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A new population analysis, ADCHα-I, based on the interpolation between the Hirshfeld (H) and the iterative Hirshfeld (H-I) methods through a parameter α and on the atomic dipole moment corrected Hirshfeld (ADCH) methodology is proposed, in combination with the constrained dipole moment density functional theory (CD-DFT) previously developed, to determine the charge distributions of force fields. Following this approach, the electronic density of the isolated molecule is determined for the value of the dipole moment that reproduces the experimental dielectric constant, in order to incorporate through this property the effects of the surrounding molecules in the liquid, and to carry on this information to the molecular simulation, the new population analysis is built to obtain the set of charges that reproduces this dipole moment. By selecting α = 1/2, one is led to charges that are larger than the ones obtained through H and ADCH and smaller than those of H-I and that incorporate, at the local level, information about the response of isolated atoms to donate or to accept charge, which is not considered in ADCH. The results obtained for several liquid properties indicate that the combination of CD-DFT with this population analysis leads to a good description of the charge distributions in force fields used in molecular simulations. [ABSTRACT FROM AUTHOR]

The high-order finite difference real-space pseudopotential density functional theory (DFT) approach is a valuable method for large-scale, massively parallel DFT calculations. A significant challenge in the approach is the oscillating "egg-box" error introduced by aliasing associated with a coarse grid spacing. To address this issue while minimizing computational cost, we developed a finite difference interpolation (FDI) scheme [Roller et al., J. Chem. Theory Comput. 19, 3889 (2023)] as a means of exploiting the high resolution of the pseudopotential to reduce egg-box effects systematically. Here, we show an implementation of this method in the PARSEC code and examine the practical utility of the combination of FDI with additional methods for improving force precision and/or reducing its computational cost, including orbital-based forces, compensating charges (namely, adding and subtracting a judiciously chosen charge density such that the total density is unaltered), and a modified spatial domain in which the real-space grid is defined. Using selected small molecules, as well as metallic Li, as test cases, we show that a combination of all four aspects leads to a significant reduction in computational cost while retaining a high level of precision that supports accurate structures and vibrational spectra, as well as stable and accurate molecular dynamics runs. [ABSTRACT FROM AUTHOR]

This study investigated how data series length and gaps in human kinematic data impact the accuracy of Lyapunov exponents (LyE) calculations with and without cubic spline interpolation. Kinematic time series were manipulated to create various data series lengths (28% and 100% of original) and gap durations (0.05–0.20 s). Longer gaps generally resulted in significantly higher LyE% error values in each plane in noninterpolated data. During cubic spline interpolation, only the 0.20-second gap in frontal plane data resulted in a significantly higher LyE% error. Data series length did not significantly affect LyE% error in noninterpolated data. During cubic spline interpolation, sagittal plane LyE% errors were significantly higher at shorter versus longer data series lengths. These findings suggest that not interpolating gaps in data could lead to erroneously high LyE values and mischaracterization of movement variability. When applying cubic spline, a long gap length (0.20 s) in the frontal plane or a short sagittal plane data series length (1000 data points) could also lead to erroneously high LyE values and mischaracterization of movement variability. These insights emphasize the necessity of detailed reporting on gap durations, data series lengths, and interpolation techniques when characterizing human movement variability using LyE values. [ABSTRACT FROM AUTHOR]

Grid is a free and open-source Python library for constructing numerical grids to integrate, interpolate, and differentiate functions (e.g., molecular properties), with a strong emphasis on facilitating these operations in computational chemistry and conceptual density functional theory. Although designed, maintained, and released as a stand-alone Python library, Grid was originally developed for molecular integration, interpolation, and solving the Poisson equation in the HORTON and ChemTools packages. Grid is designed to be easy to use, extend, and maintain; this is why we use Python and adopt many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. We leverage popular scientific packages, such as NumPy and SciPy, to ensure high efficiency and optimized performance in grid development. This article is the official release note of the Grid library showcasing its unique functionality and scope. [ABSTRACT FROM AUTHOR]

Enhanced sampling algorithms are indispensable when working with highly disconnected multimodal distributions. An important application of these is the conformational exploration of particular internal degrees of freedom of molecular systems. However, despite the existence of many commonly used enhanced sampling algorithms to explore these internal motions, they often rely on system-dependent parameters, which negatively impact efficiency and reproducibility. Here, we present fully adaptive simulated tempering (FAST), a variation of the irreversible simulated tempering algorithm, which continuously optimizes the number, parameters, and weights of intermediate distributions to achieve maximally fast traversal over a space defined by the change in a predefined thermodynamic control variable such as temperature or an alchemical smoothing parameter. This work builds on a number of previously published methods, such as sequential Monte Carlo, and introduces a novel parameter optimization procedure that can, in principle, be used in any expanded ensemble algorithms. This method is validated by being applied on a number of different molecular systems with high torsional kinetic barriers. We also consider two different soft-core potentials during the interpolation procedure and compare their performance. We conclude that FAST is a highly efficient algorithm, which improves simulation reproducibility and can be successfully used in a variety of settings with the same initial hyperparameters. [ABSTRACT FROM AUTHOR]

