Nonlinear Interaction Effects Research Articles

Estimation for semiparametric varying coefficient models with different smoothing variables under random right censoring

In this paper we study a semiparametric varying coefficient model when the response is subject to random right censoring. The model gives an easy interpretation due to its direct connectivity to the classical linear model and is very flexible since nonparametric functions which accommodates various nonlinear interaction effects between covariates are admitted in the model. We propose estimators for this model using mean-preserving transformation and establish their asymptotic properties. The estimation procedure is based on the profiling and the smooth backfitting techniques. A simulation study is presented to show the reliability of the proposed estimators and an automatic bandwidth selector is given in a data-driven way.

The evolution of free and bound waves during dispersive focusing in a numerical and physical flume

Since the introduction of the NewWave theory (Lindgren, 1970), focused wave groups are used in physical and numerical studies to investigate the interaction of marine structures and ships with extreme waves. The propagation of such wave groups is associated with high order nonlinearities that can cause considerable deviations from linear and 2nd order predictions. Consequently, nonlinear numerical models or laboratory tests are needed to accurately describe the evolution of focused wave groups. In the present study, we validate a widely used two-phase Reynolds Averaged Navier-Stokes (RANS) solver realised in OpenFOAM with experimental results for the propagation of steep focused wave groups, using a newly developed methodology based on the separation of harmonics. This approach allows for accurate focusing of wave groups and in-detail examination of the individual evolution of the high order terms, as well as identifying the source of discrepancies between experiments and numerical models. The wave groups comprise long-crested broadbanded Gaussian spectra of increasing steepness propagating in intermediate water depth. The contribution of the nonlinear harmonics to the crest height and overall shape of the wave are also discussed, together with the effect of nonlinear wave interactions on the free-wave spectrum. The rapid growth of 3rd and 4th harmonics near focusing as well as the evolution of the free-wave spectrum, cause departures of up to 29% and 22% from analytic linear and 2nd order predictions. The present results demonstrate that RANS-VoF solvers constitute accurate models to propagate nearly breaking waves.

An energy balance model exploration of the impacts of interactions between surface albedo, cloud cover and water vapor on polar amplification

We examine the effects of non-linear interactions between surface albedo, water vapor and cloud cover (referred to as climate variables) on amplified warming of the polar regions, using a new energy balance model. Our simulations show that the sum of the contributions to surface temperature changes due to any variable considered in isolation is smaller than the temperature changes from coupled feedback simulations. This non-linearity is strongest when all three climate variables are allowed to interact. Surface albedo appears to be the strongest driver of this non-linear behavior, followed by water vapor and clouds. This is because increases in longwave radiation absorbed by the surface, related to increases in water vapor and clouds, and increases in surface absorbed shortwave radiation caused by a decrease in surface albedo, amplify each other. Furthermore, our results corroborate previous findings that while increases in cloud cover and water vapor, along with the greenhouse effect itself, warm the polar regions, water vapor also significantly warms equatorial regions, which reduces polar amplification. Changes in surface albedo drive large changes in absorption of incoming shortwave radiation, thereby enhancing surface warming. Unlike high latitudes, surface albedo change at low latitudes are more constrained. Interactions between surface albedo, water vapor and clouds drive larger increases in temperatures in the polar regions compared to low latitudes. This is in spite of the fact that, due to a forcing, cloud cover increases at high latitudes and decreases in low latitudes, and that water vapor significantly enhances warming at low latitudes.

Nonlinear Effects of Social Connections and Interactions on Individual Goal Attainment and Spending: Evidences from Online Gaming Markets

Although it seems intuitive for firms to leverage social connections and interactions to influence consumers’ goal attainment and spending, the authors present a caveat of such strategies. Using two large-scale data sets with more than 5 million people-day observations from online gaming markets, Studies 1 and 2 show consistently nonlinear effects. Although some social connections and interactions boost goal attainment and spending (positive linear term), after a certain point too many of them have a diminished marginal effect (negative squared term). The results are robust to a wide array of modeling techniques addressing self-selection, unobserved individual heterogeneity, and endogeneity. In addition, novices can benefit more from greater social connections and interactions, yet also suffer more from the diminishing effects. Regarding the underlying mechanism, the follow-up experiment Study 3 shows that consistent with the information processing theory, some social connections and interactions can provide information support for goal attainment, but too many of them can introduce an information overload problem and, thus, hamper goal attainment intention. Together, these findings refute a simple, linear view of the effects of social connections and interactions and provide pivotal theoretical and practical implications.

