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interpolation function estimates post mortem interval under ambient temperature correlating with blood ATP level

FORENSIC SCIENCE INTERNATIONAL 2014年 238卷 47-52页

作者： Sun, Tingyi Yang, Tiantong Zhang, Haidong Zhuo, Luo Liu, Liang Huazhong Univ Sci & Technol Tongji Med Coll Dept Forens Med Wuhan 430030 Peoples R China Collaborat Innovat Ctr Judicial Civilizat Beijing 100040 Peoples R China China Univ Polit Sci & Law Minist Educ Key Lab Evidence Sci Beijing 100040 Peoples R China

Objective: We developed a mathematical model using interpolation function, to characterize the correlation between blood ATP levels in the right ventricle of rabbit and post mortem interval (PMI) at different ambient temperatures. Methods: Forty-eight healthy rabbits were randomly divided into 6 groups of 8 each. The sacrificed rabbits were maintained in calorstats at 10 degrees C, 15 degrees C, 20 degrees C, 25 degrees C, 30 degrees C and 35 degrees C, respectively. Blood from the right ventricle was sampled every 4 h until 72 h after death. At different time points, ATP concentrations in the blood samples were measured using an ATP fluorescence rapid detector, and then displayed on the detector screen in the form of relative light units (RLU). Relationship between PMI and ATP degradation levels was investigated statistically by SPSS 17.0 and MATLAB 10.0 software. Results: We obtained six regression equations (R-a(2) 0: 887 -0: 929_ with RLU values at PMIs of 72 h (10 degrees C), 60 h (15 degrees C), 56 h (20 degrees C), 52 h (25 degrees C), 40 h (30 degrees C) and 32 h (35 degrees C), and an interpolation function dR2a 0: 930_ was established with PMI as the dependent variable (z), RLU value as independent variable (x) and temperature as independent variable (y). Conclusion: interpolation function is an appropriate choice for PMI estimation by weakening influence of ambient temperature. (C) 2014 Elsevier Ireland Ltd. All rights reserved.

关键词： Forensic science Forensic pathology Post mortem interval interpolation function Adenosine triphosphate

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ON THE CONTINUITY AND DIFFERENTIABILITY OF AKIND OF FRACTAL interpolation function

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Applied Mathematics and Mechanics(English Edition) 2002年第4期23卷 471-478页

作者：李红达叶正麟高行山 State Key Laboratory of Information Security Graduate School C hinese Academy of Sciences Beijing 100039 P R China Department of Mathematics and Information Northwestern Polytechnical University Xi'an 710072 P R China Department of Engineering Mechanics Northwestern Polytechnical University Xi'an 710072 P R China

The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.

关键词： fractal interpolation function Holder continuity differentiability

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Cubic convolution interpolation function with variable coefficients and its application to channel estimation for IEEE 802.16 initial downlink

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IET COMMUNICATIONS 2012年第13期6卷 1979-1987页

作者： You, S. D. Chen, K. -Y. Liu, Y. -S. Natl Taipei Univ Technol Dept Comp Sci & Informat Engn Taipei 106 Taiwan Natl Taipei Univ Technol Dept Elect Engn Taipei 106 Taiwan

In this study, the authors propose to use the cubic convolution interpolation function with a free variable to generate a class of constant-coefficient interpolation functions. The interpolations functions can be applied to an orthogonal frequency-division multiplexing-based receiver for channel estimation. For a given channel, different interpolation functions from the class have different bit error rates (BERs). Therefore by using a search algorithm, a better interpolation function is chosen with the aid of a performance indicator, such as the estimated mean-squared error (EMSE). Although the uneven distribution of pilots in the IEEE 802.16e system prohibits direct utilisation of the cubic interpolation function, a simple approach has been proposed to solve this problem. The proposed method is validated in the IEEE 802.16e downlink system by Monte Carlo simulation. The simulation results also confirm that channels with different statistical properties should use different interpolation functions. In addition to the Monte Carlo simulation, we also analyse the BER of the proposed approach. We find that the BERs based on the analytical evaluation and on the simulation closely match each other. Finally, it is shown that the EMSE is an acceptable performance indicator for medium-to-high signal-to-noise ratio.

