Nonlinear Model Research Articles

Asymmetric effects of exchange rate volatility on Turkish-German commodity trade

This study investigates the asymmetric effects of exchange rate volatility on Turkish-German commodity trade using annual time-series data from 1980 to 2022. We analyze 90 industries exporting from Turkey to Germany and 114 industries importing from Germany to Turkey. The empirical results of the nonlinear ARDL model show that the volatility of the real lira-euro exchange rate had short-run asymmetric effects on trade flows for 60 (86) Turkish export (import) industries, which persisted for 46 (52) Turkish export (import) industries in the long-run. The industry-specific results show that an increase (a decrease) in lira-euro volatility increases Turkish exports (imports) to (from) Germany mostly for both small and large industries. The study suggests that export and import sectors that benefit from lira-euro volatility may consider expanding their production and trade activities, while sectors adversely affected by volatility may need to explore alternative strategies. This study highlights the importance of considering exchange rate volatility's asymmetric effects on trade between Turkey and Germany, emphasizing the varying implications across specific industries. The findings contribute valuable insights for policymakers and industry stakeholders in understanding how exchange rate fluctuations impact bilateral trade dynamics.

Bayesian fractional polynomial approach to quantile regression and variable selection with application in the analysis of blood pressure among US adults

Although the fractional polynomials (FPs) can act as a concise and accurate formula for examining smooth relationships between response and predictors, modelling conditional mean functions observes the partial view of a distribution of response variable, as distributions of many response variables such as blood pressure (BP) measures are typically skew. Conditional quantile functions with FPs provide a comprehensive relationship between the response variable and its predictors, such as median and extremely high-BP measures that may be often required in practical data analysis generally. To the best of our knowledge, this is new in the literature. Therefore, in this article, we develop and employ Bayesian variable selection with quantile-dependent prior for the FP model to propose a Bayesian variable selection with parametric non-linear quantile regression model. The objective is to examine a non-linear relationship between BP measures and their risk factors across median and upper quantile levels using data extracted from the 2007 to 2008 National Health and Nutrition Examination Survey (NHANES). The variable selection in the model analysis identified that the non-linear terms of continuous variables (body mass index, age), and categorical variables (ethnicity, gender, and marital status) were selected as important predictors in the model across all quantile levels.

Predicting anti-trypanosome effect of carbazole-derived compounds by powerful SVM with novel kernel function and comprehensive learning PSO.

In order to predict the anti-trypanosome effect of carbazole-derived compounds by quantitative structure-activity relationship, five models were established by the linear method, random forest, radial basis kernel function support vector machine, linear combination mix-kernel function support vector machine, and nonlinear combination mix-kernel function support vector machine (NLMIX-SVM). The heuristic method and optimized CatBoost were used to select two different key descriptor sets for building linear and nonlinear models, respectively. Hyperparameters in all nonlinear models were optimized by comprehensive learning particle swarm optimization with low complexity and fast convergence. Furthermore, the models' robustness and reliability underwent rigorous assessment using fivefold and leave-one-out cross-validation, y-randomization, and statistics including concordance correlation coefficient (CCC), [Formula: see text] , [Formula: see text] , and [Formula: see text] . Among all the models, the NLMIX-SVM model, which was established by support vector regression using a nonlinear combination of radial basis kernel function, sigmoid kernel function, and linear kernel function as a new kernel function, demonstrated excellent learning and generalization abilities as well as robustness: [Formula: see text] = 0.9581, mean square error (MSE) = 0.0199 for the training set and [Formula: see text] = 0.9528, MSE = 0.0174 for the test set. [Formula: see text] , [Formula: see text] , CCC, [Formula: see text] , [Formula: see text], and [Formula: see text] are 0.9539, 0.8908, 0.9752, 0.9529, 0.9528, and 0.9633, respectively. The NLMIX-SVM method proved to be a promising way in quantitative structure-activity relationship research. In addition, molecular docking experiments were conducted to analyze the properties of new derivatives, and a new potential candidate drug molecule was ultimately found. In summary, this study will provide help for the design and screening of novel anti-trypanosome drugs.