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling–Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations. [ABSTRACT FROM AUTHOR]

In this short paper, we discuss relation between an invariant distance of the bidisk and Kreĭn space geometry. In particular, an interpolation theorem for rational maps with respect to our invariant distance is proven. [ABSTRACT FROM AUTHOR]

Image muscle segmentation is useful to quantitatively assess musculoskeletal diseases by extracting biomarkers such as shape, texture and water diffusivity metrics. Although volumetric manual segmentation is time consuming and a bottleneck in practice, fully automatic approaches are still in progress to reach an acceptable accuracy. In this paper, we provide a robust semi-automated tool to segment two musculoskeletal systems, i.e. thigh and shoulder in MRI and CT modalities, respectively. The tool only needs a few manually labelled cross-sections to build a directed graph-structure of corresponding points between the successive spaced slices. The boundaries of each muscle are obtained by performing a spline interpolation based on the directed graph-structure. Each muscle label and its corresponding 3D mesh are deduced using post-processing techniques. We evaluated the tool on 26 MRI thighs and 16 CT shoulders. Three metrics along with inter-muscle overlapping were employed to evaluate the tool by comparison to an expert manual segmentation and a publicly available tools (ITK-SNAP, 3D Slicer). The results showed a mean Dice $0.988 \pm 0.003$ 0.988 ± 0.003 , and Hausdorff Distance $4.86 \pm 1.67$ 4.86 ± 1.67 mm in comparison to the manual reference for thigh muscle segmentation, and a mean Dice $0.961 \pm 0.005$ 0.961 ± 0.005 and Hausdorff Distance $2.42 \pm 0.79$ 2.42 ± 0.79 mm for shoulder muscle segmentation, outperformed the other methods. The tool is proposed as slicer module available at . [ABSTRACT FROM AUTHOR]

Their monitoring in urban regions is essential for policymakers and the population. In this study, the electromagnetic intensity (EMI) was measured around 30 stations of base transcriptive stations (BTS) at both distances lower than 20m and higher than 200m using real-time equipment SMP2-dual in summer and winter. Results have shown that EMI in summer (range: 2-6500 mW/m2) was more than in winter (1.5-5000), and the intensity of about 93% of samples exceeded WHO standards. EMI has consistently decreased with the increasing distance from BTS. There was a negative correlation between the temperature and EMI in summer and humidity and EMI for both distances. The mapping of EMI depicted the highest value of EMI across the central region from south to eastern north at a distance lower than 20 m in winter. The clustering of the EMI in this region was influenced by the geographical location of BTS. [ABSTRACT FROM AUTHOR]

The set of ST -valid inferences is neither the intersection, nor the union of the sets of K 3 -valid and LP -valid inferences, but despite the proximity to both systems, an extensional characterization of ST in terms of a natural set-theoretic operation on the sets of K 3 -valid and LP -valid inferences is still wanting. In this paper, we show that it is their relational product. Similarly, we prove that the set of TS -valid inferences can be identified using a dual notion, namely as the relational sum of the sets of LP -valid and K 3 -valid inferences. We discuss links between these results and the interpolation property of classical logic. We also use those results to revisit the duality between ST and TS . We present a notion of duality on which ST and TS are dual in exactly the same sense in which LP and K 3 are dual to each other. [ABSTRACT FROM AUTHOR]

Biogeographic studies offer valuable insights into the origin, distribution and extinction of biodiversity. As such, this study aims to identify patterns of diversity and distribution of freshwater ichthyofauna in the state of Espírito Santo, to delineate biogeographic units and to propose a hypothesis of area relationship. A database containing information on 123 fish species occurrences was compiled to conduct analyses of species richness interpolation, bioregionalization, sampling effort interpolation, endemism, and a parsimony analysis of endemism. The sampling effort in Espírito Santo is uneven, with higher representativeness of sampling sites in the highlands. Six freshwater ichthyofauna bioregions were identified, along with three major areas of increased species richness, two consensus areas of endemism and three groups of basins. The central basins of the state are characterized by a marked presence of endemic species. The southern basins also stand out as an area of endemism and density of species typical of mountainous environments, such as loricariids; they are also characterized by a significant faunal overlap with the Rio Paraíba do Sul basin. The results of this biogeographic evaluation reinforce the perception that the watersheds of the state of Espírito Santo have a diverse and characteristic freshwater fish fauna, with well-defined biogeographic units. [ABSTRACT FROM AUTHOR]

