, Lordegan, Boroujen, Ardal, and Kiar, located in Chaharmahal and Bakhtiari province, for drinking purposes. Practical information is provided regarding the status of available water resources in the region for drinking purposes. To this aim, 28 groundwater samples were collected from legally operating wells in various locations within the mentioned counties during the 2020-2021 period and subjected to chemical analysis in the laboratory. The GQI (Groundwater Quality Index) was used to assess the quality of these samples for drinking purposes. In this study, the GQI was calculated based on the concentration values of 11 parameters, including electrical conductivity, acidity, total dissolved salts, calcium ion, sodium, magnesium, potassium, carbonate, bicarbonate, chloride, and sulfate. Subsequently, spatial zoning of the overall parameter values was performed using the chemical characteristics of the collected samples and employing the inverse distance weighting (IDW) interpolation method in the GIS software environment, and the desired information layers were obtained in raster format. Furthermore, overlays were performed by applying computational functions to the available information layers,, followed by estimating the GQI values and preparing raster maps of the index. The output maps can be utilized not only to determine the qualitative characteristics within the study area but also to analyze the trends of their variations, prepare zoning maps for each parameter, and compare them with standard values. Results: The calculated GQI using measured samples categorizes a significant portion of the study area within the excellent and good quality categories suitable for drinking. Additionally, the color spectrum of the zoning map indicates better water quality in the western and southern parts of the study area than in the other sections. Generally, water quality decreases from the south toward the north and northeast. The sensitivity analysis of the model focuses on examining the impact of changing one input variable on a model's output variable. The sensitivity analysis revealed that parameters such as acidity, calcium, magnesium, total dissolved salts, and electrical conductivity had a negative effect (meaning an increase in index values and water quality improvement after removing these parameters and deterioration with their addition in the index calculation). Conversely, the concentrations of bicarbonate ions, sulfate, sodium, potassium, and chloride had a positive impact on water quality (meaning a decrease in index values and deterioration after removing these parameters and improvement with their addition in the index calculation). These parameters have allocated the highest to lowest changes in estimating the GQI index. Therefore, the GQI quality index shows greater sensitivity to the presence or absence of acidity and calcium bicarbonate than the other parameters used in determining the index, influencing decision-making regarding the classification of drinking water quality more than the other parameters. Despite having higher weights in calculating the index, some parameters show insignificant percentage changes in the index due to their presence or absence. For example, despite a lower weight of bicarbonate than magnesium ions, it shows a higher percentage change in the index after its removal than the percentage change caused by removing magnesium. Thus, higher weights for these components do not necessarily imply greater sensitivity of the model to them. Conclusion: The results of this study indicate that the groundwater quality in the studied areas is suitable for drinking purposes, and the groundwater in the study area has not been affected by changes resulting from the tested parameters in the drinking sector. Additionally, this study contributes to comprehensive and useful planning for the management and conservation of groundwater resources, enabling more informed decision-making based on groundwater quality maps in this regard.

Abstract This paper defines a family of neural-network interpolation operators. The first derivative of generalized logistic-type functions is considered as a density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators F n a , ε $F_{n}^{a,\varepsilon} $ is also introduced. The approximation of Kantorovich-type operators in L P $L_{P}$ spaces with 1 ≤ p ≤ ∞ $1 \leq p\leq \infty $ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function θ s , a $\theta _{s, a}$ are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator F n a , ε $F_{n}^{a,\varepsilon} $ and the Kantorovich variant of the operator F n a , ε $F_{n}^{a,\varepsilon} $ , the approximation of various function examples is studied.