One-step Scheme Research Articles

Efficient One-Step Second Derivative Block Numerical Scheme for Solution of first-Order Integro-differential Equations

In this work, a new class of one-step second derivative block hybrid numerical scheme is developed for the numerical solution of first-order integro-differential equations with the aid of Simpson's 1/3 quadrature method. The collocation techniques is used for the derivation of this new block method which gives high order of accuracy with very low error constants and its zero stable and convergent. The results from the numerical solution of the examples drawn from literature shows its efficiency in terms of the small errors obtained.

3D human model guided pose transfer via progressive flow prediction network

Human pose transfer is to transfer a conditional person image to a new target pose. The difficulty lies in modeling the large-scale spatial deformation from the conditional pose to the target one. However, the commonly used 2D data representations and one-step flow prediction scheme lead to unreliable deformation prediction because of the lack of 3D information guidance and the great changes in the pose transfer. Therefore, to bring the original 3D motion information into human pose transfer, we propose to simulate the generation process of real person image. We drive the 3D human model reconstructed from the conditional person image with the target pose and project it to the 2D plane. The 2D projection thereby inherits the 3D information of the poses which can guide the flow prediction. Furthermore, we propose a progressive flow prediction network consisting of two streams. One stream is to predict the flow by decomposing the complex pose transformation into multiple sub-transformations. The other is to generate the features of the target image according to the predicted flow. Besides, to enhance the reliability of the generated invisible regions, we use the target pose information which contains structural information from the flow prediction stream as the supplementary information to the feature generation. The synthesized images with accurate depth information and sharp details demonstrate the effectiveness of the proposed method.

Production of neutron-rich nuclei in the vicinity of 78Ni: Fragmentation reactions of unstable 81Ga and 82Ge beams

The fragmentation reactions of neutron-rich unstable nuclei 81Ga and 82Ge at 250 MeV/nucleon have been studied in order to search the optimal mean for the production of very neutron-rich nuclei in the vicinity of 78Ni. The newly measured cross sections were compared with various calculations, showing a good agreement with EPAX3.01. The present work provides experimental insights into the two-step scheme—fragmentation following fission—as a method to produce very neutron-rich nuclei through a combination of ISOL and fragmentation of post-accelerated beams of unstable nuclei. Our results enable an evaluation of the potential of the two-step scheme in the production of very neutron-rich nuclei for the 78Ni region. The two-step scheme using fragmentation of a post-accelerated 81Ga beam could be an option to produce neutron-rich nuclei around 78Ni when the 81Ga beam intensity reaches 1.0×108 pps, compared to the one-step scheme with fission of 238U.

Realization of quantum secure direct communication by Kitaev Abelian anyons

The quantum secure direct communication (QSDC) is provably secure and has a high capacity. The QSDC protocols are usually experimented in photon systems. Here we propose four schemes to realize the QSDC in the Kitaev Abelian anyon model: 1) the two-step scheme, 2) 2⊗2 dimensional superdense coding scheme, 3) the hyperentanglement-assisted one-step scheme and 4) one-time pad scheme. Our work provides a possibility to implement the quantum secure direct communication in many-body systems and gives a new research perspective of the quantum information on the unitary evolution of quantum field systems.

DynGMA: A robust approach for learning stochastic differential equations from data

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions, and construct likelihood-based loss by approximating the transition density to train these networks. However, these methods often rely on one-step stochastic numerical schemes, necessitating data with sufficiently high time resolution. In this paper, we introduce novel approximations to the transition density of the parameterized SDE: a Gaussian density approximation inspired by the random perturbation theory of dynamical systems, and its extension, the dynamical Gaussian mixture approximation (DynGMA). Benefiting from the robust density approximation, our method exhibits superior accuracy compared to baseline methods in learning the fully unknown drift and diffusion functions and computing the invariant distribution from trajectory data. And it is capable of handling trajectory data with low time resolution and variable, even uncontrollable, time step sizes, such as data generated from Gillespie's stochastic simulations. We then conduct several experiments across various scenarios to verify the advantages and robustness of the proposed method.

One-step block scheme with optimal hybrid points for numerical integration of second-order ordinary differential equations

In this paper, a one-step block of optimized hybrid schemes for the numerical integration of second-order initial value problems (IVP) of ordinary differential equations (ODE) is constructed via collocation techniques. The developed scheme is obtained by considering two intra-step nodal points as hybrid points, which are chosen in order to achieve optimized errors of the main formulae approximating the solution such that 0 < v1 < v 2 < 1 where v1 and v2 are defined as hybrid points. The characteristics of the developed scheme are analyzed. Application of the new scheme on some second-order IVPs shows the accuracy and effectiveness of the scheme compared with some existing methods.