We propose a benchmark for comparing gap-filling techniques used on global time-variable gravity field time-series. The Gravity Recovery and Climate Experiment (GRACE) and the GRACE Follow-On missions provide products to study the Earth’s time-variable gravity field. However, the presence of missing months in the measurements poses challenges for understanding specific Earth processes through the gravity field. We reproduce, adapt, and compare satellite-monitoring and interpolation techniques for filling these missing months in GRACE and GRACE Follow-On products on a global scale. Satellite-monitoring techniques utilize solutions from Swarm and satellite laser ranging, while interpolation techniques rely on GRACE and/or Swarm solutions. We assess a wide range of interpolation techniques, including least-squares fitting, principal component analysis, singular spectrum analysis, multichannel singular spectrum analysis, auto-regressive models, and the incorporation of prior data in these techniques. To inter-compare these techniques, we employ a remove-and-restore approach, removing existing GRACE products and predicting missing months using interpolation techniques. We provide detailed comparisons of the techniques and discuss their strengths and limitations. The auto-regressive interpolation technique delivers the best score according to our evaluation metric. The interpolation based on a least-squares fitting of constant, trend, annual, and semi-annual cycles offers a simple and effective prediction with a good score. Through this assessment, we establish a starting benchmark for gap-filling techniques in Earth’s time-variable gravity field analysis. [ABSTRACT FROM AUTHOR]

Mobile health has emerged as a major success for tracking individual health status, due to the popularity and power of smartphones and wearable devices. This has also brought great challenges in handling heterogeneous, multi-resolution data that arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model for irregular multi-resolution time series data to interpolate unsampled measurements of time series with low resolution. One major advantage of the proposed method is the capability to integrate multiple irregular time series and multiple subjects by mapping the multi-resolution data to the latent space. In addition, the proposed individualized dynamic latent factor model is applicable to capturing heterogeneous longitudinal information through individualized dynamic latent factors. Our theory provides a bound on the integrated interpolation error and the convergence rate for B -spline approximation methods. Both the simulation studies and the application to smartwatch data demonstrate the superior performance of the proposed method compared to existing methods. [ABSTRACT FROM AUTHOR]

Complex valued measures of finite total variation are a powerful signal model in many applications. Restricting to the d-dimensional torus, finitely supported measures can be exactly recovered from their trigonometric moments up to some order if this order is large enough. Here, we consider the approximation of general measures, e.g., supported on a curve, by trigonometric polynomials of fixed degree with respect to the 1-Wasserstein distance. We prove sharp lower bounds for their best approximation and (almost) matching upper bounds for effectively computable approximations when the trigonometric moments of the measure are known. A second class of sum of squares polynomials is shown to interpolate the indicator function on the support of the measure and to converge to zero outside. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel two‐step modeling method to generalize cubic Hermite interpolators on the space of probability measures P+(I)$$ {\mathcal{P}}_{+}(I) $$. First, we develop new approaches to capture the Riemannian geometric structure of P+(I)$$ {\mathcal{P}}_{+}(I) $$ when equipped with Fisher–Rao metric. Furthermore, we develop and detail all numerical tools on P+(I)$$ {\mathcal{P}}_{+}(I) $$, namely, Levi–Civita connection, minimal geodesics, parallel transport, exponential map, and logarithm map. Then, we demonstrate that preliminary analysis results yield significant benefits in constructing an optimal cubic Hermite spline on P+(I)$$ {\mathcal{P}}_{+}(I) $$ as a nonlinear Riemannian manifold, precisely where conventional numerical methods fail. [ABSTRACT FROM AUTHOR]

Given the high costs of soil sampling, low and extra-low sampling densities are still being used. Low-density soil sampling usually does not allow the computation of experimental variograms reliable enough to fit models and perform interpolation. In the absence of geostatistical tools, deterministic methods such as inverse distance weighting (IDW) are recommended but they are susceptible to the "bull's eye" effect, which creates non-smooth surfaces. This study aims to develop and assess interpolation methods or approaches to produce soil test maps that are robust and maximize the information value contained in sparse soil sampling data. Eleven interpolation procedures, including traditional methods, a newly proposed methodology, and a kriging-based approach, were evaluated using grid soil samples from four fields located in Central Alberta, Canada. In addition to the original 0.4 ha⋅sample−1 sampling scheme, two sampling design densities of 0.8 and 3.5 ha⋅sample−1 were considered. Among the many outcomes of this study, it was found that the field average never emerged as the basis for the best approach. Also, none of the evaluated interpolation procedures appeared to be the best across all fields, soil properties, and sampling densities. In terms of robustness, the proposed kriging-based approach, in which the nugget effect estimate is set to the value of the semi-variance at the smallest sampling distance, and the sill estimate to the sample variance, and the IDW with the power parameter value of 1.0 provided the best approaches as they rarely yielded errors worse than those obtained with the field average. [ABSTRACT FROM AUTHOR]

