High-resolution alignment of action potential waveforms using cubic spline interpolation

Research Article| September 01 2013 Investigating and mapping spatial patterns of arsenic contamination in groundwater using regression analysis and spline interpolation technique Pham Quy Giang; Pham Quy Giang 1Department of Environmental Health Sciences, University of Shizuoka, 52-1 Yada, Suruga-ku, Shizuoka-shi, Shizuoka 422-8526, Japan2Faculty of Natural Resources and Environment, Hanoi University of Agriculture, Hanoi, Vietnam E-mail: p11604@u-shizuoka-ken.ac.jp Search for other works by this author on: This Site PubMed Google Scholar Kosuke Toshiki; Kosuke Toshiki 1Department of Environmental Health Sciences, University of Shizuoka, 52-1 Yada, Suruga-ku, Shizuoka-shi, Shizuoka 422-8526, Japan Search for other works by this author on: This Site PubMed Google Scholar Shoichi Kunikane; Shoichi Kunikane 1Department of Environmental Health Sciences, University of Shizuoka, 52-1 Yada, Suruga-ku, Shizuoka-shi, Shizuoka 422-8526, Japan Search for other works by this author on: This Site PubMed Google Scholar Masahiro Sakata Masahiro Sakata 1Department of Environmental Health Sciences, University of Shizuoka, 52-1 Yada, Suruga-ku, Shizuoka-shi, Shizuoka 422-8526, Japan Search for other works by this author on: This Site PubMed Google Scholar Journal of Water Supply: Research and Technology-Aqua (2013) 62 (6): 385–394. https://doi.org/10.2166/aqua.2013.102 Article history Received: August 02 2012 Accepted: June 21 2013 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Share Icon Share MailTo Twitter LinkedIn Tools Icon Tools Cite Icon Cite Permissions Search Site Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsThis Journal Search Advanced Search Citation Pham Quy Giang, Kosuke Toshiki, Shoichi Kunikane, Masahiro Sakata; Investigating and mapping spatial patterns of arsenic contamination in groundwater using regression analysis and spline interpolation technique. Journal of Water Supply: Research and Technology-Aqua 1 September 2013; 62 (6): 385–394. doi: https://doi.org/10.2166/aqua.2013.102 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex The present study investigates the hypothesis that arsenic concentrations correlate with tubewell depth, and examines the effectiveness of spline interpolation, specifically completely regularized spline (CRS) and spline with tension (SWT) in estimating the magnitude of arsenic contamination in groundwater in Thanh Tri, a densely populated district located in the southern part of Hanoi City, Vietnam. Groundwater sampling conducted in 72 tubewells drilled into shallow aquifers yielded an average arsenic concentration of 82 μg/L with a maximum of 395 μg/L, far higher than the World Health Organization (WHO) guideline value of 10 μg/L. The average concentration in the lower Pleistocene aquifer was 86 μg/L, slightly higher compared with the average of 78 μg/L in the upper Holocene aquifer. Interestingly, regression analysis revealed that in the Holocene aquifer, depth of wells influenced arsenic concentrations significantly. Such an influence, however, was insignificant in the lower Pleistocene aquifer. Both the CRS and SWT spatial interpolation models resulted in plausible predictions for the arsenic concentration data. The problem of arsenic contamination in the study area should be considered seriously, as 99% of the area was estimated to be affected by arsenic levels exceeding the WHO guideline value. arsenic, groundwater contamination, regression analysis, spline interpolation This content is only available as a PDF. © IWA Publishing 2013 You do not currently have access to this content.

Researchers must be cognizant of the frequency content of analog signals that they are collecting. Knowing the frequency content allows the researcher to determine the minimum sampling frequency of the data (Nyquist critical frequency), ensuring that the digital data will have all of the frequency characteristics of the original signal. The Nyquist critical frequency is 2 times greater than the highest frequency in the signal. When sampled at a rate above the Nyquist, the digital data will contain all of the frequency characteristics of the original signal but may not present a correct time-series representation of the signal. In this paper, an algorithm known as Shannon's Sampling Theorem is presented that correctly reconstructs the time-series profile of any signal sampled above the Nyquist critical frequency. This method is superior to polynomial or spline interpolation techniques in that it can reconstruct peak values found in the original signal but missing from the sampled data time-series.

- Abstract: This study introduces an efficient super-resolution (SR) method for enhancing low-resolution fingerprint images using an autoencoder combined with spline and bicubic interpolation techniques. The approach upscales images from 129×97 to 258×194 while preserving fine details and minimizing artifacts. Trained on the FVC 2004 dataset and tested on both FVC 2004 and FVC 2002, the model achieves strong performance with SSIM of 0.968, PSNR of 35.14, and MSE of 0.007. It also attains 100% identification accuracy using the SIFT algorithm, demonstrating its effectiveness for biometric and forensic applications. Key Words: Super-Resolution, Fingerprint, Autoencoder, Spline, Bicubic, PSNR, SSIM, SIFT, Biometrics

Sampling theorem for bandlimited Hardy space functions generated by Regge problem

We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals.Graphical abstract

The advancement of computer and software technologies has facilitated the widespread adoption of spatial analysis, particularly Geographic Information Systems (GIS), representing one of the most transformative developments in modern cartographic applications. GIS capture the geographical and non-geographical data in a way that allows for visual interpretation and analysis. In the present work, the study area of Al-Mada'in is examined along with the topographic surface accuracies obtained by the Inverse Distance Weighted (IDW) and Spline methods, based on the sampling points’ number (40) and the grid size of 30 m. This study compares different interpolation algorithms using their respective prediction mean errors, prediction Root Mean Squared Error (RMSE), and Standard Deviation (STD). The IDW method showed a maximum elevation value of 48.332 m and a minimum of 39.028 m with a mean of 44.265 m, an STD of 2.512 m, and an RMSE of 1.585 m. In contrast, the Spline method achieved a higher accuracy, recording a maximum value of 47.934 m and a minimum value of 39.453 m. It also achieved a mean value of 44.339 m, an STD of 2.345 m, and a lower RMSE of 1.531 m. According to the experimental findings on biased and normalized data, Spline outperformed the IDW approach as it demonstrated a more accurate and superior interpolation inside the sample space.

