Nonlinear Functional Form Research Articles

Linear redshift parametrization of deceleration parameter in [formula omitted] gravity

In this study, we investigate the linear redshift parametrization of q(z) within the framework of f(R,Lm) gravity, using constraints derived from H(z)/Pantheon samples. We consider a non-linear functional form for f(R,Lm), specifically given by f(R,Lm)=R2+Lmn, where n represents a free parameter in the model. Subsequently, we derive the solution for the Hubble parameter by investigating the parametrization of q(z) and then apply this solution to the modified Friedmann equations. Our analysis focuses on exploring the behavior of the EoS parameter across different stages of the universe’s evolution, including radiation, matter, and dark energy eras. Furthermore, our results confirm the quintessence nature of the universe’s current accelerated expansion phase (−1<ω<−13), supporting the role of quintessence in driving the universe’s current acceleration. We also explore the redshift dependence of the deceleration parameter, statefinder, Om(z) diagnostics, energy density, pressure, and energy conditions to determine the universe’s accelerating behavior. Importantly, our findings suggest that the linear redshift parametrization of q(z), supported by additional terms in f(R,Lm) gravity, provides a compelling alternative to the cosmological constant.

Properties of new even and odd nonlinear coherent states with different parameters

We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function [Formula: see text], Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations.

A novel nonlinear spectrum estimation method and its application in on-line condition assessment of bearing-rotor system

In this paper, a novel approach for nonlinear spectrum estimation is proposed and combined with Support Vector Machine (SVM) classifier to assess the condition of bearing-rotor systems, including fault types and severity. The proposed approach involves extraction and reconstruction of target harmonics, dynamic process modeling of the reconstructed signal based on a data-driven method, and extraction of nonlinear spectrum features in the form of nonlinear output frequency response functions (NOFRFs). The focus is on the influence of model stability and accuracy evaluation on the robustness of NOFRFs. Then the robustness of the NOFRFs based on the proposed estimation approach is compared with the conventional estimation approach using simulation cases and experiments. SVM is used to classify the extracted nonlinear spectrum features. Finally, the classification accuracy of NOFRFs evaluated by the proposed approach is compared with time-domain and frequency-domain features. Neighborhood Component Analysis (NCA) is used to select sensitive features and improve classification accuracy. The proposed condition assessment strategy does not require the selection of sensitive features, ensuring the stability of assessment results, which is also a significant advantage of the proposed strategy.

Optimizing automated feeder algorithms for feed intake prediction in barramundi (Lates calcarifer)

Efficient aquaculture management requires optimizing feed intake to balance fish productivity and environmental waste. Automated feeders with daily feed intake (DFI) prediction capabilities are a popular tool for achieving this balance. The aim of this study was to optimize DFI prediction using various learning algorithms and nonlinear functional forms, while also assessing the utility of adaptive algorithms for the development of automated feeders. We selected 11 commercial feeds that represent common farm uses for barramundi (Lates calcarifer) in Southeast Asia and conducted three 8-week trials feeding 1872 juveniles to satiation. We collected 30 variables, including environmental factors (E), fish characteristics (F), feed chemical composition (C), and pellet physical characteristics (P). We compared three statistical methodologies: stepwise regression (SWR), Bayesian model averaging (BMA), and multiple factorial polynomial (MFP). The selection of commercial feed had a significant impact on fish growth, feed conversion ratio, total feed intake and nutrient retentions (P < 0.001). All three methodologies consistently identified the same 10 variables as significant (P < 0.05) for accurately describing DFI, yielding high accuracy levels (R2 = 0.85–0.88). Three variables, namely fish length, fish batch, and water temperature, accounted for the vast majority (77%) of the DFI variance. Beyond feed chemical composition, the preference for sinking pellets and the regular increase in pellet size emerged as the predominant factors enhancing DFI. SWR modelling was robust, but MFP model demonstrated the highest accuracy (R2 = 0.88), indicating that nonlinear functional relationships between variables was beneficial. BMA showed that a multimodel approach was effective in developing adaptive DFI prediction, with the most accurate models incorporating at least one variable from each category (E, F, C, P). This study proposes an optimization of DFI prediction for automated feeders, which can reduce the risk of overfeeding in barramundi farms. The use of adaptive algorithms was shown to facilitate the prioritization of sensor integration, lower development costs, and enable technology level adjustments from low-tech to high-tech. These findings provide valuable insights for the development of highly efficient and cost-effective feeding systems that align more effectively with the diverse demands of the aquaculture industry.