LiDAR-based 3D scene perception is a fundamental and important task for autonomous driving. Most state-of-the-art methods on LiDAR-based 3D recognition tasks focus on single-frame 3D point cloud data, ignoring temporal information. We argue that the temporal information across the frames provides crucial knowledge for 3D scene perceptions, especially in the driving scenario. In this paper, we focus on spatial and temporal variations to better explore temporal information across 3D frames. We design a temporal variation-aware interpolation module and a temporal voxel-point refinement module to capture the temporal variation in the 4D point cloud. The temporal variation-aware interpolation generates local features from the previous and current frames by capturing spatial coherence and temporal variation information. The temporal voxel-point refinement module builds a temporal graph on the 3D point cloud sequences and captures the temporal variation with a graph convolution module, transforming coarse voxel-level predictions into fine point-level predictions. With our proposed modules, we achieve superior performances on SemanticKITTI, SemantiPOSS and NuScenes. [ABSTRACT FROM AUTHOR]

Directional interpolation is a fast and efficient compression technique for high‐frequency Helmholtz boundary integral equations, but requires a very large amount of storage in its original form. Algebraic recompression can significantly reduce the storage requirements and speed up the solution process accordingly. During the recompression process, weight matrices are required to correctly measure the influence of different basis vectors on the final result, and for highly accurate approximations, these weight matrices require more storage than the final compressed matrix. We present a compression method for the weight matrices and demonstrate that it introduces only a controllable error to the overall approximation. Numerical experiments show that the new method leads to a significant reduction in storage requirements. [ABSTRACT FROM AUTHOR]

We introduce truncated Besov and Triebel–Lizorkin function spaces and study their main properties: embeddings, interpolation, duality, lifting, traces. These new scales allow us to improve several known results in functional analysis and PDE's. In particular, we obtain a full solution to the trace/extension problem in the critical case as well as sharp Sobolev-type embeddings with critical smoothness parameters. [ABSTRACT FROM AUTHOR]

The identification of a suitable transformation model and the calculation of correlation coefficients constitute essential steps in the simulation a nonstationary and non-Gaussian stochastic process. For stochastic ground motion, its nonstationary and non-Gaussian properties are well-known. In this paper, an easy-to-implement simulation method of a nonstationary and non-Gaussian stochastic process with known time-varying statistical moments is proposed. The approximate transformation model between the nonstationary and non-Gaussian stochastic process and the underlying Gaussian process, which contains the wider range of applicability and the availability of explicit expressions for determining the distribution parameters, is determined. The time-varying correlation coefficient of the underlying Gaussian process is calculated through the proposed interpolation method. Furthermore, the effectiveness of the proposed simulation method of the nonstationary and non-Gaussian stochastic ground motion is verified by numerical examples. [ABSTRACT FROM AUTHOR]

Let C ⊂ ℙ 3 be a general Brill–Noether curve. A classical problem is to determine when H 0 (N C (− 2)) = 0 , which controls the quadric section of C. So far this problem has only been solved in characteristic zero, in which case H 0 (N C (− 2)) = 0 with finitely many exceptions. In this paper, we extend these results to positive characteristic, uncovering a wealth of new exceptions in characteristic  2. [ABSTRACT FROM AUTHOR]

In this paper, we study a posteriori error estimates for one-dimensional and two-dimensional linear parabolic equations. The backward Euler method and the Crank–Nicolson method for the time discretization are used, and the second-order finite difference method is employed for the space discretization. Based on linear interpolation and interpolation estimate, a posteriori error estimators corresponding to space discretization are derived. For the backward Euler method and the Crank–Nicolson method, the errors due to time discretization are obtained by exploring linear continuous approximation and two different continuous, piecewise quadratic time reconstructions, respectively. As a consequence, the upper and lower bounds of a posteriori error estimates for the fully discrete finite difference methods are derived, and these error bounds depend only on the discretization parameters and the data of the model problems. Numerical experiments are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Incorporating an evidence-based approach in STEM education using data collection and analysis strategies when learning about science concepts enhances primary students' discipline knowledge and cognitive development. This paper reports on learning activities that use the nature of viscosity and the power of informal statistical inference to build students' conceptual understanding of interpolation and extrapolation without imposing on them the demands of understanding the nonlinear mathematics used to explore the concepts at the tertiary level. An exploratory research strategy was adopted to investigate the way in which Year 5 students created and analysed graphical representations from data collected when performing viscosity experiments. The data representations produced by the students and their subsequent predictions were analysed using the Structure of Observed Learning Outcomes (SOLO) model as adapted specifically for graphical representations. The results illustrate that when provided with appropriate technological tools to scaffold student learning, in this case TinkerPlots™, development of students' appreciation of interpolation and extrapolation within meaningful data contexts across the STEM curriculum does not have to wait until the tertiary level. [ABSTRACT FROM AUTHOR]

