First-order Method Research Articles

Population Pharmacokinetics of Sertraline in Psychiatric and Substance Use Disorders.

This study aimed to characterize the population pharmacokinetics of sertraline in Mexican patients with psychiatric and substance use disorders. Fifty-nine patients (13 to 76 years old) treated with doses of sertraline between 12.5 and 100 mg/day were included. Plasma sertraline concentrations were determined in blood samples and five of the main substances of abuse were determined by rapid tests in urine samples. Demographic, clinical, and pharmacogenetic factors were also evaluated. Population pharmacokinetic analysis was performed using NONMEM software with first-order conditional estimation method. A one-compartment model with proportional residual error adequately described the sertraline concentrations versus time. CYP2D6*2 polymorphism and CYP2C19 phenotypes significantly influenced sertraline clearance, which had a population mean value of 66 L/h in the final model. The absorption constant and volume of distribution were fixed at 0.855 1/h and 20.2 L/kg, respectively. The model explained 11.3% of the interindividual variability in sertraline clearance. The presence of the CYP2D6*2 polymorphism caused a 23.1% decrease in sertraline clearance, whereas patients with intermediate and poor phenotype of CYP2C19 showed 19.06% and 48.26% decreases in sertraline clearance, respectively. The model was internally validated by bootstrap and visual predictive check. Finally, stochastic simulations were performed to propose dosing regimens to achieve therapeutic levels that contribute to improving treatment response.

Modeling gas flow in low-permeability formations: An efficient combination of mixed finite elements and high order time integration schemes

Numerical simulation of gas flow in low permeability formations is a challenging task due to the high nonlinearity induced by (i) the compressibility of the gas, (ii) the Klinkenberg slippage effect and (iii) the Langmuir adsorption of the gas on the pore surface. Because of these nonlinearities, modeling gas flow in low permeability formations requires a great deal of computational effort. In this work, we develop an efficient numerical model using advanced spatial and temporal discretization methods for a simultaneous solution of the coupled equations of gas flow, cubic Peng-Robinson equation of state, slippage effect and Langmuir adsorption. The spatial discretization is performed with the lumped hybrid formulation of the mixed finite element method which is well adapted for fluid flow in heterogeneous porous media. The time integration is performed with high-order methods via the method of lines (MOL) which allows large time steps and efficient solution of the nonlinear system of equations. Numerical experiments, performed for gas extraction in a heterogeneous domain, point out the high efficiency of the new model since it can be until 10 times more efficient than the classical first-order time discretization method. Results of global sensitivity analysis show that the intrinsic gas-phase permeability and the Klinkenberg factor are the most influential parameters controlling the pumping rate in the case of gas extraction in a homogeneous domain.

Monte Carlo simulation study on the reliability of concrete-filled HSS beam-column design provisions

Revisions were recently proposed to the way in which concrete-filled hollow structural section (HSS) members are handled in CSA S16. These revisions were based on previous research, comparisons to experiments, and a first-order reliability method analysis of existing provisions for compression and flexural members. In this paper, this topic is further expanded by using Monte Carlo Simulations (MCS) to determine the inherent reliability of the previous and new design rules for concrete-filled rectangular hollow section (RHS) and circular hollow section (CHS) beam-columns. A representative set of concrete-filled RHS and CHS members with variations in concrete strength, wall slenderness, effective length, and loading eccentricity are analyzed. Using MCS, the reliability index (β+) of each is determined over a range of live-to-dead load (L/D) ratios. Inherent β+ values are compared to the code-specified target (i.e., β+ = 3.0 per Annex B of CSA S16) and the CSA S16:19 and AISC 360-16 provisions.

Reliability and sensitivity analysis of delamination growth of composite laminate structures using two efficient sampling methods

In recent years, composite structures have been used in a large number of applications in aerospace, machinery, marine, and civil engineering. However, there are inevitably many uncertainties in the whole life cycle of composite structures, which can easily lead to structural damage and failure. Therefore, it is important to analyze the reliability and sensitivity of composite structures. At present, most of the contributions use the first-order reliability method (FORM) and the second-order reliability method (SORM) to study the reliability of composite structures and compare them with the results of the Monte Carlo simulation. However, both methods have their limitations. FORM cannot guarantee the calculation accuracy for the highly nonlinear limit state equation, and the calculation efficiency of SORM is too low. Therefore, this paper proposes to use importance sampling (IS) and backpropagation neural network-based Monte Carlo (MC-BPNN) to study the reliability, sensitivity, and dispersion of delamination growth of composite laminates. The results show that compared with FORM and SORM, IS and MC-BPNN have higher calculation accuracy and efficiency and can more accurately evaluate the failure degree of composite structures and ensure their safe operation in the field of aerospace equipment. The universality of this method can make it being widely used in the reliability and sensitivity analysis of different composite materials as well as dispersion analysis.