Effect of temperature-dependent internal heat generation over exponential and dovetail convective-radiative porous fin wetted in hybrid nanofluid

The main objective of this research is to conduct a comparative study of the thermal variations in a dovetail and exponential fin, considering fully wet conditions, ternary nanofluid, and internal heat generation in the form of both linear and non-linear functions. Additionally, the influence of a magnetic field as a driving force for heat transfer systems is taken into account. The mathematical modelling involves the use of dimensionless transformations to convert the energy equation into an ordinary differential equation, which is then analytically solved using the Differential transformation method (DTM). The study focuses on exploring the effects of significant thermal parameters such as radiation conduction, wet factor, heat generation, and ambient temperature on the temperature profile. Graphical analysis is employed to investigate the thermal performance. The main findings indicate that ternary nanoliquid exhibits a higher thermal response compared to nano and hybrid nanoliquid. Moreover, the nonlinear forms of internal heat generation and ternary nanofluids demonstrate a higher rate of heat transfer.

Sensitivity of the Ramsey’s Regression Specification Error Term Test on the Degree of Nonlinearity of the Functional Form

The present paper aims to demonstrate that the Ramsey’s Regression Specification Error Term Test (RESET) is very sensitive to the degree of nonlinearity between the variables of the under-specification functional form. This widely used test, for testing the functional specification of a model, is based on the notion that if nonlinear combinations of the explanatory variables have any power in explaining the predictor, the model is mis-specified and the data generating mechanism might be approximated by a nonlinear functional form. Using Monte Carlo techniques, we find that the power of the Ramsey’s RESET test is highly influenced and related with the degree of nonlinearity between the dependent and the independent variables of the under-specification functional form.

Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates

BackgroundConfounding is a common issue in epidemiological research. Commonly used confounder-adjustment methods include multivariable regression analysis and propensity score methods. Although it is common practice to assess the linearity assumption for the exposure-outcome effect, most researchers do not assess linearity of the relationship between the confounder and the exposure and between the confounder and the outcome before adjusting for the confounder in the analysis. Failing to take the true non-linear functional form of the confounder-exposure and confounder-outcome associations into account may result in an under- or overestimation of the true exposure effect. Therefore, this paper aims to demonstrate the importance of assessing the linearity assumption for confounder-exposure and confounder-outcome associations and the importance of correctly specifying these associations when the linearity assumption is violated.MethodsA Monte Carlo simulation study was used to assess and compare the performance of confounder-adjustment methods when the functional form of the confounder-exposure and confounder-outcome associations were misspecified (i.e., linearity was wrongly assumed) and correctly specified (i.e., linearity was rightly assumed) under multiple sample sizes. An empirical data example was used to illustrate that the misspecification of confounder-exposure and confounder-outcome associations leads to bias.ResultsThe simulation study illustrated that the exposure effect estimate will be biased when for propensity score (PS) methods the confounder-exposure association is misspecified. For methods in which the outcome is regressed on the confounder or the PS, the exposure effect estimate will be biased if the confounder-outcome association is misspecified. In the empirical data example, correct specification of the confounder-exposure and confounder-outcome associations resulted in smaller exposure effect estimates.ConclusionWhen attempting to remove bias by adjusting for confounding, misspecification of the confounder-exposure and confounder-outcome associations might actually introduce bias. It is therefore important that researchers not only assess the linearity of the exposure-outcome effect, but also of the confounder-exposure or confounder-outcome associations depending on the confounder-adjustment method used.

