Explore the vast range of titles available.

In this paper, we present a numerical method of finding synchronous solutions in coupled oscillator networks. We expand the optimization method of finding the periodic solution proposed by Feng et al. (J Optim Theory Appl 143:75-86, 2009) to find the synchronous solution in networks. The synchronous solutions here can be of many types, including in-phase synchronous solutions, anti-phase synchronous solutions, periodic synchronous solutions, cluster synchronous solutions, and so on. We show that the optimization problem in coupled oscillator networks can be regarded as a nonlinear least squares problem, so the corresponding Gauss–Newton method is proposed. Numerical simulations verify our results.

The approximate linear equation A x ≈ b with some columns of A error-free can be solved via mixed least squares-total least squares (MTLS) model by minimizing a nonlinear function. This paper is devoted to the Gauss–Newton iteration for the MTLS problem. With an appropriately chosen initial vector, each iteration step of the standard Gauss–Newton method requires to solve a smaller-size least squares problem, in which the QR of the coefficient matrix needs a rank-one modification. To improve the convergence, we devise a relaxed Gauss–Newton (RGN) method by introducing a relaxation factor and provide the convergence results as well. The convergence is shown to be closely related to the ratio of the square of subspace-restricted singular values of [ A ,  b ]. The RGN can also be modified to solve the total least squares (TLS) problem. Applying the RGN method to a Bursa–Wolf model in parameter estimation, numerical results show that the RGN-based MTLS method behaves much better than the RGN-based TLS method. Theoretical convergence properties of the RGN-MTLS algorithm are also illustrated by numerical tests.

Apixaban, a factor Xa inhibitor, is a direct oral anticoagulant with a well‐balanced elimination; it is eliminated evenly via feces, urine (with no active secretion), and as metabolites after oral administration. The common understanding is that biliary secretion and enterohepatic circulation (EHC) of apixaban are limited in humans, and that fecal excretion may be attributable to intestinal secretion. However, a decrease in apixaban blood concentration with activated charcoal coadministration in humans suggests possible involvement of EHC. This study aimed to evaluate the contribution of biliary excretion, EHC, and intestinal secretion to apixaban pharmacokinetics (PK) using a physiologically‐based pharmacokinetic (PBPK) model. A top‐down analysis was performed using blood concentration and mass balance data from healthy volunteers. Model parameters were optimized using the Cluster‐Gauss Newton method (CGNM), followed by the bootstrap method. The model accurately described observed data and indicated moderate to high biliary secretion relative to metabolic clearance. Simulated biliary secretion into the duodenum well predicted the biliary secretion data in humans (< 1% of dose at 8 h post‐dose). Virtual knockout of EHC resulted in a shortened half‐life from 8.7 to 2.9 h, and 17% and 55% decrease in area under the concentration curve (AUC) and fecal excretion after intravenous dosing, respectively, confirming the significant contribution of biliary excretion and EHC. The model also accurately described apixaban PK with activated charcoal coadministration at 2 or 6 h post‐dose. Although further experimental validation (e.g., sandwich‐cultured hepatocytes) would strengthen these findings, our study demonstrates that biliary secretion and EHC play a substantial role in apixaban elimination and disposition in humans. Study Highlights What is the current knowledge on the topic? ○Apixaban elimination is thought to occur through multiple pathways: fecal excretion, metabolism, and urinary excretion where its clearance can be explained by glomerular filtration. Biliary secretion and enterohepatic circulation (EHC) are considered to play minimal roles based on animal and human studies. What question did this study address? ○This study challenged the current understanding of apixaban's elimination pathway by investigating the extent of biliary secretion and EHC in humans using PBPK modeling. What does this study add to our knowledge? ○Our analysis revealed substantial biliary secretion and EHC of apixaban in humans, which did not contradict previous interpretations from short‐term bile collection studies. How might this change drug discovery, development, and/or therapeutics? ○Neither intestinal secretion in animals nor limited bile recovery in short‐term sampling in humans should be interpreted as evidence for minimal biliary elimination and EHC in humans, highlighting the importance of comprehensive modeling approaches in drug disposition studies.

In the process industry, measurement systems are required for process development and optimization, as well as for monitoring and control. The processes often involve multiphase mixtures or flows that can be analyzed using tomography systems, which visualize the spatial material distribution within a certain measurement domain, e.g., a process pipe. In recent years, we studied the applicability of soft-field electromagnetic tomography methods for multiphase flow imaging, focusing on concepts for high-speed data acquisition and image reconstruction. Different non-intrusive electrical impedance and microwave tomography systems were developed at our institute, which are sensitive to the local contrasts of the electrical properties of the materials. These systems offer a very high measurement and image reconstruction rate of up to 1000 frames per second in conjunction with a dynamic range of up to 120 dB. This paper provides an overview of the underlying concepts and recent improvements in terms of sensor design, data acquisition and signal processing. We introduce a generalized description for modeling the electromagnetic behavior of the different sensors based on the finite element method (FEM) and for the reconstruction of the electrical property distribution using the Gauss–Newton method and Newton’s one-step error reconstructor (NOSER) algorithm. Finally, we exemplify the applicability of the systems for different measurement scenarios. They are suitable for the analysis of rapidly-changing inhomogeneous scenarios, where a relatively low spatial resolution is sufficient.

