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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]

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]

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]

To investigate the potential lane‐changing collision risks that may arise between vehicles during lane changes and those in the original lane, a model for vehicle lane‐changing collision risk is constructed specifically for this scenario, and a research analysis is conducted. First, based on vehicle trajectory data, a sample set capturing the relationships between vehicles traveling in a straight line and those changing lanes laterally is extracted and built. Interpolation methods are then applied to fill in missing values, outliers are eliminated, and data noise is smoothed during preprocessing. After preprocessing, a total of 468 vehicle pairs and 265,392 data points are obtained. Second, a real‐time collision time model is established based on the preprocessed data, and collision risk probabilities are calculated accordingly. Then, the collision risks are classified into four levels based on whether the vehicle on the side actually changes lanes and the severity of the collision risks. Finally, a light gradient boosting machine (LightGBM) learning method is adopted to predict the risk levels and analyze the main factors that significantly impact the severity of collision risks. The results indicate that the longitudinal distance between the target vehicle and the preceding vehicle is the most critical influencing factor, followed by the speed of the target vehicle itself, and then the speed difference between the target vehicle and the preceding vehicle. The influence of other factors is relatively similar and does not have a significant impact. [ABSTRACT FROM AUTHOR]

This paper develops an efficient combined interpolation/finite element approach for solving a three‐dimensional Black‐Scholes problem with stochastic volatility. The technique consists to approximate the time derivative by interpolation whereas the space derivatives are approximated using the finite element method. Both stability and error estimates of the new algorithm are deeply analyzed in the L∞$$ {L}^{\infty } $$‐norm. The proposed method is explicit, unconditionally stable, temporal second‐order accurate and fourth‐order convergence in space. This result suggests that the constructed scheme is faster and more efficient than a broad range of numerical methods widely studied in the literature for the Black‐Scholes models. Some numerical experiments are carried out to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Grid-wise Vienna Mapping Functions 1 (VMF1) and Vienna Mapping Functions 3 (VMF3) tropospheric products have been widely used to interpolate the a priori zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) over the GNSS (Global Navigation Satellite Systems) stations for the mitigation of tropospheric delays inherited in GNSS observations. Since the two products only provide ground surface ZHD and ZWD for global grid points, the ZHD and ZWD of the four grid points nearest to the GNSS site need to be reduced to the same height of the GNSS site before a horizontal interpolation (e.g., bilinear interpolation or inverse-distance weighted interpolation) is implemented. However, the accuracy of the officially recommended simple reduction model may not be as good as desired if the height of a GNSS site largely differs from that of the four ground surface grid points to be used in the interpolation. In this contribution, a new reduction model for each grid point is developed for reducing the grid-wise ZHD and ZWD to the target height to improve the interpolation performance. The sample data for the modelling were the 10-year (2010–2019) ZHD and ZWD profiles over the grid points obtained from ERA5 monthly-mean reanalysis data, while 3-year (2020–2022) ERA5 hourly reanalysis and IGS (International GNSS Service) site-wise ZTD products were used to evaluate the new model. Test results showed that the accuracy of the ZHD, ZWD (as well as the ZTD) interpolated from the VMF1/VMF3 products deduced by the new model was significantly better than the ones deduced by traditional methods, especially for sites with substantial height disparities from adjacent VMF grid points. It is expected that the new model adds good value to related fields such as GNSS positioning and GNSS meteorology for better performance. [ABSTRACT FROM AUTHOR]

We consider the extremal problem of interpolation of convex scattered data in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ by smooth edge convex curve networks with minimal Lp$$ {L}_p $$‐norm of the second derivative for 1

This paper deals with the approximation error of trigonometric interpolation for multivariate functions of bounded variation in the sense of Hardy-Krause. We propose interpolation operators related to both the tensor product and sparse grids on the multivariate torus. For these interpolation processes, we investigate the corresponding error estimates in the Lp norm for the class of functions under consideration. In addition, we compare the accuracy with the cardinality of these grids in both approaches. [ABSTRACT FROM AUTHOR]

Handling geotechnical peculiarities in specialized ground models – an experience report Dr. Spang GmbH has developed numerous specialized ground models in recent years and has gained corresponding experience in ground modeling. Within the company, a standard procedure for creating these specialized models has been established. From a software perspective, automatic meshing (triangulated 3D surface mesh of the layer boundaries) already delivers useful results for many standard cases. However, in geotechnics, there are not only standard cases and features to assess. Geotechnical peculiarities (e. g. inhomogeneous layering) result in an increased manual modeling effort. This article aims to shed light on how to handle these peculiarities in modeling, present the additional modeling steps involved, and highlight the software limitations that arise in automatic meshing (interpolation or triangulation) in such special cases. [ABSTRACT FROM AUTHOR]

