quasi-Newton Method Research Articles

Combining Sentinel-2 Data and Risk Maps to Detect Trees Predisposed to and Attacked by European Spruce Bark Beetle

The European spruce bark beetle is a major disturbance agent in Norway spruce forests in Europe, and with a changing climate it is predicted that damage will increase. To prevent the bark beetle population buildup, and to limit further spread during outbreaks, it is crucial to detect attacked trees early. In this study, we utilize Sentinel-2 data in combination with a risk map, created from geodata and forestry data, to detect trees predisposed to and attacked by the European spruce bark beetle. Random forest models were trained over two tiles (90 × 90 km) in southern Sweden for all dates with a sufficient number of cloud-free Sentinel-2 pixels during the period May–September in 2017 and 2018. The pixels were classified into attacked and healthy to study how detection accuracy changed with time after bark beetle swarming and to find which Sentinel-2 bands are more important for detecting bark beetle attacked trees. Random forest models were trained with (1) single-date data, (2) temporal features (1-year difference), (3) single-date and temporal features combined, and (4) Sentinel-2 data and a risk map combined. We also included a spatial variability metric. The results show that detection accuracy was high already before the trees were attacked in May 2018, indicating that the Sentinel-2 data detect predisposed trees and that the early signs of attack are low for trees at high risk of being attacked. For single-date models, the accuracy ranged from 63 to 79% and 84 to 94% for the two tiles. For temporal features, accuracy ranged from 65 to 81% and 81 to 92%. When the single-date and temporal features were combined, the accuracy ranged from 70 to 84% and 90 to 96% for the two tiles, and with the risk map included, the accuracy ranged from 83 to 91% and 92 to 97%, showing that remote sensing data and geodata can be combined to increase detection accuracy. The differences in accuracy between the two tiles indicate that local differences can influence accuracy, suggesting that geographically weighted methods should be applied. For the single-date models, the SWIR, red-edge, and blue bands were generally more important, and the SWIR bands were more important after the attack, suggesting that they are most suitable for detecting the early signs of a bark beetle attack. For the temporal features, the SWIR and blue bands were more important, and for the variability metric, the green band was generally more important.

Heart Rate Variability and Cerebral Autoregulation in Patients with Traumatic Brain Injury with Paroxysmal Sympathetic Hyperactivity Syndrome.

Severe traumatic brain injury (TBI) can lead to transient changes in autonomic nervous system (ANS) functioning and development of paroxysmal sympathetic hyperactivity (PSH) syndrome. Clinical manifestation of ANS disorders may be obscured by therapeutic interventions in TBI. This study aims to analyze ANS metrics and cerebral autoregulation in patients with PSH syndrome to determine their significance in early prognostication. This single-center retrospective study investigated the relationship between changes in ANS metrics, cerebral autoregulation, and PSH syndrome. Arterial blood pressure and intracranial pressure signals were monitored for 5 days post TBI. ANS metrics included time and frequency domain heart rate variability (HRV) metrics. Cerebral autoregulation was assessed using the pressure reactivity index. Sixty-six patients with severe TBI (median age 33 [interquartile range 26-50] years) were analyzed, and PSH was confirmed in nine cases. Impairment of cerebral autoregulation was observed in 67% of patients with PSH and 72% without the syndrome. Patients with PSH had higher HRV in the low-frequency range (LF; 253 ± 178 vs. 176 ± 227 ms2; p = 0.035) and lower heart rates (HRs; 70 ± 7 vs. 78 ± 19 bpm; p = 0.027) compared to those without PSH. A receiver operating characteristic curve analysis indicated that HR (area under the curve(AUC) = 0.73, p = 0.006) and HRV in the LF (AUC = 0.70, p = 0.009) are moderate predictors of PSH. In the multiple logistic regression model for PSH, diffuse axonal trauma (odds ratio(OR) = 10.82, 95% confidence interval(CI) = 1.70-68.98, p = 0.012) and HR (OR =0.91, 95% CI 0.84-0.98, p = 0.021) were significant factors. Elevated HRV in the LF and decreased HR may serve as early predictors of PSH syndrome development, particularly in patients with diffuse axonal trauma. Further research is needed to investigate the utility of the cerebral autoregulation-ANS relationship in PSH prognostication.

