Iterative Procedure Research Articles

Robust optimization of train timetables with short-length and full-length services considering uncertain passenger volume and service choice behavior

Train timetables with a combination of short-length and full-length services can adapt to spatial and temporal variations in demand. However, with such timetables, some passengers may choose to catch an earlier short-length service and then transfer to a full-length service to reach their destinations rather than waiting for a crowded full-length service. This uncertain service choice behavior frequently occurs, which, however, was not well considered in most studies on demand-oriented timetabling. Therefore, this study presents a robust timetabling approach based on the scenario-based method considering uncertain passenger volumes and service choice behavior for choosing different types of train services. A customized decomposition-based method with an iterative solution procedure is designed to solve the proposed model. In each iteration, a multi-agent-based simulation algorithm is developed to update passengers’ travel utility and the service choice preference proportion based on the previous iteration’s timetabling results. To obtain high-quality solutions in an acceptable computing time, a hybrid “ALNS + GUROBI” algorithm is developed to handle the timetabling problems for large-scale cases. The proposed method optimizes the train timetables for Xi’an Metro Line 3 in China. Our results indicate that the proposed method can account for uncertain passenger volumes and service choice behavior by adjusting the short-length plans and train headways to match the transport capacity to passenger demand.

Modified homotopy approach for diffractive production in the saturation region

In this paper we continue to develop the homotopy method for solving of the nonlinear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the nonlinear corrections as a first step of this approach. This simplified nonlinear evolution equation is solved analytically taking into account the initial and boundary conditions for the process. At the second step of our approach we demonstrated that the perturbative procedure can be used for the remaining parts of the nonlinear corrections. It turns out that these corrections are small and can be estimated in the regular iterative procedure. Published by the American Physical Society 2024

An iterative scheme for solving minimization and fixed point problems with medical image restoration

An iterative scheme for solving minimization and fixed point problems with medical image restoration

Hp-FEM for the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-Mosolov problem: a priori and a posteriori error estimates

An hp-finite element discretization for the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-Mosolov problem, a scalar variant of the Bingham flow problem but with the α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-Laplacian operator, is being analyzed. Its weak formulation is either a variational inequality of second kind or equivalently a non-smooth but convex minimization problem. For any α∈(1,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in (1,\\infty )$$\\end{document} we prove convergence, including guaranteed convergence rates in the mesh size h and polynomial degree p of the FE-solution of the corresponding discrete variational inequality. Moreover, we derive two families of reliable a posteriori error estimators which are applicable to any “approximation” of the exact solution and not only to the FE-solution and can therefore be coupled with an iterative solver. We prove that any quasi-minimizer of those families of a posteriori error estimators satisfies an efficiency estimate. All our results contain known results for the Mosolov problem by setting α=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =2$$\\end{document}. Numerical results underline our theoretical findings.

Jacobian-free Newton-Krylov method for multilevel nonlocal thermal equilibrium radiative transfer problems

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

An alternating inertial method for solving variational inequality problems on Hadamard manifolds

We propose and study an alternating inertial algorithm for approximating a solution to the variational inequality problem on an Hadamard manifold. The proposed method combines the inertial technique and the Tseng extragradient method with self-adaptive step sizes. We establish some convergence results for our iterative procedure when the variational inequality problem is governed by pseudomonotone vector fields. We present the results of some numerical experiments which show the competitive advantage of our algorithm over earlier methods in the literature.

Сalculation of fields scattered by inhomogeneous area with a large wave size

A method is proposed for finding acoustic fields scattered by an inhomogeneous area of space with a large wave size. In this case, the RAM of a personal computer is not enough to solve the direct problem at once in the entire study area. Then the area is divided into sub-areas, and the iterative procedure is organized based on problem solution in each individual sub-area.

Aptamer Insights in Targeting and Designing of Therapeutic Drugs.

In the therapy of chronic and dangerous conditions like as cancer, heart disease, neurological illnesses, or retinal angiopathy, we frequently require most effective dosage schedule with adequate precision and sufficient therapeutic potential. Among these entities with the capacity to behave in a target-specific way are aptamers. Usually, they are produced by an iterative screening procedure named “Systemic Evolution of Ligands by Exponential Enrichment (SELEX)” which is used to complicate nucleic acid libraries. For several biological purposes, including targeted treatment, aptamers are potential and could be easily molded into desirable needs and also be tested in a manner that is not very extravagant or pricey. Chemical modification can be employed to enhance their pharmacological actions or prevent enzymatic degradation, hence guaranteeing their chemical integrity and bioavailability in a physiological setting. The recent advancements made in drug targeting and design with the use of aptamers are the main topic of this review. This review will highlight current developments and go over prospects and problems in the fields of aptamer-based targeted therapy, including aptamer therapeutics.

Algebraic temporal blocking for sparse iterative solvers on multi-core CPUs

Algebraic temporal blocking for sparse iterative solvers on multi-core CPUs

On a planar equation involving [formula omitted]-Laplacian with zero mass and Trudinger–Moser nonlinearity

In this work, we study existence of positive solutions to a class of (2,q)-equations in the zero mass case in R2. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.