In this paper we construct a new basis for the cyclotomic completion of the center of the quantum gl N in terms of the interpolation Macdonald polynomials. Then we use a result of Okounkov to provide a dual basis with respect to the quantum Killing form (or Hopf pairing). The main applications are: 1) cyclotomic expansions for the gl N Reshetikhin–Turaev link invariants and the universal gl N knot invariant; 2) an explicit construction of the unified gl N invariants for integral homology 3-spheres using universal Kirby colors. These results generalize those of Habiro for sl 2 . In addition, we give a simple proof of the fact that the universal gl N invariant of any evenly framed link and the universal sl N invariant of any 0-framed algebraically split link are Γ -invariant, where Γ = Y / 2 Y with the root lattice Y. [ABSTRACT FROM AUTHOR]

In this paper, we consider how to accurately solve the singular value problem and the linear system for a class of Polynomial-Vandermonde-type (PVT) matrices, which belongs to the class of negative matrices introduced by Huang and Xue (Adv Comput Math 47:73, 2021), and these negative matrices arise in some applications such as interpolation problems. In order to parameterize PVT matrices, we present the explicit expressions of initial minors of such matrices. An algorithm is designed to accurately compute the parametrization matrix for PVT matrices. Based on the accurate parametrization algorithm, all the singular values, both large and small, of PVT matrices are computed, and the linear systems associated with PVT matrices are solved to high relative accuracy. Numerical experiments are performed to confirm the claimed high relative accuracy. [ABSTRACT FROM AUTHOR]

In this paper, after recalling the main properties of the voice transform, we prove its inversion formula, then we present some qualitative uncertainty principles associated with this transform. Finally, we find a solution to an interpolation problem. [ABSTRACT FROM AUTHOR]

Round-off error is inevitable in computer numerical control (CNC) systems because it is challenging to ensure that the interpolation time is an integer multiple of the interpolation period. This error can affect both machining precision and motion smoothness. To eliminate the round-off error and improve machining speed and precision, a novel round-off error elimination method is proposed that modifies the S-shaped acceleration/deceleration (ACC/DEC) feedrate scheme. Firstly, an adapted bidirectional scanning algorithm is applied to a jerk-limited S-shaped feedrate profile to improve machining efficiency while respecting feedrate constraints. Secondly, during the interpolation stage, the velocity round-off error is first introduced. Based on the novel properties of the modified S-shaped scheme, the displacement round-off error is then analyzed and addressed using different strategies, such as modifying the S-shaped profile with one-cycle rounding-up in a specified section or segment transition, without crossing the end point. Finally, a series of simulation and real machining experiments are conducted to compare the proposed method with existing round-off error compensation algorithms. The results show that the proposed method offers more flexible and effective round-off error compensation, with significant improvements in machining efficiency and the smoothness of the motion profile, including velocity, acceleration, and jerk. The real machining experiments, conducted in a CNC system with a 250-µs real-time control period and focused on 3D complex surface engraving, verified the practicality of the proposed method. [ABSTRACT FROM AUTHOR]

Inference using fuzzy rules enables decision-making that is supported with imprecise knowledge. Unlike conventional fuzzy reasoning approaches which directly perform pattern-matching in response to an input observation, recent techniques have integrated rule-firing-based and rule interpolating-based inference methods. This is in order to address challenging issues where observations are of different matching degrees to the rules within a given rule base, including unmatched ones. While applied generally, such a unified inference mechanism may become too complex to exploit the entire rule base for deriving a reasonable conclusion. In practice, only a small number of 'appropriate' rules are selected to accomplish the required inference. This paper presents an enhanced integrated fuzzy inference mechanism, which is fed with fewer rules returned by a weight-guided selection procedure. In particular, the weights of rule attributes are utilised in a dual manner: guiding the selection of appropriate rules for rule firing and determining the nearest neighbouring rules for rule interpolation. The resulting mechanism is applied to a real-world problem, empirically demonstrating its significant efficacy. [ABSTRACT FROM AUTHOR]

We construct some smooth functions defined over a sphere that interpolate large sets of scattered data, using some modified Shepard methods, the least squares thin-plate spline and the inverse multiquadric functions. We illustrate the benefits of our methods in numerical examples for some test functions and some real data applications. [ABSTRACT FROM AUTHOR]

