Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Julia (2)
- Least squares (2)
- Uncertainty (2)
- ALS (1)
- Cubic spline (1)
-
- Curve fitting (1)
- Data (1)
- Fit (1)
- Fitting (1)
- Hermite (1)
- Interpolation (1)
- Irregular grid (1)
- Jacobian covariance (1)
- Julia data (1)
- Linear (1)
- Linear least squares (1)
- Nonlinear (1)
- PCHIP (1)
- Polynomial (1)
- Polynomial curve fitting (1)
- Python (1)
- Reflectance (1)
- Regression (1)
- Residual (1)
- VUV (1)
- XUV (1)
- Publication
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Linear Least Squares Curve Fitting, R. Steven Turley
Linear Least Squares Curve Fitting, R. Steven Turley
Faculty Publications
This article is a review of the theory and practice behind linear least squares curve fitting. It outlines how to find the optimal parameters to match experimental data with theory and how to estimate the uncertainty in those parameters. The article demonstrates and validates these calculations in Excel, MATLAB, Mathematica, Python, and Julia.
Fitting Parameter Uncertainties In Least Squares Fitting, R. Steven Turley
Fitting Parameter Uncertainties In Least Squares Fitting, R. Steven Turley
Faculty Publications
This article review the theory and practice of computing uncertainties in the fit parameters in least squares fits. It shows how to estimate the uncertainties and gives some numerical examples in Julia of their use. Examples are given and validated for both linear and nonlinear fits.
Polynomial Fitting, R. Steven Turley
Polynomial Fitting, R. Steven Turley
Faculty Publications
This article reviews the theory and some good practice for fitting polynomials to data. I show by theory and example why fitting using a basis of orthogonal polynomials rather than monomials is desirable. I also show how to scale the independent variable for a more stable fit. I also demonstrate how to compute the uncertainty in the fit parameters. Finally, I discuss regression analysis: how to determine whether adding an additional term to the fit is justified.
Cubic Interpolation With Irregularly-Spaced Points In Julia 1.4, R. Steven Turley
Cubic Interpolation With Irregularly-Spaced Points In Julia 1.4, R. Steven Turley
Faculty Publications
This article shows how to interpolate between regularly- or irregularly-spaced points in Julia 1.4. It has derivations of the theory behind cubic splines, and piece-wise cubic hermite polynomial interpolation. The spline interpolants are continuous and have continuous first and second derivatives. The hermite polynomial interpolants are continuous and have continuous first derivatives. Three techniques are implemented to determine the slope at the data points for the interpolation (knots). One uses the average slope of the neighboring segments. Another use the quadratic polynomial passing through the point and its two neighbors. The third, PCHIP, is similar to the first method, but …
Fitting Als Reflectance Data Using Python, R. Steven Turley
Fitting Als Reflectance Data Using Python, R. Steven Turley
Faculty Publications
This article describes how to use the python refl library in https://bitbucket.org/steve_turley/reflectance-fitting to fit thin film reflectance data from the Advanced Light Source (ALS) at Lawrence Berkeley National Labs. It uses data taken for a thin film of aluminum capped by a thin film of aluminum fluoride on a silicon nitride substrate. The single fit in the example shown here shows the importance of taking into account the oxidation of the aluminum layer as part of the fit.
14-3-3zeta Role In Promoting Survival Of Cells To Facilitate Progression Of Cancer, Katie Pennington, Eranga Roshan, Joshua Andersen, Katherine K. Mccormack
14-3-3zeta Role In Promoting Survival Of Cells To Facilitate Progression Of Cancer, Katie Pennington, Eranga Roshan, Joshua Andersen, Katherine K. Mccormack
Student Works
The regulatory protein 14-3-3z promotes cellular growth and survival, and high expression levels of 14-3-3z are associated with mortality in multiple cancer types. 14-3-3z binds cellular proteins in a phosphorylation-dependent manner to modulate their functions. We have been characterizing the interactome of 14-3-3z which will likely lead to candidates for novel therapies for chemoresistant cancers. Tumor cells must be able to survive in a variety of stresses within the tumor microenvironment, including hypoxia, which occurs when tumors lack adequate blood supply. Previous data from our lab suggested that 14-3-3z promotes the adaptation of tumor cells to hypoxic stress. Our hypothesis …