Step Size Research Articles

On Implementing a Two-Step Interior Point Method for Solving Linear Programs

A new two-step interior point method for solving linear programs is presented. The technique uses a convex combination of the auxiliary and central points to compute the search direction. To update the central point, we find the best value for step size such that the feasibility condition is held. Since we use the information from the previous iteration to find the search direction, the inverse of the system is evaluated only once every iteration. A detailed empirical evaluation is performed on NETLIB instances, which compares two variants of the approach to the primal-dual log barrier interior point method. Results show that the proposed method is faster. The method reduces the number of iterations and CPU time(s) by 27% and 18%, respectively, on NETLIB instances tested compared to the classical interior point algorithm.

Modulation of dlPFC function and decision-making capacity by repetitive transcranial magnetic stimulation in methamphetamine use disorder

This study explores the impact of repetitive transcranial magnetic stimulation (rTMS) on decision-making capabilities in individuals with methamphetamine use disorder (MUD), alongside potential underlying psychological mechanisms. Employing the Iowa Gambling Task (IGT) and computational modeling techniques, we assessed the decision-making processes of 50 male MUD participants (24 underwent rTMS treatment, 26 received no treatment) and 39 healthy controls (HC). We compared pre- and post-rTMS treatment alterations in the left dorsolateral prefrontal cortex (dlPFC). Results revealed inferior performance in the IGT among the MUD group, characterized by aberrant model parameters in the Value-Plus-Perseverance (VPP) model, including heightened learning rate, outcome sensitivity, and reinforcement learning weight, alongside diminished response consistency and loss aversion. RTMS treatment demonstrated efficacy in reducing craving scores, enhancing decision-making abilities, and partially restoring normalcy to certain model parameters in the MUD cohort. Nonetheless, no linear relationship between changes in model parameters and craving was observed. These findings lend support to the somatic marker hypothesis, implicating the dlPFC in the decision-making deficits observed in MUD, with rTMS potentially ameliorating these deficits by modulating the function of these brain regions. This study not only offers novel insights and methodologies for MUD rehabilitation but also underscores the necessity for further research to corroborate and refine these findings. Trial Registration www.chictr.org.cn Identifier: No. ChiCTR17013610.

Establishment of a novel DNNSS-MOVES prediction model for carbon emissions of trucks driving on dirt roads

This study proposes a novel prediction model to accurately quantify the carbon emissions of the trucks driving on dirt roads based on the deep learning neural network for small sample (DNNSS) and the motor vehicle emission simulator (MOVES). The application range of the MOVES model was extended to the transportation of asphalt mixtures on the temporary road. The model correction method was also established based on the rolling resistance coefficient (CR) and the correction coefficient (μ). By comparing the measured fuel consumption of the truck with the carbon emissions calculated by the MOVES model, the values of CR × μ can be back-calculated. DNNSS was constructed for estimating the CR × μ. The Adaptive Moment Estimation (Adam) algorithm was used to dynamically adjust the learning rate and accelerate the convergence of the network; the Dropout function was used to alleviate overfitting; and the Rectified Linear Unit (ReLU) function was used as the activation function to solve the gradient vanishing problem. The test results showed that the vehicle speed and load greatly influence the CR × μ. The DNNSS algorithm was better at predicting the CR × μ. The proposed DNNSS-MOVES model was more accurate than the conventional methods.

Prediction of Aerodynamic Forces at the Tip of the Compressor Blades Based on Multi-scale 1DCNN Combined with CBAM

The compressor is a crucial component of aircraft engines, and the blades are the critical factor affecting the performance of the compressor. Based on multi-scale one-dimensional convolution neural network (1DCNN) with Convolutional Block Attention Module (CBAM), a data-driven model is proposed for predicting the aerodynamic characteristics of the blade tips. The model is trained using the Adam with decoupled weight decay (AdamW) optimizer and a staged learning rate scheduling strategy. Due to the distinct aerodynamic pressure distributions on the suction and pressure sides, separate models are constructed in order to reveal the aerodynamic performance of the blade tips accurately. During the model validation, Root Mean Square Error (RMSE) and the coefficient of determination (R2) are taking as evaluation criterions, where high reliability is demonstrated compared to Computational Fluid Dynamics (CFD) results.