Accurately predicting errors incurred in a cross-section model for two-step reactor analysis enables the development of optimal case matrices and more efficient cross-section models. In a companion paper, we developed a systematic methodology for the partial derivatives cross-section model through rigorous analytic error analysis. In this paper, we verify our methodology against the conventional "brute force" numerical approach using a typical pressurized water reactor (PWR) lattice. By successfully reproducing known results, we gain confidence in our methodology's application to advanced reactor environments, where optimal case matrices are generally not known. Our error methodology relies on accurately estimating bounds on the derivatives of the cross-section functions, a task we achieve through an order of convergence study. We use these derivative bounds in derived error expressions to obtain pointwise and setwise cross-section error bounds and verify these results with reference solutions of various two-group cross sections. We then propagate the cross-section error bounds to reactivity error using first-order perturbation theory and analyze their combined effect. Application of this approach to our test problem corroborates our prior qualitative findings with quantitative evidence and reveals the relative magnitudes of interpolation and model form error sources across diverse PWR cross-section functionalizations. Our results suggest systematic pathways for improving case matrix construction to minimize the overall error. These findings also confirm what is well known to the light water reactor design community, which is that interpolation error of cross sections for standard interpolation procedures and case matrix structures is on the order of 10 pcm or less. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multi-lattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model. [ABSTRACT FROM AUTHOR]

The paper concerns the weighted Hilbert transform of locally continuous functions on the semiaxis. By using a filtered de la Vallée Poussin type approximation polynomial recently introduced by the authors, it is proposed a new "truncated" product quadrature rule (VP- rule). Several error estimates are given for different smoothness degrees of the integrand ensuring the uniform convergence in Zygmund and Sobolev spaces. Moreover, new estimates are proved for the weighted Hilbert transform and for its approximation (L-rule) by means of the truncated Lagrange interpolation at the same Laguerre zeros. The theoretical results are validated by the numerical experiments that show a better performance of the VP-rule versus the L-rule. [ABSTRACT FROM AUTHOR]

Laguerre spectral approximations play an important role in the development of efficient algorithms for problems in unbounded domains. In this paper, we present a comprehensive convergence rate analysis of Laguerre spectral approximations for analytic functions. By exploiting contour integral techniques from complex analysis, we prove that Laguerre projection and interpolation methods of degree n converge at the root-exponential rate O(\exp (-2\rho \sqrt {n})) with \rho >0 when the underlying function is analytic inside and on a parabola with focus at the origin and vertex at z=-\rho ^2. As far as we know, this is the first rigorous proof of root-exponential convergence of Laguerre approximations for analytic functions. Several important applications of our analysis are also discussed, including Laguerre spectral differentiations, Gauss-Laguerre quadrature rules, the scaling factor and the Weeks method for the inversion of Laplace transform, and some sharp convergence rate estimates are derived. Numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the real interpolation theory for variable Lorentz–Karamata spaces as well as for the corresponding martingale Hardy spaces. As a consequence, the generalization of Doob's maximal inequality will be proved. Moreover, the atomic decompositions of the variable martingale Hardy–Lorentz–Karamata spaces are also presented. The results obtained here are new even for martingale Hardy–Lorentz–Karamata spaces. [ABSTRACT FROM AUTHOR]

We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation. We apply the general result to non-conjugate series priors, showing that these priors give near optimal and adaptive recovery in some generality, Gaussian priors, and mixtures of Gaussian priors, where the latter are also shown to be near optimal and adaptive. [ABSTRACT FROM AUTHOR]

Event sequence data widely exists in real life, where each event is typically represented as a tuple, event type and occurrence time. Recently, neural point process (NPP), a probabilistic model that learns the next event distribution with events history given, has gained a lot of attention for event sequence modelling. Existing NPP models use one single vector to encode the whole events history. However, each type of event has its own historical events of concern, which should have led to a different encoding for events history. To this end, we propose Type-wise Neural Point Process (TNPP), with each type of event having a history vector to encode the historical events of its own interest. Type-wise encoding further leads to the realization of type-wise decoding, which together makes a more effective neural point process. Experimental results on six datasets show that TNPP outperforms existing models on the event type prediction task under both extrapolation and interpolation setting. Moreover, the results in terms of scalability and interpretability show that TNPP scales well to datasets with many event types and can provide high-quality event dependencies for interpretation. The code and data can be found at https://github.com/lbq8942/TNPP. [ABSTRACT FROM AUTHOR]