关键词： Pilots INSTITUTE OF ELECTRICAL AND ELECTRONIC ENGINEERS performance indicators Convolution channel estimation manipulated variable Cubic simplicial approximation Downlink SEARCHING ALGORITHM Monte Carlo technique interpolation function Ziziphus mauritiana interpolation

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Study on interpolation function of image reconstruction

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11th Joint International Computer Conference (JICC 2005)

作者： Qu, Z Yang, D Wen, JH Chongqing Univ Post & Telecommun Coll Comp Sci & Technol Chongqing 400065 Peoples R China

ISBN: (纸本)9812565329

In this paper, an efficient image reconstruction algorithm in industrial computed tomography with the fan-beam projection was discussed in detail. In order to improve the quality of image reconstruction, a new algorithm of image reconstruction of convolution back projection based on interpolation function was proposed. The new method ameliorates the process of image reconstruction, which can improve the quality of image reconstruction. The efficiency of the algorithm of convolution back projection is evaluated in contrast to that of its traditional serial counterpart. The entire procedure from data acquisition to image reconstruction on computer was completed. Experiment results clearly demonstrate that interpolation function can efficiently improve quality of images reconstruction.

关键词： interpolation function the algorithm of convention back projection image reconstruction

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Comparison of Interpolating functions and Interpolating Points in Full-Wave Multilevel Green's function interpolation Method (vol 58, pg 2691, 2010)

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2010年第10期58卷 3437-3437页

作者： Shi, Yan Chan, Chi Hou Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China City Univ Hong Kong State Key Lab Millimeter Waves Hong Kong Hong Kong Peoples R China

The difficulty for the solution of full-wave electromagnetic problems using multilevel Green's function interpolation method (MLGFIM) lies in applying interpolating approaches to efficiently and accurately approximate Green's function with rapidly changing phase term. We compare various interpolating schemes when radial basis function (RBF) is employed for the interpolation of scattered data of Green's function. We show that the infinitely smooth Gaussian (GA) RBF has the best interpolation accuracy. In order to improve the interpolation efficiency, a new kind of staggered Tartan grid is proposed. A good calculation method for the shape parameter in GA RBF is given to solve its sensitivity to the group size and the number of interpolation points. Based on the analysis of variation of the number of interpolation points with electric length of the group, adaptive choice of the types of interpolation functions and interpolation points are employed. Numerical examples show that the computational efficiency of this new interpolation scheme is much improved over the previously reported ones.

关键词： Gaussian (GA) multilevel Green's function interpolation method (MLGFIM) radial basis function (RBF) staggered Tartan grid full-wave Group Size shape parameter Green's function interpolation function interpolation discrete data

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Image super-resolution based on multifractals in transfer domain

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SIGNAL PROCESSING-IMAGE COMMUNICATION 2025年 133卷

作者： Yao, Xunxiang Wub, Qiang Zhange, Peng Baod, Fangxun Shandong Univ Finance & Econ Sch Comp Sci & Technol Jinan Peoples R China Univ Technol Sydney Fac Engn & Informat Technol Sydney Australia Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao Peoples R China Shandong Univ Sch Math Jinan Peoples R China

The goal of image super-resolution technique is to reconstruct high-resolution image with fine texture details from its low-resolution *** Fourier domain,such fine details are more related to the information in the highfrequency spectrum. Most of existing methods do not have specific modules to handle such high-frequency information adaptively. Thus, they cause edge blur or texture disorder. To tackle the problems, this work explores image super-resolution on multiple sub-bands of the corresponding image, which are generated by NonSubsampled Contourlet Transform (NSCT). Different sub-bands hold the information of different frequency which is then related to the detailedness of information of the given low-resolution *** this work, such image information detailedness is formulated as image roughness. Moreover, fractals analysis is applied to each sub-band image. Since fractals can mathematically represent the image roughness, it then is able to represent the detailedness (i.e. various frequency of image information). Overall, a multi-fractals formulation is established based on multiple sub-bands image. On each sub-band, different fractals representation is created adaptively. In this way, the image super-resolution process is transformed into a multifractal optimization problem. The experiment result demonstrates the effectiveness of the proposed method in recovering high-frequency details.