Performance analysis of linearization schemes for modelling multi-phase flow in porous media

Reservoir simulation is crucial for understanding the flow response in underground reservoirs, and it significantly helps reduce uncertainties in geological characterization and optimize methodologies for field development strategies. However, providing efficient and accurate solutions for the strong heterogeneity remains challenging, as most of the discretization methods cannot handle this complexity. In this work, we perform a comprehensive assessment of various numerical linearization techniques employed in reservoir simulation, particularly focusing on the performance of the nonlinear solver for problem dealing with fluid flow in porous media. The primary linearization methods examined are finite difference central (FDC), finite forward difference (FDF), and operator-based linearization (OBL). These methods are rigorously analyzed and compared in terms of their accuracy, computational efficiency, and adaptability to changing reservoir conditions. The results demonstrate that each method has distinct strengths and limitations. The FDC method is more accurate particularly in complex simulations where strong heterogeneity are introduced but is generally slower in convergence. The OBL on the other hand, is more efficient and converges quickly, which makes it suitable for scenarios with limited computational resources and simple physics, while the FDF method provides a balanced combination of precision and computational speed, contingent upon careful step size management of the derivative estimations. This paper aims to guide the selection of appropriate linearization techniques for enhancing nonlinear solvers’ accuracy and efficiency in reservoir simulation .

Molecular dynamics simulation on crystal morphology of NH4ClO4.

Ammonium perchlorate (NH4ClO4, abbreviated as AP) has the advantages of high oxygen content, high density, and good compatibility, and has significant application prospects in the field of energetic materials. The crystal morphology has a great influence on the properties and sensibility of energetic materials, and a single experimental means is difficult in exploring the crystals; therefore, the crystal morphology of AP is investigated using molecular dynamics simulation complemented with experiments, to theoretically analyze the differences in AP crystal habit and the interactions between solvent molecules and the main growing crystal surfaces of AP. The results show that AP crystal is mainly composed of five independent crystal surfaces (0 0 1), (0 1 0), (1 0 0), (1 0 1), and (1 0 -1) in vacuum using the BFDH laws, with (0 0 1) surface being the main growth crystal surface. In contrast, in H2O solvent, the (1 0 1) and (1 0 -1) surfaces disappear, and the AP mainly consists of (0 0 1), (0 1 0), and (1 0 0) surfaces with a rectangular shape. The crystal morphology obtained from theoretical prediction is in good agreement with that obtained from experimental culture. This paper can provide a new idea for the cultivation and preparation of AP large crystals, and promote the application of AP crystals in energetic materials. The crystal morphologies of AP in vacuum and H2O solvent under Dreiding force field were predicted based on attachment energy model by using molecular dynamics method in Materials Studio 2019 software. The entire molecular dynamics simulation was carried out under the NTV system, the temperature control method was selected as Anderson, and the system temperature was set to 298 K. The simulation time was set to 40 ps, the step size was set to 1 fs, and the data were outputted every 5000 steps.

Selection effect of learning rate parameter on estimators of [formula omitted] exponential populations under the joint hybrid censoring

A Bayesian method based on the learning rate parameter η is called a generalized Bayesian method. In this study, joint hybrid censored type I and type II samples from k exponential populations were examined to determine the influence of the parameter η on the estimation results. To investigate the selection effects of the learning rate and the loss parameters on the estimation results, we considered two additional loss functions in the Bayesian approach: the linear and the generalized entropy loss functions. We then compared the generalized Bayesian algorithm with the traditional Bayesian algorithm. We performed Monte Carlo simulations to compare the performance of the estimation results with the losses and different values of η. The effects of different losses with different values and learning rate parameters are examined using an example.

Technological evolution of large-scale blue hydrogen production toward the U.S. Hydrogen Energy Earthshot

Hydrogen potentially has a crucial role in the U.S. transition to a net-zero emissions economy. Learning from large-scale hydrogen projects will boost technological evolution and innovation toward the U.S. Hydrogen Energy Earthshot. We apply experience curves to estimate the evolving costs of blue hydrogen production and to further examine the economic effect on technological evolution of the Inflation Reduction Act’s tax credits for carbon sequestration and clean hydrogen. Learning-by-doing alone can decrease the production cost of blue hydrogen. Without tax incentives, however, it is hard for blue hydrogen production to reach the cost target of $1/kg H2. Here we show that the breakeven cumulative production capacity required for gas-based blue hydrogen to reach the $1/kg H2 target highly depends on tax credit, natural gas price, inflation rate, and learning rates. We make recommendations for hydrogen hub development and for accelerating technological progress toward the Hydrogen Energy Earthshot.