Beat-to-beat analysis of hemodynamic response to mental and psychological stress in sickle cell anemia

Abstract Vaso-occlusive crises are a hallmark symptom of sickle cell disease. Physical stressors can trigger decreased microvascular blood flow and increase the risk for vaso-occlusive crises. However, the effect of mental and psychological stressors on vascular physiology in sickle cell disease is not well-established. We hereby examined fluctuations in continuous blood pressure to evaluate hemodynamic changes in sickle cell disease patients during mental and psychological stress. Thirteen sickle cell disease subjects from the Children’s Hospital Los Angeles and 11 healthy volunteers were recruited. Continuous blood pressure was recorded during two mental tasks and one psychological stress task. Systolic beat-to-beat blood pressure variability measurements were calculated for each subject. Three very short-term blood pressure variability metrics served as outcome measures: standard deviation, coefficient of variation, and average real variability. Peripheral augmentation index was calculated from arterial waveforms. Linear mixed effects models evaluated associations between patient factors and outcome measures. Sickle cell disease patients exhibit increased systolic blood pressure variability in response to psychological stress. All subjects exhibited a decrease in systolic blood pressure variability in response to mental stress tasks. During mental stress, both groups displayed increased augmentation index, reflective of stress-induced vasoconstriction, while psychological stress in sickle cell disease patients led to both decreased mean arterial pressure and increased augementation index, suggestive of uncompensated vasoconstriction. These findings emphasize the impact of mental and psychological stressors on vascular function in sickle cell disease and the potential for monitoring physiological signals to predict vaso-occlusive crisis events.

Temporal variability and predictability predict alpine plant community composition and distribution patterns.

One of the most reliable features of natural systems is that they change through time. Theory predicts that temporally fluctuating conditions shape community composition, species distribution patterns, and life history variation, yet features of temporal variability are rarely incorporated into studies of species-environment associations. In this study, we evaluated how two components of temporal environmental variation-variability and predictability-impact plant community composition and species distribution patterns in the alpine tundra of the Southern Rocky Mountains in Colorado (USA). Using the Sensor Network Array at the Niwot Ridge Long-Term Ecological Research site, we used in situ, high-resolution temporal measurements of soil moisture and temperature from 13 locations ("nodes") distributed throughout an alpine catchment to characterize the annual mean, variability, and predictability in these variables in each of four consecutive years. We combined these data with annual vegetation surveys at each node to evaluate whether variability over short (within-day) and seasonal (2- to 4-month) timescales could predict patterns in plant community composition, species distributions, and species abundances better than models that considered average annual conditions alone. We found that metrics for variability and predictability in soil moisture and soil temperature, at both daily and seasonal timescales, improved our ability to explain spatial variation in alpine plant community composition. Daily variability in soil moisture and temperature, along with seasonal predictability in soil moisture, was particularly important in predicting community composition and species occurrences. These results indicate that the magnitude and patterns of fluctuations in soil moisture and temperature are important predictors of community composition and plant distribution patterns in alpine plant communities. More broadly, these results highlight that components of temporal change provide important niche axes that can partition species with different growth and life history strategies along environmental gradients in heterogeneous landscapes.

The Effects of a Single Vagus Nerve’s Neurodynamics on Heart Rate Variability in Chronic Stress: A Randomized Controlled Trial

