Nonlinear Model Research Articles

External Debt and Economic Growth in Sierra Leone: A Threshold Analysis

The main focus of this study is to investigate the impact of external debt on economic growth and determine the threshold level of external debt that is favourable for economic growth in Sierra Leone, within the framework of a non-linear model (quadratic function). The study employs the Ordinary Least Squares estimation technique with annual time series data for the period 1980 to 2022. The empirical findings reveal that, lagged GDP, external debt, external debt squared and investment are the main drivers of economic growth in Sierra Leone. Specifically, the result reveals that external debt, investment and lagged GDP have a positive impact on growth whilst, external debt squared has a harmful impact on growth. Furthermore, the study establishes a nonlinear relationship between external debt and economic growth. The result indicates that the optimal threshold level of external debt (as a % of GDP) in Sierra Leone is 115%. The findings reveal that, external debt below the threshold level is growth enhancing. However, the accumulation of external debt beyond the threshold level of 115% is detrimental to growth. The diagnostic result confirms that about 76% of the variation in economic growth is explained by the regressors (independent variables). Also, the granger causality test result suggests a unidirectional causality from external debt to economic growth with no reverse causality, indicating that external debt granger caused economic growth at the 5% level. Based on the findings, the study recommends that, government should develop a robust debt management policy, to keep debt levels within sustainable limits and also cultivate an economic culture of transparency, on the issue of debt management and contract negotiations.

Epistatic Features and Machine Learning Improve Alzheimer's Disease Risk Prediction Over Polygenic Risk Scores.

Polygenic risk scores (PRS) are linear combinations of genetic markers weighted by effect size that are commonly used to predict disease risk. For complex heritable diseases such as late-onset Alzheimer's disease (LOAD), PRS models fail to capture much of the heritability. Additionally, PRS models are highly dependent on the population structure of the data on which effect sizes are assessed and have poor generalizability to new data. The goal of this study is to construct a paragenic risk score that, in addition to single genetic marker data used in PRS, incorporates epistatic interaction features and machine learning methods to predict risk for LOAD. We construct a new state-of-the-art genetic model for risk of Alzheimer's disease. Our approach innovates over PRS models in two ways: First, by directly incorporating epistatic interactions between SNP loci using an evolutionary algorithm guided by shared pathway information; and second, by estimating risk via an ensemble of non-linear machine learning models rather than a single linear model. We compare the paragenic model to several PRS models from the literature trained on the same dataset. The paragenic model is significantly more accurate than the PRS models under 10-fold cross-validation, obtaining an AUC of 83% and near-clinically significant matched sensitivity/specificity of 75%. It remains significantly more accurate when evaluated on an independent holdout dataset and maintains accuracy within APOE genotype strata. Paragenic models show potential for improving disease risk prediction for complex heritable diseases such as LOAD over PRS models.

On the direct quantization of Maxwell field

In this paper, we apply the generalized integration constants (GCI) method (Belhadi 2023 https://arxiv.org/abs/2303.08236), in field theory to quantize Maxwell and the Klein–Gordon free fields. The study is performed in both position and momentum spaces, to obtain the equal-time Dirac brackets among the fields and their conjugate momenta. The idea is to compute the brackets near the initial instant using the Taylor polynomial expansion, and then deduce directly their expressions at any later time. In the case of the Maxwell field, the interdependence of the field components (constraints) requires the use of the Helmholtz theorem to separate the transversal and longitudinal parts. Our work finishes with the study of the O(3) nonlinear sigma model using the GCI approach.

Laboratory simulation to study the nonlinear evolution of right-hand circularly polarised wave in laser-produced plasmas

To simulate the astrophysical scenarios at the scale of laboratory astrophysics, the interaction of high-power lasers with plasmas is increasingly being used. So, in this perspective, a nonlinear wave-wave interaction between right-hand circularly polarised wave (R-mode wave) and electron plasma wave (EPW) is proposed to understand the localization of the pump R-mode wave and associated magnetic turbulence at electron scale in magnetized plasma relevant to laboratory astrophysics. The ponderomotive force and relativistic variation of electron mass are accountable for this nonlinear wave-wave interaction model. For this nonlinear dynamics, coupled model equations for EPW and R-mode wave are developed and solved by laboratory simulations utilizing finite difference and pseudo-spectral methods. The observed simulation findings, like the nonlinear evolution of the pump wave, typical scale size of the formed localized structures, and electron scale turbulent spectra associated with the coherent structures resemble various laboratory and space plasma scenarios. A semi-analytical model in the paraxial limits is also developed to understand the physics behind the localization process of the pump wave inside the plasma medium.