Application of growth models to South African Boer goat castrates and does under feedlot conditions

Mathematical models may aid researchers in describing biological processes, like growth, in animals. This study aimed to collect the body weight data of 18 Boer goat castrates and 20 Boer goat does, from birth until maturity, to model growth and determine growth trends. This is a novel investigation as sufficient information on an age-weight database for these two Boer goat sexes from birth to maturity, is lacking. Using age-weight data, four nonlinear models, namely the Brody, Gompertz, Logistic and Von Bertalanffy growth models, were plotted and evaluated. The model parameters of each growth model were compared for differences between the two sexes. The statistical effectiveness of fit was determined for each model using AIC and RMSE, with R2 also being considered. All models except the Brody model, predicted significantly heavier mature weights for castrates. The Brody model was deemed unfit to describe Boer goat growth as the function severely over-predict weights from birth until maturity for both sexes. The Von Bertalanffy (R2 = 91.3) and Gompertz functions (R2 = 91.3) showed the best fit for Boer goat castrates, while the Gompertz model (R2 = 95.1) showed the best fit for Boer goat does. The Gompertz function is the preferred model to depict Boer goat growth overall, as it accurately characterized growth of both sexes. According to the Gompertz model the age at which the inflection point of the growth curve was reached, did not differ significantly between castrates and does (141.80 days versus 136.31 days). There was also no significant difference in maturation rate between the two sexes.

Supply chain network design based on Big Data Analytics: heuristic-simulation method in a pharmaceutical case study

Digital technology is a pivotal aspect of the ongoing digital transformation upon which supply chain networks (SCNs) heavily rely. Through the utilization of Big Data Analytics (BDA), organizations can gain insights into sales, production and formulate decision support systems. The pharmaceutical supply chain emerges as a crucial player in producing and distributing medications vital for treating COVID-19 patients. In this study, we have innovatively designed a multi-echelon Pharmaceutical Supply Chain Network (PSCN) using BDA during the COVID-19 pandemic. We have developed a novel Mixed-Integer Non-Linear Programming model addressing allocation, production planning, and inventory control decisions, known as the LAPI problem. A transformation method is employed to convert the non-linear model into a linear one to enhance computational efficiency. The primary objective of our mathematical model is to minimize the total cost and CO2 emissions of the transportation system and established centres while maximizing the shelf life of medicines. Our experiments reveal that medium- and large-scale problems, characterized by the three main attributes of BDA – variety, velocity and volume (3 V‟s), pose challenges for optimal solutions. We present a case study of Iran to validate the mathematical model for large-scale problems. Employing a simulation approach, we estimate the demand for required pharmaceuticals, underscoring our proposed model’s real-world applicability and effectiveness. This research contributes to the growing necessity of eco-friendly and efficient supply chain strategies, especially in the critical domain of pharmaceuticals during pandemic situations.

Linear and Non-Linear Modelling Methods for a Gas Sensor Array Developed for Process Control Applications.

New process developments linked to Power to X (energy storage or energy conversion to another form of energy) require tools to perform process monitoring. The main gases involved in these types of processes are H2, CO, CH4, and CO2. Because of the non-selectivity of the sensors, a multi-sensor matrix has been built in this work based on commercial sensors having very different transduction principles, and, therefore, providing richer information. To treat the data provided by the sensor array and extract gas mixture composition (nature and concentration), linear (Multi Linear Regression-Ordinary Least Square "MLR-OLS" and Multi Linear Regression-Partial Least Square "MLR-PLS") and non-linear (Artificial Neural Network "ANN") models have been built. The MLR-OLS model was disqualified during the training phase since it did not show good results even in the training phase, which could not lead to effective predictions during the validation phase. Then, the performances of MLR-PLS and ANN were evaluated with validation data. Good concentration predictions were obtained in both cases for all the involved analytes. However, in the case of methane, better prediction performances were obtained with ANN, which is consistent with the fact that the MOX sensor's response to CH4 is logarithmic, whereas only linear sensor responses were obtained for the other analytes. Finally, prediction tests performed on one-year aged sensor platforms revealed that PLS model predictions on aged platforms mainly suffered from concentration offsets and that ANN predictions mainly suffered from a drop of sensitivity.