关键词： Image super-resolution Nonsubsampled contourlet transform fractal interpolation function Image roughness Fractal dimension Multifractal

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interpolation functions Of General Type-2 Fuzzy Systems

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2024年 1-17页

作者： Zhao, Shan Shi, Kaibo Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Sichuan Peoples R China

This paper focuses on simplifying the use procedure and calculation of general type-2 fuzzy systems by way of extracting their the interpolation functions. Firstly, four kinds of fuzzification methods with special laws are designed to construct the general type-2 fuzzy sets in the antecedents and consequents of type-2 inference rules. On this basis, together with the KM algorithm, alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-plane representation and interpolation conclusions of interval type-2 fuzzy systems, three types of interpolation functions of general type-2 fuzzy systems are obtained. In the meantime, all of the interpolation functions have been proved as universal approximators. It can be seen that in future applications of general type-2 fuzzy systems, interpolation functions can be applied directly instead of conventional blocks. Because of the ingenious design of the general type-2 fuzzy sets on operations, the computation of general type-2 fuzzy systems has been greatly reduced. In order to verify the validity and superiority of the proposed methods, simulation results with a type-1 fuzzy system, an interval type-2 fuzzy system and two general type-2 fuzzy systems for the approximation problem of dynamic systems are presented. The simulations exhibit that the suggested approaches have good and desired performance.

关键词： Type-2 fuzzy set General type-2 fuzzy system interpolation function Universal approximator

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interpolation functions of interval type-2 fuzzy systems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第2期41卷 3183-3200页

作者： Zhao, Shan Li, Zhao Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Sichuan Peoples R China Chengdu Univ Sch Comp Sci Chengdu Sichuan Peoples R China

The interpolation functions of interval type-2 fuzzy systems and their universal approximation are investigated in this paper. Two types of fuzzification methods are designed to construct the antecedents and consequents of the type-2 inference rules. Then the properties of the fuzzy operator and the type-reduction algorithm are used to integrate all parts of the fuzzy system. interpolation functions of interval type-2 fuzzy systems, which are proved to be universal approximators, are obtained based on three models, namely single input and single output, double inputs and single output, and multiple inputs and single output. The proposed approach is applied to approximate experiments of dynamic systems so as to evaluate the system performance. The system parameters are optimized by the QPSO algorithm. Experimental results for several data sets are given to show the approximation performances of the proposed interpolation functions are better than those of the interpolation function of the classical type-1 fuzzy system.

关键词： Interval type-2 fuzzy system interval type-2 fuzzy set interpolation function universal approximation

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interpolation functions of feedforward neural networks

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2003年第12期46卷 1861-1874页

作者： Li, HX Lee, ES Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Kansas State Univ Dept Ind & Mfg Syst Engn Manhattan KS 66506 USA

Mathematical essence and structures of the feedforward neural networks are investigated in this paper. The interpolation mechanisms of the feedforward neural networks are explored. For example, the well-known result, namely, that a neural network is an universal approximator, can be concluded naturally from the interpolative representations. Finally, the learning algorithms of the feedforward neural networks are discussed. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： neural network fuzzy neural network interpolation function mathematical neuron mathematical neural network

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interpolation functions in control volume finite element method

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COMPUTATIONAL MECHANICS 2003年第4期30卷 303-309页

作者： Abbassi, H Turki, S Ben Nasrallah, S Fac Sci Tunis Dept Phys Sfax 3018 Tunisia Ecole Natl Ingn Dept Energet Monastir 5000 Tunisia

The main contribution of this paper is the study of interpolation functions in control volume finite element method used in equal order and applied to an incompressible two-dimensional fluid flow. Especially, the exponential interpolation function expressed in the elemental local coordinate system is compared to the classic linear interpolation function expressed in the global coordinate system. A quantitative comparison is achieved by the application of these two schemes to four flows that we know the analytical solutions. These flows are classified in two groups: flows with privileged direction and flows without. The two interpolation functions are applied to a triangular element of the domain then;a direct comparison of the results given by each interpolation function to the exact value is easily realized. The two functions are also compared when used to solve the discretized equations over the entire domain. Stability of the numerical process and accuracy of solutions are compared.

关键词： control volume finite element method incompressible fluid flow interpolation function flow-oriented interpolation laminar flow

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