Iterative Procedure Research Articles

Iterative Immunostaining and NEDD Denoising for Improved Signal-To-Noise Ratio in ExM-LSCM.

Expansion microscopy (ExM) has significantly reformed the field of super-resolution imaging, emerging as a powerful tool for visualizing complex cellular structures with nanoscale precision. Despite its capabilities, the epitope accessibility, labeling density, and precision of individual molecule detection pose challenges. We recently developed an iterative indirect immunofluorescence (IT-IF) method to improve the epitope labeling density, improving the signal and total intensity. In our protocol, we iteratively apply immunostaining steps before the expansion and exploit signal processing through noise estimation, denoising, and deblurring (NEDD) to aid in quantitative image analyses. Herein, we describe the steps of the iterative staining procedure and provide instructions on how to perform NEDD-based signal processing. Overall, IT-IF in ExM-laser scanning confocal microscopy (LSCM) represents a significant advancement in the field of cellular imaging, offering researchers a versatile tool for unraveling the structural complexity of biological systems at the molecular level with an increased signal-to-noise ratio and fluorescence intensity. Key features • Builds upon the method developed by Mäntylä et al. [1] and introduces the IT-IF method and signal-processing platform for several nanoscopy imaging applications. • Retains signal-to-noise ratio and significantly enhances the fluorescence intensity of ExM-LSCM data. • Automatic estimation of noise, signal reconstruction, denoising, and deblurring for increased reliability in image quantifications. • Requires at least seven days to complete.

A Fully Implicit Coupled Scheme for Mixed Elastohydrodynamic Problems on Co-Allocated Grids

In the modeling of elastohydrodynamic lubrication problems considering mixed friction, strongly coupled dependencies occur due to piezo-viscous effects and asperities, which can make a numerical solution exceptionally difficult. A fully implicit coupled scheme for solving mixed elastohydrodynamic lubrication problems is presented. Our scheme uses finite-volume discretization and co-allocated grids for hydrodynamic pressure and elastic deformation. To provide strong coupling between pressure and deformation even in the highly loaded zone, a correction term that adds numerical diffusion is used. The resulting linear equation system of this scheme can be efficiently solved by Krylov subspace methods. This results in an improved accuracy and computational efficiency compared to the existing methods. This approach was validated and has been shown to be accurate.

Decentralized learning control for high-speed trains with unknown time-varying speed delays

Treating the multi-point-mass dynamic model of high-speed trains as an interconnected system, this study proposes a decentralized iterative learning control scheme for high-speed trains to achieve the trajectory tracking goal. By making reasonable estimates of the interaction term and compensating for it, the proposed control scheme utilizes only local information from each carriage and does not need any inter-carriage information exchange. The zero-error tracking of the desired trajectory is guaranteed even in a restricted communication environment. Considering unknown time-varying speed delays in the actual high-speed train operations, a modified decentralized iterative learning control scheme is also provided to address the negative impact of speed delays. The convergence of tracking errors is strictly proven by constructing appropriate composite energy functions. Numerical simulations further verify the theoretical results.

A novel unified variational finite difference (VFD) solution method for optimal control problems

This article is aimed to propose a simple yet efficient unified numerical strategy for solving both linear and non-linear optimal control problems. To do so, the general form of quadratic performance index function and nonlinear state equations are considered first. Then, the idea of variational differential quadrature method is used to convert the integral/differential equations to the equivalent algebraic form. Since time is the only independent variable is this research, the finite difference method with an equally-spaced discretization scheme would be a more appropriate technique rather than the differential quadrature approach. So, the implemented numerical solution is called now as the variational finite difference method. The method of Lagrange multipliers is then utilized for minimization purpose and, as a result, the final set of nonlinear algebraic equations are obtained. Finally, the quadratic and triadic forms of non-linearity are considered and an explicit formulation is represented for the residual and Jacobian of the Newton-based iterative solution procedure. To demonstrate the accuracy and efficiency of the proposed approach in the quadratic optimal control area, several benchmark problems involving linear time-invariant, linear time-variant and nonlinear examples are successfully solved and the results are confirmed with those existed in the literature.