Space deformations deform the ambient space and thus implicitly deform the embedded objects. Free-Form Deformation allows high-order deformation to the embedding space, yet the lattice may fail to conform to the object and involves many internal control points. Cage-based Deformation utilizes a cage space that conforms to the object, obviating the need for additional internal control points, but it is typically linear at edges. In this paper, we propose a simple and general method with both advantages while avoiding their drawbacks, allowing users to implement high-order cage-based deformation. To achieve this goal, we introduce a new parametric transfinite interpolation scheme based on generalized barycentric coordinates, which unifies and generalizes the rectangular and triangular Coons patch. This C0 Generalized Coons patch can be defined not only over 2D domains but also 3D domains or even higher-dimensional domains, with arbitrary polytopes, even including non-manifold topologies. Moreover, the C0 Generalized Coons patch has an elegant mathematical expression. [ABSTRACT FROM AUTHOR]

Real-time rendering has been embracing ever-demanding effects, such as ray tracing. However, rendering such effects in high resolution and high frame rate remains challenging. Frame extrapolation methods, which do not introduce additional latency as opposed to frame interpolation methods such as DLSS 3 and FSR 3, boost the frame rate by generating future frames based on previous frames. However, it is a more challenging task because of the lack of information in the disocclusion regions and complex future motions, and recent methods also have a high engine integration cost due to requiring G-buffers as input. We propose a G-buffer free frame extrapolation method, GFFE, with a novel heuristic framework and an efficient neural network, to plausibly generate new frames in real time without introducing additional latency. We analyze the motion of dynamic fragments and different types of disocclusions, and design the corresponding modules of the extrapolation block to handle them. After that, a light-weight shading correction network is used to correct shading and improve overall quality. GFFE achieves comparable or better results than previous interpolation and G-buffer dependent extrapolation methods, with more efficient performance and easier integration. [ABSTRACT FROM AUTHOR]

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination. [ABSTRACT FROM AUTHOR]

We introduce ToonCrafter, a novel approach that transcends traditional correspondence-based cartoon video interpolation, paving the way for generative interpolation. Traditional methods, that implicitly assume linear motion and the absence of complicated phenomena like dis-occlusion, often struggle with the exaggerated non-linear and large motions with occlusion commonly found in cartoons, resulting in implausible or even failed interpolation results. To overcome these limitations, we explore the potential of adapting live-action video priors to better suit cartoon interpolation within a generative framework. ToonCrafter effectively addresses the challenges faced when applying live-action video motion priors to generative cartoon interpolation. First, we design a toon rectification learning strategy that seamlessly adapts live-action video priors to the cartoon domain, resolving the domain gap and content leakage issues. Next, we introduce a dual-reference-based 3D decoder to compensate for lost details due to the highly compressed latent prior spaces, ensuring the preservation of fine details in interpolation results. Finally, we design a flexible sketch encoder that empowers users with interactive control over the interpolation results. Experimental results demonstrate that our proposed method not only produces visually convincing and more natural dynamics, but also effectively handles dis-occlusion. The comparative evaluation demonstrates the notable superiority of our approach over existing competitors. Code and model weights are available at https://doubiiu.github.io/projects/ToonCrafter [ABSTRACT FROM AUTHOR]

We propose MiNNIE, a simple yet comprehensive framework for real-time simulation of nonlinear near-incompressible elastics. To avoid the common volumetric locking issues at high Poisson's ratios of linear finite element methods (FEM), we build MiNNIE upon a mixed FEM framework and further incorporate a pressure stabilization term to ensure excellent convergence of multigrid solvers. Our pressure stabilization strategy injects bounded influence on nodal displacement which can be eliminated using a quasiNewton method. MiNNIE has a specially tailored GPU multigrid solver including a modified skinning-space interpolation scheme, a novel vertex Vanka smoother, and an efficient dense solver using Schur complement. MiNNIE supports various elastic material models and simulates them in real-time, supporting a full range of Poisson's ratios up to 0.5 while handling large deformations, element inversions, and self-collisions at the same time. [ABSTRACT FROM AUTHOR]

