Least-squares best fit of a deterministic model to experimental data using linear prediction: estimating confidence intervals of the rms with prediction and application to dimensional metrology of mirrors

2002 ◽  
Vol 4 (2) ◽  
pp. 145-154 ◽  
Author(s):  
Manuel Mestre ◽  
Jean-Pierre Rozelot
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Confidence Intervals ◽  
Linear Prediction ◽  
Deterministic Model ◽  
Dimensional Metrology ◽  
Best Fit

Characteristics of statistical parameters used to interpret least-squares results.

1978 ◽  
Vol 24 (4) ◽  
pp. 611-620 ◽  
Author(s):  
R B Davis ◽  
J E Thompson ◽  
H L Pardue
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Confidence Intervals ◽  
Standard Error ◽  
Statistical Parameters ◽  
Average Value ◽  
Data Points ◽  
Independent Variable ◽  
Highly Correlated

Abstract This paper discusses properties of several statistical parameters that are useful in judging the quality of least-squares fits of experimental data and in interpreting least-squares results. The presentation includes simplified equations that emphasize similarities and dissimilarities among the standard error of estimate, the standard deviations of slopes and intercepts, the correlation coefficient, and the degree of correlation between the least-squares slope and intercept. The equations are used to illustrate dependencies of these parameters upon experimentally controlled variables such as the number of data points and the range and average value of the independent variable. Results are interpreted in terms of which parameters are most useful for different kinds of applications. The paper also includes a discussion of joint confidence intervals that should be used when slopes and intercepts are highly correlated and presents equations that can be used to judge the degree of correlation between these coefficients and to compute the elliptical joint confidence intervals. The parabolic confidence intervals for calibration cures are also discussed briefly.

scholarly journals Simulating tubulin-associated unit transport in an axon: using bootstrapping for estimating confidence intervals of best-fit parameter values obtained from indirect experimental data

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170045 ◽  
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov
Keyword(s):  
Experimental Data ◽  
Confidence Intervals ◽  
Surrogate Data ◽  
Model Parameters ◽  
Model Predictions ◽  
Estimate Parameter ◽  
Minimum Number ◽  
Percentile Bootstrap ◽  
Parameter Values ◽  
Best Fit

In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate ‘experimental’ data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.

scholarly journals Pathways of reducing equivalents in hepatocytes from rats. Estimation of cytosolic fluxes by means of 3H-labelled substrates for either A- or B-specific dehydrogenases

1987 ◽  
Vol 243 (3) ◽  
pp. 625-630 ◽  
Author(s):  
C Vind ◽  
A Hunding ◽  
N Grunnet
Keyword(s):  
Experimental Data ◽  
Lactate Dehydrogenase ◽  
Alcohol Dehydrogenase ◽  
Least Squares ◽  
Oxidation Rate ◽  
Isolated Hepatocytes ◽  
Glycerol Phosphate ◽  
Hydrogen Atoms ◽  
Best Fit ◽  
Glycerol Phosphate Dehydrogenase

The metabolism of [2-3H]lactate and [2-3H]glycerol was studied in isolated hepatocytes from fed rats. In order to estimate the rate of equilibrium between the 4A and 4B hydrogen atoms of NADH, we compared the flow of 3H from [2-3H]lactate and [2-3H]glycerol, the oxidations of which are catalysed by A- and B-type dehydrogenases, respectively. Hepatocytes were incubated with lactate, glycerol and ethanol and tracer amounts of [2-3H]lactate or [2-3H]glycerol and the labelling rates of lactate, ethanol, glucose and glycerol phosphate were determined. The data were used to calculate the oxidation rate of NADH catalysed by lactate dehydrogenase, alcohol dehydrogenase, triosephosphate dehydrogenase and glycerol phosphate dehydrogenase. The rates were calculated by obtaining the best fit of a model to the experimental data by using a least-squares procedure. The results support our model and suggest that the fluxes through various dehydrogenases are sufficient to equilibrate the 4A and 4B hydrogen atoms of cytosolic NADH. The validity of the metabolic models used was evaluated by comparison of rates of NADH oxidation catalysed by cytosolic dehydrogenases as calculated by two different models.

scholarly journals Smart Design Nano-Hybrid Formulations by Machine Learning

Proceedings ◽  
2020 ◽  
Vol 78 (1) ◽  
pp. 5
Author(s):  
Raquel de Melo Barbosa ◽  
Fabio Fonseca de Oliveira ◽  
Gabriel Bezerra Motta Câmara ◽  
Tulio Flavio Accioly de Lima e Moura ◽  
Fernanda Nervo Raffin ◽  
...  
Keyword(s):  
Machine Learning ◽  
Experimental Data ◽  
Water Solubility ◽  
Inorganic Materials ◽  
Fine Tuning ◽  
Support Vector ◽  
Drug Solubility ◽  
Physical Behavior ◽  
Best Fit