Exploring a Dynamic Homotopy Technique to Enhance the Convergence of Classical Power Flow Iterative Solvers in Ill-Conditioned Power System Models

This paper presents a dynamic homotopy technique that can be used to calculate a preliminary result for a power flow problem (PFP). This result can then be used as an initial estimate to efficiently solve the PFP using either the classical Newton-Raphson (NR) method or its fast decoupled version (FDXB) while still maintaining high accuracy. The preliminary stage for the dynamic homotopy problem is formulated and solved by employing integration techniques, where implicit and explicit schemes are studied. The dynamic problem assumes an initial condition that coincides with the initial estimate for a traditional iterative method such as NR. In this sense, the initial guess for the FPF is adequately set as a flat start, which is a starting for the case when this initialization is of difficult assignment for convergence. The static homotopy method requires a complete solution of a PFP per homotopy pathway point, while the dynamic homotopy is based on numerical integration methods. This approach can require only one LU factorization at each point of the pathway. Allocating these points properly helps avoid several PFP resolutions to build the pathway. The hybrid technique was evaluated for large-scale systems with poor conditioning, such as a 109,272-bus model and other test systems under stressed conditions. A scheme based on the implicit backward Euler scheme demonstrated the best performance among other numerical solvers studied. It provided reliable partial results for the dynamic homotopy problem, which proved to be suitable for achieving fast and highly accurate solutions using both the NR and FDXB solvers.

A coupled steady thermo-electromagnetic problem in axisymmetric geometries. Mathematical and numerical analysis

Abstract This paper focuses on the analysis of a steady thermo-electromagnetic problem related to the modeling of induction heating processes. Taking advantage of the cylindrical symmetry, the original three-dimensional problem can be reduced to a two-dimensional one on a meridional section, provided that the current density has only the azimuthal component. A variational formulation is presented in appropriately weighted Sobolev spaces, and the existence of a solution is established by employing a fixed-point argument. Furthermore, uniqueness and additional regularity results are proved under reasonable assumptions on the physical coefficients. A finite element approximation combined with a fixed-point iteration scheme is proposed for the numerical solution of the problem. A priori error estimates are obtained to quantify the accuracy of the approximation. Finally, numerical results are reported to validate the theoretical estimates and assess the performance of the method in a physical application.

Theoretical model of ultimate shear capacity and flexural capacity design method of boundary elements for reinforced concrete frames with steel plate shear walls

AbstractThe steel plate shear walls (SPSWs) have been proven effective in reinforced concrete frames (RCFs) as a lateral force‐resistant structure. Despite of advancements, accurately predicting the ultimate shear capacity of RCFs with SPSWs remains challenging using current simplified models. Additionally, the flexural capacity design procedure for the boundary elements (beams and columns) in previous studies of RCF‐SPSWs involved intricate iterative procedures, hindering its widespread implementation. To address the two issues, this paper investigates the pushover responses and the plate‐frame interaction (PFI) of an RCF‐SPSWs system using theoretical and numerical methods. There are three main contributions. First, a theoretical model of ultimate shear capacity for RCF‐SPSWs is proposed, which can also be used to predict shear contributions of boundary frames in RCF‐SPSWs. Calculation errors for ultimate shear capacity of RCF‐SPSWs and shear contribution from the boundary frame are only 3.7% and 6.7% respectively, which are reduced dramatically compared with the traditional model. A simplified schematic diagram for the global collapse mechanism (uniform distribution of plastic hinges within a structure) of RCF‐SPSWs is developed to facilitate the calculation of internal work and reaction forces. Secondly, a flexural capacity design method for the boundary elements to avoid in‐span plastic hinges is proposed. The proposed method enables the achievement of direct estimation of the flexural demands that could trigger a global collapse mechanism, all without intricate iterative procedures. The applicability of current assumptions for the design of steel boundary frame in RCF‐SPSWs system is discussed, and engineering suggestions are provided to ensure safer and more economic designs. Comparison results confirmed the applicability of the proposed design method, which can be adopted to achieve the global collapse mechanism for RCF‐SPSW system. Thirdly, impacts of yielding panel actions on the flexural capacity of boundary elements of RCF‐SPSWs are clarified. Comparison results demonstrated that adding SPSWs to an RCF alters the axial force on boundary elements and significantly impacts the flexural capacity. A design suggestion is made to emphasize the importance of avoiding the balanced failure of boundary elements. The proposed theoretical model can be used to economize the cross‐section of boundary elements in RCF‐SPSWs system under seismic loads due to accurate prediction of their shear contribution; the proposed flexural capacity design method can achieve a global collapse mechanism, and thus the structural safety and energy dissipation capacity are improved; moreover, the building design efficiency is also improved due to avoidance of intricate iterative procedures.