Synthesis of multi-mode electric-mechanical variable transmission based on 4-DOF planetary gear mechanisms

Synthesis of multi-mode electric-mechanical variable transmission (EVT) mainly involves two contents: the topology of planetary gear mechanism (PGM) and the determination of their characteristic parameters. This article deals with the computationally intensive problems caused by numerous potential schemes and proposes an automatic and systematic design process for multi-mode EVTs based on 3-row PGM. First, all the non-isomorphic 4-degree-of-freedom (4-DOF) topologies are enumerated by combining the modified digraph model with the determinants of their adjacency matrices. Second, the rules with guiding significance for configuring shift elements and motor/generators (M/Gs) are summarized to eliminate all infeasible configurations. And all the mechanical points (MPs) that come from the kinematic equations play an important role in the selection of new schemes. Third, the method of Monte Carlo simulation handles the problem of solving many different forms of multivariate nonlinear functions to sort the rational mode sequences. Finally, the characteristic parameters of each planetary gear set are optimized by NSGA-II. The feasibility of the method is verified by synthesizing six novelty 3-mode EVTs and it is also applicable to similar problems.

Ridge Regression for Functional Form Identification of Continuous Predictors of Clinical Outcomes in Glomerular Disease

Introduction: Penalized regression models can be used to identify and rank risk factors for poor quality of life or other outcomes. They often assume linear covariate associations, but the true associations may be nonlinear. There is no standard, automated method for determining optimal functional forms (shapes of relationships) between predictors and the outcome in high-dimensional data settings. Methods: We propose a novel algorithm, ridge regression for functional form identification of continuous predictors (RIPR) that models each continuous covariate with linear, quadratic, quartile, and cubic spline basis components in a ridge regression model to capture potential nonlinear relationships between continuous predictors and outcomes. We used a simulation study to test the performance of RIPR compared to standard and spline ridge regression models. Then, we applied RIPR to identify top predictors of Patient-Reported Outcomes Measurement Information System (PROMIS) adult global mental and physical health scores using demographic and clinical characteristics among N = 107 glomerular disease patients enrolled in the Nephrotic Syndrome Study Network (NEPTUNE). Results: RIPR resulted in better predictive accuracy than the standard and spline ridge regression methods in 56–80% of simulation repetitions under a variety of data characteristics. When applied to PROMIS scores in NEPTUNE, RIPR resulted in the lowest error for predicting physical scores, and the second-lowest error for mental scores. Further, RIPR identified hemoglobin quartiles as an important predictor of physical health that was missed by the other models. Conclusion: The RIPR algorithm can capture nonlinear functional forms of predictors that are missed by standard ridge regression models. The top predictors of PROMIS scores vary greatly across methods. RIPR should be considered alongside other machine learning models in the prediction of patient-reported outcomes and other continuous outcomes.

Inspecting the stability of non-linear IS-LM model with dual time delay

Capital stock is a strong pillar in the macroeconomics paradigm and plays a significant role when dealing with macroeconomic problems. Also, implementation of the investment decisions and employment of capital into productive use are two ignored time delays in accumulation of capital. Hence, a mathematical model with dual time delays in capital accumulation is formulated in this work. Furthermore, by adhering to functions that do not follow regularity, i.e., considering non-linear functional forms will not only influence policy making but also broaden our viewpoint towards realistic scenarios. Therefore, non-linear functional forms for investment, liquidity preference and government expenditure are considered. First, the equilibrium point is established, which is unique in this case. For analysing stability around the equilibrium point, the work is divided into three delay-dependent cases. When the time delay reaches a critical value, the complex dynamics of the system, such as stability switches and Hopf bifurcation, are investigated. The system is sensitive to a few parameters, such as depreciation rate, propensity to invest in capital stock, and average tax rate. The behavioural change is observed by altering these parameters. This study establishes a time limit within which the available capital for production should be put to productive use, and investment decisions should be made, which will aid in effective policymaking.

Assessing mediational processes using piecewise linear growth curve models with individual measurement occasions.

