Parametric Model-based Methods Research Articles

PolyWeight: A free and open-source program for determination of molecular weight distribution of linear polymers

This paper introduces PolyWeight, a Python software featuring a user-friendly graphical user interface (GUI), which offers two distinct approaches for MWD determination: an analytical relation-based method and a parametric model-based method. By utilizing dynamic moduli, users can calculate MWD as well as molecular weight averages such as Mn, Mw, and Mz. The functionality of PolyWeight is validated using synthetic data and real data obtained from the literature, exhibiting good agreement. Log files and datasets used in this work are available on GitHub. Program summaryProgram Title: PolyWeightCPC Library link to program files:https://doi.org/10.17632/rn8t4mmvyd.1Developer's repository link:https://github.com/a-minotto/PolyWeightLicensing provisions: GPLv3Programming language: Python 3.xNature of problem: Analytical rheology enables the determination of molecular weight distribution (MWD) by solving inverse problems. The reptation theory establishes a liaison between the viscoelastic behavior and MWD, permitting the application of mathematical resolution methods like regularization and parameterization. PolyWeight offers two solutions: a parameterization-based method that assumes a generalized exponential distribution (GEX) for the MWD, and an analytical relationship-based method that utilizes the relaxation spectrum.Solution method: The analytical relationship-based solution incorporates a mathematical formulation that considers the relaxation spectrum obtained from the dynamic moduli using the NLREG software. The numerical integration of the relaxation spectrum is performed utilizing the integrate.quad function from the SciPy library. An optimization process is employed in the parametric solution to perform a multiobjective fit of the viscoelastic models to the dynamic moduli. The integrals in this case are also calculated using the integrate.quad package from the SciPy library. The optimization procedure utilizes the lmfit library, where a Minimizer object is created based on the optimization function and subsequently utilized with the minimize function, employing the default Levenberg-Marquardt algorithm for the fit.

Bayesian optimization for estimating the maximum tolerated dose in Phase I clinical trials

We introduce a Bayesian optimization method for estimating the maximum tolerated dose in this article. A number of parametric model-based methods have been proposed to estimate the maximum tolerated dose; however, parametric model-based methods need an assumption that dose–toxicity relationships follow specific theoretical models. This assumption potentially leads to suboptimal dose selections if the dose–toxicity curve is misspecified. Our proposed method is based on a Bayesian optimization framework for finding a global optimizer of unknown functions that are expensive to evaluate while using very few function evaluations. It models dose–toxicity relationships with a nonparametric model; therefore, a more flexible estimation can be realized compared with existing parametric model-based methods. Also, most existing methods rely on point estimates of dose–toxicity curves in their dose selections. In contrast, our proposed method exploits a probabilistic model for an unknown function to determine the next dose candidate without ignoring the uncertainty of posterior while imposing some dose-escalation limitations. We investigate the operating characteristics of our proposed method by comparing them with those of the Bayesian-based continual reassessment method and two different nonparametric methods. Simulation results suggest that our proposed method works successfully in terms of selections of the maximum tolerated dose correctly and safe dose allocations.

Uncertainty-guided intelligent sampling strategy for high-efficiency surface measurement via free-knot B-spline regression modelling

Intelligent sampling can be used to influence the efficiency of surface geometry measurement. With no design model information provided, reconstruction from prior sample points with a surrogate model has to be carried out iteratively, thus the next best sample point(s) can be intelligently selected. But, a lack of accurate and fast reconstruction models hinders the development of intelligent sampling techniques. In this paper, a smart surrogate model based on free-knot B-splines is used for intelligent surface sampling design with the aid of uncertainty modelling. By implementing intelligent sampling in a Cartesian, parametric or specific error space, the proposed method can be flexibly applied to reverse engineering and geometrical tolerance inspection, especially for high-dynamic-range structured surfaces with sparse and sharply edged features. Extensive numerical experiments on simulated and real surface data are presented. The results show that this parametric model-based method can achieve the same or higher sampling efficiency as some recent non-parametric methods but with far less computing time cost.

OnlineCall: fast online parameter estimation and base calling for illumina's next-generation sequencing.

Next-generation DNA sequencing platforms are becoming increasingly cost-effective and capable of providing enormous number of reads in a relatively short time. However, their accuracy and read lengths are still lagging behind those of conventional Sanger sequencing method. Performance of next-generation sequencing platforms is fundamentally limited by various imperfections in the sequencing-by-synthesis and signal acquisition processes. This drives the search for accurate, scalable and computationally tractable base calling algorithms capable of accounting for such imperfections. Relying on a statistical model of the sequencing-by-synthesis process and signal acquisition procedure, we develop a computationally efficient base calling method for Illumina's sequencing technology (specifically, Genome Analyzer II platform). Parameters of the model are estimated via a fast unsupervised online learning scheme, which uses the generalized expectation-maximization algorithm and requires only 3 s of running time per tile (on an Intel i7 machine @3.07GHz, single core)-a three orders of magnitude speed-up over existing parametric model-based methods. To minimize the latency between the end of the sequencing run and the generation of the base calling reports, we develop a fast online scalable decoding algorithm, which requires only 9 s/tile and achieves significantly lower error rates than the Illumina's base calling software. Moreover, it is demonstrated that the proposed online parameter estimation scheme efficiently computes tile-dependent parameters, which can thereafter be provided to the base calling algorithm, resulting in significant improvements over previously developed base calling methods for the considered platform in terms of performance, time/complexity and latency. A C code implementation of our algorithm can be downloaded from http://www.cerc.utexas.edu/OnlineCall/.