This paper proposes a novel dynamic model considering manufacturing errors and eccentricity errors to analyze the dynamics of planetary gear transmission (PGT). The dynamic model is established based on the fractional-order calculus and solved by an enhanced fourth-order Lagrange interpolation polynomials method. Three numerical examples and the vibration experiments of PGT are employed for verification. The comparison results indicate that the proposed solution method has higher solution accuracy and efficient than the existing algorithms in solving fractional equations, and the relative errors of the proposed solution method in three examples are 0.32%, 0.78% and 0.16%, respectively. The proposed dynamic model of PGT has better agreement with the experimentally measured signal compared with the integer-order dynamic model, and the maximum error and average error of the characteristic frequency amplitude between the proposed dynamic model and the measured signal are 4.76% and 3.57%, respectively. The proposed method contributes to the theoretical foundation for the signal monitoring of PGT. [ABSTRACT FROM AUTHOR]

Groundwater analysis across the Oum Rbia watershed is currently hampered by technical constraints and high costs. This research aimed to produce comprehensive groundwater quality maps throughout the basin 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 conducted over twelve campaigns during the 2021 and 2022 seasons involved sample collection from fifty-four locations across the six aquifers of the watershed. 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. WQI indicated that groundwater in most of the studied basin is of excellent quality, though water quality deteriorates in the 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 such factors as temperature, river flow, human activities, and seasonal pollution sources. These maps enhance the understanding of water table information for non-experts as well as 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. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear abstract Cauchy problem with an m-accretive operator. If the initial value and the right-hand side lie in some interpolation sets with parameter α , then we obtain the rate of convergence O (| π | α / 2) for solutions of the corresponding implicit Euler schemes and for the Euler solution as the limit, we obtain Hölder continuity of exponent α . [ABSTRACT FROM AUTHOR]

Copyright of Automatisierungstechnik is the property of De Gruyter 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.)

Copyright of Methods in Ecology & Evolution is the property of Wiley-Blackwell 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.)

Multispectral imaging systems with a multispectral filter array (MSFA) provide an affordable and portable way to capture multispectral images (MSIs) that have a variety of applications in different fields. These systems generate raw images initially and require an effective multispectral image demosaicking technique for reconstructing the MSI from the raw data. These demosaicking methods require proper usage of the spectral correlation available between the bands of MSI to generate high quality MSI. However, the existing demosaicking methods only partially utilize this spectral correlation, as they use spectral correlation only in the initial estimation of MSI. In this work, we utilize the spectral correlation between bands iteratively and finally enhance the quality of the generated image using median filtering based image enhancement. The exploratory results on the two standard datasets publicise the quality of the presented method on the various metrics. [ABSTRACT FROM AUTHOR]

Current mask processing operations rely on interpolation algorithms that do not produce extra pixels, such as nearest neighbor (NN) interpolation, as opposed to algorithms that do produce extra pixels, like bicubic (BIC) or bilinear (BIL) interpolation. In our previous study, the author proposed an alternative approach to NN-based mask processing and evaluated its effects on deep learning training outcomes. In this study, the author evaluated the effects of both BIC-based image and mask processing and BIC-and-NN-based image and mask processing versus NN-based image and mask processing. The evaluation revealed that the BIC-BIC model/network was an 8.9578% (with image size 256 × 256) and a 1.0496% (with image size 384 × 384) increase of the NN-NN network compared to the NN-BIC network which was an 8.3127% (with image size 256 × 256) and a 0.2887% (with image size 384 × 384) increase of the NN-NN network. [ABSTRACT FROM AUTHOR]

The main objective of the current study was to use seven lots in Hartford, CT that are planned for community reuse to determine the optimal sampling density that allows for the detection of hotspots of lead pollution while limiting the labor of the sampling process. The sampling density was investigated using soil Pb measured by in situ X-ray Fluorescence as the indicator to evaluate soil health, with a new threshold of 200-mg/kg proposed by the USEPA in January of 2024. Even though this study takes place in an urban setting, where the new USEPA policy requires the use of a 100-mg/kg threshold for Pb due to the fact that there are other identifiable sources of the contaminant, only the 200-mg/kg threshold is discussed because it is evident from the analysis that compliance of a 100 mg/kg threshold in urban plots is highly unlikely (five out of seven sites would require complete site excavation prior to reuse). Using the inverse distance weighted geospatial interpolation of in situ pXRF determined lead measurements, grid sampling resolutions of 3-m, 4-m, 5-m, 6-m, 8-m, 10-m, and 12-m were compared. Ultimately, the case study finds that the largest grid resolution that can be implemented for soil screening to maintain hotspots of pollution to properly inform soil management decisions is a 6-m grid, or a density of approximately 1/36-m2. [ABSTRACT FROM AUTHOR]