Physically based vs. data-driven models for streamflow and reservoir volume prediction at a data-scarce semi-arid basin.

Physically based or data-driven models can be used for understanding basinwide hydrological processes and creating predictions for future conditions. Physically based models use physical laws and principles to represent hydrological processes. In contrast, data-driven models focus on input-output relationships. Although both approaches have found applications in hydrology, studies that compare these approaches are still limited for data-scarce, semi-arid basins with altered hydrological regimes. This study aims to compare the performances of a physically based model (Soil and Water Assessment Tool (SWAT)) and a data-driven model (Nonlinear AutoRegressive eXogenous model (NARX)) for reservoir volume and streamflow prediction in a data-scarce semi-arid region. The study was conducted in the Tersakan Basin, a semi-arid agricultural basin in Türkiye, where the basin hydrology was significantly altered due to reservoirs (Ladik and Yedikir Reservoir) constructed for irrigation purposes. The models were calibrated and validated for streamflow and reservoir volumes. The results show that (1) NARX performed better in the prediction of water volumes of Ladik and Yedikir Reservoirs and streamflow at the basin outlet than SWAT (2). The SWAT and NARX models both provided the best performance when predicting water volumes at the Ladik reservoir. Both models provided the second best performance during the prediction of water volumes at the Yedikir reservoir. The model performances were the lowest for prediction of streamflow at the basin outlet (3). Comparison of physically based and data-driven models is challenging due to their different characteristics and input data requirements. In this study, the data-driven model provided higher performance than the physically based model. However, input data used for establishing the physically based model had several uncertainties, which may be responsible for the lower performance. Data-driven models can provide alternatives to physically-based models under data-scarce conditions.

Cross-border political competition.

Individuals are increasingly exposed to news and opinion from beyond national borders. This news and opinion are often concentrated in clusters of ideological homophily, such as political parties, factions, or interest groups. But how does exposure to cross-border information affect the diffusion of ideas across national and ideological borders? Here, we develop a non-linear mathematical model for the cross-border spread of two ideologies. First, we describe the standard deterministic model where the populations of each country are assumed to be constant and homogeneously mixed. We solve the system of differential equations numerically by the Runge-Kutta method and show how small changes in the influence of a minority ideology can trigger shifts in the global political equilibrium. Second, we simulate recruitment as a stochastic differential process for each political affiliation and fit model solutions to population growth rates and voting populations in US presidential elections from 1932 to 2020. We also project the dynamics of several possible scenarios from 2020 to the end of the century. We show that cross-border influence plays a fundamental role in determining election outcomes. An increase in foreign support for a national party's ideas could change the election outcome, independent of domestic recruitment capacity. One key finding of our study suggests that voter turnout in the US will grow at a faster rate than non-voters in the coming decades. This trend is attributed to the enhanced recruitment capabilities of both major parties among non-partisans over time, making political disaffection less prominent. This phenomenon holds true across all simulated scenarios.

Seismic fragility analysis of simply supported bridges considering uncertainty in scour condition