Research on the Data-Driven Differential Equation-Solving Algorithm Based on Artificial Intelligence

Data-driven DEs has gained popularity in the past few years. This work proposes the new framework, named Adam Gannet Optimization Algorithm (AdamGOA), that combines Adam Optimization and Gannet Optimization Algorithm (GOA) to improve a stability, solve higher order Differential Equations (DE) and accuracy of DE. Adam is a first-order gradient-based methods, optimizes stochastic objectives using adaptive lower-order moments. In contrast, GOA represents a different distinct action of a gannets mathematically during foraging and is employed to facilitate exploitation and exploration. In addition, a Shepard Convolutional Neural Network (ShCNN) processed data to construct meta-data and estimate derivatives. After that, the unified integral form is established to determine optimal structure. Heterogeneous parameters are used to estimate and are labeled as constants or variables. Furthermore, the experimental findings showed that the AdamGOA_ ShCNN beat leading models in Accuracy, Convergence, and Mean Square Error (MSE), with values of 0.989, 4, and 0.539, respectively.

Pseudo-Helmholtz decomposition for an elastic VTI wavefield based on wavefront phase direction

P and S waves are coupled when propagating in anisotropic elastic media. The separation of P and S waves helps to study the characteristics of different types of seismic waves as well as mitigating crosstalk artifacts in elastic reverse time migration and elastic full-waveform inversion. At present, the methods of seismic wave mode separation in anisotropic media are mainly built on divergence- and curl-like operations, pseudo-Helmholtz decomposition, and low-rank approximation. We develop a new pseudo-Helmholtz decomposition operator based on eigenform analysis and the wavefront phase direction to decompose vertically transversely isotropic elastic wavefields. The corresponding P-/S-wave decoupling formulas are also derived in detail. Compared with the divergence- and curl-like methods, the new method does not change the phase of P and S waves. Compared with existing pseudo-Helmholtz decomposition methods based on eigenform analysis, our method achieves more accurate wavefield separation than the zero-order pseudo-Helmholtz decomposition operator. Our method requires solving one vector Poisson equation only, resulting in much less computational cost than the existing first-order pseudo-Helmholtz decomposition methods. In addition, the accuracy of our method is analyzed by providing homogeneous media with different parameter settings. Finally, the numerical examples demonstrate that the new pseudo-Helmholtz decomposition method is effective, efficient, and robust against random noise.

Weighted Least Squares Regression with the Best Robustness and High Computability

A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual as equally important, the new procedure exponentially down-weights squared residuals that lie far away from the cloud of all residuals and assigns a constant weight (one) to squared residuals that lie close to the center of the squared-residual cloud. The new procedure can keep a good balance between robustness and efficiency; it possesses the highest breakdown point robustness for any regression equivariant procedure, being much more robust than the classic least squares, yet much more efficient than the benchmark robust method, the least trimmed squares (LTS) of Rousseeuw. With a smooth weight function, the new procedure could be computed very fast by the first-order (first-derivative) method and the second-order (second-derivative) method. Assertions and other theoretical findings are verified in simulated and real data examples.

Potential Energy Optimization Approach in the Form-Finding of Tensegrities and Cable–Strut Systems

A form-finding process for tensegrities and cable–strut systems is determined as a minimum problem of potential energy that is constructed considering initial estimated pre-stress states. Both the Jacobian and Hessian matrices of a potential energy function are derived explicitly regarding free nodal coordinates. Based on these derivations, both the first-order geodesic dynamic relaxation optimization method and the second-order optimization method of Newton can be applied to solve form-finding problems involving tensegrities and cable–strut structures. It should be noted that both the pre-stress state and the configuration of the systems are adjusted during the optimization process to satisfy self-equilibrium conditions. The geometrical constraints are then included in the proposed work as equality constraint conditions to find the final forms satisfying not only the self-equilibrium states but also the designers’ demands. Two well-known and complex systems are investigated to assess the efficiency of the proposed method, i.e. free-standing truncated icosahedral tensegrity and the Kiewitt Dome.