Longitudinal processes often unfold concurrently where the growth patterns of two or more longitudinal outcomes are associated. Additionally, if the study under investigation is long, the growth curves may exhibit nonconstant change with respect to time. Multiple existing studies have developed multivariate growth models with nonlinear functional forms to explore joint development where two longitudinal records are correlated over time. However, the relationship between multiple longitudinal outcomes may also be unidirectional. Accordingly, it is of interest to estimate regression coefficients of such unidirectional paths. One statistical tool for such analyses is longitudinal mediation models. In this study, we develop two models to evaluate mediational processes where the linear-linear piecewise functional form is utilized to capture the change patterns. We define the mediational process as either the baseline covariate or the change in covariate influencing the change in the mediator, which, in turn, affects the change in the outcome. We present the proposed models through simulation studies and real-world data analyses. Our simulation studies demonstrate that the proposed mediational models can provide unbiased and accurate point estimates with target coverage probabilities with a 95% confidence interval. The empirical analyses demonstrate that the proposed models can estimate covariates' direct and indirect effects on the change in the outcome. We also provide the corresponding code for the proposed models.

Supervised Regularized Multidimensional Scaling Using Weighted Stress Measure

Supervised Regularized Multidimensional Scaling (SRMDS), a non-linear variant of classical Multi-Dimensional Scaling (cMDS) is proposed recently which involves Radial basis function. The method is focused on the effective selection of centers of the radial basis functions in transforming data from a higher dimensional space to a lower dimension. The transformation matrix is determined by minimizing stress. Weights of components of the stress that are of great importance for classification of data got less focus in Supervised Regularized Multidimensional Scaling. In this article, we have investigated several forms of non-linear functions which may be used as weights of the stress measure. A new form of Z-shape weight function dependent on intraclass information of the dataset is introduced which prefers to preserve global structure of the dataset. The efficiency of the proposed approach is illustrated on several benchmarking datasets which shows that the weighted Supervised Regularized Multidimensional Scaling (WSRMDS) outperforms the base method and some other state of the art approaches such as Linear Discriminant Analysis (LDA), and Supervised Principal Component Analysis (SPCA). Observing the finding of this research, among different weight functions, Z-shape weight function is recommended to use since it works better then any other weight functions for most of the data sets.

The Impact of Functional Form Complexity on Model Overfitting for Nonlinear Mixed-Effects Models

Nonlinear mixed-effects models (NLMEMs) allow researchers to model curvilinear patterns of growth, but there is ambiguity as to what functional form the data follow. Often, researchers fit multiple nonlinear functions to data and use model selection criteria to decide which functional form fits the data “best.” Frequently used model selection criteria only account for the number of parameters in a model but overlook the complexity of intrinsically nonlinear functional forms. This can lead to overfitting and hinder the generalizability and reproducibility of results. The primary goal of this study was to evaluate the performance of eight model selection criteria via a Monte Carlo simulation study and assess under what conditions these criteria are sensitive to model overfitting as it relates to functional form complexity. Results highlighted criteria with the potential to capture overfitting for intrinsically nonlinear functional forms for NLMEMs. Information criteria and the stochastic information complexity criterion recovered the true model more often than the average or conditional concordance correlation. Results also suggest that the amount of residual variance and sample size have an impact on model selection for NLMEMs. Implications for future research and recommendations for application are also provided.

Development of urban freight trip generation models concerning establishment classification process for a developing country

The objective of this study is to develop the Freight Trip Generation (FTG) models concerning establishment classification process for estimating freight trip activity. Establishment Based Freight Survey (EBFS) was performed to collect various supply chain variables involved in the urban freight system. Extensive data of 647 samples were collected from Tiruchirappalli city, India. Economic activity analysis shows that pure receiver and intermediate establishments do not follow the uniform freight trip activity among the industrial segments. Hence, a suitable methodology for the establishment classification process is developed using traditional and machine learning (ML) techniques to classify the establishment into an intermediate and pure receiver before estimating the freight trip activity. Supply chain variables like employment, FTA, industrial segment, mode of the commercial vehicle, type of delivery, number of suppliers, and gross floor area play a crucial role in the establishment classification process. Then, employment-based FTG models are developed with the classified data using linear and non-linear functional forms for each industrial segment. Finally, it is observed that FTG models result enhanced, when the establishment classification process is performed as an initial stage, with lower error and accurate estimation of urban freight trip activity.