Background: The modulation of the autonomic nervous system’s activity, particularly increasing its parasympathetic tone, is of significant interest in clinical physiotherapy due to its potential benefits for stress-related conditions and recovery processes. This study evaluated the effectiveness of the addition of neurodynamics in enhancing parasympathetic activation in subjects with chronic stress. Methods: A clinical trial randomly assigned participants to a group with neurodynamics (6 bpm breathing protocol + manual therapy + neurodynamic technique) or a group without neurodynamics (6 bpm breathing protocol + manual therapy only). Metrics of heart rate variability (HRV), including the Mean Heart Rate (Mean HR), standard deviation of intervals between consecutive heartbeats (SDNN), Heart Rate Difference (Diff. HR), Root Mean Square of Successive Differences (RMSSD), number of intervals differing by more than 50 ms (NN50), percentage of consecutive NN intervals that differed by more than 50 ms (pNN50), and the high-frequency component measured in standardized units (HF), were assessed before, during, and after the intervention. Results: During the intervention, the group with neurodynamics showed significant changes in all variables except in the pNN50 and HF while the group without neurodynamics only showed improvements in the Mean HR, SDNN, and RMSSD. In the post-intervention phase, the group with neurodynamics maintained an increase in HRV while the group without neurodynamics experienced a decrease, suggesting an increase in sympathetic activity. Conclusions: Vagal nerve neurodynamics appear to represent an effective method for enhancing parasympathetic activation in patients with chronic stress. The results highlight the importance of a more comprehensive analysis of HRV variables in order to obtain a correct picture of the impact of interventions on the complex and multifaceted functioning of the autonomic nervous system.

Prediction of Resilient Modulus Value of Cohesive and Non-Cohesive Soils Using Artificial Neural Network

This paper investigates the application of Artificial Neural Networks (ANNs) for predicting the resilient modulus (Mr) of subgrade and subbase soils, which is a critical parameter in pavement design. Utilizing a dataset of 1683 Mr observations, the ANN model incorporates eight input variables, including soil gradation, plasticity, and stress conditions. The model was optimized using a quasi-Newton method, achieving high predictive accuracy, with a coefficient of determination (R2) of 0.9613 and low error rates for both selection and testing datasets. To further enhance model interpretability, SHAP (SHapley Additive exPlanations) analysis was conducted, revealing the significant influence of specific input parameters, such as saturation ratio, plasticity index and soil gradation, on Mr predictions. This study underscores the potential of ANNs as a practical tool for estimating resilient modulus, offering a reliable alternative to conventional laboratory testing methods. The findings suggest that integrating ANNs into pavement design processes can lead to more accurate predictions of pavement performance, ultimately supporting the development of more efficient and durable road structures.

The consequences of cardiac autonomic nervous system modulation during pulmonary vein isolation: A review.

Pulmonary vein isolation (PVI) is a well-established treatment modality for atrial fibrillation (AF). Apart from the desired effect regarding the arrhythmic substrate within the left atrium, PVI commonly leads to modulation of the intrinsic cardiac autonomic nervous system (ICANS). Using the available literature, this article presents the anatomy of ICANS and describes methods of assessing its function, mainly focusing on heart rate (HR) variability metrics. Then, we summarize the modern pathophysiological outlooks on the onset and recurrence of AF and explain how the arrhythmia and the activation of ICANS are intertwined. Further, the article discusses the extent, dynamics and persistence of ICANS modulation during PVI, accounting for various modalities and procedural strategies. Both the potential benefits and pitfalls of such modulation are explored, considering AF recurrence, HR and HR variability changes, as well as the unclear effect on ventricular arrhythmias and nerve remodeling. Finally, the article aims to outline further directions of research necessary to improve our understanding of ICANS and its modulation.

Determining the optimum number of cycles for calculating joint coordination and its variability during running at different speeds: A timeseries analysis

Understanding the intricacies of human movement coordination and variability during running is crucial to unraveling the dynamics of locomotion, identifying potential injury mechanisms and understanding skill development. Identification of minimum number of cycles for calculation of reliable coordination and its variability could help with better test organization and efficient assessment time. By adopting a cross-sectional study design, this study investigated the minimum required cycles for calculating hip-knee, hip-ankle and knee-ankle coordination and their variability using a continuous relative phase (CRP) method. Twenty-nine healthy adults ran on a treadmill at speeds of 9, 12.5, and 16 km.h−1 while 3D kinematic data of their lower limbs were recorded using 6 optoelectronic cameras. Using Intraclass Correlation Coefficient (ICC) analysis, reliability between CRP and its variability (CRPv) in different gait cycles (3, 5, 10, 20, 30) was assessed for each speed. A minimum of 10 cycles was required for CRP calculation across all speeds, whereas CRPv necessitated a minimum of 30 cycles for moderate to good reliability. While increasing the number of cycles improved ICC values for inter-joint CRP, the same trend was not consistently observed for CRPv, emphasizing the importance of separately assessing CRP and its variability metrics.

