scholarly journals Estimation of non-constant variance in isothermal titration calorimetry using an ITC measurement model

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0244739
Author(s):  
Xiujie Ge ◽  
Lan Chen ◽  
Dexing Li ◽  
Renxiao Liu ◽  
Guanglu Ge
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Isothermal Titration Calorimetry ◽  
Weighted Least Squares ◽  
Measurement Model ◽  
Variance Function ◽  
Titration Calorimetry ◽  
Least Squares Regression ◽  
Error Components ◽  
Constant Variance

Isothermal titration calorimetry (ITC) is the gold standard for accurate measurement of thermodynamic parameters in solution reactions. In the data processing of ITC, the non-constant variance of the heat requires special consideration. The variance function approach has been successfully applied in previous studies, but is found to fail under certain conditions in this work. Here, an explicit ITC measurement model consisting of main thermal effects and error components has been proposed to quantitatively evaluate and predict the non-constant variance of the heat data under various conditions. Monte Carlo simulation shows that the ITC measurement model provides higher accuracy and flexibility than variance function in high c-value reactions or with additional error components, for example, originated from the fluctuation of the concentrations or other properties of the solutions. The experimental design of basic error evaluation is optimized accordingly and verified by both Monte Carlo simulation and experiments. An easy-to-run Python source code is provided to illustrate the establishment of the ITC measurement model and the estimation of heat variances. The accurate and reliable non-constant variance of heat is helpful to the application of weighted least squares regression, the proper evaluation or selection of the reaction model.

Least Squares Regression Estimates of the Schaefer Production Model: Some Monte Carlo Simulation Results

1980 ◽  
Vol 37 (8) ◽  
pp. 1284-1294 ◽  
Author(s):  
Russell S. Uhler
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Population Size ◽  
Analytical Methods ◽  
Production Model ◽  
Parameter Estimates ◽  
Errors In Variables ◽  
Least Squares Regression ◽  
Harvest Rate

Both analytical methods and Monte Carlo experiments are used to determine the amount of bias in the regression estimates of the Schaefer model when it is estimated with catch and effort data. It is shown that the use of the catch–effort ratio and effort as regressors leads to the classical errors in variables problem which produces asymptotically biased parameter estimates. Since the seriousness of the bias, and even its direction in the case of certain formulations of the model, cannot be determined by analytical methods, Monte Carlo simulation experiments were used. Four variations of the Schaefer model were investigated; two of which come from a discrete formulation of the model and two of which come from a continuous formulation. The least squares regression estimates of all formulations result in substantial bias although one formulation is considerably better than the others.Bias in the optimal levels of the population size, the harvest rate, and fishing effort are also calculated. It is found that under likely conditions regarding the model equation errors that the optimal population size and harvest rate may be as much as 40–50% in error depending on the model used. In general, however, the bias in these quantities is much smaller than the bias in the parameter estimates themselves.Key words: Schaefer model, Monte Carlo, optimal fishery management, errors in variables, biased estimates

scholarly journals TOA-based source localization using ML estimation

2018 ◽  
Vol 7 (2.7) ◽  
pp. 742
Author(s):  
Ram Prasad Gundu ◽  
P Pardhasaradhi ◽  
S Koteswara Rao ◽  
V Gopi Tilak
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Method ◽  
Measurement Model ◽  
Optimization Techniques ◽  
Time Of Arrival ◽  
Two Dimensional ◽  
Single Trial ◽  
Ml Estimation ◽  
First Case

This paper proposes the Time of arrival (TOA) measurement model for finding the position of a stationary emitting source for Line-of-Sight (LOS) scenario. Here Maximum Likelihood Estimation (MLE) is used as the positioning algorithm. For approximation of the roots of the solution, which directly corresponds to the source location, the optimization techniques used are Gauss-Newton, Gradient descent and Newton-Raphson methods. Two different cases are considered for investigation in this paper. The first case compares the three different optimization techniques in terms of convergence rate. In the second case the error values obtained from two different scenarios are compared, one involving a single trial only, while the second scenario uses Monte Carlo method of simulations. Firstly, the error values, for both the coordinates (two-dimensional), obtained by getting the difference between the measured source positions and the initially guessed source position are obtained for a single trial. Later using Monte Carlo simulation method, the Root-Mean-Square (RMS) error values, for both the coordinates (two-dimensional), for the optimization techniques are obtained. To improve the performance of the algorithm, Monte Carlo simulation has been used for multiple trials.  

scholarly journals pytc: a python package for analysis of Isothermal Titration Calorimetry experiments

2017 ◽  
Author(s):  
Hiranmayi Duvvuri ◽  
Lucas C. Wheeler ◽  
Michael J. Harms
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Isothermal Titration Calorimetry ◽  
Titration Calorimetry ◽  
Thermodynamic Models ◽  
Extensive Documentation ◽  
Cross Platform ◽  
Key Features ◽  
Python Package

AbstractHere we describe pytc, an open-source Python-package for global fits of thermodynamic models to multiple Isothermal Titration Calorimetry experiments. Key features include simplicity, the ability to implement new thermodynamic models, a robust maximum likelihood fitter, a fast Bayesian Markov-Chain Monte Carlo sampler, rigorous implementation, extensive documentation, and full cross-platform compatibility. pytc can be used as either a programming API or with a GUI. It is available for download at: https://github.com/harmslab/pytc.

scholarly journals A Novel Robust Method for Solving CMB Receptor Model Based on Enhanced Sampling Monte Carlo Simulation

Processes ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 169 ◽  
Author(s):  
Wen Hou ◽  
Yunlei Yang ◽  
Zheng Wang ◽  
Muzhou Hou ◽  
Qianhong Wu ◽  
...  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Least Squares ◽  
Source Apportionment ◽  
Environmental Protection Agency ◽  
Weighted Least Squares ◽  
Chemical Mass Balance ◽  
Enhanced Sampling ◽  
Protection Agency ◽  
Mass Balance Models

The traditional effective variance weighted least squares algorithms for solving CMB (Chemical Mass Balance) models have the following drawbacks: When there is collinearity among the sources or the number of species is less than the number of sources, then some negative value of contribution will appear in the results of the source apportionment or the algorithm does not converge to calculation. In this paper, a novel robust algorithm based on enhanced sampling Monte Carlo simulation and effective variance weighted least squares (ESMC-CMB) is proposed, which overcomes the above weaknesses. In the following practical instances for source apportionment, when nine species and nine sources, with no collinearity among them, are selected, EPA-CMB8.2 (U.S. Environmental Protection Agency-CMB8.2), NKCMB1.0 (NanKai University, China-CMB1.0) and ESMC-CMB can obtain similar results. When the source raise dust is added to the source profiles, or nine sources and eight species are selected, EPA-CMB8.2 and NKCMB1.0 cannot solve the model, but the proposed ESMC-CMB algorithm can achieve satisfactory results that fully verify the robustness and effectiveness of ESMC-CMB.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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