Improved YOLOv8 algorithm for vehicle image target detection based on learning rate optimisation strategy

Vehicle image target detection is of great significance in the field of computer vision, which is mainly applied in the fields of traffic safety, intelligent traffic management and automatic driving. This study adopts a learning rate decay strategy for the YOLOv8 algorithm, which achieves the purpose of dynamically adjusting the learning rate. Through the analysis of model confusion matrix, F1 confidence, precision confidence, accuracy, recall, and recall confidence curve, the results show that the YOLOv8 algorithm adjusted by the learning rate attenuation strategy is able to efficiently and accurately detect and identify the car target in the image, and all the evaluation indexes have reached the optimal level. Comparison of the target detection results with the labels in the test set verifies that the optimised learning rate YOLOv8 algorithm achieves 100% prediction accuracy, successfully identifying and labelling the car target in the image. In conclusion, the learning rate optimised YOLOv8 algorithm performs well in vehicle image target detection and provides an effective solution for efficient and accurate car recognition.

Comparison of postoperative gait parameters after total ankle arthroplasty and ankle fusion: A systematic review.

Ankle pathology, such as severe arthritis, often necessitates surgical intervention to restore mobility and alleviate pain. Two commonly performed procedures for end-stage ankle disease are ankle fusion (AF) and total ankle arthroplasty (TAA). This review aims to compare the impact of AF and TAA on postoperative gait parameters. An extensive search in PubMed, Scopus, and Web of Science electronic databases was conducted with the use of the keywords ("ankle arthrodesis" OR "ankle fusion") AND ("ankle replacement" OR "ankle arthroplasty") AND "gait." Clinical studies in terms of postoperative gait parameters were included in this review. At least one of the following gait parameters, included in gait analysis, should be researched: spatiotemporal variables and joint kinematics and kinetics. An initial search revealed 221 studies. After the removal of duplicates and screening of titles,10 studies (7 prospective and 3 retrospective case series) were included for qualitative analysis. In the majority of studies, there is no significant difference in spatiotemporal parameters, such as walking speed, cadence, stance duration, step length, and stride length among AF and TAA patients. Postoperative sagittal ankle ROM, mainly maximum ankle dorsiflexion angle is significantly higher in TAA patients, while results concerning hip and knee ROM are variable. The comparison of AF and TAA in terms of postoperative gait parameters has shown variable results. In the majority of studies, there is no significant difference in spatiotemporal and kinetic parameters among AF and TAA patients. Further high-quality prospective studies are needed to fully elucidate the comparison of postoperative gait parameters.

The impact of diffusion tensor imaging tractography settings on muscle fascicle architecture and diffusion parameter estimates: Tract length, completion, and curvature are most sensitive to tractography settings.

Diffusion-tensor (DT)-MRI tractography provides information about properties relevant to muscle health and function, including estimates of architectural properties such as fascicle length, pennation angle, and curvature and diffusion properties such as mean diffusivity (MD) and fractional anisotropy (FA). Tractography settings, including integration algorithms, thresholds for early tract termination, and tract smoothing approaches, impact the accuracy of the muscle property estimates. However, muscle DT-MRI tractography is performed using a variety of these settings, complicating comparisons between different studies. The effects of different tractography settings on muscle architecture estimates have not been fully explored, and optimized settings for muscle tractography have not yet been determined. We examined the influence of integration algorithm and termination check settings combined with a range of step sizes, termination criteria, and smoothing polynomial orders on tract characteristics, completion/reason for termination, and goodness of fit between fiber tracts and smoothing polynomials using 3-T DT-MR images of the lower leg muscles of seven healthy adults. We found that tract length and completion were highly sensitive to strict FA and intersegment angle thresholds (25%-69% reduction in complete fiber tracts from lowest to highest minimum FA threshold and 11%-36% reduction from highest to lowest intersegment angle threshold). Higher order polynomials (third and fourth order vs. second order) better fit the muscle fiber trajectories, but curvature estimates were highly sensitive to smoothing polynomial order (3.9-6.6 m-1 increase for second- vs. fourth-order fitting polynomials). Step size impacted curvature estimates, albeit to a lesser degree. Integration algorithm had little impact, and mean pennation angle, and tract-based FA and MD, were relatively insensitive to all parameters. The results demonstrate which muscle diffusion measures and architectural estimates are most sensitive to varying tractography settings and support the need for consistent reporting of tractography details to aid interpretation and comparison of results between studies.