This paper presents a novel non-linear least squares enhanced proper orthogonal decomposition (POD)-based 4DVar algorithm (referred as NLS-4DVar) for the non-linear ensemble-based 4DVar. In the algorithm, the Gauss-Newton iterative method is employed to handle the non-quadratic non-linearity of the 4DVar cost function while the overall structure of the algorithm still resembles the original POD-4DVar algorithm. It is proved that the original POD-4DVar algorithm is a special case of the proposed NLS-4DVar algorithm under the assumption of the linear relationship between the model perturbations (MPs) and the simulated observation perturbations (OPs). Under the assumption it is also shown that the solution of POD-4DVar algorithm coincides with the solution of the proposed NLS-4DVar algorithm. On the contrary, if the linear relationship assumption is dropped, the solution of the POD-4DVar algorithm is only the first iteration of the proposed NLS-4DVar algorithm. As a result, our analysis provides an explanation for the degraded and inaccurate performance of the POD-4DVar algorithm when the underlying forecast model or (and) the observation operator is strongly non-linear. The potential merits and advantages of the proposed NLS-4DVar are demonstrated by a group of Observing System Simulation Experiments with Advanced Research WRF (ARW) using accumulated rainfall-observations.

Due to the existence of environmental or human factors, and because of the instrument itself, there are many uncertainties in point clouds, which directly affect the data quality and the accuracy of subsequent processing, such as point cloud segmentation, 3D modeling, etc. In this paper, to address this problem, stochastic information of point cloud coordinates is taken into account, and on the basis of the scanner observation principle within the Gauss–Helmert model, a novel general point-based self-calibration method is developed for terrestrial laser scanners, incorporating both five additional parameters and six exterior orientation parameters. For cases where the instrument accuracy is different from the nominal ones, the variance component estimation algorithm is implemented for reweighting the outliers after the residual errors of observations obtained. Considering that the proposed method essentially is a nonlinear model, the Gauss–Newton iteration method is applied to derive the solutions of additional parameters and exterior orientation parameters. We conducted experiments using simulated and real data and compared them with those two existing methods. The experimental results showed that the proposed method could improve the point accuracy from 10−4 to 10−8 (a priori known) and 10−7 (a priori unknown), and reduced the correlation among the parameters (approximately 60% of volume). However, it is undeniable that some correlations increased instead, which is the limitation of the general method.

This paper presents a method for estimating the conditional or posterior distribution of the parameters of deterministic dynamical systems. The procedure conforms to an EM implementation of a Gauss–Newton search for the maximum of the conditional or posterior density. The inclusion of priors in the estimation procedure ensures robust and rapid convergence and the resulting conditional densities enable Bayesian inference about the model parameters. The method is demonstrated using an input–state–output model of the hemodynamic coupling between experimentally designed causes or factors in fMRI studies and the ensuing BOLD response. This example represents a generalization of current fMRI analysis models that accommodates nonlinearities and in which the parameters have an explicit physical interpretation. Second, the approach extends classical inference, based on the likelihood of the data given a null hypothesis about the parameters, to more plausible inferences about the parameters of the model given the data. This inference provides for confidence intervals based on the conditional density.

In this paper, we propose a new version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems based on the transformation to the nonsmooth equation, which is equivalent to some unconstrained optimization problem. The B-differential plays the role of the derivative. We present two types of algorithms (usual and inexact), which have superlinear and global convergence for semismooth cases. These results can be applied to efficiently find all solutions of the nonlinear complementarity problems under some mild assumptions. The results of the numerical tests are attached as a complement of the theoretical considerations.

The Levenberg–Marquardt method is a fundamental regularization technique for the Newton method applied to nonlinear equations, possibly constrained, and possibly with singular or even nonisolated solutions. We review the literature on the subject, in particular relating to each other various convergence frameworks and results. In this process, the analysis is performed from a unified perspective, and some new results are obtained as well. We discuss smooth and piecewise smooth equations, inexact solution of subproblems, and globalization techniques. Attention is also paid to the LP-Newton method, because of its relations to the Levenberg–Marquardt method.

Quantile regression is an increasingly popular method for estimating the quantiles of a distribution conditional on the values of covariates. Regression quantiles are robust against the influence of outliers and, taken several at a time, they give a more complete picture of the conditional distribution than a single estimate of the center. This article first presents an iterative algorithm for finding sample quantiles without sorting and then explores a generalization of the algorithm to nonlinear quantile regression. Our quantile regression algorithm is termed an MM, or majorize-minimize, algorithm because it entails majorizing the objective function by a quadratic function followed by minimizing that quadratic. The algorithm is conceptually simple and easy to code, and our numerical tests suggest that it is computationally competitive with a recent interior point algorithm for most problems.