Nonlinear Growth Models Research Articles

Effects of cadmium toxicity on sesame seed germination explained by various nonlinear growth models

This experiment was conducted to evaluate the effects of cadmium toxicity on the seed germination properties of sesame cultivars (Halil, Nazok Shakhei, Oltan, and Yellow White) using non-linear growth models. Seeds were germinated in petri dishes (90 mm diameter), with a double layered of filter paper soaked in distilled water as control treatment or cadmium (CdSO4) solutions in concentrations of 0, 100, 200, 400, 600, 800 and 1000 ppm. Each treatment was replicated four times and included 50 seeds in each petri dishes. Hyperbolastic growth models for the description of seed germination data were compared to Richards, Weibull, Logistic and Gompertz models. Our results revealed that all studied cultivars were germinated at the cadmium-polluted germination medium to a maximum of 200 ppm without reduction in germination fraction, while seed germination rate was decreased at this concentration compared to 0 and 100 ppm. Increasing cadmium concentration resulted in the germination fraction reduction from 1 to 0.4 at the 400 ppm. The recommended hyperbolastic growth model was type III or (H3) as it provided the best model with the lowest Corrected Akaike Information Criterion for cv. Halil (AICc = −14.6) and cv. Nazok Shakhei, (AICc = −14.2).

Effect of insulin-like growth factor 1 gene on growth traits of Kejobong goat and its growth analysis.

Aim:This study aimed to identify the effect of the insulin-like growth factor 1 (IGF1) gene on growth, to uncover the genetic marker at the IGF1 gene, and to predict growth performance by analyzing growth models of Kejobong goats based on their genotype.Materials and Methods:DNA and records of body weight (BW) and body measurements (BM) of Kejobong goats were collected, the IGF1 gene was amplified from the DNA template by polymerase chain reaction (PCR); the PCR products were then sequenced to determine single nucleotide polymorphisms (SNP). Linear mixed model (LMM) was used to analyze the association between SNP and growth traits. Four non-linear growth models were analyzed using non-LMM to describe the growth model and to compare the growth within genotypes.Results:An SNP at intron 4 (g5752G→C) genotyped into GG and CC was significantly associated with BW and BM. Goats of genotype GG had a significantly higher BW and BM (p<0.05) than those of genotype CC. Growth analysis showed that the von Bertalanffy model was the most fit for describing BW, the Brody model for chest width and hip height, the Gompertz and Logistic models for heart girth, and the von Bertalanffy and Gompertz models for hip width.Conclusion:An SNP at intron 4 of the IGF1 gene was associated with the growth trait and was usable as a genetic marker candidate for improvement of growth traits of Kejobong goats while von Bertalanffy model provides proper and accurate estimates of parameters to describe the growth performance of Kejobong goats.

Robust positive control of a nonlinear tumor growth model

Control of physiological systems, like tumor growth dynamics, can contribute to modern medicine by designing optimized therapies or automating treatments. Typical challenges in physiological control are the positivity of the input and the interpatient variability of model parameters. We use positive dynamics extension to ensure the positivity of the input, and design a robust controller for a nominal model acquired after exact linearization and stabilizing feedback. During the controller design, we minimize the effect of the model perturbation in the worst-case sense and minimize the energy of the performance criteria. The results show enhanced performance compared to our similar robust control approach where only the performance was minimized in the worst-case sense with similar characteristics in the input signals.

On the Nonlinear Growth of Multiphase Richtmyer–Meshkov Instability in Dilute Gas-Particles Flow**Supported by the National Natural Science Foundation of China under Grant Nos. 91852207, 11801036, 11502029, and the NSAF under Grant No. U1630247.