Nano-hybrid formulations combine organic and inorganic materials in self-assembled platforms for drug delivery. Laponite is a synthetic clay, biocompatible, and a guest of compounds. Poloxamines are amphiphilic four-armed compounds and have pH-sensitive and thermosensitive properties. The association of Laponite and Poloxamine can be used to improve attachment to drugs and to increase the solubility of β-Lapachone (β-Lap). β-Lap has antiviral, antiparasitic, antitumor, and anti-inflammatory properties. However, the low water solubility of β-Lap limits its clinical and medical applications. All samples were prepared by mixing Tetronic 1304 and LAP in a range of 1–20% (w/w) and 0–3% (w/w), respectively. The β-Lap solubility was analyzed by UV-vis spectrophotometry, and physical behavior was evaluated across a range of temperatures. The analysis of data consisted of response surface methodology (RMS), and two kinds of machine learning (ML): multilayer perceptron (MLP) and support vector machine (SVM). The ML techniques, generated from a training process based on experimental data, obtained the best correlation coefficient adjustment for drug solubility and adequate physical classifications of the systems. The SVM method presented the best fit results of β-Lap solubilization. In silico tools promoted fine-tuning, and near-experimental data show β-Lap solubility and classification of physical behavior to be an excellent strategy for use in developing new nano-hybrid platforms.

scholarly journals Unbinding of Hyaluronan Accelerates the Enzymatic Activity of Bee Hyaluronidase

2011 ◽  
Vol 286 (41) ◽  
pp. 35699-35707 ◽  
Author(s):  
Attila Iliás ◽  
Károly Liliom ◽  
Brigitte Greiderer-Kleinlercher ◽  
Stephan Reitinger ◽  
Günter Lepperdinger
Keyword(s):  
Experimental Data ◽  
Quartz Crystal ◽  
Surface Loop ◽  
X Ray ◽  
Site Model ◽  
Substrate Interaction ◽  
Close Proximity ◽  
Binding Groove ◽  
The One ◽  
Best Fit

Hyaluronan (HA), a polymeric glycosaminoglycan ubiquitously present in higher animals, is hydrolyzed by hyaluronidases (HAases). Here, we used bee HAase as a model enzyme to study the HA-HAase interaction. Located in close proximity to the active center, a bulky surface loop, which appears to obstruct one end of the substrate binding groove, was found to be functionally involved in HA turnover. To better understand kinetic changes in substrate interaction, binding of high molecular weight HA to catalytically inactive HAase was monitored by means of quartz crystal microbalance technology. Replacement of the delimiting loop by a tetrapeptide interconnection increased the affinity for HA up to 100-fold, with a KD below 1 nm being the highest affinity among HA-binding proteins surveyed so far. The experimental data of HA-HAase interaction were further validated showing best fit to the theoretically proposed sequential two-site model. Besides the one, which had been shown previously in course of x-ray structure determination, a previously unrecognized binding site works in conjunction with an unbinding loop that facilitates liberation of hydrolyzed HA.

Comparative study of isotherm parameters of lead biosorption by two wastes of olive-oil production

2015 ◽  
Vol 72 (5) ◽  
pp. 711-720 ◽  
Author(s):  
G. Blázquez ◽  
A. Ronda ◽  
M. A. Martín-Lara ◽  
A. Pérez ◽  
M. Calero
Keyword(s):  
Experimental Data ◽  
Olive Tree ◽  
Langmuir Equation ◽  
Equilibrium Isotherm ◽  
Chemical Treatments ◽  
Olive Stone ◽  
Loss Of Mass ◽  
Best Fit ◽  
Tree Pruning ◽  
Effectiveness Coefficient

Batch isotherm studies were carried out on a laboratory scale: (i) to investigate the effectiveness to remove lead of two wastes (olive stone (OS) and olive tree pruning (OTP)), untreated and chemically treated; and (ii) to examine the applicability of various adsorption isotherms to fit the experimental data. Results from tests were analyzed using seven equilibrium isotherm correlations (Langmuir, Freundlich, Dubinin–Radushkevich, Temkin, Redlich–Peterson, Sips, and Toth equations). The sum of the squares of the errors was determined for each isotherm and the Langmuir equation provided the best fit. Chemical treatments increased the biosorption properties of these materials. The maximum biosorption capacities were: 6.33, 49.13, 14.83, and 38.93 mg g−1 for untreated OS, HNO3-OS, H2SO4-OS, and NaOH-OS, respectively, and 26.72, 86.40, 72.78, and 123.80 mg g−1 for untreated OTP, HNO3-OTP, H2SO4-OTP, and NaOH-OTP, respectively. Finally, the loss of mass for each waste (13.9, 14.3, and 36.8% for HNO3-OS, H2SO4-OS, and NaOH-OS and 35.1, 27.5, and 46.7% for HNO3-OTP, H2SO4-OTP, and NaOH-OTP, respectively) was taken into account and an effectiveness coefficient was determined for each adsorbent material.

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