Hardware-accelerated neural network model for early prediction of sudden cardiac arrest based on heart rate variability metrics

AbstractSudden Cardiac Arrest (SCA) constitutes a dire medical condition, marked by the abrupt cessation of effective blood circulation due to the heart's failure to contract properly. This leads to acute circulatory collapse, often culminating in loss of consciousness within an hour and potentially resulting in fatality within minutes if left unattended. Heart rate variability (HRV) serves as a critical biometric, derived from electrocardiogram (ECG) signals with ventricular depolarization waves to further calculate the R-R Intervals (RRIs). These intervals provide the basis for extracting various characteristics of cardiac rhythm, encompassing time-domain, frequency-domain, and nonlinear features. This study presents a neural network-based classification algorithm that leverages HRV metrics to categorize patients into SCA and Normal Sinus Rhythm (NSR) cohorts. The proposed neural network (NN) model showcased impressive results, achieving an accuracy of 96.23%, a sensitivity of 94.35%, and a specificity of 98.12% in detecting SCA, as evaluated through leave-one-subject-out analysis. In order to harness the benefits of hardware acceleration, the algorithm is implemented on a Field-Programmable Gate Array (FPGA). Its computational efficiency is subsequently benchmarked against traditional software-based methodologies. The hardware-level implementation is made possible in Verilog hardware description language (HDL) and was verified successfully with expected performance by register-transfer level (RTL) simulation via Vivado 2020.2.

Analytical ab initio hessian from a deep learning potential for transition state optimization

Identifying transition states—saddle points on the potential energy surface connecting reactant and product minima—is central to predicting kinetic barriers and understanding chemical reaction mechanisms. In this work, we train a fully differentiable equivariant neural network potential, NewtonNet, on thousands of organic reactions and derive the analytical Hessians. By reducing the computational cost by several orders of magnitude relative to the density functional theory (DFT) ab initio source, we can afford to use the learned Hessians at every step for the saddle point optimizations. We show that the full machine learned (ML) Hessian robustly finds the transition states of 240 unseen organic reactions, even when the quality of the initial guess structures are degraded, while reducing the number of optimization steps to convergence by 2–3× compared to the quasi-Newton DFT and ML methods. All data generation, NewtonNet model, and ML transition state finding methods are available in an automated workflow.

Home blood pressure stability score is associated with better cardiovascular prognosis: data from the nationwide prospective J-HOP study.

A home blood pressure (BP)-centered strategy is emerging as the optimal approach to achieve adequate BP control in individuals with hypertension, but a simple cardiovascular risk score based on home BP level and variability is lacking. This study used prospective data from the Japan Morning Surge-Home Blood Pressure (J-HOP) extended study to develop a simple home BP stability score for the prediction of cardiovascular risk. The J-HOP extended study included 4070 participants (mean age 64.9 years) who measured home BP three times in the morning and evening for 14 days at baseline. During the mean 6.3-year follow-up, there were 260 cardiovascular events. A home BP stability score was calculated based on the average of morning and evening systolic BP (SBP; MEave), and three home BP variability metrics: average real variability (average absolute difference between successive measurements); average peak (average of the highest three SBP values for each individual), and time in therapeutic range (proportion of time spent with MEave home SBP 100-135 mmHg). There was a curvilinear association between the home BP stability score and the risk of cardiovascular events. Compared with individuals in the optimal home SBP stability score group (9-10 points), those in the very high-risk group (0 points) had significantly higher cardiovascular event risk during follow-up (adjusted hazard ratio 3.97, 95% confidence interval 2.22-7.09; p < 0.001), independent of age, sex, medication, cardiovascular risk factors, and office BP. These data show the potential for a simple home BP-based score to predict cardiovascular event risk in people with hypertension.