Bridges are vital infrastructures but face compounding risks from scouring and seismic events. Although recent studies have explored these individual and overlapping hazards, they often utilize deterministic approaches and focus on specific bridge types in limited geographical areas. This study addresses these gaps by introducing a probabilistic framework for assessing the seismic performance of multi-span reinforced concrete (RC) highway bridges in the presence of scour-related uncertainties. A time-dependent scour model, informed by a Bayesian approach and literature-based uncertainties, is integrated into the framework. Probabilistic Seismic Hazard Analysis (PSHA) and record selection strategies are employed to define the seismic demand probabilistically. Monte Carlo simulation (MCS) is utilized to propagate combined uncertainties during the analysis, considering different scour scenarios defined according to the discharge peak condition of the flood event at the specific location of the bridge. In the last step of the probabilistic framework, fragility analyses are conducted on individual components and the entire system by means of nonlinear dynamic models and multiple stripe analysis (MSA). An actual five-span bridge with simply supported prestressed concrete girders, located in Chile, is used as application example of the proposed approach, considering measured hydrological data and seismic hazard of the real location of the bridge. The study identifies distinct vulnerabilities across various bridge components under scour conditions. Elastomeric bearings are particularly susceptible in scenarios characterized by low scour depths (low discharge peak condition). Conversely, abutments display heightened vulnerabilities as scour depth increases (medium discharge peak condition). Piles also exhibit notable vulnerability, escalating in scenarios with great scour depth (medium discharge peak condition). Notably, piles tend to be more susceptible than columns to scour effects, especially in bents featuring shorter columns. These disparities in vulnerability are influenced by the bridge design philosophy, as well as the synergistic effects of seismic forces and varying scour depths. System fragility curves further elucidate that the likelihood of exceeding specific damage thresholds varies according to different scour scenarios, with the deeper scour depth scenario, displaying the higher vulnerabilities.

One-loop Bern-Carrasco-Johansson numerators on quadratic propagators from the worldsheet

We introduce a novel approach for deriving one-loop Bern-Carrasco-Johansson (BCJ) numerators and reveal the world-sheet origin of the one-loop double copy. Our work shows that expanding Cachazo-He-Yuan half-integrands into generalized Parke-Taylor factors intrinsically generates BCJ numerators on quadratic propagators satisfying Jacobi identities. We validate our methodology by successfully reproducing one-loop BCJ numerators for the nonlinear sigma model as well as those of pure Yang-Mills theory in four dimensions with all-plus or single-minus helicities. Published by the American Physical Society 2024

An encoding generative modeling approach to dimension reduction and covariate adjustment in causal inference with observational studies

In this article, we develop CausalEGM, a deep learning framework for nonlinear dimension reduction and generative modeling of the dependency among covariate features affecting treatment and response. CausalEGM can be used for estimating causal effects in both binary and continuous treatment settings. By learning a bidirectional transformation between the high-dimensional covariate space and a low-dimensional latent space and then modeling the dependencies of different subsets of the latent variables on the treatment and response, CausalEGM can extract the latent covariate features that affect both treatment and response. By conditioning on these features, one can mitigate the confounding effect of the high dimensional covariate on the estimation of the causal relation between treatment and response. In a series of experiments, the proposed method is shown to achieve superior performance over existing methods in both binary and continuous treatment settings. The improvement is substantial when the sample size is large and the covariate is of high dimension. Finally, we established excess risk bounds and consistency results for our method, and discuss how our approach is related to and improves upon other dimension reduction approaches in causal inference.

Exploiting residual errors in nonlinear online prediction

AbstractWe introduce a novel online (or sequential) nonlinear prediction approach that incorporates the residuals, i.e., prediction errors in the past observations, as additional features for the current data. Including the past error terms in an online prediction algorithm naturally improves prediction performance significantly since this information is essential for an algorithm to adjust itself based on its past errors. These terms are well exploited in many linear statistical models such as ARMA, SES, and Holts-Winters models. However, the past error terms are rarely or in a certain sense not optimally exploited in nonlinear prediction models since training them requires complex nonlinear state-space modeling. To this end, for the first time in the literature, we introduce a nonlinear prediction framework that utilizes not only the current features but also the past error terms as additional features, thereby exploiting the residual state information in the error terms, i.e., the model’s performance on the past samples. Since the new feature vectors contain error terms that change with every update, our algorithm jointly optimizes the model parameters and the feature vectors simultaneously. We achieve this by introducing new update equations that handle the effects resulting from the changes in the feature vectors in an online manner. We use soft decision trees and neural networks as the nonlinear prediction algorithms since these are the most widely used methods in highly publicized competitions. However, as we show, our methods are generic and any algorithm supporting gradient calculations can be straightforwardly used. We show through our experiments on the well-known real-life competition datasets that our method significantly outperforms the state-of-the-art. We also provide the implementation of our approach including the source code to facilitate reproducibility (https://github.com/ahmetberkerkoc/SDT-ARMA).