An ANFIS based approach for predicting the weld strength of resistance spot welding in artificial intelligence development

Artificial intelligence (AI) is a modern approach which has the ability to capture nonlinear relationships and interaction effects. Frequently, AI methods have been used by researchers to predict output responses of the Resistance spot welding (RSW) due to the complex- ity during the welding process and numerous interferential factors, especially the short-time property of the process. The present study is to investigate the weld strength of spot weld for high strength steel sheets of CR780 using the Adaptive neuro fuzzy inference system (ANFIS). These results were compared with those obtained by conventional Artificial neural network (ANN). The input parameters were extracted through the dynamic resistance signal which was obtained from the primary circuit of the welding machine. Both the ANN and ANFIS models were utilized for the formulation of mathematical model with an off-line dynamic resistance response of the RSW at a particular parameters setting. The performances of both models were compared in terms of correlation coefficient value (R), Root mean squared error (RMSE), and Mean absolute percentage error (MAPE). While both methods were capable of predicting the weld strength, it was found that ANFIS model could predict more precisely than ANN.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Soliton dynamics for trapped Bose-Einstein condensate with higher-order interaction

We model the three-dimensional (3D) trapped Bose-Einstein condensate with the Gross-Pitaevskii equation (GPE) incorporating higher-order nonlinear interaction effects. Based on the F-expansion method and self-similar approach, we analytically derive the exact soliton solutions of the 3D GPE, identifying the oscillatory mode under certain experimental settings. The oscillatory kinetic parameter values we obtained coincide very well with those reported in previous work, which is based on the variational approach, showing the applicability of the theoretical treatment presented in this work.

EpiACO - a method for identifying epistasis based on ant Colony optimization algorithm

BackgroundIdentifying epistasis or epistatic interactions, which refer to nonlinear interaction effects of single nucleotide polymorphisms (SNPs), is essential to understand disease susceptibility and to detect genetic architectures underlying complex diseases. Though many works have been done for identifying epistatic interactions, due to their methodological and computational challenges, the algorithmic development is still ongoing.ResultsIn this study, a method epiACO is proposed to identify epistatic interactions, which based on ant colony optimization algorithm. Highlights of epiACO are the introduced fitness function Svalue, path selection strategies, and a memory based strategy. The Svalue leverages the advantages of both mutual information and Bayesian network to effectively and efficiently measure associations between SNP combinations and the phenotype. Two path selection strategies, i.e., probabilistic path selection strategy and stochastic path selection strategy, are provided to adaptively guide ant behaviors of exploration and exploitation. The memory based strategy is designed to retain candidate solutions found in the previous iterations, and compare them to solutions of the current iteration to generate new candidate solutions, yielding a more accurate way for identifying epistasis.ConclusionsExperiments of epiACO and its comparison with other recent methods epiMODE, TEAM, BOOST, SNPRuler, AntEpiSeeker, AntMiner, MACOED, and IACO are performed on both simulation data sets and a real data set of age-related macular degeneration. Results show that epiACO is promising in identifying epistasis and might be an alternative to existing methods.

Frame nonlinear analysis by force method

The focus of this paper is on the force-based finite element for analysis of planar frames. Both material and geometrical nonlinear behavior are considered in this study. The formulations are based on the two-field Hellinger-Reissner functional. Nonlinear effects of the internal forces interactions are considered by using 2D tangent material stiffness and fiber discretization technique. Due to presence of the rigid body modes in the global coordinates, the element is formulated in a basic coordinate system. Corotational approach transforms responses of the basic coordinate system to the global one and makes the element applicable for structures with arbitrarily large rigid body displacements and rotations. Moreover, shear-locking problem is removed in this formulation. Two iterative and non-iterative algorithms for the element state determinations are proposed. Finally, the new element accuracy and also efficiency are verified by some numerical examples.