We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions. [ABSTRACT FROM AUTHOR]

The primary challenge in CNC machining is optimizing arc interpolation for better smoothness and precision, as traditional methods often fail to maintain a consistent curvature, resulting in inefficiencies and inaccuracies. This study utilizes the Archimedes spiral, comprising a series of seamlessly connected circular arcs, as an innovative interpolation curve to improve arc interpolation efficiency and accuracy. The proposed methodology addressed the issue of constant arc interpolation curvature and facilitated the implementation of the spiral's interpolation algorithm. It employs the parametric equation of the Archimedes spiral to define tangent vectors, which is pivotal for the execution of the algorithm. In the context of speed planning, the curve was segmented into different sections, allowing the calculation of maximum acceleration based on the interval segmentation angle of the tangent vector. This segmentation facilitates the analysis of speed variations, which are consequently integrated to determine the speed distribution across different curve sections. Through this integration, the motion process is categorized, thereby achieving a refined speed distribution curve. This study introduces a realtime interpolation algorithm capable of calculating the largest axis of the tangent vector, thereby enabling precise pulse coordinates. This coordinate information are then effortlessly derived from the simple geometric relationships inherent in the spiral's structure. The effectiveness of the proposed method is demonstrated through simulation and practical machining on two distinct graphical representations. Compared with the traditional linear interpolation algorithm, the proposed method improves the machining efficiency of heart-shaped curves by 6.85% while ensuring the machining accuracy. Comprehensive evaluation, encompassing track error, and surface roughness assessments, validates the enhanced performance of this interpolation technique. [ABSTRACT FROM AUTHOR]

This study represents a pioneering effort to integrate geographic information systems (GIS) and ensemble machine learning methods to predict noise levels on a university campus. Three ensemble models including random forest (RF), gradient boosting (GB), and extreme gradient boosting (XGB) were developed to predict traffic noise based on data collected over a 4-week period at the Universiti Teknologi Malaysia (UTM) campus. Noise measurements were obtained during peak morning hours (7:30 to 9:30 a.m.) on weekdays within the UTM campus in Johor. Additional predictor variables, including data from the digital elevation model (DEM) and land use, were incorporated to capture the complex nonlinear relationships influencing noise levels. The models were optimized through hyperparameter tuning, resulting in high precision, as evidenced by performance metrics such as the coefficient of determination (R2), mean absolute error (MAE), and mean squared error (MSE). The XGB model emerged as the most accurate, with R2 = 0.96, MAE = 0.9, and MSE = 0.3. Noise maps generated using the inverse distance weighting (IDW) interpolation technique highlighted the spatial distribution of noise levels, classified into five classes considering WHO standards. The findings identified distance from roads, the number of light vehicles, and proximity to green areas as the most significant predictors. However, challenges remain in accurately predicting noise levels associated with other predictors. The outcomes of the study indicate the superior performance of the XGB model compared to the GB and RF models. The study recommends several measures to manage and control noise pollution on the UTM campus, including raising awareness, regulating and enforcing vehicle speed limits, reevaluating land use, installing sound insulation systems, and planting trees and vegetation buffer zones around and within educational buildings. [ABSTRACT FROM AUTHOR]

Kriging-based finite element method (K-FEM) is an enhancement of the FEM using Kriging interpolation in place of the conventional polynomial interpolation. This paper presents the development of the K-FEM for analysis of curved beams based on a deep arc theory, which accounts for membrane and shear deformation. The discrete strain gap technique is employed to circumvent shear locking and membrane locking. The numerical tests show that the Kriging-based elements are free from any locking, are able to provide highly accurate solutions with a regular course mesh discretization, and have excellent convergence characteristics, especially for circular beams. [ABSTRACT FROM AUTHOR]