We discuss evolutions of nonlinear features in Richtmyer–Meshkov instability (RMI), which are known as spikes and bubbles. In single-phase RMI, the nonlinear growth has been extensively studied but the relevant investigation in multiphase RMI is insufficient. Therefore, we illustrate the dynamic coupling behaviors between gas phase and particle phase and then analyze the growth of the nonlinear features theoretically. A universal model is proposed to describe the nonlinear finger (spike and bubble) growth velocity qualitatively in multiphase RMI. Both the effects of gas and particles have been taken into consideration in this model. Further, we derive the analytical expressions of the nonlinear growth model in limit cases (equilibrium flow and frozen flow). A novel compressible multiphase particle-in-cell (CMP-PIC) method is used to validate the applicability of this model. Numerical finger growth velocity matches well with our model. The present study reveals that particle volume fraction, particle density and Stokes number are the three key factors, which dominate the interphase momentum exchange and further induce the unique property of multiphase RMI.

Forecasting fish yield using statistical nonlinear growth models – A reparameterization concept

The concept of reparameterization is rarely employed in forecasting fish yield, even though reparameterization method is computationally more efficient especially when estimation involves an iterative method. Further, a reparameterization of the growth functions whose new parameters correspond to scientifically interesting characteristics of the growth process (Choi et al, 2009). Reparameterization of the same basic model produce the same goodness-of-fit and the same fitted values, etc. but they may differ greatly in their estimation behavior. Further, a class of parameters that exhibits close-to-linear behavior is the class of expected-value parameters. The extent of non-normality and excess variance of the least squares estimates of an expected value parameter is generally small (Ratkowsky, 1990). The only restriction on expected-value parameters is that they should fall within the observed range of the data and not correspond to asymptotes or extrapolations outside the data range. Expected-value parameters outside the range of the observed data are less efficacious. Also, the derived expressions due to expected-value parameters are usually more cumbersome in appearance than the original expressions, and the expected-value parameters may appear more than once. As compensation for this loss of aesthetics, however, parameterizations with expected-value parameters offer three advantages. First, one obtains rapid convergence to the leastsquares estimates using the new parameterization, since the new model close-to-linear. A second benefit is that initial parameter estimates are very easy to obtain. Third, the expected-value parameters are more suitable for inference than the original parameters since their least-squares estimates are close-to being unbiased, normally distributed, minimum variance estimators. Although the role of expected-value parameters is very important, algebraic limitations prevent the universal application of expected-value parameters. However, in most of the cases a few parameters (one or two parameters only) are responsible for the far-from-linear behavior of a nonlinear regression model, it is seldom necessary to replace all the parameters of a model by expected-value parameters (Ratkowsky, 1990). Singh (2011) derived an explicit expression for partial reparameterization of Schaefer model with autoregressive of order one using expected-value parameters and fitted to catch-effort fishery data.

Dynamic growth metrics for examining prenatal exposure impacts on child growth trajectories: Application to perfluorooctanoic acid (PFOA) and postnatal weight gain

BackgroundEpidemiologic studies investigating prenatal exposures in relation to growth typically rely on cumulative growth measures such as weight or BMI. However, less is known about how prenatal exposure may impact other aspects of growth dynamics, including timing and velocity. ObjectivesTo describe and apply a nonlinear growth model previously used in other health science fields to characterize postnatal growth trajectories for use in environmental epidemiology studies. MethodsWe used a double logistic function to model child weight trajectories from birth to 5.5 years using data from the Swedish Environmental Longitudinal Mother and Child, Asthma and Allergy (SELMA) study. From this, we approximated several infant growth metrics: 1) duration of time needed to complete 90% of the infant growth spurt (Δt1), 2) the maximum growth rate in infancy or infant peak growth velocity (PGV), 3) the age at infant PGV (δ1), a measure of growth tempo, and 4) the weight plateau at the end of the infant growth spurt (α1). We assessed these metrics in relation to prenatal perfluorooctanoic acid (PFOA) exposure among 1334 mother-child pairs, and differences between boys and girls. ResultsAverage estimated infant PGV and its timing (δ1) were 0.68 kg/month and 3.4 months, respectively. Mean infant growth spurt duration (Δt1) was 13 months, ending at an average weight plateau (α1) of 8.2 kg. Higher prenatal PFOA concentrations were related to a longer duration of infant growth (Δt1: 0.06; 95% CI = 0.01, 0.11). PGV was not impacted, but higher prenatal PFOA concentrations were significantly related to delayed infant PGV (δ1: 0.58; 95% CI = 0.17, 0.99) and a higher post-spurt weight plateau (α1: 0.81; 95% CI = 0.21, 1.41). After adjusting for false discovery, results were only significant for δ1 and α1. We observed a significant interaction by sex for the association with δ1, and stratified analyses revealed the association was only significant among girls. ConclusionModel-derived growth metrics were consistent with published growth standards. This novel application of nonlinear growth modeling enabled detection of altered infant growth dynamics in relation to prenatal PFOA exposure. Our results may help describe how PFOA yields lower birthweights, but higher weight later in childhood. Future applications may characterize adolescent growth or additional metrics of biological interest.