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

The Immediate Effect of the Novel Hybrid Passive Spring Damper Ankle-Foot Orthosis on Spatiotemporal Parameters of Walking in Patients with Multiple Sclerosis

ABSTRACT Introduction Patients with multiple sclerosis (PwMS) experience damage to their central nervous system, which can lead to unilateral or bilateral drop foot. The presently utilized ankle-foot orthoses (AFOs) for PwMS have exhibited limited clinical efficacy. Objective This current study evaluated the immediate effects of the Novel Hybrid Passive Spring Damper Ankle-Foot Orthosis (HPSDAFO) on walking in PwMS. Study design A cohort trial. Methods Twelve PwMS suffering of unilateral drop foot took part in this study. They were given the novel HPSDAFO and underwent kinematic assessment including walking along a 10-m walkway at a self-selected speed, both with and without the HPSDAFO. Results The novel HPSDAFO device significantly changed gait parameters of ankle range of motion, single limb support duration, and step and stride length of the affected side (P < 0001). Furthermore, the device also improved the symmetry index and resulted in increased walking speed and cadence. Conclusions The application of the novel HPSDAFO on the affected side of PwMS resulted in a notable enhancement in the symmetry of spatial parameters, which highlights the need for additional research in this area. Clinical Relevance Using the novel HPSDAFO, PwMS can walk without adverse effects, promoting the normalization of their spatiotemporal walking parameters.

The Immediate Effect of the Novel Hybrid Passive Spring Damper Ankle-Foot Orthosis on Spatiotemporal Parameters of Walking in Patients with Multiple Sclerosis

ABSTRACT Introduction Patients with multiple sclerosis (PwMS) experience damage to their central nervous system, which can lead to unilateral or bilateral drop foot. The presently utilized ankle-foot orthoses (AFOs) for PwMS have exhibited limited clinical efficacy. Objective This current study evaluated the immediate effects of the Novel Hybrid Passive Spring Damper Ankle-Foot Orthosis (HPSDAFO) on walking in PwMS. Study design A cohort trial. Methods Twelve PwMS suffering of unilateral drop foot took part in this study. They were given the novel HPSDAFO and underwent kinematic assessment including walking along a 10-m walkway at a self-selected speed, both with and without the HPSDAFO. Results The novel HPSDAFO device significantly changed gait parameters of ankle range of motion, single limb support duration, and step and stride length of the affected side (P < 0001). Furthermore, the device also improved the symmetry index and resulted in increased walking speed and cadence. Conclusions The application of the novel HPSDAFO on the affected side of PwMS resulted in a notable enhancement in the symmetry of spatial parameters, which highlights the need for additional research in this area. Clinical Relevance Using the novel HPSDAFO, PwMS can walk without adverse effects, promoting the normalization of their spatiotemporal walking parameters.

The effect of balance training using touch controller-based fully immersive virtual reality devices on balance and walking ability in patients with stroke: A pilot randomized controlled trial.

Fully immersive virtual reality (FIVR) removes information from the real world and replaces it with computer-generated data, creating the impression of being in a genuine virtual world. To evaluate the effects of balance training using touch controller-based FIVR devices on balance and walking abilities in patients with stroke. The participants were randomly categorized into the FIVR group (n = 18) and control group (n = 18). The control group received conventional therapy for 5 sessions, 30 minutes per week, for 5 weeks. The FIVR group practiced additional touch controller-based FIVR balance training for 3 sessions of 30 minutes per week for 5 weeks and changes in balance and walking ability were measured for both groups. Touch controller-based FIVR balance training significantly improved the Berg Balance Scale (BBS) and, timed up-and-go (TUG) test results (P < .01). There was also significant improvement in gait abilities, including gait velocity, step length of the affected side, stride length, and single limb support of the affected side (P < .01). Touch controller-based FIVR balance training improved balance and gait in patients with stroke. These results indicate that touch controller-based FIVR balance training is feasible and suitable for patients with stroke, providing a promising avenue for rehabilitation.

A modified quasi-Newton method for uncertain multiobjective optimization problems under a finite uncertainty set

ABSTRACT In this article, a modified quasi-Newton method is developed for the robust counterpart (RC) of an uncertain multiobjective optimization problem (UMOP). Specifically, the RC of a UMOP is the minimum of an objective-wise worst-case (OWWC) type RC. To determine the descent direction for the RC, a subproblem using a common Hessian approximation is constructed. An inexact line search technique based on the Armijo technique is employed to find an appropriate step length. Furthermore, a modified version of the Davidon–Fletcher–Powell (DFP) update formula is developed for the RC. A modified quasi-Newton algorithm is built using descent direction step length, and DFP Hessian update formula. Furthermore, the convergence of the modified quasi-Newton algorithm is also discussed. Finally, the modified quasi-Newton algorithm is illustrated with a set of test problems and compared with the weighted sum method. Moreover, it is demonstrated that the algorithm is effective for both convex and non-convex problems.