Interpolation techniques can be used to determine the approximate value of a parameter if it is known that two values are bound to a certain interval. Interpolation can be done numerically or fractal. The fractal interpolation value is influenced by the vertical scale factor and the fractal interpolation function (FIF). This research introduces fractal interpolation technique with FIF which is constructed from Sierspinski triangles. As an example of application, the interpolation technique is applied to determine the approximate value of the rice demand parameter in the inventory model. The accuracy of the interpolation results is determined using the mean absolute percentage error (MAPE). The number of triangles obtained and the interpolation values for each successive iteration are 3n and 3n+1. MAPE values from 6 to 9 iteration were 24.603%, 24.603%, 23.858%, 23.772% respectively. There is a decrease in the value of MAPE, this indicates an increase in the value of the accuracy of the interpolation results. It can be concluded that the MAPE value is also influenced by the number of iterations of the interpolation technique. [ABSTRACT FROM AUTHOR]

Although conceptually attractive, the use of ensemble data assimilation methods, such as the ensemble Kalman filter (EnKF), can be constrained by intensive computational requirements. In such cases, the ensemble optimal interpolation scheme (EnOI), which works on a single model run instead of ensemble evolution, may offer a sub‐optimal alternative. This study explores different approaches of dynamic covariance matrix generation from predefined state vector repositories for assimilating synthetic water level observations with the EnOI scheme into a distributed rainfall‐runoff‐inundation model. Repositories are first created by storing open loop state vectors from the simulation of past flood events. The vectors are later sampled during the assimilation step, based on their closeness to the model forecast (calculated using vector norm). Results suggest that the dynamic EnOI scheme is inferior to the EnKF, but can improve upon the deterministic simulation depending on the sampling approach and the repository used. Observations can also be used for sampling to increase the background spread when the system noise is large. A richer repository is required to reduce analysis degradation, but increases the computation cost. This can be resolved by using a sliced repository consisting of only the vectors with norm close to the model forecast. [ABSTRACT FROM AUTHOR]

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 weekly monitoring sites at Can Tho city during the rice cropping season of 2016-2017 were collected to find the correlation between the occurrence frequency and density of BPH. 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, as well as forecast plant protection. As a result, in the 2nd rice cropping stage, the population of brown planthoppers was found to be highly significantly influenced by the following 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 BPH 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 BPH in rice fields. However, the factors influencing the brown planthopper would determine the accuracy of the prognosis. [ABSTRACT FROM AUTHOR]

In this paper, we prove jet interpolation and approximation theorems for symplectic holomorphic automorphisms, symplectic holomorphic embeddings and symplectic holomorphic self-maps of C 2 n respectively. We discuss the symplectic tame set and give a criterion and some properties on it, on which some of our main theorems are built. [ABSTRACT FROM AUTHOR]

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Taking advantage of the gradual change characteristic of the curvature of the conventional conic ellipse, this paper proposes a method of fitting a non-uniform rational B-spline (NURBS) curve with an elliptical arc and, thereafter, performing speed planning and interpolation of the elliptical arc itself. First, the method of elliptical arc fitting is introduced and then proven by simulation with comparative previous linear and arc fittings to obtain better fitting accuracy with fewer segments. Subsequently, the tangent vector of any point of an ellipse is used to complete the speed planning and interpolation of that ellipse. In terms of speed planning, the maximum acceleration of any point in the elliptical arc can be obtained by using a tangent vector, and the time speed curve in this work is completed based on this phenomenon. In the interpolation stage, the longest axis of the current point is determined by using the tangent vector of any point of the elliptical arc, according to which the pulse is sent, thereby completing the interpolation operation via this iterative cycle. This method unifies the processing model of the interpolation algorithm, the simplicity and efficiency of which is verified by subsequent simulation data. This method can also be universally applied to processing most other types of curve. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we present two constructions: the Lipschitz closed injective hull ideals and the Lipschitz interpolative ideals of a Lipschitz operator ideal. These procedures aim to construct new Lipschitz operator ideals between pointed metric spaces and Banach spaces. The new ideals are characterized by specific criteria that determine whether a Lipschitz operator belongs to them, using summability properties and interpolation formulas. [ABSTRACT FROM AUTHOR]

Radio environment maps (REMs) have demonstrated their significance in spectrum sensing, control, and sharing, particularly in relation to unmanned systems, the Internet of Things (IoT), and 5G communication. However, they encounter challenges related to meeting the increasing accuracy requirements. This paper introduces the BHM-RK algorithm, a novel approach for constructing REMs in scenarios with multiple transmitters. The algorithm utilizes spatial clustering for transmitter partitioning, Bayesian posterior inference within partitions, and residual Kriging interpolation to address challenges posed by diverse transmitter influences. Experimental validation demonstrates the superior performance of the BHM-RK algorithm in terms of construction accuracy compared to existing methods, highlighting its effectiveness in enhancing precision in REM construction for scenarios with multiple transmitters. [ABSTRACT FROM AUTHOR]