Estimating New Quantities from Longitudinal Test Scores to Improve Forecasts of Future Performance

Psychometric models for longitudinal test scores typically estimate quantities associated with single-administration tests, like ability at each time-point. However, models for longitudinal tests have not considered opportunities to estimate new quantities that are unavailable from single-administration tests. Specifically, we discuss dynamic measurement models – which combine aspects of longitudinal IRT, nonlinear growth models, and dynamic assessment – to directly estimate capacity, defined as the expected future score once the construct has fully developed. After discussing the history and connecting these areas into a single framework, we apply the model to verbal test scores from the Intergenerational Studies, which follow 494 people from 3 to 72 years old. The goal is to predict adult verbal scores (Age ≥ 34) from adolescent scores (Age ≤ 20). We held-out the adult data for prediction and compared predictions from traditional longitudinal IRT ability scores and proposed dynamic measurement capacity scores from models fit to the adolescent data. Results showed that the R2 from capacity scores were 2.5 times larger than the R2 from longitudinal IRT ability scores (43% vs. 16%), providing some evidence that exploring new quantities available from longitudinal testing could be worthwhile when an interest in testing is forecasting future performance.

Incorporating Parameter Estimability Into Model Selection

We investigate a class of information criteria based on the informational complexity criterion (ICC), which penalizes model fit based on the degree of dependency among parameters. In addition to existing forms of ICC, we develop a new complexity measure that uses the coefficient of variation matrix, a measure of parameter estimability, and a novel compound criterion that accounts for both the number of parameters and their informational complexity. We compared the performance of ICC and these variants to more traditionally used information criteria (i.e., AIC, AICc, BIC) in three different simulation experiments: simple linear models, nonlinear population abundance growth models, and nonlinear plant biomass growth models. Criterion performance was evaluated using the frequency of selecting the generating model, the frequency of selecting the model with the best predictive ability, and the frequency of selecting the model with the minimum Kullback-Leibler divergence. We found that the relative performance of each criterion depended on the model set, process variance, and sample size used. However, one of the compound criteria performed best on average across all conditions at identifying both the model used to generate the data and at identifying the best predictive model. This result is an important step forward in developing information criterion that select parsimonious models with interpretable and tranferrable parameters.

Control charts for detection of dead batches during hydrogenation of edible oil

Purpose Modeling and inferring about the process using growth models are the problems of enormous practical importance. Growth behavior of melting point (MP) during hydrogenation is found to be nonlinear. The purpose of this paper is to propose a control chart based method for on-line detection of a growth process becoming dead. Design/methodology/approach The nonlinear growth kinetics of MP during hydrogenation is modeled as a random walk with drift. In earlier work, the random walk model is developed based on a linear approximation and the control chart is constructed based on this approximate model. Here, an alternative model that does not make use of any such approximation is proposed. The variable drift component of the random walk is estimated following an innovative method of instrumental variable estimation. The model thus obtained is then used to construct a new control chart. Findings It is shown that both the control charts are able to detect dead batches satisfactorily, but the new chart is superior to the earlier one. Originality/value The authors are not aware of any relevant literature which provides an implementable and practitioner friendly approach to model the usually cumbersome variance function using signal-to-noise ratio and then use the same for estimating the parameters of a nonlinear dynamic growth model.