Floating-point photonic iterative solver demonstrated for Newton–Raphson method

Though photonic computing systems offer advantages in speed, scalability, and power consumption, they often have a limited dynamic encoding range due to low signal-to-noise ratios. Compared to digital floating-point encoding, photonic fixed-point encoding limits the precision of photonic computing when applied to scientific problems. In the case of iterative algorithms such as those commonly applied in machine learning or differential equation solvers, techniques like precision decomposition and residue iteration can be applied to increase accuracy at a greater computing cost. However, the analog nature of photonic symbols allows for modulation of both amplitude and frequency, opening the possibility of encoding both the significand and exponent of floating-point values on photonic computing systems to expand the dynamic range without expending additional energy. With appropriate schema, element-wise floating-point multiplication can be performed intrinsically through the interference of light. Herein, we present a method for configurable, signed, floating-point encoding and multiplication on a limited precision photonic primitive consisting of a directly modulated Mach–Zehnder interferometer. We demonstrate this method using Newton's method to find the Golden Ratio within ±0.11%, with six-level exponent encoding for a signed trinary digit-equivalent significand, corresponding to an effective increase of 243× in the photonic primitive's dynamic range.

Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space

We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for their finding are obtained in the case when the operator in linear part of the problem hasn't inverse and can have nonclosed set of values. As an application we consider boundary-value problem for van der Pol equation in a separable Hilbert space.

Weak solvability of elliptic variational inequalities coupled with a nonlinear differential equation

In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modeling the antiplane shear deformation of a static frictional adhesive contact problem. The adhesion process has been extensively studied, but it is usual to assume a priori that the intensity of adhesion is bounded by introducing truncation operators. The aim of this article is to remove this restriction.The proof is based on an iterative approximation scheme showing that the problem has a unique solution. A key ingredient is finding uniform a priori bounds for each iterate. These are obtained by adapting versions of the Moser iteration to our system of equations.

Numerical Simulation and On-Site Measurement of Dynamic Response of Flexible Marine Aquaculture Cages

Flexible cages are widely used in marine aquaculture, yet their mechanical features in extreme seas are still unclear. This study proposes a numerical algorithm to solve the coupled response of the multiple cage systems. The net and mooring lines are modeled using the lumped-mass model, while the flexible floating collar system is assessed with the large-deformation FEM model, and the two models are coupled through an iterative scheme. Sea trials are conducted, and the motion of the cage is obtained using an image processing technique, which validates the numerical algorithm. Using the proposed numerical algorithm, a series of simulations are performed to investigate the response of flexible cages in extreme seas. Motions, line tensions, and structural sectional forces are studied, and the effects of factors such as the wavelength of incident waves and the diameter of collar pipes are investigated.