Short-Term Schedule Optimization with Nonlinear Blending Models for Improved Metallurgical Recovery in Mining

Short-Term Schedule Optimization with Nonlinear Blending Models for Improved Metallurgical Recovery in Mining

Higher-order asymptotic refinements in a multivariate regression model with general parameterization

This paper derives a general Bartlett correction formula to improve the inference based on the likelihood ratio test in a multivariate model under a quite general parameterization, where the mean vector and the variance-covariance matrix can share the same vector of parameters. This approach includes a number of models as special cases such as non-linear regression models, errors-in-variables models, mixed-effects models with non-linear fixed effects, and mixtures of the previous models. We also employ the Skovgaard adjustment to the likelihood ratio statistic in this class of multivariate models and derive a general expression of the correction factor based on Skovgaard approach. Monte Carlo simulation experiments are carried out to verify the performance of the improved tests, and the numerical results confirm that the modified tests are more reliable than the usual likelihood ratio test. Applications to real data are also presented for illustrative purposes.

Semi-physiological Pharmacokinetic Model of Clozapine and Norclozapine in Healthy, Non-smoking Volunteers: The Impact of Race and Genetics.

Healthy volunteers were recruited in a population pharmacokinetic study. Blood samples were collected at 30 min and 1, 2, 3, 5 and 8 h following a single flat dose of clozapine (12.5 mg). The clozapine and norclozapine concentrations were measured via high-performance liquid chromatography-ultraviolet method. A semi-physiological pharmacokinetic model of clozapine and norclozapine was developed using nonlinear mixed-effects modeling. Clinical and genetic predictors were evaluated, including CYP1A2 (rs762551) and ABCB1 (rs2032582), using restriction fragment length polymorphism. A total of 270 samples were collected from 33 participants. The data were best described using a two-compartment model for clozapine and a two-compartment model for norclozapine with first-order absorption and elimination and pre-systemic metabolism. The estimated (relative standard error) clearance of clozapine and norclozapine were 27 L h-1 (31.5 %) and 19.6 L h-1 (30%), respectively. Clozapine clearance was lower in sub-Saharan Africans (n = 4) and higher in Caucasians (n = 9) than Asians (n = 20). Participants with CYP1A2 (rs762551) (n = 18) and ABCB1 (rs2032582) (n = 12) mutant alleles had lower clozapine clearance in the univariate analysis. This is the first study to develop a semi-physiological pharmacokinetic model of clozapine and norclozapine accounting for the pre-systemic metabolism. Asians required lower doses of clozapine as compared with Caucasians, while clozapine pharmacokinetics in sub-Saharan Africans should be further investigated in larger trials.

Using Data Science Tools to Reveal and Understand Subtle Relationships of Inhibitor Structure in Frontal Ring-Opening Metathesis Polymerization.

The rate of frontal ring-opening metathesis polymerization (FROMP) using the Grubbs generation II catalyst is impacted by both the concentration and choice of monomers and inhibitors, usually organophosphorus derivatives. Herein we report a data-science-driven workflow to evaluate how these factors impact both the rate of FROMP and how long the formulation of the mixture is stable (pot life). Using this workflow, we built a classification model using a single-node decision tree to determine how a simple phosphine structural descriptor (Vbur-near) can bin long versus short pot life. Additionally, we applied a nonlinear kernel ridge regression model to predict how the inhibitor and selection/concentration of comonomers impact the FROMP rate. The analysis provides selection criteria for material network structures that span from highly cross-linked thermosets to non-cross-linked thermoplastics as well as degradable and nondegradable materials.

Symmetry and complexity: a Lie symmetry method to bifurcation, chaos, multistability and soliton solutions of the nonlinear generalized advection-diffusion-reaction equation

This paper deals with the complexities of nonlinear dynamics within the nonlinear generalized advection-diffusion-reaction equation, which describes intricate transport phenomena involving advection, diffusion, and reaction processes occurring simultaneously. Through the utilization of the Lie symmetry approach, we thoroughly examine this proposed model, transforming the partial differential equation into an ordinary differential equation using similarity reduction techniques to facilitate a more comprehensive analysis. Exact solutions for this transformed equation are derived employing the extended simplest equation method and the new extended direct algebraic method. To enhance understanding, contour plots along with 2D and 3D visualizations of solutions are employed. Additionally, we explore bifurcation and chaotic behaviors through a qualitative analysis of the model. Phase portraits are meticulously scrutinized across various parameter values, offering insights into system behavior. The introduction of an external periodic strength allows us to utilize various tools including time series, 3D, and 2D phase patterns to discern chaotic and quasi-periodic behaviors. Furthermore, a multistability analysis is conducted to examine the impacts of diverse initial conditions. These findings underscore the efficacy and practicality of the proposed methodologies in evaluating soliton solutions and elucidating phase dynamics across a spectrum of nonlinear models, offering novel perspectives on intricate physical phenomena

Epidemic Characteristics and Meteorological Risk Factors of Hemorrhagic Fever With Renal Syndrome in 151 Cities in China From 2015 to 2021: Retrospective Analysis.