On the clinotron effect in a backward-wave tube

The results of a theoretical study of the clinotron effect in a clinotron model, which takes into account static electron trajectories in the focusing magnetic field and the initial spacing between the lower beam boundary and the surface of the slow-wave structure, are presented. Physical processes of interaction between a thick electron beam with transverse dimensions comparable with the length of the slow wave and the RF field at its oblique incidence onto the structure are considered. It is demonstrated that, as the current is increased from the starting to the working value, a beam tilt is necessary to reduce the nonlinear effects of interaction between the beam and the RF field and prevent the complex self-oscillation dynamics in the clinotron; in the small amplitude mode (start), the beam tilt is related to optimization of the beam supply into the interaction space, which ensures the minimum starting current. In addition, it is shown that, in the presence of the initial spacing between the beam and structure, the reduced clinotron efficiency η/С increases and, at the optimum tilt angle, is no less than the normalized efficiency of classical backward-wave tubes with a thin electron beam.

Signature of nonlinear damping in geometric structure of a nonequilibrium process.

We investigate the effect of nonlinear interaction on the geometric structure of a nonequilibrium process. Specifically, by considering a driven-dissipative system where a stochastic variable x is damped either linearly (∝x) or nonlinearly (∝x^{3}) while driven by a white noise, we compute the time-dependent probability density functions (PDFs) during the relaxation towards equilibrium from an initial nonequilibrium state. From these PDFs, we quantify the information change by the information length L, which is the total number of statistically distinguishable states which the system passes through from the initial state to the final state. By exploiting different initial PDFs and the strength D of the white-noise forcing, we show that for a linear system, L increases essentially linearly with an initial mean value y_{0} of x as L∝y_{0}, demonstrating the preservation of a linear geometry. In comparison, in the case of a cubic damping, L has a power-law scaling as L∝y_{0}^{m}, with the exponent m depending on D and the width of the initial PDF. The rate at which information changes also exhibits a robust power-law scaling with time for the cubic damping.

Progressive Seismic Failure of a Highway Bridge, Including Abutment-Backfill Interaction

Current engineering practice pays little attention, if any, to nonlinear abutment-backfill soil interaction (ABSI) effects on seismic behaviour of bridges. The primary focus of this article is to assess the influence of ABSI on the progressive seismic failure of bridge structures. Emphasis is placed on the significance of ABSI effects, including abutment behaviour and backfill soil flexibility. Nonlinear dynamic analysis is performed using a bilinear hysteretic model for the bridge superstructure and nonlinear characteristics of the expansion joint. Results indicate that ABSI has a significant effect on the seismic response in the longitudinal direction and can effectively reduce bridge seismic demands. ABSI affects rotational ductility demand at pier ends of the bridges, relative displacements, pounding and axial forces in the restrainers. Thus, it is essential that numerical models used in seismic assessment of bridge structures properly consider abutment-backfill interaction.

The moderating effect of supervisor and coworker support for error management on service recovery performance and helping behaviors

PurposeThe purpose of this paper is to amend and extend the emerging research that has utilized an employee-focused approach to examining the service recovery process. In doing so, the authors examine the influences of supervisor and coworker support for error management on two measures of employee service performance: service recovery performance and helping behaviors during service failure and recoveries. Specifically, this study examines the linear and non-linear interaction effects of supervisor and coworker support for error management on the outcome variables.Design/methodology/approachTo examine the proposed relationships, the authors conducted a field study that utilized survey data from a sample of 243 restaurant employees and their immediate supervisors. Employee ratings of supervisor and coworker support for error management were matched with the data gathered for the two dependent variables (i.e. supervisory ratings of service recovery performance and helping behaviors). Structural equation modeling was used to examine the linear interaction effects on the outcome variables. To examine the non-linear interaction effects on the outcome variables the authors utilized polynomial regression and response surface modeling.FindingsThe results showed that the interaction effects of supervisor and coworker support for error management was significantly positively related to both service recovery performance and helping behaviors. In addition, an alternative analysis of the shape of the interaction effects using polynomial regression and response surface modeling showed that the moderating effects may be better conceptualized as non-linear.Originality/valueThese findings offer new insights about the roles and impact of various forms of support in the service recovery process. First, the current study focuses specifically on supervisor and coworker support for error management and the impact on employees’ service recovery performance and helping behaviors. Second, this research investigates the interaction effects of these two forms of support on service recovery performance and helping behaviors. Third, along with linear interaction effects, the current work examines non-linear interaction effects. These relationships examined in this study have not been tested before. Thus, the findings of this research make a unique contribution to research in service management. The findings of this study provide more prescriptive insights about the means to prevent and respond effectively to service errors.