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

A Quasi-Newton Subspace Trust Region Algorithm for Nonmonotone Variational Inequalities in Adversarial Learning over Box Constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon $$\\end{document}-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

A class of regularized adaptive multichannel equalization algorithms for speech dereverberation

The multiple input/output inverse theorem (MINT) is a typical speech dereverberation technique based on acoustic channel equalization. Although the adaptive MINT (A-MINT) method has been developed to meet the requirements of real-time application systems, its performance often deteriorates due to the effect of the identification errors of room impulse responses (RIRs). In this paper, we present a regularized A-MINT approach to reduce the sensitivity of the adaptive equalizer to the RIR identification errors. According to the regularized MINT criterion, Newton's and quasi-Newton methods are used to establish two adaptive speech dereverberation algorithms, respectively, which obtain faster convergent rate and better dereverberation performance. The effectiveness of the proposed algorithms is validated through numerical experiments with the RIRs measured in real acoustic environments.

An Efficient Optimization Model and Tabu Search–Based Global Optimization Approach for the Continuous p-Dispersion Problem

Continuous p-dispersion problems with and without boundary constraints are NP-hard optimization problems with numerous real-world applications, notably in facility location and circle packing, which are widely studied in mathematics and operations research. In this work, we concentrate on general cases with a nonconvex multiply connected region that are rarely studied in the literature due to their intractability and the absence of an efficient optimization model. Using the penalty function approach, we design a unified and almost everywhere differentiable optimization model for these complex problems and propose a tabu search–based global optimization (TSGO) algorithm for solving them. Computational results over a variety of benchmark instances show that the proposed model works very well, allowing popular local optimization methods (e.g., the quasi-Newton methods and the conjugate gradient methods) to reach high-precision solutions due to the differentiability of the model. These results further demonstrate that the proposed TSGO algorithm is very efficient and significantly outperforms several popular global optimization algorithms in the literature, improving the best-known solutions for several existing instances in a short computational time. Experimental analyses are conducted to show the influence of several key ingredients of the algorithm on computational performance. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search &amp; Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72122006, 71821001, and 72471100] Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0089 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0089 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Adapting the population size in CMA-ES using nearest-better clustering method for multimodal optimization

The covariance matrix adaptation evolution strategy (CMA-ES) is one of the advanced algorithms for solving continuous single-objective optimization. In this algorithm, the population size is an important parameter which represents the number of candidate points generated in each iteration. A larger population size allows for better exploration of the search space and is typically required for handling multimodal functions, while a smaller population size facilitates quicker convergence. Adapting the population size in this algorithm raises a question about how to increase/decrease/keep it in an efficient way to solve specific problems. In this paper, we propose a novel approach for this purpose based on the information of niches observed during the evolution process. Firstly, the nearest-better clustering (NBC) technique is employed to detect the number of niches in each iteration, then the information will be used to adapt the population size accordingly. Additionally, a quasi-Newton method, which serves as a local search, can be incorporated into the algorithm in order to speed it up. We evaluate the effectiveness of our method through numerical simulations on multimodal test functions, the black-box optimization benchmarking (BBOB) noiseless testbed, and the CEC 2014 and CEC 2017 benchmark testing suites.

New objective functions for streamflow calibrations to specific model applications

