Research on the Model of Linear Data Fitting Method

By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.

Large Scattered Data Fitting Based on Radial Basis Functions

Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.

Dynamics and data fitting of a time-delayed SIRS hepatitis B model with psychological inhibition factor and limited medical resources

Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to describe hepatitis B transmission dynamics.In order to describe the behavior changes caused by people's psychological changes,the non-monotonic incidence rate is adopted in the model.We use the saturated treatment rate to describe the limited medical resources.Mathematical analysis shows the existence conditions of the equilibria,forward or backward bifurcation,Hopf bifurcation and the Bogdanov-Takens bifurcation.During the observation of the case data of hepatitis B in China,it is found that there are mainly three features,periodic outbreaks,aperiodic outbreaks,and periodic outbreaks turns to aperiodic outbreaks.According to the above features,we select three different representative regions,Jiangxi,Zhejiang province and Beijing,and then use our model to fit the actual monthly hepatitis B case data.The basic reproduction numbers that we estimated are 1.7712,1.4805 and 1.4132,respectively.The results of data fitting are consistent with those of theoretical analysis.According to the sensitivity analysis of Ro,we conclude that reducing contact,increasing treatment rate,strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B.

SOLVING THE BACKWARD HEAT CONDUCTION PROBLEM BY DATA FITTING WITH MULTIPLE REGULARIZING PARAMETERS

We propose a new reconstruction scheme for the backward heat conduction problem. By using the eigenfunction expansions, this ill-posed problem is solved by an optimization problem, which is essentially a regularizing scheme for the noisy input data with both the number of truncation terms and the approximation accuracy for the final data as multiple regularizing parameters. The convergence rate analysis depending on the strategy of choosing regularizing parameters as well as the computational accuracy of eigenfunctions is given. Numerical implementations are presented to show the validity of this new scheme.

HERMITE SCATTERED DATA FITTING BY THE PENALIZED LEAST SQUARES METHOD

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 （2002）, pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.

Comparison of Data Screening Methods for Evaluating School-Level Fitness Patterns in Youth: Findings from the NFL PLAY 60 FITNESSGRAM Partnership Project

Background: There has been a great interest in tracking health-related fitness across the United States. The NFL PLAY 60 FITNESSGRAM Partnership Project (NFL P60FGPP) is a large participatory research network that involves the surveillance of fitness among more than 1000 schools spread throughout the country. Fitness data are collected by school staff and therefore these data can vary in quality and representativeness. Therefore, careful screening procedures are needed to ensure that the data can reflect actual patterns in the schools. This study examined the impact of different data screening procedures on outcomes of aerobic fitness (AF) collected from the NFL P60FGPP. Methods: Data were compiled from 149,101 youth from 504 schools and were processed using the established age- and gender-specific AF FITNESSGRAM health-related standards. Data were subjected to three different screening procedures (based on grade size and boy-to-girl ratio per grade). Linear models were computed to obtain unadjusted and adjusted (for age, BMI-Z, and socio-economic status) estimates of % youth in the Healthy Fitness Zone (HFZ) in order to determine if, 1) there were differences in % in the HFZ and 2) if differences could be explained by changes in the representativeness of the sample due to the different data screening procedures. Results: Depending on the screening procedure used, the final sample ranged from 96,999 (no screening) to 46,572 youth (most stringent criteria). The proportion of youth achieving appropriate levels of AF ranged from 56% to 61% with unscreened data resulting in consistently lower percentages of youth achieving the standard (P < 0.05). Overall, these differences were not explained by possible changes in demographic characteristics as the result of applying different screening criteria. Conclusions: The findings demonstrate the importance of establishing appropriate screening procedures that maximize sample size while also ensuring generalizability of the findings.

Plane wave fitting of the internal tidal sea-surface height signatures extracted from the TOPEX/Poseidon altimeter data along satellite tracks

The sea-surface height （SSH） signatures of internal tides extracted from the TOPEX/Poseidon （T/P） altimeter data along satellite tracks are fitted with superposition of several plane waves which have different wavenumber vectors. The key problem of plane wave fitting with iterative method is how to determine the initial value of wavenumber of each plane wave. The previous solving method is to analyze the internal tidal SSH signatures along each track with wavenumber spectrum. But it is found that the problem cannot be solved completely with the wavenumber spectrum analysis method only. The method based on the combination of wavenumber spectrum analysis method and the exhaustive method is proposed to determine the initial values of wavenumbers for iteration. Numerical results indicate that the proposed method is not only reasonable and feasible but also better than the previous method. The proposed method is an improvement of the previous one, which is beneficial to improving the precision of plane wave fitting of the T/P internal tidal SSH signatures and deepening the understanding of the internal tides in ocean.