Hemorrhagic fever with renal syndrome (HFRS) continues to pose a significant public health threat to the population in China. Previous epidemiological evidence indicates that HFRS is climate sensitive and influenced by meteorological factors. However, past studies either focused on too-narrow geographical regions or investigated time periods that were too early. There is an urgent need for a comprehensive analysis to interpret the epidemiological patterns of meteorological factors affecting the incidence of HFRS across diverse climate zones. In this study, we aimed to describe the overall epidemic characteristics of HFRS and explore the linkage between monthly HFRS cases and meteorological factors at different climate levels in China. The reported HFRS cases and meteorological data were collected from 151 cities in China during the period from 2015 to 2021. We conducted a 3-stage analysis, adopting a distributed lag nonlinear model and a generalized additive model to estimate the interactions and marginal effects of meteorological factors on HFRS. This study included a total of 63,180 cases of HFRS; the epidemic trends showed seasonal fluctuations, with patterns varying across different climate zones. Temperature had the greatest impact on the incidence of HFRS, with the maximum hysteresis effects being at 1 month (-19 ºC; relative risk [RR] 1.64, 95% CI 1.24-2.15) in the midtemperate zone, 0 months (28 ºC; RR 3.15, 95% CI 2.13-4.65) in the warm-temperate zone, and 0 months (4 ºC; RR 1.72, 95% CI 1.31-2.25) in the subtropical zone. Interactions were discovered between the average temperature, relative humidity, and precipitation in different temperature zones. Moreover, the influence of precipitation and relative humidity on the incidence of HFRS had different characteristics under different temperature layers. The hysteresis effect of meteorological factors did not end after an epidemic season, but gradually weakened in the following 1 or 2 seasons. Weather variability, especially low temperature, plays an important role in epidemics of HFRS in China. A long hysteresis effect indicates the necessity of continuous intervention following an HFRS epidemic. This finding can help public health departments guide the prevention and control of HFRS and develop strategies to cope with the impacts of climate change in specific regions.

Effective Nonlinear Predictive and CTC-PID Control of Rigid Manipulators

Effective nonlinear control of manipulators with dynamically coupled arms, like those with direct drives, is the subject of the paper. The main proposal of the paper are model-based predictive control (MPC) algorithms, with nonlinear state-space models and most recent disturbance attenuation technique. This technique makes controller design and calculations simpler, avoiding necessity of dynamic modeling of disturbances or resorting to additional techniques like SMC. The core of the paper are computationally effective MPC-NPL (Nonlinear Prediction and Linearization) algorithms, where computations at every sample are divided into two parts: prediction of initial trajectories using nonlinear model, then optimization using simplified linearized model. For a comparison a known CTC-PID algorithm, which is also model-based, is considered. It is applied in standard form and also proposed in more advanced CTC-PID2dof version. For all algorithms a comprehensive comparative simulation study is performed, for a direct drive manipulator under disturbances. Additional contribution of the paper is an investigation of influence of sampling period length and computational delay time on performance of the algorithms, which is practically important when using model-based algorithms and fast sampling.

On the analytical soliton approximations to fractional forced Korteweg-de Vries equation arising in fluids and Plasmas using two novel techniques

Abstract The current investigation examines the fractional forced Korteweg-de Vries (FF-KdV) equation, a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method (YHPM) and the Yang transform decomposition method (YTDM), along with the Caputo operator, for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.

The Added Value of Statistical Seasonal Forecasts

Seasonal climate predictions can assist with timely preparations for extreme episodes, such as dry or wet periods that have associated additional risks of droughts, fires and challenges for water management. Timely warnings for extreme warm summers or cold winters can aid in preparing for increased energy demand. We analyse seasonal forecasts produced by three different methods: (1) a multi-linear statistical forecasting system based on observations only; (2) a non-linear random forest model based on observations only; and (3) process-based dynamical forecast models. The statistical model is an empirical system based on multiple linear regression that is extended to include the trend over the previous 3 months in the predictors, and overfitting is further reduced by using an intermediate multiple linear regression model. This results in a significantly improved El Niño forecast skill, specifically in spring. Also, the Indian Ocean dipole (IOD) index forecast skill shows improvements, specifically in the summer and autumn months. A hybrid multi-model ensemble is constructed by combining the three forecasting methods. The different methods are used to produce seasonal forecasts (three-month means) for near-surface air temperature and monthly accumulated precipitation seasonal forecast with a lead time of one month. We find numerous regions with added value compared with multi-model ensembles based on dynamical models only. For instance, for June, July and August temperatures, added value is observed in extensive parts of both Northern and Southern America, as well as Europe.