The individual private cost of problematic alcohol use: a compensating income variation approach

ABSTRACT While the social cost of problematic alcohol use has been examined, limited information exists on the private cost incurred by consumers. Using Icelandic panel data and the compensating income variation (CIV) method we estimate this individual private cost. We examine results using different measures of problematic alcohol use, two non-linear functional forms for income, and two utility proxies. We estimate the yearly individual cost, or CIV, to be 4–62 thousand USD. These estimates are considerably higher if not adjusted for income endogeneity. Results suggest that the CIV method is highly sensitive to model specifications in two areas: (i) The modelling of income; log-transformation contrasted with a piecewise-linear form shows that high-income groups affect full sample CIVs substantially, highlighting differences between mean and median value-estimates. This raises ethical questions on the trade-off between utilitarian policies based on means and largely driven by high-income groups, versus policies guided by median values that benefit most individuals. (ii) The choice of utility proxy; the CIV using happiness is substantially higher than that obtained using life satisfaction. This highlights the need for policy makers to consider whether their objectives should focus on cognitive measures of subjective well-being or affective measures.

Are there non-linear relationships between alcohol consumption and long-term health?: a systematic review of observational studies employing approaches to improve causal inference

BackgroundResearch has long found ‘J-shaped’ relationships between alcohol consumption and certain health outcomes, indicating a protective effect of moderate consumption. However, methodological limitations in most studies hinder causal inference. This review aimed to identify all observational studies employing improved approaches to mitigate confounding in characterizing alcohol–long-term health relationships, and to qualitatively synthesize their findings.MethodsEligible studies met the above description, were longitudinal (with pre-defined exceptions), discretized alcohol consumption, and were conducted with human populations. MEDLINE, PsycINFO, Embase and SCOPUS were searched in May 2020, yielding 16 published manuscripts reporting on cancer, diabetes, dementia, mental health, cardiovascular health, mortality, HIV seroconversion, and musculoskeletal health. Risk of bias of cohort studies was evaluated using the Newcastle-Ottawa Scale, and a recently developed tool was used for Mendelian Randomization studies.ResultsA variety of functional forms were found, including reverse J/J-shaped relationships for prostate cancer and related mortality, dementia risk, mental health, and certain lipids. However, most outcomes were only evaluated by a single study, and few studies provided information on the role of alcohol consumption pattern.ConclusionsMore research employing enhanced causal inference methods is urgently required to accurately characterize alcohol–long-term health relationships. Those studies that have been conducted find a variety of linear and non-linear functional forms, with results tending to be discrepant even within specific health outcomes.Trial registrationPROSPERO registration number CRD42020185861.

The dynamics of early-stage transmission of COVID-19: A novel quantification of the role of global temperature

The global outbreak of COVID-19 has emerged as one of the most devastating and challenging threats to humanity. As many frontline workers are fighting against this disease, researchers are struggling to obtain a better understanding of the pathways and challenges of this pandemic. This paper evaluates the concept that the transmission of COVID-19 is intrinsically linked to temperature. Some complex nonlinear functional forms, such as the cubic function, are introduced to the empirical models to understand the interaction between temperature and the “growth” in the number of infected cases. An accurate quantitative interaction between temperature and the confirmed COVID-19 cases is obtained as log(Y) = -0.000146(temp_H)3 + 0.007410(temp_H)2 –0.063332 temp_H + 7.793842, where Y is the periodic growth in confirmed COVID-19 cases, and temp_H is the maximum daily temperature. This equation alone may be the first confirmed way to measure the quantitative interaction between temperature and human transmission of COVID-19. In addition, four important regions are identified in terms of maximum daily temperature (in Celsius) to understand the dynamics in the transmission of COVID-19 related to temperature. First, the transmission decreases within the range of −50 °C to 5.02 °C. Second, the transmission accelerates in the range of 5.02 °C to 16.92 °C. Essentially, this is the temperature range for an outbreak. Third, the transmission increases more slowly in the range of 16.92 °C to 28.82 °C. Within this range, the number of infections continues to grow, but at a slower pace. Finally, the transmission decreases in the range of 28.82 °C to 50 °C. Thus, according to this hypothesis, the threshold of 16.92 °C is the most critical, as the point at which the infection rate is the greatest. This result sheds light on the mechanism in the cyclicity of the ongoing COVID-19 pandemic worldwide. The implications of these results on policy issues are also discussed concerning a possible cyclical fluctuation pattern between the Northern and Southern Hemispheres.