Updating to Optimal Parametric Values by Memory-Dependent Methods: Iterative Schemes of Fractional Type for Solving Nonlinear Equations

In the paper, two nonlinear variants of the Newton method are developed for solving nonlinear equations. The derivative-free nonlinear fractional type of the one-step iterative scheme of a fourth-order convergence contains three parameters, whose optimal values are obtained by a memory-dependent updating method. Then, as the extensions of a one-step linear fractional type method, we explore the fractional types of two- and three-step iterative schemes, which possess sixth- and twelfth-order convergences when the parameters’ values are optimal; the efficiency indexes are 6 and 123, respectively. An extra variable is supplemented into the second-degree Newton polynomial for the data interpolation of the two-step iterative scheme of fractional type, and a relaxation factor is accelerated by the memory-dependent method. Three memory-dependent updating methods are developed in the three-step iterative schemes of linear fractional type, whose performances are greatly strengthened. In the three-step iterative scheme, when the first step involves using the nonlinear fractional type model, the order of convergence is raised to sixteen. The efficiency index also increases to 163, and a third-degree Newton polynomial is taken to update the values of optimal parameters.

Numerical Solution of Fourth-order Initial Value Problems Using Novel Fourth-order Block Algorithm

In this paper, a one-step fourth-order block scheme for solving fourth order Initial Value Problems (IVPs) of Ordinary Differential Equations (ODE) is developed using interpolation and collocation techniques. The derived schemes contain two hybrid points which are chosen such that 0 < w1 < w2 < 1 where w1 and w2 are defined as hybrid points. The characteristics of the developed schemes are analyzed. The obtained schemes are applied in block form to solve some fourth-order IVPs and the numerical results show the accuracy and effectiveness of the block scheme compared with some existing methods.

Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem

In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values f′(r), f″(r), and f‴(r) of a nonlinear equation f(x)=0 with r being its simple root. We can achieve high values of the efficiency index (E.I.) over the bound 22/3=1.587 with three function evaluations and over the bound 21/2=1.414 with two function evaluations. The third-degree Newton interpolatory polynomial is derived to update these critical values per iteration. We introduce relaxation factors into the Dzˇunic´ method and its variant, which are updated to render fourth-order convergence by the memory-accelerating technique. We developed six types optimal one-step iterative schemes with the memory-accelerating method, rendering a fourth-order convergence or even more, whose original ones are a second-order convergence without memory and without using specific optimal values of the parameters. We evaluated the performance of these one-step iterative schemes by the computed order of convergence (COC) and the E.I. with numerical tests. A Lie symmetry method to solve a second-order nonlinear boundary-value problem with high efficiency and high accuracy was developed.

Spectral CT image reconstruction using a constrained optimization approach-An algorithm for AAPM 2022 spectral CT grand challenge and beyond.

CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner-upteam. This paper reports details of our PROSPECT algorithm (Prior-based Restricted-variable Optimization for SPEctral CT) and follow-up studies regarding the algorithm's accuracy and enhancement of its convergencespeed. We formulated the reconstruction task as an optimization problem. PROSPECT employed a one-step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam-hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projectiondata. Prior knowledge allowed a reduction of the number of unknown variables by . PROSPECT algorithm achieved the average root of mean square error (RMSE) of in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double-precision projection data reduced RMSE to . Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computationtime. PROSPECT algorithm achieved a high degree of accuracy and computationalefficiency.

One-step scheme in continuous carbon nanofilament–carbon fiber multi-scale reinforcement fabrication at ultra-low temperature with simultaneous tensile and interfacial improvement

Current reports on carbon fiber (CF) modification mainly emphasize its interfacial improvement, yet often sacrifice the strength of CF itself. The comprehensive mechanical improvement of composite requires deeper understanding about the reinforcement. In this work, a process was established based on one-step growth of carbon nanofilament on continuous CF at ultra-low temperature. Both single-factor and orthogonal experiments were executed, while the conversion of catalyst, the generation of carbon nanostructures, and the damage and repair of CF were comprehensively studied. When using Cu5Ni5 catalyst, 0.4 L/min hydrogen, 0.3 L/min acetylene, and 350 ℃ chemical vapor deposition for 5 min, the obtained carbon nanofilament–carbon fiber reached 5.26 GPa tensile and 113 MPa interfacial shear strength. The interlaminar shear strength of its epoxy-based composite was also recorded as 134 MPa. Consequently, this composite far exceeded that of pristine CF in not only tensile strength and modulus by 78.4 % and 55.3 %, but also flexural strength and modulus by 216.0 % and 99.2 %, respectively. This work has fully unleashed the impressive reinforcing potential of CF in composite by extending the theory. Finally, it also contributes to energy conservation and cost reduction for mass production.

Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients

Abstract We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Milstein’s weak error analysis on the one-step approximation of SDEs, we prove a general result on weak convergence of the one-step discretization of the SDEs mentioned above. As applications, we show the weak convergence rates for several numerical schemes of half-order strong convergence, such as tamed and balanced schemes. Numerical examples are presented to verify our theoretical analysis.

Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications

It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu’s lemma and Maingé’s fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations.