Efficient nanoscale characterization of wafer surfaces using intelligent sampling and Bayesian optimization

The geometrical attributes of a wafer, such as thickness, uniformity, and local curvature, serve as eminent determinants of its quality. Therefore, measurements that are both rapid and accurate are paramount as multi-stage fabrication processes hinge on them to ensure high product reliability, proper process control, and maximum efficiency. The manual wafer profiling measurement approach in use today is, unfortunately, a time-consuming process. This creates a need for fast and prompt analysis of wafer attributes. This research thus proposes an iterative sampling method that boasts reducing the number of samplings down to a minimum without the need to discard a sufficient level of accuracy for the purpose of reliable attribute estimation. Subsequently, we suggest a series of methods to improve the monitoring and evaluation of the surface topography, all within the context of ultra-precision/nanoscale manufacturing processes, such as ultra-precision machining (UPM) and chemical–mechanical planarization (CMP). For the purpose of both real-time and exception-based detection of anomalies in the UPM process, we constructed a process-machine interaction (PMI) model with Bayesian learning, which amalgamates the received data across heterogeneous sensors such as force, vibration, and acoustic emission in situ. Similarly, the CMP process is quantitatively characterized by a multi-scaled multilayer nonlinear decomposition model with predictive capabilities. This model helps understand the physio-mechanical phenomena underlying both CMP and the UPM processes and describe and predict the nonlinear interactions, as evidenced by the experimentally collected vibration signal patterns.

Efficiently localizing system anomalies for cloud infrastructures: a novel Dynamic Graph Transformer based Parallel Framework

Cloud environment is a virtual, online, and distributed computing environment that provides users with large-scale services. And cloud monitoring plays an integral role in protecting infrastructures in the cloud environment. Cloud monitoring systems need to closely monitor various KPIs of cloud resources, to accurately detect anomalies. However, due to the complexity and highly dynamic nature of the cloud environment, anomaly detection for these KPIs with various patterns and data quality is a huge challenge, especially those massive unlabeled data. Besides, it’s also difficult to improve the accuracy of the existing anomaly detection methods. To solve these problems, we propose a novel Dynamic Graph Transformer based Parallel Framework (DGT-PF) for efficiently detect system anomalies in cloud infrastructures, which utilizes Transformer with anomaly attention mechanism and Graph Neural Network (GNN) to learn the spatio-temporal features of KPIs to improve the accuracy and timeliness of model anomaly detection. Specifically, we propose an effective dynamic relationship embedding strategy to dynamically learn spatio-temporal features and adaptively generate adjacency matrices, and soft cluster each GNN layer through Diffpooling module. In addition, we also use nonlinear neural network model and AR-MLP model in parallel to obtain better detection accuracy and improve detection performance. The experiment shows that the DGT-PF framework have achieved the highest F1-Score on 5 public datasets, with an average improvement of 21.6% compared to 11 anomaly detection models.

Behavior of steel fiber-reinforced coal gangue concrete beams under impact load

In order to promote the use of new sustainable steel fibers (SF) reinforced coal gangue aggregates (CGA) concrete, impact tests were performed in this paper. The impact resistance of steel fiber-reinforced coal gangue concrete was investigated using a self-developed drop-weight facility. The test variables were the CGA replacement rate (0 %, 50 %, and 100 %), the SF volume content (0 %, 0.75 %, and 1.5 %), and the drop height of the drop-weight (0.5 m and 1.0 m). Using 15 kg of hard steel as a drop-weight, the drop-weight impact test was performed on steel fiber-reinforced coal gangue concrete beams with a span of 300 mm; the damage pattern, impact reaction force-time, displacement-time relationships, and energy absorbed by steel fiber-reinforced coal gangue concrete beams were studied. The test shows that, compared with natural aggregate, CGA reduces concrete's static mechanical properties and impact resistance, and adding SF improves the static mechanical properties and impact resistance of coal gangue concrete. As the CGA replacement rate increased from 0 % to 50 % and 100 %, the reaction force of impact of the specimens decreased by 2.54 %− 6.06 % and 3.69 %− 12.33 %. The SF volume content was increased from 0 % to 0.75 % and 1.5 %, and the reaction force of impact of the specimens was increased by 23.05 %− 32.34 % and 72.27 %− 81.84 %, respectively. The impact resistance of steel fiber-reinforced concrete beams under impact loading was investigated numerically using a nonlinear explicit finite element model in LS-DYNA. The Finite Element results were validated with experimental results. Based on the validated finite element model, a parametric study was carried out to investigate the effects of coal gangue replacement rate, steel fiber volume content, and drop height of the drop weight on the behavior of the beams. This study might provide a basis for the future engineering project applications of steel fiber-reinforced coal gangue concrete under impact conditions.