A Bayesian approach for describing the growth of Chukar partridges

Abstract In this article, a Bayesian approach was employed for estimating the body growth of Chukar partridge ( Alectoris chukar). Nonlinear growth models commonly used to estimate the growth curve of birds were fitted to weight-age data and estimates of model parameters and their credible intervals were obtained via a formal Bayesian framework. More specifically, the Gompertz, Brody, Logistic and von Bertalanffy growth models were fitted to weekly body weight data of 108 female and 72 male partridge chicks from hatch to 20 weeks of age. Deviance Information Criteria (DIC) and the coefficient of determination ( R 2) were employed as the goodness of fit for comparing the fitted models. The DIC and R 2 values of the models ranged from 172.9 to 204.2 and 0.9765 to 0.9913, respectively. The von Bertalanffy model was found to provide the best fit in terms of lower DIC and higher R 2 values, followed by the Gompertz model for both male and female partridge data. The Bayesian approach was found to be adequate for fitting complex nonlinear functions to weight-age data of Chukar partridges.

A comparison of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability growth

The growth dynamics of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability are compared systematically using data from high-resolution implicit large-eddy simulations of a model of the Mach 1.3 air(acetone) and sulfur hexafluoride (Jacobs and Krivets, 2005) shock tube experiment. The vorticity deposition by the incident shock and the dynamics of interface evolution are examined quantitatively and qualitatively. The perturbation amplitudes from the two- and three-dimensional simulations are compared to the experimental data and to the predictions of several nonlinear instability growth models. It is shown that the perturbation amplitudes from the two- and three-dimensional simulations with matching initial Richtmyer velocity are in excellent agreement with the experimental data. In addition, the dynamics of reshock (not considered in the experiment) are described in detail, and the post-reshock mixing layer amplitude growth rate is compared to the predictions of several reshock models. It is shown that using two-dimensional simulations to understand three-dimensional dynamics is valid only at early-to-intermediate times before reshock; at intermediate-to-late times after reshock the three-dimensional growth is generally larger than the corresponding two-dimensional growth. The reshock dynamics are also different between two and three dimensions. The quantitative results, together with visualizations of the flow field, were also used to contrast the difference between two- and three-dimensional vorticity and enstrophy dynamics.

First-passage time study of a stochastic growth model

In this paper, a stochastic nonlinear growth model is proposed, which can be considered a generalization of the stochastic logistic model. It can be applied to the growth of a generic population as well as to the propagation of the fracture in engineering materials. The excitation is assumed to be a stationary Gaussian white noise stochastic process, which affects the system parametrically. A preliminary study of the stochastic differential equation governing the model reveals that there is a phase transition when the nonlinearity parameter c reaches one: when $$c<1$$ , the system tends to the stationary state, while it is never stationary when $$c\ge 1$$ . Then, attention is focused on the first-passage time problem, which is of crucial importance for dynamical systems. The first-order stochastic differential equation (SDE) that describes the model is transformed into an Ito’s SDE by adding the Wong–Zakai–Stratonovich corrective term. For the last equation, the backward Kolmogorov equation is formulated. By solving it with appropriate initial and boundary conditions, the probability of survival is obtained, that is, the probability of not exceeding a given threshold. The solution is looked for three cases $$c 1$$ . In any case, the numerical analyses show that the survival probability decays fast.