One-step implementation of multiqubit controlled–controlled-Z gates with Rydberg atoms

In this paper, we propose a one-step scheme for generating a multiqubit controlled–controlled-Z (CCZ) gate based on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. The Rydberg atoms can form a Rabi oscillation between the ground state and the collective excited state effectively, so a one-step three-qubit CCZ gate can be easily achieved through a Rabi cycle. Numerical simulation results show that the scheme has a high fidelity and robustness against errors which are caused by parameter errors, intrinsic errors, and atomic decays. Therefore, we hope that this scheme will enable fast and robust quantum computing in the near future.

A Review of the Some Fixed Point Theorems for Different Kinds of Maps

The focus of this article, reviewed a generalized of contraction mapping and nonexpansive maps and recall some theorems about the existence and uniqueness of common fixed point and coincidence fixed-point for such maps under some conditions. Moreover, some schemes of different types as one-step schemes ,two-step schemes and three step schemes (Mann scheme algorithm, Ishukawa scheme algorithm, noor scheme algorithm, .scheme algorithm, scheme algorithm Modified scheme algorithm arahan scheme algorithm and others. The convergence of these schemes has been studied .On the other hands, We also reviewed the convergence, valence and stability theories of different types of near-plots in convex metric space.

Cubature Kalman Filters Model Predictive Static Programming Guidance Method with Impact Time and Angle Constraints Considering Modeling Errors

This paper proposes a CKF-MPSP guidance method for hitting stationary targets with impact time and angle constraints for missiles in the presence of modeling errors. This innovative guidance scheme is composed of three parts: First, the model predictive static programming (MPSP) algorithm is used to design a nominal guidance method that simultaneously satisfies impact time and angle constraints. Second, the cubature Kalman filter (CKF) is introduced to estimate values of the influence of the inevitable modeling errors. Finally, a one-step compensation scheme is proposed to eliminate the modeling errors’ influence. The proposed method uses a real missile dynamics model, instead of a simplified one with a constant-velocity assumption, and eliminates the effects of modeling errors with the compensation scheme; thus, it is more practical. Simulations in the presence of modeling errors are conducted, and the results illustrate that the CKF-MPSP guidance method can reach the target with a high accuracy of impact time and angles, which demonstrates the high precision and strong robustness of the method.

Adaptive Jamming Attack Detection Under Noise Uncertainty in mmWave Massive MIMO Systems

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

A Review of Building Energy Retrofit Measures, Passive Design Strategies and Building Regulation for the Low Carbon Development of Existing Dwellings in the Hot Summer–Cold Winter Region of China

Retrofitting buildings to achieve improved levels of energy performance is a key strategy in the transition to a low-/net zero carbon future. In China, there has been an enormous growth in residential construction in recent decades in response to the country’s economic development and population growth. However, although these buildings are structurally solid and have long functional life spans, most have very poor thermal performance. Therefore, they would be very suitable for energy retrofitting. Because of the variety of retrofitting options, it is important to review the retrofit measures, regulations and possible outcomes to find effective, long-term solutions that strike a balance between the energy saved, the carbon emitted and the financial costs over a building’s lifetime. This paper reviews suitable retrofit measures for the hot summer–cold winter region of China, because this is an area with huge numbers of residential buildings that are suitable for energy retrofitting. The study explores the current conditions of targeted residential buildings, retrofit schemes, building regulations, and policy gaps towards achieving China’s 2060 carbon neutrality goal. The review indicates that current mandatory building energy regulations in this region are not ambitious enough to achieve a significantly lower carbon future, and one-step deep Passivhaus retrofit schemes are recommended to achieve decarbonization goals.

One-step generation of Bell state on nonlocal acoustics wave resonators assisted by nitrogen-vacancy center ensembles

Recently, quantum information processing (QIP) on acoustics wave resonators (AWRs) has attracted much attention as the quality factor of AWR has been increased to 1011, which means the time of phonons stored in the AWR can reach the order of seconds. To achieve the large-scale QIP on AWRs, one should complete quantum entangled operations on nonlocal AWRs. Different from previous work, we propose a one-step all-resonance scheme to generate Bell states on two nonlocal AWRs coupled to two nitrogen-vacancy center ensembles (linked by an AWR quantum bus) respectively. One-step all-resonance operation makes the scheme easier to be experimentally implemented.

Finite-Element Method for the Simulation of Lipid Vesicle/Fluid Interactions in a Quasi–Newtonian Fluid Flow

We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty which allows computational savings and facilitates implementation. A high-order Galerkin finite element approximation allows accurate calculations of the membrane force with high-order derivatives. The time discretization is based on the double composition of the one-step backward Euler scheme, while the time step size is flexibly controlled using a time integration error estimation. Numerical examples are presented with particular attention paid to the validation and assessment of the model’s relevance in terms of physiological significance. Optimal convergence rates of the time discretization are obtained.