Unconditional optimal [formula omitted]-norm error estimate and superconvergence analysis of a linearized nonconforming finite element variable-time-step BDF2 method for the nonlinear complex Ginzburg–Landau equation

In this paper, a linearized fully discrete scheme combining the variable-time-step two-step backward differentiation formula (VSBDF2) in time and the nonconforming finite element methods (FEMs) in space is constructed and analyzed for the nonlinear complex Ginzburg–Landau equation. A novel convergence analysis approach is proposed, which shows that the H1-norm error of this scheme can reach optimal order in space and sharp second-order convergence in time. The key ingredients of our analysis are temporal–spatial error splitting approach, a new positive definiteness property of discrete orthogonal convolution (DOC) kernels with respect to complex sequences, an energy projection operator and a discrete Laplace operator Δh related to the nonconforming element space, and a relationship between Δh and classical L2 projection operator in complex space. Furthermore, through a specific treatment of the error equation and the combination technique of interpolating operator and projection operator, we prove that the proposed scheme has the global superconvergence result of order O(τ2+h2) in H1-norm for the first time, which further improves the efficiency of numerical computation. Here τ and h are the maximum time and spatial step sizes, respectively. It should be pointed out that all these error results are rigorously established under mild assumptions of the time step, and get rid of the usual grid ratio constraints between temporal and spatial step sizes in linearized scheme. At last, numerical experiments are provided to verify the theoretical analysis.

Subgradient-projection-based stable phase-retrieval algorithm for X-ray ptychography.

X-ray ptychography is a lensless imaging technique that visualizes the nano-structure of a thick specimen which cannot be observed with an electron microscope. It reconstructs a complex-valued refractive index of the specimen from observed diffraction patterns. This reconstruction problem is called phase retrieval (PR). For further improvement in the imaging capability, including expansion of the depth of field, various PR algorithms have been proposed. Since a high-quality PR method is built upon a base PR algorithm such as ePIE, developing a well performing base PR algorithm is important. This paper proposes an improved iterative algorithm named CRISP. It exploits subgradient projection which allows adaptive step size and can be expected to avoid yielding a poor image. The proposed algorithm was compared with ePIE, which is a simple and fast-convergence algorithm, and its modified algorithm, rPIE. The experiments confirmed that the proposed method improved the reconstruction performance for both simulation and real data.

PLM-Res-U-Net: A light weight binarization model for enhancement of multi-textured palm leaf manuscript images

This paper proposes a deep semantic binarization model, PLM-Res-U-Net, for enhancing palm-leaf manuscripts. PLM-Res-U-Net is a lightweight model comprising encoding and decoding blocks with skip connections. The model enhances the palm leaf manuscript by efficiently retaining the text strokes by removing the degradations such as uneven illumination, aging marks, brittleness, and background discolorations. Two datasets of palm leaf manuscript collections with multiple degradation patterns and diverse textured backgrounds are used for experimentation. PLM-Res-U-Net is trained from scratch with 50 epochs with a learning rate of1e−8 with three sampling strategies. The performance of state-of-the-art deep learning models ResUnet, Pspnet, U-Net++, and Segnet are also evaluated along with two diverse benchmark datasets. Analysis shows that results obtained by the proposed PLM-Res-U-Net prove generalizability and computational efficacy with a dice score of 0.986. Additionally, PLM-Res-U-Net successfully preserves the edge strokes of the text compared with state-of-the-art models.

Physics-Informed Online Learning for Temperature Prediction in Metal AM.

In metal additive manufacturing (AM), precise temperature field prediction is crucial for process monitoring, automation, control, and optimization. Traditional methods, primarily offline and data-driven, struggle with adapting to real-time changes and new process scenarios, which limits their applicability for effective AM process control. To address these challenges, this paper introduces the first physics-informed (PI) online learning framework specifically designed for temperature prediction in metal AM. Utilizing a physics-informed neural network (PINN), this framework integrates a neural network architecture with physics-informed inputs and loss functions. Pretrained on a known process to establish a baseline, the PINN transitions to an online learning phase, dynamically updating its weights in response to new, unseen data. This adaptation allows the model to continuously refine its predictions in real-time. By integrating physics-informed components, the PINN leverages prior knowledge about the manufacturing processes, enabling rapid adjustments to process parameters, geometries, deposition patterns, and materials. Empirical results confirm the robust performance of this PI online learning framework in accurately predicting temperature fields for unseen processes across various conditions. It notably surpasses traditional data-driven models, especially in critical areas like the Heat Affected Zone (HAZ) and melt pool. The PINN's use of physical laws and prior knowledge not only provides a significant advantage over conventional models but also ensures more accurate predictions under diverse conditions. Furthermore, our analysis of key hyperparameters-the learning rate and batch size of the online learning phase-highlights their roles in optimizing the learning process and enhancing the framework's overall effectiveness. This approach demonstrates significant potential to improve the online control and optimization of metal AM processes.