Model-Based Material Parameter Estimation for Terahertz Reflection Spectroscopy

One important yet commonly overlooked phenomenon in terahertz (THz) reflection spectroscopy is the etalon effect-interference caused by multiple reflections from dielectric layers. Material layers are present in many THz applications from the monitoring of pharmaceutical tablet coating thickness to the detection of drugs, explosives, or other contraband concealed beneath layers of packaging and/or clothing. This paper focuses on the development and implementation of a model-based material parameter estimation technique, primarily for use in reflection mode THz spectroscopy that takes the etalon effect into account. The technique is adapted from techniques developed for transmission spectroscopy of thin samples and includes a priori information; namely, the assumption that a material's complex refractive index behaves consistently with the Lorentz dispersion model. The inclusion of the multiple returns provides additional information about the material and its structure, alleviating the need for short time windows in the fast Fourier transform (FFT) processing, which can limit spectral resolution. In addition, the parametrization of the material's dielectric function offers the potential for material classification based on these estimated dispersion model parameters. The parametric model-based method is validated by comparison with results from a conventional, non-parametric method applied to transmission mode data before being applied to reflection mode data for further validation with transmission mode results. Tests are also conducted to evaluate the parametric technique's robustness against measurement noise and ambiguity in sample thickness.

Bayesian hybrid dose-finding design in phase I oncology clinical trials

In oncology, dose escalation is often carried out to search for the maximum tolerated dose (MTD) in phase I clinical trials. We propose a Bayesian hybrid dose-finding method that inherits the robustness of model-free methods and the efficiency of model-based methods. In the Bayesian hypothesis testing framework, we compute the Bayes factor and adaptively assign a dose to each cohort of patients based on the adequacy of the dose-toxicity information that has been collected thus far. If the data observed at the current treatment dose are adequately informative about the toxicity probability of this dose (e.g. whether this dose is below or above the MTD), we make the decision of dose assignment (e.g. either to escalate or to de-escalate the dose) directly without assuming a parametric dose-toxicity curve. If the observed data at the current dose are not sufficient to deliver such a definitive decision, we resort to a parametric dose-toxicity curve, such as that of the continual reassessment method (CRM), in order to borrow strength across all the doses under study to guide dose assignment. We examine the properties of the hybrid design through extensive simulation studies, and also compare the new method with the CRM and the '3 + 3' design. The simulation results show that our design is more robust than parametric model-based methods and more efficient than nonparametric model-free methods.

Model-based analysis of optically mapped epicardial activation patterns and conduction velocity.

A novel parametric model-based method was developed to quantify epicardial conduction patterns and velocity in an isolated Langendorff-perfused rabbit heart. The method incorporated geometric and anatomical features of the left and right ventricles into the analysis. Optical images of propagation were obtained using the voltage-sensitive dye DI-4-ANEPPS, and a high-speed digital camera. Activation maps were extracted from these images and interpolated onto a three-dimensional finite-element model of epicardial geometry and fiber structure. Activation time was expressed as a function of local parametric coordinates, and a conduction velocity vector field was computed from the gradient of the scalar field. Activation times measured using bipolar electrodes did not differ significantly from times measured using the optical mapping technique. The method was able to detect a 34% decrease in average fiber velocity and a 28% decrease in average cross-fiber velocity following the addition of 0.5 mM heptanol into the perfusate. The combination of optical mapping with a three-dimensional geometric model of the ventricles provides a new tool to quantify wave-front propagation relative to anatomy at a relatively high spatial resolution.

Regional myocardial perfusion and mechanics: a model-based method of analysis.

A new parametric model-based method has been developed that allows epicardial strain distributions to be computed on the left ventricular free wall in normal and ischemic myocardium and integrated with the regional distributions of anatomic and physiological measurements so that underlying relationships can be explored. An array of radiopaque markers was sewn on the anterior wall of the left ventricle (LV) in three anesthetized open-chest canines, and their positions were recorded using biplane video fluoroscopy before and 2 min after occlusion of the left anterior descending coronary artery. The three-dimensional (3D) anatomy of the LV and epicardial fiber angles were measured post-mortem using a 3D probe. A prolate spheroidal finite element model was fitted to the epicardial surface points (with <0.2 mm accuracy) and fiber angles (<5 degrees error). Regional myocardial blood flows (MBFs) were measured using fluorescent microspheres and fitted into the model (<0.3 ml min(-1) g(-1) error). Epicardial fiber and cross-fiber strain distributions were computed by allowing the model to deform from end-diastole to end-systole according to the recorded motion of the surface markers. Systolic fiber strain varied from -0.05 to 0.01 within the region of the markers during baseline, and regional MBF varied from 1.5 to 2.0 ml min(-1) g(-1). During 2 min ischemia, regional MBF was less than 0.3 ml min(-1) g(-1) in the ischemic region and 1.0 ml min(-1) g(-1) in the nonischemic region, and fiber strain ranged from 0.05 in the central ischemic zone to -0.025 in the remote nonischemic tissue. This analysis revealed a zone of impaired fiber shortening extending into the normally perfused myocardium that was significantly wider at the base than the apex. A validation analysis showed that a regularizing function can be optimized to minimize both fitting errors and numerical oscillations in the computed strain fields.