ABSTRACT The ν$$ \nu $$‐gap metric has a clear frequency domain interpolation of system uncertainties. However, the ν$$ \nu $$‐gap metric between lightly damped systems may be very close to one, and causes difficulty for robust stability analysis as well as control design. In this article, the problem is addressed by adjusting the weight in the H∞$$ {H}_{\infty } $$ loop‐shaping method to reduce the corresponding weighted ν$$ \nu $$‐gap metric at the resonance frequency (RF). To this end the selection of the weight is essential. The RFs of lightly damped systems with different perturbations often appear in a frequency band rather than at a single frequency. Thus, it is hard to investigate the weight's impact on the weighted ν$$ \nu $$‐gap metric based on any specific perturbation. Particularly, the weight W$$ W $$ may change the sequencing of ν$$ \nu $$‐gap metric of diverse perturbations to the nominal plant, and raises additional issue to the robust stability analysis. The expression of the maximum ν$$ \nu $$‐gap metric in the RF band is derived to tackle these problems. Then, the impact of the weight on the single‐input single‐output weighted ν$$ \nu $$‐gap metric is quantitatively analyzed. This provides a guidance to the H∞$$ {H}_{\infty } $$ loop‐shaping of lightly damped systems. An iterative design of the weight optimization is applied by limiting the upper bound of the frequency response of the shaped plant. The feasibility and advantages of the iterative design is shown by an illustrative example of a single‐phase pulse width modulation rectifier. [ABSTRACT FROM AUTHOR]

Semi-supervised learning techniques utilize both labeled and unlabeled images to enhance classification performance in scenarios where labeled images are limited. However, challenges such as integrating unlabeled images with incorrect pseudo-labels, determining appropriate thresholds for the pseudo-labels, and label prediction fluctuations on low-confidence unlabeled images, hinder the effectiveness of existing methods. This research introduces a novel framework named Interpolation Consistency for Bad Generative Adversarial Networks (IC-BGAN) that utilizes a new loss function. The proposed model combines bad adversarial training, fusion techniques, and regularization to address the limitations of semi-supervised learning. IC-BGAN creates three types of image augmentations and label consistency regularization in interpolation of bad fake images, real and bad fake images, and unlabeled images. It demonstrates linear interpolation behavior, reducing fluctuations in predictions, improving stability, and facilitating the identification of decision boundaries in low-density areas. The regularization techniques boost the discriminative capability of the classifier and discriminator, and send a better signal to the bad generator. This improves the generalization and the generation of diverse inter-class fake images as support vectors with information near the true decision boundary, which helps to correct the pseudo-labeling of unlabeled images. The proposed approach achieves notable improvements in error rate from 2.87 to 1.47 on the Modified National Institute of Standards and Technology (MNIST) dataset, 3.59 to 3.13 on the Street View House Numbers (SVHN) dataset, and 12.13 to 9.59 on the Canadian Institute for Advanced Research, 10 classes (CIFAR-10) dataset using 1000 labeled training images. Additionally, it reduces the error rate from 22.11 to 18.40 on the CINIC-10 dataset when using 700 labeled images per class. The experiments demonstrate the IC-BGAN framework outperforms existing semi-supervised methods, providing a more accurate classification solution with smoother class label estimates, especially for low-confidence unlabeled images. [ABSTRACT FROM AUTHOR]

Semi-supervised learning has gained significant attention in the field of remote sensing due to its ability to effectively leverage both a limited number of labeled samples and a large quantity of unlabeled data. An effective semi-supervised learning approach utilizes unlabeled samples to enforce prediction consistency under minor perturbations, thus reducing the model's sensitivity to noise and suppressing false positives in change-detection tasks. This principle underlies consistency regularization-based methods. However, while these methods enhance noise robustness, they also risk overlooking subtle but meaningful changes, leading to information loss and missed detections. To address this issue, we introduce a simple yet efficient method called Sample Inflation Interpolation (SII). This method leverages labeled sample pairs to mitigate the information loss caused by consistency regularization. Specifically, we propose a novel data augmentation strategy that generates additional change samples by combining existing supervised change samples with calculated proportions of change areas. This approach increases both the quantity and diversity of change samples in the training set, effectively compensating for potential information loss and reducing missed detections. Furthermore, to prevent overfitting, small perturbations are applied to the generated sample pairs and their labels. Experiments conducted on two public change detection (CD) datasets validate the effectiveness of our proposed method. Remarkably, even with only 5% of labeled training data, our method achieves performance levels that closely approach those of fully supervised learning models. [ABSTRACT FROM AUTHOR]