Thinking Inside the Bounds: Improved Error Distributions for Indifference Point Data Analysis and Simulation Via Beta Regression using Common Discounting Functions

AbstractStandard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable distribution-based framework for indifference points, which limits its ability to adequately describe the inherent variability in the data. Software commonly assumes data follow a normal distribution with constant variance. However, typical indifference points do not follow a normal distribution or exhibit constant variance. To address these limitations, this paper introduces a class of nonlinear beta regression models that offers excellent fit to discounting data and enhances simulation-based approaches. This beta regression model can accommodate popular discounting functions. This work proposes three specific advances. First, our model automatically captures non-constant variance as a function of delay. Second, our model improves simulation-based approaches since it obeys the natural boundaries of observable data, unlike the ordinary assumption of normal residuals and constant variance. Finally, we introduce a scale-location-truncation trick that allows beta regression to accommodate observed values of 0 and 1. A comparison between beta regression and standard nonlinear regression reveals close agreement in the estimated discounting rate k obtained from both methods.

Partial reformulation-linearization based optimization models for the Golomb ruler problem

In this paper, we provide a straightforward proof of a conjecture proposed in \cite{Duxbury2021} regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in \cite{Kocuk2019}, utilizing the reformulation-linearization technique. \modif{Finally, we provide the correct outputs of the greedy heuristic proposed in \cite{Duxbury2021} and correct some false conclusions stated or implied therein.}

Multi-objective location-routing model and algorithm study of material reserve bases for large-scale railway engineering construction projects

Material supply is an important support for engineering construction and an important factor affecting the progress and quality of engineering construction. A multi-objective mixed-integer nonlinear programming model is proposed for the location routing problem of the material reserve base of large-scale railway engineering construction projects, considering realistic factors like the construction period, the cycle of the material reserve, the variety of materials, the heterogeneous fleet, and demand splitting. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA- II) is developed for solving this model. This paper optimises obtaining the initial population based on the linear feature of railway engineering, improves the fitness function, and designs a two-stage crossover operator. In addition, the algorithm is compared with the augmented ϵ-constraint method with the help of a practical example. Three metrics are used to assess the performance of the algorithm's outputs, and two metrics are used to assess the similarity of the Pareto fronts obtained by the two algorithms. The results show that the proposed algorithm performs better in terms of ‘quantity’ and ‘spacing’, that the Pareto solutions obtained are accurate, and that the speed of solution is almost 10 times that of the augmented ϵ-constraint (AUGMECON) method.

Parametric study on the flexural behavior of steel fiber reinforced concrete beams utilizing nonlinear finite element analysis

Reinforced concrete beams undergo significant internal forces and deformations under extensive loading and have flexural or shear failure based on the reinforcement detailing and geometric properties. The addition of steel fibers increases the deformation and load carrying capacities that leads to ductile behavior. The main contribution of fibers is the improvement of the composite tensile capacity, which results in improved flexural and shear responses. This study numerically investigates the effect of fiber properties on the flexural behavior of steel fiber reinforced concrete (SFRC) beams for both compression and tension failure. First, three specimens from prior experimental studies are modeled using the nonlinear finite element program ABAQUS and the analytical results are verified by comparison with the test results. Contrary to prior nonlinear models, the developed model accurately predicts the damage pattern, descending portion of the load-displacement relationship, and ultimate displacement, which lead to a reliable estimation of energy dissipation capacity and ductility. A comprehensive parametric study is then conducted to examine the effect of tension reinforcement ratio, fiber volume fraction, and fiber aspect ratio on the flexural behavior of both reinforced concrete and SFRC beams. The influence of these key parameters is investigated by comparing the peak load, displacement ductility, peak stiffness, service stiffness, energy dissipation capacity, and damage pattern for both reinforced concrete and SFRC beams. The analytical results indicate that the addition of steel fibers up to 2.0 % leads to a slight increase in the load carrying capacity, while the displacement ductility and energy dissipation capacity are significantly improved. Furthermore, the utilization of 1.0 % steel fibers is observed to be sufficient to modify the failure mode of over reinforced concrete beams from brittle compression failure to tension failure.