Analysis of harmonic functions under lower bounds of N-weighted Ricci curvature with ε-range

The behavior of harmonic functions on Riemannian manifolds under lower bounds of the Ricci curvature has been studied from both analytic and geometric viewpoints. For example, some Liouville type theorems are obtained under lower bounds of the Ricci curvature. Recently, those results are generalized under lower bounds of the N-weighted Ricci curvature RicψN with N∈[n,∞]. In this paper, we present a Liouville type theorem for harmonic functions of sublinear growth and a gradient estimate of harmonic functions on weighted Riemannian manifolds under weaker lower bounds of RicψN with N<0. We also prove an Lp-Liouville theorem under lower bounds of RicψN with N∈[n,∞] in a different way from previous studies. Our results are obtained as a consequence of an argument under lower bounds of RicψN with ε-range, which is a unification of constant and variable curvature bounds. Among various methods considered for the analysis of harmonic functions, this paper focuses on methods using the Moser's iteration procedure.

Erlangization/Canadization of Phase-Type Jump Diffusions, with Applications to Barrier Options

For a jump diffusion with upward phase-type jumps with p phases, the maximum before an independent Erlang time eηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^q_\\eta$$\\end{document} with q stages and rate parameter η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document} is again phase-type with q(p+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q(p+1)$$\\end{document} phases. An iterative scheme for computing the phase generator is presented and applied to representing the price of a barrier option with time horizon eηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^q_\\eta$$\\end{document} as a single ordinary integral. Canadization then means to approximate a fixed horizon T with an eηq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^q_\\eta$$\\end{document} satisying Eeηq=T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {E}}e^q_\\eta =T$$\\end{document} for a sufficiently large q. Similar results holds for Greeks like the delta and the gamma. A numerical example is given for a down-and-in call option and the Canadization is combined with Richardson extrapolation. Finally, a recursion is developed that only requires the iteration to be performed in p+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p+1$$\\end{document} dimensions.

General synthetic iterative scheme for rarefied gas mixture flows

The numerical simulation of rarefied gas mixtures with disparate mass and concentration is a huge research challenge. Based on our recent kinetic modeling for monatomic gas mixture flows, this problem is tackled by the general synthetic iterative scheme (GSIS), where the mesoscopic kinetic and macroscopic synthetic equations are alternately solved by the finite-volume discrete velocity method. Three important features of GSIS are highlighted. First, the synthetic equations are precisely derived from the kinetic equation, naturally reducing to the Navier-Stokes equations in the continuum flow regime; in other flow regimes, the kinetic equation provides high-order closure of the constitutive relations to capture the rarefaction effects. Second, these synthetic equations, which can be solved quickly, help to adjust the kinetic system to relax rapidly toward the steady state. Furthermore, in such a two-way coupling, the constraint on the spatial cell size is relieved. Third, the linear Fourier stability analysis demonstrates that the error decay rate in GSIS is smaller than 0.5 for various combinations of mass, concentration and viscosity ratios, such that the error can be reduced by three orders of magnitude after 10 iterations. The efficiency and accuracy of GSIS are demonstrated through several challenging cases covering a wide range of mass ratio, species concentration, and flow speed.

Generation of Mandelbrot and Julia sets by using M-iteration process

In this manuscript, we introduce the M-iteration process for generating Mandelbrot and Julia sets. We establish an escape criterion for a polynomial of the form xk+1+c in the complex plane corresponding to the M-iteration process. Next, we present some graphical examples of Mandelbrot and Julia sets generated using the proven escape criterion and the escape-time algorithm. We also compare the images generated with the M, Mann, and Picard–Mann iterations. Moreover, we study the dependency between the iterations’ parameters and three numerical measures (the average escape time, non-escaping area index, and box-counting dimension) used in the literature. The results show that fractal images generated using the M-iteration are entirely different from those generated using the other two analysed iteration schemes. Moreover, the dependencies are highly non-linear and vary between the iterations.