Seismically induced uplift effects on nuclear power plants. Part 2: Demand on internal equipment

This work focuses on the dynamic response of nuclear power plant mechanical sub-systems (i.e., main cooling system, steam generators, emergency cooling injection tanks and piping) that are housed within the containment structure and are associated with power generation. More specifically, the numerical modeling procedure focuses on the internal R/C wall structural system used for supporting the mechanical equipment. Next, the complex grid of the mechanical components is modeled with shell finite elements. This internal equipment configuration is then excited by the ground motion numerically predicted in Part I οf this work by considering geometrically nonlinear soil-structure interaction effects. Following extensive parametric studies, the seismic demand imposed on the internal equipment is assessed on the basis of dynamic stress analysis of the critical components. Depending on frequency content of the incoming seismic motion, it is shown that abrupt uplift may take place. This is true even for moderate earthquake intensity, particularly when the containment structure rests on soft soils and the vertical component of ground motion is not negligible. This situation may produce peaks in the pipe elbow strains that could potentially affect serviceability, operation and under extreme conditions, the safety of the entire nuclear power plant.

Local Logit Regression for Recovery Rate

We propose a flexible and robust non-parametric local logit regression for modelling and predicting defaulted loans' recovery rates that lie in [0,1]. Applying the model to the widely studied Moody's recovery dataset and estimating it by a data-driven method, the local logit regression uncovers the underlying nonlinear relationship between the recovery and covariates, which include loan/borrower characteristics and economic conditions. We find some significant nonlinear marginal and interaction effects of conditioning variables on recoveries of defaulted loans. The presence of such nonlinear economic effects enriches the local logit model specification that supports the improved recovery prediction. This paper is the first to study a non-parametric regression model that not only generates unbiased and improved recovery predictions of defaulted loans relative to the parametric counterparts, it also facilitates reliable inference on marginal and interaction effects of loan/borrower characteristics and economic conditions. Moreover, incorporating these nonlinear marginal and interaction effects, we improve the specification of parametric regression for fractional response variable, which we call a model, the predictive performance of which is comparable to that of local logit model. This calibrated parametric model will be attractive to applied researchers and industry professionals working in the risk management area and unfamiliar with non-parametric machinery.

Estimating Heritability from Nuclear Family and Pedigree Data.

Heritability is a measure of familial resemblance. Estimating the heritability of a trait could be one of the first steps in the gene mapping process. This chapter describes how to estimate heritability for quantitative traits from nuclear and pedigree data using the ASSOC program in the Statistical Analysis in Genetic Epidemiology (S.A.G.E.) software package. Estimating heritability rests on the assumption that the total phenotypic variance of a quantitative trait can be partitioned into independent genetic and environmental components. In turn, the genetic variance can be divided into an additive (polygenic) genetic variance, a dominance variance (nonlinear interaction effects between alleles at the same locus) and an epistatic variance (interaction effects between alleles at different loci). The last two are often assumed to be zero. The additive genetic variance represents the average effects of individual alleles on the phenotype and reflects transmissible resemblance between relatives. Heritability in the narrow sense (h 2 ) refers to the ratio of the additive genetic variance to the total phenotypic variance. Heritability is a dimensionless population-specific parameter. ASSOC estimates association parameters (regression coefficients) and variance components from family data. ASSOC uses a linear regression model in which the total residual variance is partitioned, after regressing on covariates, into the sum of random components such as an additive polygenic component, a random sibship component, random nuclear family components, a random marital component, and an individual-specific random component. Assortative mating, nonrandom ascertainment of families, and failure to account for key confounding factors may bias heritability estimates.

