Applicability of mathematical curve-fitting procedures to late mixed dentition patients with crowding: A clinical-experimental evaluation

2007 ◽  
Vol 131 (2) ◽  
pp. 160.e17-160.e25 ◽  
Author(s):  
Hans Wellens
Keyword(s):  
Curve Fitting ◽  
Experimental Evaluation ◽  
Mixed Dentition ◽  
Fitting Procedures

Comparison of reaction theories for multilevel interference—the 14C + p reactions

1969 ◽  
Vol 47 (24) ◽  
pp. 2763-2777 ◽  
Author(s):  
C. T. Tindle ◽  
E. Vogt
Keyword(s):  
Compound Nucleus ◽  
Cross Sections ◽  
Curve Fitting ◽  
Low Energy ◽  
Analytic Method ◽  
R Matrix ◽  
Strong Interference ◽  
S Matrix ◽  
Fitting Procedures ◽  
Good Agreement

A comparison is made between the R-matrix and S-matrix theories of low-energy compound nucleus resonances for the particular case of two-level interference. The (p,γ) and (p,n) cross sections of 14C for proton energies between 0.7 and 1.5 MeV are analyzed using both theories. The 15N compound nucleus in this region exhibits strong two-level interference. The two theories provide equally good fits to the data, but the parameters describing the compound-nucleus levels are quite different. A general analytic method of relating the two sets of parameters is derived and shown to give good agreement with the results obtained by curve-fitting procedures. Remarks are made concerning the general behavior of the parameters under strong interference conditions and also on the inclusion of many channels into the analysis.

Improved curve fitting procedures to determine equilibrium binding constants

The Analyst ◽  
2006 ◽  
Vol 131 (10) ◽  
pp. 1145 ◽  
Author(s):  
Frank H. Stootman ◽  
Dianne M. Fisher ◽  
Alison Rodger ◽  
Janice R. Aldrich-Wright
Keyword(s):  
Curve Fitting ◽  
Binding Constants ◽  
Equilibrium Binding ◽  
Fitting Procedures

A Comparison of Five Curve-Fitting Procedures in Radioimmunoassay

1986 ◽  
Vol 23 (6) ◽  
pp. 694-698 ◽  
Author(s):  
Jennifer A Nisbet ◽  
J A Owen ◽  
Gail E Ward
Keyword(s):  
Binding Site ◽  
Curve Fitting ◽  
The Other ◽  
Practical Advantage ◽  
Analytical Precision ◽  
Fitting Procedures ◽  
Best Fit ◽  
Single Binding Site ◽  
Better Than

Data obtained from routine analytical radioimmunoassays were processed using five curve-fitting procedures, viz. ‘Amersham’, single binding site, four parameter logistic, a linear logit-log and a polynomial logit-log. The polynomial logit-log procedure gave the best fit, but this was probably due to the inherent flexibility of this curve-fitting process since the analytical precision achieved with it was no better than what was obtained with most of the other procedures. A limited study failed to show that statistical weighting of data before curve fitting had any practical advantage.

Analysis of X-ray Photoelectron Spectra through Their Even Derivatives

1979 ◽  
Vol 33 (5) ◽  
pp. 502-509 ◽  
Author(s):  
Attila E. Pavlath ◽  
Merle M. Millard
Keyword(s):  
Curve Fitting ◽  
Photoelectron Spectroscopy ◽  
Least Square ◽  
Photoelectron Spectra ◽  
Original Position ◽  
Noise Background ◽  
X Ray ◽  
Fitting Procedures ◽  
Higher Derivatives ◽  
Derivatives Of

The analysis of organic and inorganic surfaces can be carried out very effectively with the aid of x-ray photoelectron spectroscopy. In many cases, however, the presently available methods and techniques for data treatment resolutions are not suitable for the qualitative and quantitative identification of the various forms of a given atom on the same surface. The number of components and a good approximation of their original position in the composite curve must be known to use the available curve fitting procedures, otherwise the evaluation can be unreliable. It is suggested that the second and higher even derivatives of the composite could provide these data. The possibility of applying even derivatives of composite curves in combination with a nonlinear least square curve fitting program was investigated. It was found that depending on the noise background of the spectra, the resolution could be improved through this method. The resolution is dependent on the half-width of the component curves, their separation, and ratio. Both Gaussian and Lorentzian curves can be resolved, but the resolution of the latter is easier. The resolution is increasing with higher derivatives; however, increased smoothing must be applied at each step to neutralize the influence of the noise background.

Direct Use of Second Derivatives in Curve-Fitting Procedures

1989 ◽  
Vol 43 (5) ◽  
pp. 877-882 ◽  
Author(s):  
Farida Holler ◽  
David H. Burns ◽  
James B. Callis
Keyword(s):  
Curve Fitting ◽  
A Priori ◽  
Simulated Data ◽  
Relevant Information ◽  
Second Derivative ◽  
Unknown Variable ◽  
Fitting Method ◽  
Second Derivatives ◽  
Fitting Procedures ◽  
Ft Ir