Cloud computing liberates enterprises and organizations from expensive data centers and complex IT infrastructures by offering the on-demand availability of vast storage and computing power over the internet. Among the many service models in practice, the public cloud for its operation cost saving, flexibility, and better customer support popularity in individuals and organizations. Nonetheless, this shift in the trusted domain from the concerned users to the third-party service providers pops up many privacy and security concerns. These concerns hindrance the wide adaptation for many of its potential applications. Furthermore, classical encryption techniques render the encrypted data useless for many of its valuable operations. The combined concept of attribute-based encryption (ABE) and searchable encryption (SE), commonly known as attribute-based keyword searching (ABKS), emerges as a promising technology for these concerns. However, most of the contemporary ABE-based keyword searching schemes incorporate costly pairing and computationally heavy secret sharing mechanisms for its realization. Our proposed scheme avoids the expensive bilinear pairing operation during the searching operation and costly Lagrange interpolation for secret reconstruction. Besides, our proposed scheme enables the updation of access control policy without entirely re-encrypting the ciphertext. The security of our scheme in the selective-set model is proved under the Decisional Bilinear Diffie-Hellmen (DBDH) assumption and collision-free. Finally, the experimental results and performance evaluation demonstrate its communication and overall efficiency. [ABSTRACT FROM AUTHOR]

Failure probability function (FPF) can reflect quantitative effects of random input distribution parameter (DP) on failure probability, and it is significant for decoupling reliability‐based design optimization (RBDO). But the FPF estimation is time‐consuming since it generally requires repeated reliability analyses at different DPs. For efficiently estimating FPF, an augmented directional sampling (A‐DS) is proposed in this paper. By using the property that the limit state surface (LSS) in physical input space is independent of DP, the A‐DS establishes transformation of LSS samples in standard normal spaces corresponding to different DPs. By the established transformation in different standard normal spaces, the LSS samples obtained by DS at a given DP can be transformed to those at other DPs. After simple interpolation post‐processing on those transformed samples, the failure probability at other DPs can be estimated by DS simultaneously. The main novelty of A‐DS is that a strategy of sharing DS samples is designed for estimating the failure probability at different DPs. The A‐DS avoids repeated reliability analyses and inherits merit of DS suitable for solving problems with multiple failure modes and small failure probability. Compared with other FPF estimation methods, the examples sufficiently verify the accuracy and efficiency of A‐DS. [ABSTRACT FROM AUTHOR]

In the present work the geometrically exact beam model is formulated in terms of unit quaternions. A projection‐based discretization approach is proposed which is based on a normalization of the quaternion approximation. The discretization relies on NURBS shape functions and, alternatively, on Lagrangian interpolation. The redundancy of the quaternions is resolved by applying the method of Lagrange multipliers. In a second step the Lagrange multipliers are eliminated circumventing the need to solve saddle point systems. The resulting finite elements retain the objectivity of the underlying beam formulation. Optimal rates of convergence are observed in representative numerical examples. [ABSTRACT FROM AUTHOR]

Herein, an improved mechanical metamaterial is proposed, which is derived from the decomposition, rotation, and reassembly of reentrant structures. The structure is parametric, allowing for rapid redesign. The study focuses on the variations in equivalent stiffness and Poisson's ratio of the structure within the linear elastic range when internal rib angle θ changes. First, based on homogenization simulation analyses, it has been verified that this design achieves the tailorable equivalent elastic modulus and Poisson's ratio over a wide range, meanwhile, maintaining equal elastic properties in the orthogonal direction at all times. Second, to reduce future repetitive experiments, an interpolation model is established to expand the design domain. The fitting formula indicates that by modifying θ and relative wall thickness t/L0, the elastic performance of the structures can be tailored. Additionally, the impact of boundary conditions is discussed to minimize experimental costs. Finally, the accuracy of the simulations is validated through uniaxial compression tests. [ABSTRACT FROM AUTHOR]

Due to the high level of information similarity between camouflage soldier objects and their background, traditional deep learning-based object detection networks encounter distinct error detection rates and miss detection rates when attempting to detect camouflage soldiers. To address these challenges, we proposed a camouflage soldier object detection network (AFSNet) based on attention mechanism and multi-scale feature fusion strategy. We employed an attention module to enhance the network's capability for feature extraction. Furthermore, we proposed a novel strategy for multi-scale feature fusion based on pyramidal feature shrinking, aiming to mitigate interference caused by interpolation and prevent information loss resulting from pooling during the process of feature fusion. Moreover, we introduced a novel information handle module that enhances the network's capability for feature fusion by regulating the information transmission pathway. Experiments demonstrated that our network exhibits a better camouflage object detection performance than state-of-arts networks. Compared to YOLOv7, our network can achieve 93 % AP, which is increased by 6.7 % with almost no computation overhead. [ABSTRACT FROM AUTHOR]