Irrotational Flow over Ogee Spillway Crest: New Solution Method and Flow Geometry Analysis

A spillway is a hydraulic structure of major importance in dam safety, and its current analysis usually involves a hybrid approach combining CFD modeling with experimental research, either using well-known WES design charts or conducting new model experiments in the laboratory. Flow over spillway crests involves fluid accelerations, making irrotationality an adequate simplification of the Navier–Stokes (NS) equations. However, an efficient tool using this method is currently lacking for spillway flow, particularly for ogee spillway flow. This work focuses on this aspect of the problem, and a new method for computing irrotational flow solutions over ogee spillways is proposed by developing flow net computational solutions. The proposed method entails a new iterative procedure in the complex potential plane where free surface pressures are exactly set to zero, contrary to other methods, and an automatic determination of the critical point, the unknown energy head, and the free surface profile. The model generates solutions efficiently in only a few seconds on a personal workstation, permitting a fast estimate of spillway flow operation, and is thus an effective complement to experimental and NS-CFD modeling. The solutions produced are compared with observations of a high operational head equal to five times the design head of the ogee crest, resulting in reasonable agreement. The application of the new model to investigate the limitations of analytical equations used in spillway flow, like Jaeger’s theory, establishes limits for its use by relating its curvature parameter to the spillway chute slope.

Decay time estimate for LEO spacecraft

The growing concerns posed by orbital debris represent a serious threat to the future of space operations in low Earth orbit. With the goal of limiting the formation of new debris, space agencies are proposing international guidelines that satellites should be able to deorbiting within 25 years of the end of their operational life. Orbital decay is typically caused by atmospheric drag, so estimating the decay time of a satellite subject to drag is critical to assessing whether the guidelines are met. However, such estimate is a very challenging task because of the difficulty of accurately modeling atmospheric properties and because of the coupling of orbital dynamics with spacecraft attitude. In this paper, a simplified algorithm based on the King-Hele formulation is proposed to rapidly estimate the decay time of an orbiting satellite without imposing any assumptions on the spacecraft’s nominal size, mass, geometry or attitude. The algorithm accounts for the effect of solar activity level variations on atmospheric properties and drag coefficient through an iterative procedure and can be applied to any object in orbit. Numerical tests show that the predictions in terms of decay times are very accurate for satellites that are quite different in size and geometry, including the presence of an aerodynamic drag augmentation system such as a drag sail.

An Iteratively Reweighted Importance Kernel Bayesian Filtering Approach for High-Dimensional Data Processing

This paper proposes an iteratively re-weighted importance kernel Bayes filter (IRe-KBF) method for handling high-dimensional or complex data in Bayesian filtering problems. This innovative approach incorporates importance weights and an iterative re-weighting scheme inspired by iteratively re-weighted Least Squares (IRLS) to enhance the robustness and accuracy of Bayesian inference. The proposed method does not require explicit specification of prior and likelihood distributions; instead, it learns the kernel mean representations from training data. Experimental results demonstrate the superior performance of this method over traditional KBF methods on high-dimensional datasets.

Natural Gradient Variational Bayes Without Fisher Matrix Analytic Calculation and Its Inversion

This article introduces a method for efficiently approximating the inverse of the Fisher information matrix, a crucial step in achieving effective variational Bayes inference. A notable aspect of our approach is the avoidance of analytically computing the Fisher information matrix and its explicit inversion. Instead, we introduce an iterative procedure for generating a sequence of matrices that converge to the inverse of Fisher information. The natural gradient variational Bayes algorithm without analytic expression of the Fisher matrix and its inversion is provably convergent and achieves a convergence rate of order O ( log s / s ) , with s the number of iterations. We also obtain a central limit theorem for the iterates. Implementation of our method does not require storage of large matrices, and achieves a linear complexity in the number of variational parameters. Our algorithm exhibits versatility, making it applicable across a diverse array of variational Bayes domains, including Gaussian approximation and normalizing flow Variational Bayes. We offer a range of numerical examples to demonstrate the efficiency and reliability of the proposed variational Bayes method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

The SOR and AOR Methods with Stepwise Optimized Values of Parameters for the Iterative Solutions of Linear Systems

We modify the successive overrelaxation (SOR) method and accelerated overrelaxation (AOR) method for solving linear equations systems. The optimal value of the acceleration parameter is determined, using the maximal reduction method of the residual vector’s length, or equivalently an orthogonality condition. Rather than the constant value, the MAOR method endows a step-by-step varying acceleration parameter to possess the property of absolute convergence and the orthogonality of consecutive residual vector. In SOR, the relaxation parameter is also optimized by using the orthogonality condition. Numerical examples ensure that the MSOR and MAOR iterative schemes converge faster than the original SOR and AOR iterative schemes. They are easily implemented with low computational cost, and without needing of a detailed spectral analysis to determine the optimal values of parameters has a great advantage.