This study introduces a new modelling approach that leads to a more efficient process for constructing the matrix system arising from the discretization of integral equations by the boundary element method. This method uses the matrix structure employed in the direct interpolation technique, yielding computational efficiency while maintaining precise outcomes and ensuring convergence as the mesh is refined. To demonstrate the effectiveness of this novel numerical technique, it is applied to solve two-dimensional problems governed by the Laplace equation. [ABSTRACT FROM AUTHOR]

In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott–Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included. [ABSTRACT FROM AUTHOR]

AbstractSpatial interpolation is essential for handling sparsity and missing spatial data. Current machine learning-based spatial interpolation methods are subject to the statistical constraints of spatial stratified heterogeneity (SSH), normally involving separate modeling of each stratum and simple weighted averaging to integrate intra-stratum and inter-strata features. However, these models overlook the different contributions of inter-strata features to different locations within a stratum (heterogeneous inter-strata associations, HIA) and the explanation of spatial effects on the interpolation process, leading to suboptimal and unreliable interpolation outcomes. This article proposes a novel explainable spatial interpolation method considering SSH (X-SSHM). Spatial and environmental features are utilized to describe intra-stratum and inter-strata information, which are fed into random forest-based learners to achieve high-level semantic feature mapping. Geographically weighted regression is employed to integrate intra-stratum and inter-strata features to achieve a unified expression of SSH and HIA, obtaining the final interpolation result. Geographically weighted Shapley (GSHAP) is proposed to decompose the marginal contributions of intra-stratum and inter-strata features. Model performance is evaluated on simulated and soil organic matter datasets. X-SSHM outperformed five baselines regarding interpolation accuracy. Moreover, statistical methods validated X-SSHM’s ability to elucidate the mechanisms by which SSH, spatial autocorrelation and HIA affect the model interpolation process. [ABSTRACT FROM AUTHOR]

This study focuses on the analytical identification and quantification of one type of spurious responses in the context of response history analysis. The spurious response is caused by linear interpolation of input loads. Through analytical derivations and numerical simulations, it is shown that the identified spurious response is fully caused by the interpolation and can significantly affect both damping and inertial forces. Furthermore, the spurious response is not bounded, thus, resistance-based designs could potentially be non-conservative. The findings are applicable to (non-)linear MDOF systems. To address this issue and improve the quality of numerical results, remedies and recommendations are proposed. [ABSTRACT FROM AUTHOR]

Solar proxies are a valuable tool used in most atmospheric models to simulate or predict the state and variation of the different layers linked to the solar source. In this work, we analyze the performance, through correlation analysis, of six solar EUV proxies, and different combination of them, to reproduce annual ionospheric F2 critical frequency (foF2) from ten different stations. We find that certain combinations of traditional proxies outperform the capacity to reproduce interannual ionospheric foF2 variability, resulting in better statistical correlation and time stability, these new proxies could be a valuable tool to predict the state of the atmosphere and for interpolation in case of missing data. Different combinations of proxies such as F30, MgII, Sn or Lya, creates better indicators than using them alone. These new EUV proxies are also used to estimate long-term trends along the ten stations. As we increase the correlation, the estimated trend decrease as expected by definition. However, a key point is that the average trends, after filtering solar activity, result negative as was predicted by the increase of the greenhouse gases. [ABSTRACT FROM AUTHOR]

Consideration in this paper is the global well-posedness for the 3D axisymmetric MHD equations with only vertical dissipation and vertical magnetic diffusion. The existence of unique low-regularity global solutions of the system with initial data in Lorentz spaces is established by using higher-order energy estimates and real interpolation method. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to explore the nonlinear static bending analysis of functionally graded porous sandwich plates with a ceramic core (FSCC) subjected to a transverse uniform load resting on Kerr foundation (KF) using the mixed interpolation of tensorial components for the four-node rectangular element (called MITC4). Porosity appearing in two skin layers is assumed according to the uneven porosity distribution with a porosity factor Ω. The advantage of this element is fast convergence, high accuracy and cancels the shear-locking phenomenon. The present study considers the geometrical nonlinearity resulting from mid-plane stretching based on the von Kármán geometrical nonlinearity. The first-order shear deformation theory (FSDT) is employed to approximate the displacement field of the plate due to its simplicity and efficiency. The current formulation's authenticity is evaluated by comparing it with previously published works. For the first time, the nonlinear bending of FSCC subjected to a transverse uniform load resting on the Kerr foundation is investigated. Furthermore, the influence of input parameters on the nonlinear bending behavior of FSCC is fully provided. [ABSTRACT FROM AUTHOR]