First-order formalism for Alice string

We apply the first-order formalism method to obtaining BPS equations for Alice string. This is done by generalizing the well-known first-order formalism to the case of non-Abelian strings. We do not assume any specific gauge group nor the shape of the kinetic term function, but require only that the fields are axially-symmetric and static. With this formalism we reproduce the BPS equations of SU(2)×U(1) Alice strings (Chatterjee and Nitta, 2017), and present their corresponding numerical solutions.

A novel train–bridge interaction computational framework based on a meshless box girder model

In traditional train–bridge coupled system (TBCS), simply supported box girder bridges are often modeled using Euler beam elements, neglecting their spatial structure. This simplification may yield inaccurate results, impacting the running safety analysis of high-speed railway. To address this issue, a novel train–bridge interaction computational framework based on first-order shear deformation theory (FSDT) and radial point interpolation method (RPIM) for the box girder bridge model is proposed. In this model, the displacement fields of top, bottom, and web plates are represented using FSDT and numerically discretized by RPIM. The traditional TBCS is upgraded by replacing the Euler beam model with the novel model. This is the first time that the framework has been applied to TBCS field. Several numerical examples are presented to highlight the accuracy of this novel model, and illustrate the differences, and advantages of it over the traditional model. The results indicate that the proposed model closely matches the accuracy of the solid element (C3D20) model; it can provide a comprehensive bridge response compared to traditional TBCS, and the latter may underestimate the dynamic response of the structure. The proposed model holds significant potential for the simulation of box structures and widespread application in the field of TBCS.

Sensitivity of fatigue reliability in wind turbines: effects of design turbulence and the Wöhler exponent

Abstract. Fatigue assessment of wind turbines involves three main sources of uncertainty: material resistance, load, and the damage accumulation model. Many studies focus on increasing the accuracy of fatigue load assessment to improve the fatigue reliability. Probabilistic modeling of the wind's turbulence standard deviation is an example of an approach used for this purpose. Editions 3 and 4 of the IEC standard for the design of wind energy generation systems (IEC 61400-1) suggest different probability distributions as alternatives for the representative turbulence in the normal turbulence model (NTM) of edition 1. There are debates on whether the suggested distributions provide conservative reliability levels, as the established design safety factors are calibrated based on the representative turbulence approach. The current study addresses the debate by comparing annual reliability based on different scenarios of NTM using a probabilistic approach. More importantly, it elaborates on the relative importance of load assessment accuracy in defining the fatigue reliability. Using the DTU 10 MW reference wind turbine and the first-order reliability method (FORM), we study the changes in the annual reliability level and its sensitivity to the three main random inputs. We perform the study considering the blade root flapwise and the tower base fore–aft moments, assuming different fatigue exponents in each load channel. The results show that integration over distributions of turbulence in each mean wind speed results in less conservative annual reliability levels than representative turbulence. The difference in the reliability levels varies according to turbulence distribution and the fatigue exponent. In the case of the tower base, the difference in the annual reliability index after 20 years can be up to 50 %. However, the model and material uncertainty have much higher effects on the reliability levels compared to load uncertainty. Knowledge about such differences in the reliability levels due to the choice of turbulence distribution is especially important, as it impacts the extent of lifetime extension through reliability reassessments.

Population Pharmacokinetic Modeling of Posaconazole in Japanese Patients Receiving Fungal Prophylaxis.

Posaconazole is a vital drug to treat and prevent invasive fungal infections. Several factors, such as sex, body weight, total serum proteins, dietary intake, and severe mucositis, affect posaconazole pharmacokinetics (PKs). However, the relevance of other factors that affect the PKs of posaconazole in hematopoietic stem cell transplantation (HSCT) is unknown. This study explored factors influencing the PKs of posaconazole in HSCT recipients and nontransplant patients with hematological diseases. The authors conducted a single-institution, retrospective study. Forty-two Japanese inpatients receiving oral posaconazole tablets as prophylaxis for fungal infections were enrolled in this study. A one-compartment model with first-order absorption was used as the structural pharmacokinetic model. A population PK (PopPK) analysis was performed using a nonlinear mixed-effects modeling program, using a first-order conditional estimation method with interactions. Perl-speaks-NONMEM and R were used to evaluate the goodness of fit and visualize the output. In 29% of the enrolled patients, the serum concentration of posaconazole was <0.5 mcg/mL, considered the effective range. PopPK analysis revealed that the patient had undergone HSCT within 1 year, diarrhea occurred more than 5 times a day, and aspartate aminotransferase were covariates that influenced apparent clearance (CL/F). The CL/F of posaconazole was 1.43-fold higher after HSCT and 1.26-fold higher during diarrhea. PopPK analysis revealed that HSCT, diarrhea, and aspartate aminotransferase were factors associated with the CL/F of posaconazole. The trough concentration of posaconazole may be below the therapeutic range in a few patients with diarrhea and/or after HSCT. As invasive fungal infections in patients with hematologic diseases can be life-threatening, therapeutic drug monitoring of posaconazole is strongly recommended, and patients should be carefully monitored.