Steering control for handling and stability and wear resistance of multi-axle vehicles

The steering performance of a vehicle directly affects its handling and stability, and tire wear during steering. For multi-axle vehicles equipped with a mechanical hydraulic steering system (MHS), this paper describes a steering-by-wire hydraulic system (SHS) for a third axle that can reduce the steering wear of third-axle tires while improving the handling and stability. A hydraulic steering system based on a reliable self-locking alignment cylinder was designed in this study, and a nonlinear dynamics model of a multi-axle vehicle was developed. In terms of the control strategy, the upper controller was a decision selector with a lateral acceleration threshold of 0.3 g , at which point the system entered the nonlinear kinematic state as a criterion for decision-making. The suboptimal linear time-varying model predictive control (S-LTV-MPC) method or Ackermann steering theory was used to calculate the target steering angle of the third axle. The lower controller was a fuzzy proportional–integral–derivative controller for tracking the steering angle of the third axle. The simulation and test results showed that the S-LTV-MPC method can meet the requirements of real-time control and accuracy. The designed SHS exhibited good handling and stability, and anti-wear properties during steering.

Conditions for the existence of soliton solutions: An analysis of coefficients in the generalized Wu–Zhang system and generalized Sawada–Kotera model

Abstract Exploring nonlinear equations and systems with predetermined coefficient values constrains the depth of understanding of the dynamics inherent in various applications and phenomena represented by such equations. On the contrary, exploration of nonlinear models with free coefficients offers avenues for improved development and ongoing refinement. In light of this, this study aimed to reassess the Wu–Zhang (WZ) system and Sawada–Kotera (SK) model by introducing arbitrary coefficients. Our goal is to identify the constraints necessary to ensure the existence of soliton solutions. Through the application of two distinct approaches, namely, the sine–cosine function method and tanh–coth expansion method, we systematically examine the conditions that facilitate the emergence of solitons within the WZ system and SK model. The insights gained from this analysis are supported by the presentation of 2D and 3D plots, providing a visual depiction of the propagation characteristics exhibited by the obtained solutions. The findings of the current work on conditions for the existence of soliton solutions for both generalized Wu–Zhang and generalized Sawada–Kotera models are novel and presented here for the first time.

Schauder and Calderón–Zygmund type estimates for fully nonlinear parabolic equations under “small ellipticity aperture” and applications

In this manuscript, we derive some Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations of the form: ∂tu−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Hólder continuous functions, and F enjoys a small ellipticity aperture. Furthermore, for problems with merely bounded data, we prove that such solutions are C1,Log-Lip-regular. We also obtain Calderón-Zygmund estimates for such a class of non-convex operators. Finally, we connect our results and recent estimates for fully nonlinear models in certain solution classes.

A comprehensive analysis of COVID-19 nonlinear mathematical model by incorporating the environment and social distancing

This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model’s equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V–L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures.

Double layer capacitors in dye sensitized solar cells with large charge and energy storage capacity and controlled shape of output voltage signals.

The output signals in natural dyes-based solar cells (DSSC) can be either rising or decaying depending on the type of ions present in the system; these ions called added ions, are introduced by the additives: mordant and brighteners. The photon-dye interaction produces electrons, which eventually reach the electrode giving place to a superficially charged electrode in contact with an electrolyte where are the added ions. This combination produces, automatically, an electrical double-layer EDL structure which has important effects on the performance of the system: a) the added ions control, to a large extent, the initial shape of the output signal, giving rise to rising or decaying profiles; b) it is possible to store large amounts of energy and charge at high electric fields. This structure is found in many other systems that have a surface charged in contact with an electrolyte like piezoelectric materials in human body. This assertion was supported by determining important parameters such as the force between charged surfaces on both sides of the interface, the charge density, the energy density, and the capacitance. The Debye length has very small values then, many important quantities depend on this; it is possible to obtain large values for energy UDL ~ 3.6x105 Jm-3 and charge density ρDL ≈ 1.1x107 Cm-3 for double layer capacitors; these values are orders of magnitude larger than the corresponding values for electrostatic capacitors: Uelec ≈ 4.5x10-3 Jm-3 and ρelec ≈ 1.2 Cm-3. A non-linear model was also developed to fit unstable oscillations found in the output profiles produced by abrupt lighting.