Some Real-Life Applications of a Newly Designed Algorithm for Nonlinear Equations and Its Dynamics via Computer Tools

In this article, we design a novel fourth-order and derivative free root-finding algorithm. We construct this algorithm by applying the finite difference scheme on the well-known Ostrowski’s method. The convergence analysis shows that the newly designed algorithm possesses fourth-order convergence. To demonstrate the applicability of the designed algorithm, we consider five real-life engineering problems in the form of nonlinear scalar functions and then solve them via computer tools. The numerical results show that the new algorithm outperforms the other fourth-order comparable algorithms in the literature in terms of performance, applicability, and efficiency. Finally, we present the dynamics of the designed algorithm via computer tools by examining certain complex polynomials that depict the convergence and other graphical features of the designed algorithm.

Neural‐network transformation models for counting processes

AbstractWhile many survival models have been invented, the Cox model and the proportional odds model are among the most popular ones. Both models are special cases of the linear transformation model. The linear transformation model typically assumes a linear function on covariates, which may not reflect the complex relationship between covariates and survival outcomes. Nonlinear functional form can also be specified in the linear transformation model. Nonetheless, the underlying functional form is unknown and mis‐specifying it leads to biased estimates and reduced prediction accuracy of the model. To address this issue, we develop a neural‐network transformation model. Similar to neural networks, the neural‐network transformation model uses its hierarchical structure to learn complex features from simpler ones and is capable of approximating the underlying functional form of covariates. It also inherits advantages from the linear transformation model, making it applicable to both time‐to‐event analyses and recurrent event analyses. Simulations demonstrate that the neural‐network transformation model outperforms the linear transformation model in terms of estimation and prediction accuracy when the covariate effects are nonlinear. The advantage of the new model over the linear transformation model is also illustrated via two real applications.

Dose‐response association between nurse staffing and patient outcomes following major cancer surgeries using a nationwide inpatient database in Japan

To examine the non-linear dose-response associations between nurse staffing levels and patient outcomes using a nationwide inpatient database in Japan. Previous studies showed that higher nurse staffing levels were associated with better patient outcomes. However, it remains unclear whether there are thresholds for the associations between higher nurse staffing levels and improved patient outcomes. Retrospective observational study design following the STROBE guideline. We identified all patients aged ≥20years who underwent one of six major cancer surgeries between July 2010 and March 2018 using data from the Diagnosis Procedure Combination database, a nationwide database for acute-care inpatients in Japan. Restricted cubic spline regression analyses, the statistical method that allows non-linear functional form, were performed with several scenarios of cut-off points to examine the dose-response associations between patient-to-nurse ratio per shift and failure to rescue, 30-day in-hospital mortality and postoperative complications. Among 645,687 patients, restricted cubic spline regression analyses showed insignificant associations of patient-to-nurse ratio with failure to rescue and 30-day in-hospital mortality with no threshold, but a reverse J-shaped association with postoperative complications with a threshold of patient-to-nurse ratio per shift of 5.4. In terms of postoperative complications, additional registered nurses were associated with decreased postoperative complications. However, this incremental benefit of additional registered nurses may disappear if hospitals allocate five to six number of registered nurses in general wards. This study suggested that additional registered nurses over one per five to six patients may not bring the incremental benefit to decrease postoperative complications.