Development and experimental validation of computational methods for human antibody affinity enhancement.

High affinity is crucial for the efficacy and specificity of antibody. Due to involving high-throughput screens, biological experiments for antibody affinity maturation are time-consuming and have a low success rate. Precise computational-assisted antibody design promises to accelerate this process, but there is still a lack of effective computational methods capable of pinpointing beneficial mutations within the complementarity-determining region (CDR) of antibodies. Moreover, random mutations often lead to challenges in antibody expression and immunogenicity. In this study, to enhance the affinity of a human antibody against avian influenza virus, a CDR library was constructed and evolutionary information was acquired through sequence alignment to restrict the mutation positions and types. Concurrently, a statistical potential methodology was developed based on amino acid interactions between antibodies and antigens to calculate potential affinity-enhanced antibodies, which were further subjected to molecular dynamics simulations. Subsequently, experimental validation confirmed that a point mutation enhancing 2.5-fold affinity was obtained from 10 designs, resulting in the antibody affinity of 2nM. A predictive model for antibody-antigen interactions based on the binding interface was also developed, achieving an Area Under the Curve (AUC) of 0.83 and a precision of 0.89 on the test set. Lastly, a novel approach involving combinations of affinity-enhancing mutations and an iterative mutation optimization scheme similar to the Monte Carlo method were proposed. This study presents computational methods that rapidly and accurately enhance antibody affinity, addressing issues related to antibody expression and immunogenicity.

Noise suppression in photon-counting computed tomography using unsupervised Poisson flow generative models

Deep learning (DL) has proven to be important for computed tomography (CT) image denoising. However, such models are usually trained under supervision, requiring paired data that may be difficult to obtain in practice. Diffusion models offer unsupervised means of solving a wide range of inverse problems via posterior sampling. In particular, using the estimated unconditional score function of the prior distribution, obtained via unsupervised learning, one can sample from the desired posterior via hijacking and regularization. However, due to the iterative solvers used, the number of function evaluations (NFE) required may be orders of magnitudes larger than for single-step samplers. In this paper, we present a novel image denoising technique for photon-counting CT by extending the unsupervised approach to inverse problem solving to the case of Poisson flow generative models (PFGM)++. By hijacking and regularizing the sampling process we obtain a single-step sampler, that is NFE = 1. Our proposed method incorporates posterior sampling using diffusion models as a special case. We demonstrate that the added robustness afforded by the PFGM++ framework yields significant performance gains. Our results indicate competitive performance compared to popular supervised, including state-of-the-art diffusion-style models with NFE = 1 (consistency models), unsupervised, and non-DL-based image denoising techniques, on clinical low-dose CT data and clinical images from a prototype photon-counting CT system developed by GE HealthCare.

Three-Dimensional Probe Mispositioning Errors Compensation: A Feasibility Study in the Non-Redundant Helicoidal Near to Far-Field Transformation Case

A feasibility study on the compensation of 3D mispositioning errors of the probe occurring in the characterization of a long antenna, via a non-redundant (NR) near to far-field (NTFF) transformation with helicoidal scan, is conducted in this article. Such types of errors can result from imperfections in the rail driving the linear motion of the probe and from an imprecise synchronization of the linear and rotational movements of the probe and the antenna when drawing the scan helix. To correct them, an approach, which proceeds through two steps, is proposed. The former step uses a technique called cylindo rical wave (CW) correction for compensating the phase of the near-field (NF) samples, which, owing to the rail imperfections, result in not being acquired over the measurement cylinder surface. The latter exploits an iterative scheme to restore the samples at the sampling points required by the adopted NR representation along the scan helix from those obtained by applying the CW correction technique and impaired by 2D mispositioning errors. The so compensated NF samples are then effectively recovered via a 2D optimal sampling interpolation (OSI) scheme to accurately obtain the input data required to carry out the standard cylindrical NTFF transformation. The OSI representation is determined here by assuming a long antenna under test as enclosed in a prolate ellipsoid or cylinder ending into two hemispheres (cigar) in order to make, depending on the particular geometry of the considered antenna, the representation effectively non-redundant. The reported numerical simulation results show the capability of the proposed approach to compensate even severe 3D mispositioning errors, thus enabling its usage in a real measurement scenario.

Computational Analysis of a Novel Iterative Scheme with an Application

The computational study of fixed-point problems in distance spaces is an active and important research area. The purpose of this paper is to construct a new iterative scheme in the setting of Banach space for approximating solutions of fixed-point problems. We first prove the strong convergence of the scheme for a general class of contractions under some appropriate assumptions on the domain and a parameter involved in our scheme. We then study the qualitative aspects of our scheme, such as the stability and order of convergence for the scheme. Some nonlinear problems are then considered and solved numerically by our new iterative scheme. The numerical simulations and graphical visualizations prove the high accuracy and stability of the new fixed-point scheme. Eventually, we solve a 2D nonlinear Volterra Integral Equation (VIE) via the application of our main outcome. Our results improve many related results in fixed-point iteration theory.

A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.