FITS数据文件的检索和访问

普适图像传输系统(Flexible Image Transport System,FITS)是天文学领域应用最广泛的数据格式。自从20世纪80年代FITS格式被国际天文联合会(IAU)正式公布为国际标准以来,大部分的天文数据都是以FITS文件的形式在世界各地的数据中心和天文学家手中保存和交换。采用文件系统方式保存管理的FITS数据文件,很难适应程序化的检索和定位需求。随着FITS文件数量的不断增加以及虚拟天文台技术的发展,为这些以文件形式保存的天文数据提供检索功能的需求越来越迫切。FITS头以关键词值对的形式确切定义了所属FITS文件的结构,还提供了数据本身诸多特性的重要信息。FITS头中保存的这些信息可以满足大部分FITS数据文件查询检索的需求。将FITS头中的信息利用数据库来保存和管理,可以极大的方便对FITS文件的检索和定位。FITS头归档入库系统(FitHAS)是中国虚拟天文台项目开发的一个简单实用的FITS头信息归档入库工具,能够方便的将单个或者多个FITS文件的主FITS头信息导入到数据库中,为FITS数据文件的查询检索奠定基础,进而为虚拟天文台等更高层次的数据访问服务部署创造条件。本文介绍FITS数据格式,FITS头的基本结构;探讨虚拟天文台环境下FITS数据文件检索定位的实现方式;阐述FitHAS的功能特点、设计开发和使用方法。

SOME SHAPE-PRESERVING QUASI-INTERPOLANTS TO NON-UNIFORMLY DISTRIBUTED DATA BY MQ-B-SPLINES

Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.

分布式实时存储环境下的FITS数据一致性研究

在大型太阳望远镜观测数据的分布式高速实时存储过程中,作为元数据的FITS头和FITS数据文件的不一致,导致应用程序不能根据构建在元数据上的索引信息检索到相对应的FITS数据文件。研究了这种环境下,两类数据的一致性模型;分析总结了二者在实时存储时的一致性保障机制和解决方案,提出了应用改进的两段提交协议来协商这两种数据之间的一致性关系,并给出了两段提交协议在高速数据存储背景下的算法实现,研究过程和方法能够对其他科学领域的相关应用提供参考。

Real and Fitted Spherical Indentations

Spherical indentations that rely on original date are analyzed with the physically correct mathematical formula and its integration that take into account the radius over depth changes upon penetration. Linear plots, phase-transition onsets, energies, and pressures are algebraically obtained for germanium, zinc-oxide and gallium-nitride. There are low pressure phase-transitions that correspond to, or are not resolved by hydrostatic anvil onset pressures. This enables the attribution of polymorph structures, by comparing with known structures from pulsed laser deposition or molecular beam epitaxy and twinning. The spherical indentation is the easiest way for the synthesis and further characterization of polymorphs, now available in pure form under diamond calotte and in contact with their corresponding less dense polymorph. The unprecedented results and new possibilities require loading curves from experimental data. These are now easily distinguished from data that are “fitted” to make them concur with widely used unphysical Johnson’s formula for spheres (“P = (4/3)h3/2R1/2E∗”) not taking care of the R/h variation. Its challenge is indispensable, because its use involves “fitting equations” for making the data concur. These faked reports (no “experimental” data) provide dangerous false moduli and theories. The fitted spherical indentation reports with radii ranging from 4 to 250 μm are identified for PDMS, GaAs, Al, Si, SiC, MgO, and Steel. The detailed analysis reveals characteristic features.

Application of Newtonian approximate model to LIGO gravitational wave data processing

With the observation of a series of ground-based laser interferometer gravitational wave(GW)detectors such as LIGO and Virgo,nearly 100 GW events have been detected successively.At present,all detected GW events are generated by the mergers of compact binary systems and are identified through the data processing of matched filtering.Based on matched filtering,we use the GW waveform of the Newtonian approximate(NA)model constructed by linearized theory to match the events detected by LIGO and injections to determine the coalescence time and utilize the frequency curve for data fitting to estimate the parameters of the chirp masses of binary black holes(BBHs).The average chirp mass of our results is 22.05_(-6.31)^(+6.31)M_(⊙),which is very close to 23.80_(-3.52)^(+4.83)M_(⊙)provided by GWOSC.In the process,we can analyze LIGO GW events and estimate the chirp masses of the BBHs.This work presents the feasibility and accuracy of the low-order approximate model and data fitting in the application of GW data processing.It is beneficial for further data processing and has certain research value for the preliminary application of GW data.