Non-linear interaction of buoyancy with von Kármán’s swirling flow in mixed convection above a heated rotating disc

In this paper, a systematic computational and theoretical study of the thermo-fluid-dynamics governing the flow above a heated horizontal rotating disc is presented. The fluid flow field is much more complex here as compared to von Kármán’s original solution (which took into account only the effect of disc rotation), and the effects of non-linear interaction between buoyancy and rotation are critically analysed here by studying the separate and combined roles of disc rotation and buoyancy on the fluid dynamic and heat transfer characteristics. The self-similarity of von Kármán’s flow field is lost, and the present paper establishes, for the first time, that the flow field above a heated rotating disc is divided into three distinct fluid dynamic regions. The three regions are demarcated by the loci of V̂z=0 and V̂r=0. In region 1 (R-1), V̂r is positive and V̂z is negative (such directions of the velocity components are characteristic of von Kármán’s flow or pure forced convection). In region 2 (R-2), V̂r is negative and V̂z is positive (such directions of the velocity components are characteristic of pure natural convection near a static disc surface). In region 3 (R-3), both V̂r and V̂z are negative. The forced convection results are obtained asymptotically at a large non-dimensional radius R within the region R-1 showing the dominance of forced convection mechanism, however, the fluid retains the signature of natural convection even at large values of R in the region R-3 where there is an inward radial velocity. Similarly, although a plume forms in the central portion of the disc where the solution is dominated by the effects of buoyancy, the fluid retains a signature of the disc rotation in the helical pathlines of fluid particles rising in the plume (whereas there is no swirl velocity present in pure natural convection above a static disc). The non-linear interaction between buoyancy and rotation results in several peculiar, rather non-intuitive, flow phenomena. Examples of such peculiarity include (i) the presence of a very sensitive spot on the upper boundary such that for a small change in this initial position the fluid pathlines may face drastically different final outcomes, (ii) the presence of a small portion near the centre of the disc where the fluid supplies energy to the disc, (iii) the effect of rotation on the rate of convective heat transfer being diminished by buoyancy over certain part of the disc while being enhanced over another part. This non-linear effect on Nusselt number is quantified here in terms of a Grashof number defined for mixed convection (Grmc).

Time-dependent probability density function in cubic stochastic processes.

We report time-dependent probability density functions (PDFs) for a nonlinear stochastic process with a cubic force using analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x,t) in general involves a time integral, and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g., in the short and long time limits). Numerical simulations of the Fokker-Planck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that transient PDFs behave drastically differently from the stationary PDFs in regard to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric with the kurtosis smaller than 3, transient PDFs are skewed with the kurtosis larger than 3; transient PDFs are much broader than stationary PDFs. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in the relaxation process.

Validation of the alternating conditional estimation algorithm for estimation of flexible extensions of Cox's proportional hazards model with nonlinear constraints on the parameters.

Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure.

Non-linear Interaction between Air pollutants and Ambient Temperature

Introduction: Air pollution has been associated with mortality, but most studies only focused on overall effects of air pollutants. Recently, a few studies have reported that the effect of air pollutions on mortality has an interactive relationship with season. However, the definition of season is ambiguous and varies by country since it depends on climates. In order to estimate varying effects of air pollutants by season more accurately, we estimated non-linear interactions between air pollutions and ambient temperature. Methods: This study included data of three cities in Taiwan for 1994–2007, seven cities in Korea for 1992–2010, and six cities in Japan for 1972–2009. We used three representative air pollutants, PM10, NO2, and CO and all causes of mortality count data. We used non-linear temperature basis to estimate non-linear interaction with air pollution. Results: We found non-linear interaction effects between air pollutions and ambient temperature on mortality in many cities. These interactive relationships showed U or J shape, which means that the effect of air pollutants increases in extremely high or low temperature. Conclusions: We found suggestive evidence of air pollution effect on mortality, which had non-linear relationship with ambient temperature and was increased in extremely hot and cold temperature. These results can be used for making public health policy be more evidence-informed and further studies will determine biological and epidemiological causes of this results.