High-efficiency parametric iterative schemes for solving nonlinear equations with and without memory

Many practical problems, such as the Malthusian population growth model, eigenvalue computations for matrices, and solving the Van der Waals' ideal gas equation, inherently involve nonlinearities. This paper initially introduces a two-parameter iterative scheme with a convergence order of two. Building on this, a three-parameter scheme with a convergence order of four is proposed. Then we extend these schemes into higher-order schemes with memory using Newton's interpolation, achieving an upper bound for the efficiency index of 7.8874813≈1.99057. Finally, we validate the new schemes by solving various numerical and practical examples, demonstrating their superior efficiency in terms of computational cost, CPU time, and accuracy compared to existing methods.

Convergence and stability analyses of a novel iterative scheme

Convergence and stability analyses of a novel iterative scheme

Analytical equation for camera imaging with refractive interfaces

Camera imaging through refractive interfaces is a crucial issue in photogrammetric measurements. Most past studies adopted numerical optimization algorithms based on refractive ray tracing procedures. In these studies, the camera and interface parameters are usually calculated iteratively with numerical optimization algorithms. Inappropriate initial values can cause iterations to diverge. Meanwhile, these iterations cannot efficiently reveal the accurate nature of refractive imaging. Therefore, obtaining camera calibration results that are both flexible and physically interpretable continues to be challenging. Consequently, in this study, we modeled refractive imaging by employing ray transfer matrix analysis. Subsequently, we deduced an analytical refractive imaging (ARI) equation that explicitly describes the refractive geometry in a matrix form. Although this equation is built upon the paraxial approximation, we executed a numerical experiment that shows that the developed analytical equation can accurately illustrate refractive imaging with a considerable object distance and a slightly tilted angle of the flat interface. This ARI equation can be used to define the expansion center and the normal vector of the flat interface. Finally, we also propose a flexible measurement method to determine the orientation of the flat interface, wherein the orientation can be measured rather than calculated by iterative procedures.

Space Quasi-Periodic Steady Euler Flows Close to the Inviscid Couette Flow

We prove the existence of steady space quasi-periodic stream functions, solutions for the Euler equation in a vorticity-stream function formulation in the two dimensional channel R×[-1,1]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}\ imes [-1,1]$$\\end{document}. These solutions bifurcate from a prescribed shear equilibrium near the Couette flow, whose profile induces finitely many modes of oscillations in the horizontal direction for the linearized problem. Using a Nash–Moser implicit function iterative scheme, near such equilibrium we construct small amplitude, space reversible stream functions, slightly deforming the linear solutions and retaining the horizontal quasi-periodic structure. These solutions exist for most values of the parameters characterizing the shear equilibrium. As a by-product, the streamlines of the nonlinear flow exhibit Kelvin’s cat eye-like trajectories arising from the finitely many stagnation lines of the shear equilibrium.

Impact of Previous Abdominal Surgery and Timing of Peritoneal Metastases on Accuracy of Imaging in Predicting the Surgical PCI: A Report From the PRECINCT Study.

In this report from Phase 1 of the prospective, observational, PRECINCT (Pattern of peritoneal dissemination and REsponse to systemic Chemotherapy IN Common and uncommon peritoneal Tumours) study, a correlation was performed between the radiological PCI (peritoneal cancer index; rPCI) and surgical PCI (sPCI). The impact of timing of peritoneal malignancy (PM) and previous abdominal surgery was also studied. The rPCI and sPCI were considered the 'same' if they differed by ≤ 3 points. The agreement was assessed using Bland-Altman analysis and the strength of the agreement was assessed using the concordance correlation coefficient (CCC). The extent of prior surgery was classified according to prior surgical score (PSS). In 707 (79.4%) patients, rPCI and sPCI concurred in 280 (39.6%). In the Bland-Altman analysis, < 40% patients were in the ±3 PCI points limit of acceptable difference. The average difference between the two scores was 4.5 points (95% CI- -5.16 to -3.92). The CCC- was 0.59 for the whole cohort ('moderate' concordance) and was not influenced by imaging modality, timing of PM or PSS. The rPCI underestimated sPCI by an average of 4.5 points. The role of peritoneal MRI in patients undergoing iterative procedures and the performance of imaging according to sites of recurrence need further evaluation.