Most curve-fitting procedures deal with an unknown, variable baseline by modeling it with a function involving a number of parameters. In view of the facts that (1) there is often no analytically relevant information in the baseline, and (2) there is usually no functional form known, a priori, for the baseline, we have chosen to eliminate it by means of the second-derivative transformation. The resulting profile is deconvoluted by fitting it with the second derivative of the sum of an appropriate number of component curves. The utility of this procedure is demonstrated on simulated data with typical baselines and noise levels, and on real FT-IR data. Peak parameters (such as position, width, and area) obtained from this technique are comparable to those obtained by fitting the original spectrum with Lorentzian curves and a simple baseline. The major advantage of this procedure is the reduction in the number of parameters that must be optimized in the fitting method. Applications of the technique could eliminate contributions from other complex baseline profiles in the quantitative analysis of spectral components.

scholarly journals Investigating bias in the application of curve fitting programs to atmospheric time series

2014 ◽  
Vol 7 (7) ◽  
pp. 7085-7136 ◽  
Author(s):  
P. A. Pickers ◽  
A. C. Manning
Keyword(s):  
Time Series ◽  
Curve Fitting ◽  
Data Sets ◽  
Mathematical Functions ◽  
Data Set ◽  
Zero Crossing ◽  
Sensitivity Tests ◽  
Input Parameters ◽  
Fitting Procedures ◽  
Gas Measurement

Abstract. The decomposition of an atmospheric time series into its constituent parts is an essential tool for identifying and isolating variations of interest from a data set, and is widely used to obtain information about sources, sinks and trends in climatically important gases. Such procedures involve fitting appropriate mathematical functions to the data, however, it has been demonstrated that the application of such curve fitting procedures can introduce bias, and thus influence the scientific interpretation of the data sets. We investigate the potential for bias associated with the application of three curve fitting programs, known as HPspline, CCGCRV and STL, using CO2, CH4 and O3 data from three atmospheric monitoring field stations. These three curve fitting programs are widely used within the greenhouse gas measurement community to analyse atmospheric time series, but have not previously been compared extensively. The programs were rigorously tested for their ability to accurately represent the salient features of atmospheric time series, their ability to cope with outliers and gaps in the data, and for sensitivity to the values used for the input parameters needed for each program. We find that the programs can produce significantly different curve fits, and these curve fits can be dependent on the input parameters selected. There are notable differences between the results produced by the three programs for many of the decomposed components of the time series, such as the representation of seasonal cycle characteristics and the long-term growth rate. The programs also vary significantly in their response to gaps and outliers in the time series. Overall, we found that none of the three programs were superior, and that each program had its strengths and weaknesses. Thus, we provide a list of recommendations on the appropriate use of these three curve fitting programs for certain types of data sets, and for certain types of analyses and applications. In addition, we recommend that sensitivity tests are performed in any study using curve fitting programs, to ensure that results are not unduly influenced by the input smoothing parameters chosen. Our findings also have implications for previous studies that have relied on a single curve fitting program to interpret atmospheric time series measurements. This is demonstrated by using two other curve fitting programs to replicate work in Piao et al. (2008) on zero-crossing analyses of atmospheric CO2 seasonal cycles to investigate terrestrial biosphere changes. We highlight the importance of using more than one program, to ensure results are consistent, reproducible, and free from bias.

scholarly journals Investigating bias in the application of curve fitting programs to atmospheric time series

2015 ◽  
Vol 8 (3) ◽  
pp. 1469-1489 ◽  
Author(s):  
P. A. Pickers ◽  
A. C. Manning
Keyword(s):  
Time Series ◽  
Curve Fitting ◽  
Data Sets ◽  
Mathematical Functions ◽  
Data Set ◽  
Zero Crossing ◽  
Sensitivity Tests ◽  
Input Parameters ◽  
Fitting Procedures ◽  
Gas Measurement

Abstract. The decomposition of an atmospheric time series into its constituent parts is an essential tool for identifying and isolating variations of interest from a data set, and is widely used to obtain information about sources, sinks and trends in climatically important gases. Such procedures involve fitting appropriate mathematical functions to the data. However, it has been demonstrated that the application of such curve fitting procedures can introduce bias, and thus influence the scientific interpretation of the data sets. We investigate the potential for bias associated with the application of three curve fitting programs, known as HPspline, CCGCRV and STL, using multi-year records of CO2, CH4 and O3 data from three atmospheric monitoring field stations. These three curve fitting programs are widely used within the greenhouse gas measurement community to analyse atmospheric time series, but have not previously been compared extensively. The programs were rigorously tested for their ability to accurately represent the salient features of atmospheric time series, their ability to cope with outliers and gaps in the data, and for sensitivity to the values used for the input parameters needed for each program. We find that the programs can produce significantly different curve fits, and these curve fits can be dependent on the input parameters selected. There are notable differences between the results produced by the three programs for many of the decomposed components of the time series, such as the representation of seasonal cycle characteristics and the long-term (multi-year) growth rate. The programs also vary significantly in their response to gaps and outliers in the time series. Overall, we found that none of the three programs were superior, and that each program had its strengths and weaknesses. Thus, we provide a list of recommendations on the appropriate use of these three curve fitting programs for certain types of data sets, and for certain types of analyses and applications. In addition, we recommend that sensitivity tests are performed in any study using curve fitting programs, to ensure that results are not unduly influenced by the input smoothing parameters chosen. Our findings also have implications for previous studies that have relied on a single curve fitting program to interpret atmospheric time series measurements. This is demonstrated by using two other curve fitting programs to replicate work in Piao et al. (2008) on zero-crossing analyses of atmospheric CO2 seasonal cycles to investigate terrestrial biosphere changes. We highlight the importance of using more than one program, to ensure results are consistent, reproducible, and free from bias.

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