Distributed adaptive greedy quasi-Newton methods with explicit non-asymptotic convergence bounds

Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence which is not easy to implement in the distributed setting. In this work, we first propose a line search free greedy quasi-Newton (GQN) method with adaptive steps and establish explicit non-asymptotic bounds for both the global convergence rate and local superlinear rate. Our novel idea lies in the design of multiple GQN updates, which only involves computing Hessian-vector products, to control the Hessian approximation error, and a simple mechanism to adjust stepsizes to ensure the objective function improvement per iterate. Then, we extend it to the master–worker framework and propose a distributed adaptive GQN method whose communication cost is comparable with that of first-order methods, yet it retains the superb convergence property of its centralized counterpart. Finally, we demonstrate the advantages of our methods via numerical experiments.

Simultaneous biosorption of acid violet and reactive yellow dyes by Cladosporium cladosporioides

The synthetic dye mixture of Acid Violet 90 and Reactive Yellow 145 was treated with dead Cladosporium cladosporioides biomass. The individual concentrations were calculated with the first-order derivative spectrophotometric method. The calibration curves were plotted at wavelengths of 578.4 nm and 318.2 nm in the derivative spectrum for Acid Violet 90 and Reactive Yellow 145, respectively. The calculated limit of quantitation value is ~ 2.5 mg/L for Acid Violet 90 and ~ 1.5 mg/L for Reactive Yellow 145. The achieved mean recovery percentage values are around 100%. The highest removal efficiency (100%) was obtained for both dyes at pH 4 using 0.25 g biomass and 50 mg/L of each dye in 60 min reaction time with 150 rpm shaking speed. The hydrochloric acid solution was used for biomass regeneration, and the removal efficiencies remained at 99% and 89% for Acid Violet 90 and Reactive Yellow 145 in the third cycle.Graphical abstractBiosorption process

A-stable spectral deferred correction method for nonlinear Allen-Cahn model

This paper presents a type of A-stable spectral deferred correction (SDC) method. The scheme is initiated by the first-order backward Euler method. We adopt the linear stabilization approach for the Allen-Cahn model to get the linear semi-implicit SDC scheme. This is done by the addition and subtraction of the linear stabilization operators that have been provided for the Allen-Cahn problem. The ranges of the stabilization factors are then given. The aim is to achieve A-stability and error estimates for the implicit part of the scheme. Finally, the semi-implicit SDC scheme coupled with the Fourier spectral method is used to simulate the Allen-Cahn problem, which is also suitable for the highly nonlinear problem. Numerical experiments are given to numerically demonstrate the high-order accuracy and the energy decay property of the scheme with A-stability parameters.

Reliability analysis of fatigue crack growth in shallow shell structures using the Dual Boundary Element Method

This work presents a novel methodology for fatigue life reliability analysis using a newly developed Dual Boundary Element Method-based Implicit Differentiation Method (DBEM-IDM) in shallow shell structures. The proposed DBEM formulations evaluate stress intensity factors and fatigue life sensitivities in shallow shells considering geometrical variables and curvature. The IDM formulations, obtained through direct differentiation of the shallow shell DBEM formulations, uses the First-Order Reliability Method (FORM) to assess the reliability index and probability of failure of shallow shell structures with multiple cracks. Two numerical examples were simulated to illustrate the effectiveness of the proposed methodology. The first example examines a shallow shell with a centre hole and cracks subjected to various loads. The critical crack length required to ensure structural reliability and inspectability is determined. Fatigue reliability assessment is performed for the same example, employing limit state functions expressed in terms of fatigue life. FORM results are compared with the results of Monte Carlo Simulations (MCS), and provided a maximum difference of 3.67%. Parametric analyses are conducted to identify significant variables that affect reliability, and it was found that precise determination of design parameters is necessary to reduce the probability of failure, particularly for the Paris law constants. The second example, featuring more complex geometry, involved assessing fatigue reliability in a cylindrical shallow shell structure with multiple cracks. The results of this example indicate a 3.49% maximum difference between FORM and MCS. The results exhibit a low error compared to the MCS, and the inherent efficiency of the IDM-based FORM underscores its suitability for addressing uncertainty in reliability analysis.