基于遗传Data Farming的公共政策优化仿真模型

为了解决公共政策优化仿真时考察点不全面及耗费时间大的问题,提出了基于遗传Data Farming的公共政策优化仿真模型。所提出的模型中,Data Farming被用于全面地考察输入参数空间中各输入参数水平对应的输出响应,通过把仿真过程的输出过程看作适应度的计算,遗传算法被用于优化仿真过程,提高优化效率。分析了公共政策作用效果的影响因素,并介绍了传统的Data Farming技术,然后从仿真目标、模型框架、算法等三方面介绍了所提出的优化仿真模型。最后进行了实验,证明了所提出模型的有效性。

中国频谱射电日像仪FITS-IDI文件格式研究

我国新一代中国频谱射电日像仪(Chinese Spectral Radio Heliograph,CSRH)原始观测数据采用自定义格式,在进行后续处理与共享使用时必须转换相应的格式。在分析FITS-IDI(FITS Interferometry Data Interchange)格式的基础上,结合CSRH的实际观测模式与数据产出方式,定义与设计了符合项目情况的FITS-IDI格式及字段,并对FITS-IDI文件中若干字段的值如何获取、计算进行了深入讨论。根据定义生成的FITS-IDI文件已成功导入CASA软件,并可以进行后续处理。经过对CASA测量集文件的核实,证明了数据生成的正确性。本研究有效地推进了CSRH的建设工作,也对其他射电干涉阵数据存储有一定的参考价值。

PeakFit、1stOpt在弗兰克-赫兹实验数据处理中的应用

引入了两种新的弗兰克-赫兹实验数据处理方法。1.运用峰值分析软件PeakFit实现数据的拟合与自动寻峰。2.通过数学优化软件1stOpt实现多峰与单峰拟合,然后编写1stOpt求最值程序获得其峰值信息。PeakFit操作简单,无需编程,多峰拟合效果良好,峰值信息精确。1stOpt获得的相关系数可达0.999 9,拟合效果极好,峰值信息准确可靠。

FITS图像处理技术荟萃及在太阳观测中的应用

针对FITS图像文件的特点,结合其在天文学领域的广泛应用,对其各种处理技术进行了简明扼要的介绍。包括FITS文件完整性的检查、文件头和数据内容的查看、图像特性的伪彩编码、文件格式的转换、数据的压缩及相关太阳物理信息的提取等内容。

Hubble Diagram Test of 280 Supernovae Redshift Data

We compare the Hubble diagram calculated from the observed redshift (RS)/magnitude (μ) data of 280 Supernovae in the RS range of z = 0.0104 to 8.1 with Hubble diagrams inferred on the basis of the exponential tired light and the Lambda Cold Dark Matter (ΛCDM) cosmological model. We show that the experimentally measured Hubble diagram follows clearly the exponential photon flight time (tS)/RS relation, whilst the data calculated on the basis of the ΛCDM model exhibit poor agreement with the observed data.

Estimation of Extreme Coastal Wave Heightsfrom Time Series of Wave Data

A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.

基于Datasheet的两电平逆变器损耗模型研究

为进一步提高市电领域中应用广泛的SPWM两电平逆变器输出效率并降低器件损耗,深入分析了双极性调制模式下的两电平无源逆变电源的工作过程,建立了基于数学分析方法的损耗模型并进行了仿真验证。采用基于非理想条件下的CMF10120D型SiC-MOS管与C4D05120A型SiC肖特基二极管(SBD),通过数据提取工具image2data与数据拟合方法获得Datasheet内功率管损耗与漏极电流、结温函数关系式,建立SiC-MOS与SBD的影响因子函数,最终得出两电平逆变器损耗模型。仿真分析表明所建立的模型正确可靠,脉冲宽度相对误差计算控制在0.75%以下,具有实用价值,能够为后续开展实验研究提供理论支撑。

Uncertainty analysis of gravity data inversion

The traditional gravity modelling methods fail to deal with ambiguity zones. These zones are likely to be associated with uncertain boundaries. Source boundaries can be divided into "hard "and "soft "types."Hard"boundary stands for distinguished margin of discontinuity of source distributions. Traditional modelling method is based on this type of boundary. Uncertain boundaries of ambiguity zones belong to "soft"boundary.The authors put forward the uncertainty analysis because lots of uncertainty factors need to be taken into consideration. Any powerful system designed to interpret gravity data for a real source distribution must be able to deal with uncertain information. Uncertainty analysis( UA) is a useful tool to estimate the ambiguity of the data interpretation. It is often applied in conjunction with a specific modelling or inversion method. In this study,we use an iterative inversion and its results are evaluated using uncertainty analysis and proved to be effective.