Nonlinear subband adaptive filter based on Andrew’s sine estimator for Van der Pol system identification

Echo cancellation has been effectively achieved through the successful application of subband adaptive filtering (SAF) algorithms. However, the performance of these algorithms may significantly deteriorate when the system exhibits nonlinear distortion. The Van der Pol–Duffing oscillator (VDPDO) system is widely recognized as a complex nonlinear system that displays intricate dynamical behaviors, emphasizing the importance of identifying this nonlinear model. This paper proposes a novel SAF, termed nonlinear SAF (NLSAF) for VDPDO system identification. The NLSAF is based on the functional link artificial neural network (FLANN) to achieve superior nonlinear modeling capability. In particular, the Andrew’s sine estimator is integrated into the NLSAF, generating NLSAF-ASE algorithm for performance improvement. The simulation results provide evidence of the accurate identification of the Van der Pol system through the effective utilization of the NLSAF-ASE algorithm.

Integrated impact of urban mixed land use on TOD ridership: A multi-radius comparative analysis

The global trend toward urbanization has spurred the widespread adoption of transit-oriented development (TOD). While previous research has extensively explored the relationship between land use and TOD ridership, much of it has focused on linear associations at a singular scale. Leveraging recent advancements in nonlinear modeling and the accessibility of open-source data, this study employs a comprehensive two-step methodology. Firstly, K-means clustering algorithm categorizes TOD sites in Shenzhen into three distinct clusters, providing a site-based understanding of their characteristics. Subsequently, a Light Gradient Boosting Machine (LightGBM) classification model, complemented by SHapley Additive exPlanations (SHAP) values for interpretation, quantitatively evaluates the influence of mixed land use on TOD ridership across various catchment areas. As for the findings, we discover that land-use factors have different effects on TOD site patronage at different buffer radii and delve into the intricacies of these effects. Further results reveal non-linear relationships with varying degrees of positivity and negativity. For instance, residents and health sites positively impact patronage across all buffer radii, while certain commercial land uses exhibit a negative influence. The study demonstrates how the importance of different land-use structures varies across these clusters, shedding light on the nuanced impacts of land use on TOD catchment areas. Our research optimizes land-use mixes based on predominant cluster characteristics by offering actionable recommendations for urban managers.

Wind-Induced Dynamic Response of Inter-Story Isolated Tall Buildings with Friction Pendulum Bearing Based on an Enhanced Simplified Model

Isolation technology, especially for base isolation, is increasingly being applied in earthquake-prone areas. To satisfy some special demands (such as prevention from seawater erosion of an isolation layer, story-adding retrofit of existing buildings, avoidance of collision between base-isolated tall buildings, and so on), the isolation layer sometimes has to be set in the middle of a building to constitute inter-story isolated buildings. This special structural form inevitably encounters strong wind loads during service life, and its wind-resistant performance deserves to be investigated. This study conducts the wind-induced vibration analysis of inter-story isolated tall buildings with friction pendulum bearing (FPB). The nonlinear time domain analysis model and statistical linearization method to compute the wind-induced response of FPB inter-story isolated tall buildings are addressed based on an enhanced simplified model. Considering the independence of the upper and lower structures, two structural design schemes for inter-story isolated tall buildings are provided. Their dynamic characteristics are analyzed, and wind-induced responses are compared. Finally, the accuracy of the statistical linearization method is verified. This study provides an important theoretical basis for the structural design and wind resistance of inter-story isolated tall buildings.