Probabilistically modelled geometrical imperfections for reliability analysis of vertically loaded steel frames

The article explores the stochastic modelling of 3D steel frames under static vertical load, with a main focus on random initial geometrical imperfections. The random input parameters for initial geometrical imperfections are derived from the tolerance criteria in accordance with European standard. In order to derive statistical parameters from the corresponding standard tolerances, two methods noted as #RSS (random storey sway) and #RSP (random storey position) have been utilized and compared. Both of these methods are used along with the first-order reliability method (FORM) and the advanced finite element method (FEM) – geometrically and materially nonlinear imperfect analysis (GMNIA) to numerically analyse several geometries of steel frame structures. Ultimate resistances of these structures are monitored and basic sensitivity studies are conducted. The results are also compared with the deterministic approach of the European standard. The stochastic approach of the FORM to estimate the ultimate resistance of steel frame structures serves as a verification tool of the classic, in engineering praxis widely used, deterministic approach. This study provides useful provisions for the advanced numerical analyses of steel frames of various geometries. Additionally, the estimations of ultimate resistance by the deterministic European standard approach is verified for selected frame geometries.

Accelerated analysis on the triple momentum method for a two-layer ReLU neural network

The momentum method has become the workhorse in the deep learning community. To theoretical understand its success, researchers put efforts in demystifying its convergence properties when optimizing neural networks. For the convex problem, it is well-known that the triple momentum (TM) method owns the fastest theoretical convergence rate among all first-order methods. However, there exists no theoretical convergence results about the TM method in solving the non-convex neural networks training problem, let alone its acceleration guarantee. In this paper, we focus on the training process of the TM method for a two-layer ReLU neural network. Inspired by the accurate characterization of the high-resolution dynamical system, we consider the high-resolution ordinary differential equation (ODE) of the TM method. Under the over-parameterized assumption, we derive that the original non-convex optimization problem can be transformed to a strongly convex task. By applying an appropriate Lyapunov function, we prove that the TM method can linearly converge to a global minimum. Compared to the heavy ball method and Nesterov’s accelerated gradient method, our result provides the first guarantee for the acceleration of the TM method in training neural networks. Through empirical experiments, the accelerated convergence of the TM method and the effect of over-parameterization are validated.

Approximate Integral Method for Nonlinear Reliability Analysis

In the realm of reliability analysis methods, the First-Order Reliability Method (FORM) exhibits excellent computational accuracy and efficiency in linear problems. However, it fails to deliver satisfactory performance in nonlinear ones. Therefore, this paper proposes an Approximate Integral Method (AIM) to calculate the failure probability of nonlinear problems. Firstly, based on the Most Probable Point (MPP) of failure and the reliability index β obtained from the FORM, the Limit State Function (LSF) can be equivalent to an Approximate Parabola (AP) which divides the hypersphere space into feasible and failure domains. Secondly, through the ratio of the approximate region occupied by a parabolic curve to the entire hypersphere region, the failure probability can be calculated by integration. To avoid the computational complexity in the parabolic approximate area due to high dimensionality, this paper employs a hyper-rectangle, constructed from chord lengths corresponding to different curvatures, as a substitute for the parabolic approximate area. Additionally, a function is utilized to adjust this substitution, ensuring accuracy in the calculation. Finally, compared with the calculated result of the Monte Carlo simulation (MCS) and the FORM, the feasibility of this method can be demonstrated through five numerical examples.

Sketched Newton Value Iteration for Large-Scale Markov Decision Processes

Value Iteration (VI) is one of the most classic algorithms for solving Markov Decision Processes (MDPs), which lays the foundations for various more advanced reinforcement learning algorithms, such as Q-learning. VI may take a large number of iterations to converge as it is a first-order method. In this paper, we introduce the Newton Value Iteration (NVI) algorithm, which eliminates the impact of action space dimension compared to some previous second-order methods. Consequently, NVI can efficiently handle MDPs with large action spaces. Building upon NVI, we propose a novel approach called Sketched Newton Value Iteration (SNVI) to tackle MDPs with both large state and action spaces. SNVI not only inherits the stability and fast convergence advantages of second-order algorithms, but also significantly reduces computational complexity, making it highly scalable. Extensive experiments demonstrate the superiority of our algorithms over traditional VI and previously proposed second-order VI algorithms.