This research introduces a method with a pragmatic approach for measuring the contour of shaft workpieces. The algorithm utilizes dual-stage Canny edge detection and sub-pixel localization techniques. This study focuses on the challenges associated with edge detection in the context of back-light lighting systems, with the aim of enhancing both accuracy and stability. The proposed technique integrates adaptive threshold-based Canny edge detection, weighted fusion, and morphological algorithms in order to improve the continuity of edges. The process of identifying the location of a coarse edge is accomplished through the utilization of cubic spline interpolation and curve fitting techniques to determine sub-pixel coordinates. The RANSAC fitting algorithm is employed to estimate lines that best match a set of edge points, hence enabling the computation of accurate values for axis-type components. The error analysis and compensation under various lighting conditions were completed through experimental analysis. The method described in this study demonstrates a notable level of accuracy and reliability in the recognition of cylindrical standard parts. It exhibits the capability of precisely identifying standard parts of varying sizes, with an absolute error margin of 8 micrometers. In addition, the algorithm has anti-interference capability, and we deployed the algorithm on Nvidia's Jetson orin nano, so that the entire system design can be more compact. In conclusion, this algorithm offers a viable solution for the efficient and accurate recognition of part contours in diverse settings.

The traditionally diameter-varying tube is a combination part of cylinder and cone with unsmooth transition region, which is usually a weak link. Using spline technique, we present a smooth diameter-varying tube consisting of cylinder and revolution surface with interpolation spline as meridian, and study the stability of three categories of typical curves used for filament winding, geodesics, semi-geodesics, and constant winding angle curve. A sufficient condition that makes fiber path non-bridging is introduced by analyzing normal curvature, and furthermore there is a sufficient and necessary condition of non-bridging geodesics. For constant angle winding, an efficient algorithm for determining whether constant winding angle curve is stable or not is presented by investigating its slippage coefficient , and a novel winding pattern design metthod is proposed for filament winding diameter-varying tube. These methods have been applied to our computer aided filament winding software. The experimental and simulation results show that our method can design winding pattern of uniformly covering the mandrel, and efficiently shortens the design time.

The sampling theorem can be described as a economic way of representing a limited bandwidth function. A sample of points is chosen and an interpolation function of these points is used to represent the function. The great importance of this fact is that paves the way to discrete computation. The sample points act as a sort of “highlight” points of the original function, and computation involving the entire function may be restricted to calculation using only the sample points. Moreover we were able to find some refining of the classical outline of the sampling theorem that improves its precision bringing also some physical insight into the core of the theorem. Of course also these consideration are not restricted to optics, they can be construed as general properties of the signal theory. But we were optically minded at all times and most of the applications are in optics.

The measurement of the characteristic parameters of a circularly polarized antenna can be realized by a measurement system of a linear polarization antenna. However, before its parameters can be synthesized from the linear polarization measured data, the vertical and horizontal polarization parameters of the circularly polarized antenna need to be tested several times. In this paper, a radial point interpolation method is introduced into the test system to reduce the test time. The performance of the algorithm is compared with the moving least square method which is based on a cubic spline interpolation technique. The numerical experiments show that the proposed method outperforms the moving least square approach in the case of fewer sampling points.

本文在分析了三次样条插值里三转角算法的基础上，对第二种边界条件的情形进行了推广，研究了此情形下任意两插值点二阶导数已知的样条函数的解法。文章的最后，通过一个例子，说明了此计算方法。 In this article, based on analysis of three turning angles algorithm of cubic spline interpolation, the cubic spline interpolation is generalized on the condition of the second boundary. The methods are presented on the condition that the second derivative of arbitrary two nodes is given. At the end of the article, this cal- culation method is illustrated through an example.

The procedure for composing the spline function of order m that interpolates n data is roughly divided into two stages: (1) constructing the matrix An that transforms the fl-spline coefficient vector c into the sample value vector s; and (2) calculating the vector c. Then the effects of boundary conditions and the locations of the sampling points and the knots on the number of computations for spline interpolation are evaluated. There are no boundary condition effects of the construction of A" for equispacing. Non-periodic boundary conditions reduce the number of computations needed to calculate c from O(m2n) to O(m2n/4). In the construction of An, choosing equispaced sampling points reduces the number of computations from O(m2n) to O(m2) in the case of sampling points located at a constant interval between each pair of adjacent knots. In the calculation of c, equispaced sampling points reduce the number of computations from O(m2n) to O(m2n /2) in the case where m is even and the locations of the knots are identical with those of the sampling points.

Dyadic calculus and sampling theorems for functions with multidimensional domain II. Applications to dyadic sampling representations

Path following of marine surface vehicles with dynamical uncertainty and time-varying ocean disturbances

In this chapter, a comprehensive review is made on the application of cubic spline interpolation techniques in the field of power systems. Domains like available transfer capability (ATC), electric arc furnace modeling, static var. compensation, voltage stability margin, and market power determination in deregulated electricity market are taken as samples to illustrate the significance of cubic spline interpolation.