Most hydrological models require a calibration process, performed usually using objective functions that measure the differences between observed and simulated data. Objective functions are typically based on statistical metrics, such as the mean squared error (MSE), which penalizes extreme values in statistics, or mean absolute error (MAE), which assigns equal weight to each measure. Although the MSE is effective in capturing model prediction bias or variability, the calibration results with MSE-based objective functions tend to focus on high flow events at the expense of low flow errors. As different objective functions may emphasize different model response aspects, an appropriate objective function is critical to successful model calibration for model application suitability to a given task. The primary aim of this study is not to directly compare the MSE and MAE to determine which is more relevant to model performance. Instead, as an extended formulation for the Kling–Gupta efficiency (KGE), the new objective functions were designed to incorporate performance metrics based on both the MSE and MAE to evaluate model performance more comprehensively across different flow regimes. The case study has investigated the influence of the proposed objective functions on long-term daily streamflow simulations from a land surface model (LSM) over four study watersheds in the Republic of Korea. The proposed objective functions can help simulate streamflow for the specific purpose of model applications through trade-offs between the MSE- and MAE-based variability metrics in the constituent components. The proposed calibration method allows for a more balanced consideration of various flow regime aspects, compared with the results obtained using traditional objective functions.

Surface Variability Mapping and Roughness Analysis of the Moon Using a Coarse‐Graining Decomposition

AbstractThe lunar surface contains a wide variety of topographic shapes and features, each with different distributions and scales, and any analysis technique to objectively measure roughness must respect these qualities. Coarse‐graining is a naturally scale‐dependent filtering technique that preserves scale‐dependent symmetries and produces coarse elevation maps that gradually erase the smaller features from the original topography. In this study of the lunar surface, we present two surface variability metrics obtained from coarse‐graining lunar topography: fine elevation and coarse curvature. Both metrics are isotropic, deterministic, slope‐independent, and coordinate‐agnostic. Fine (detrended) elevation is acquired by subtracting the coarse elevation from the original topography and contains features that are smaller than the coarse‐graining length‐scale. Coarse curvature is the Laplacian of coarsened topography, and naturally quantifies the curvature at any scale and indicates whether a location is elevated or depressed relative to its neighborhood at that scale. We find that highlands and maria have distinct roughness characteristics at all length‐scales. Our topographic spectra reveal four scale‐breaks that mark characteristic shifts in surface roughness: 100, 300, 1,000, and 4,000 km. Comparing fine elevation distributions between maria and highlands, we show that maria fine elevation is biased toward smaller‐magnitude elevations and that the maria–highland discrepancies are more pronounced at larger length‐scales. We also provide local examples of selected regions to demonstrate that these metrics can successfully distinguish geological features of different length‐scales.

A nested primal–dual iterated Tikhonov method for regularized convex optimization

AbstractProximal–gradient methods are widely employed tools in imaging that can be accelerated by adopting variable metrics and/or extrapolation steps. One crucial issue is the inexact computation of the proximal operator, often implemented through a nested primal–dual solver, which represents the main computational bottleneck whenever an increasing accuracy in the computation is required. In this paper, we propose a nested primal–dual method for the efficient solution of regularized convex optimization problems. Our proposed method approximates a variable metric proximal–gradient step with extrapolation by performing a prefixed number of primal–dual iterates, while adjusting the steplength parameter through an appropriate backtracking procedure. Choosing a prefixed number of inner iterations allows the algorithm to keep the computational cost per iteration low. We prove the convergence of the iterates sequence towards a solution of the problem, under a relaxed monotonicity assumption on the scaling matrices and a shrinking condition on the extrapolation parameters. Furthermore, we investigate the numerical performance of our proposed method by equipping it with a scaling matrix inspired by the Iterated Tikhonov method. The numerical results show that the combination of such scaling matrices and Nesterov-like extrapolation parameters yields an effective acceleration towards the solution of the problem.

Assessment of effective factors on student performance based on machine learning methods

Machine learning methods have gained increasing attention in the field of education due to advancing technological tools and rapidly growing data. The general focus of this attention is on identifying the best method, but it is also critical to determine the extent to which the methods under consideration differ statistically and to correctly identify variable importance metrics. In this study, we benchmarked the performance of twenty-three machine learning algorithms on real educational data via cross-validation based on criteria such as accuracy, AUC and F1-score. Besides, the methods were statistically compared using DeLong and McNemar tests. The findings showed that the LightGBM method appeared to be the best method and presented the most important factors determining student achievement according to this method. The systematic process followed in the study is considered to yield valuable insights for data-driven studies as well as the field of education.