Modeling growth curves for Indian Native vs Exotic chicken breeds to assist in selection strategies

The knowledge of growth curves in poultry is worth for determining economic efficiencies. With the availability of advance and potent computing algorithm, we can develop suitable statistical procedures for model evaluation which suites for the estimation of parameters influencing body weight in native and exotic chicken breeds. In this study, three breeds of chicken . Brown Nicobari (119), Ghagus (118) and Dahlem Red (125) were taken which were hatched at the same time using 20 sires and eighty dams from each breed and maintained at ICAR-Directorate of Poultry Research, Hyderabad under same milieu. Genetic parameters, for body weight up to 14 weeks of age, of all the three breeds have been evaluated. Data on parameters like egg weight (at the time of incubation), birth weight and weight at weekly intervals up to 14 weeks of age were recorded. The animal growth data are generally non-linear in nature so an attempt has been made to fit non-linear growth models, viz. exponential, logistic, Gompertz and monomolecular on data pertaining to body weight of native and exotic poultry breeds. The study concludes that the two criteria Mean Absolute Error and Root Mean Square Error support the logistic model which was found to be most suitable growth model for poultry birds.

Development of a non-linear growth model for predicting temporal evolution of Scenedesmus obliquus with varying irradiance.

In the present study, the effect of irradiance on growth performance of Scenedesmus obliquus was investigated, and various non-linear growth models were evaluated to predict its temporal evolution. This microalga was cultured in a LED-illuminated flat-panel gas-lift photobioreactor operated in batch mode at varying irradiance ranging from 50 to 200µmol/m2/s keeping all the other physico-chemical parameters constant. When growth data in terms of optical density were fitted in sigmoidal growth models, three non-linear models, namely, Richards model, Gompertz model, and logistic model, were found to be the best fit. Comparing these models based on statistical information, the logistic model could more appropriately and precisely describe algal growth under varying light intensity. Finally, the parameters of the logistic model were determined using regression analysis and were incorporated in the logistic equation to investigate the kinetic characteristics of S. obliquus. The optimum light intensity (Iopt) for growth was found to be 150µmol/m2/s, at which a maximum specific growth rate (µopt) of 0.35/day was obtained. The model developed was validated experimentally and could successfully explain the photo-inhibition phenomenon occurring at light intensity above 150µmol/m2/s.

Development of non-linear stochastic fatigue crack growth models for structural grade steel

This paper describes the analysis and quantification of within specimen and between specimen fatigue crack growth variability from tests undertaken on BS 4360: 1990 Grade 50DD (now BS EN 10025: Part 2: 2004, Grade S355K2) steel specimens. A non-linear fatigue crack growth model is presented which draws upon within and between specimen variability, the application of a newly identified and unique intersection point (referred to as the Gurney Point) and the use of reliability updating. This model, which aggregates fatigue crack growth variability over defined increments of growth, provides crisp fatigue life predictions at a sufficiently early stage of fatigue life.

Growth and diffusion dynamics of tractor in Punjab

Over the last few decades, India has seen an incessant increase of tractor use as well as expansion in its domestic tractor manufacturing industry, in spite of comparatively slow wage growth and a slow decline in the employment share of the agricultural sector. If the present situation is to be accounted, arguably as much as 90% of the country’s farm area may be prepared by tractors. Monomolecular nonlinear growth model methodology was applied to Punjab’s tractor density time-series data to capture the diffusion of tractor. Levenberg-Marquardt iterative method was applied with the help of SAS by using PROC NLIN statement and the obtained results show that the model is a good fit for the data under consideration. Further, Compound annual growth rate (CAGR) of tractor density was also calculated to infer about the changes in tractor density over the time (1982–2015 ) and found that CAGR was high during 80s and 90s than 2000s. Despite of low growth in last decade, Punjab is expected to have more adopters of tractor in coming years. From this empirical study, we also infer that 90 per cent tractor penetration will be achieved by 2032 in Punjab.

Evaluating the most suitable nonlinear growth model for turbot (Scophthalmus maximus) in aquaculture 2 (weight application): Multi‐criteria model selection and growth prediction

Seeking the most suitable model to describe the growth of turbot, we analysed growth data of two different turbot (Scophthalmus maximus) strains reared communally in a recirculating aquaculture system. We fitted 10 different nonlinear growth models to individual weight gain data (n = 2,010) during the grow-out phase. Analyses were carried out for each strain, for sexes within strains and for a pooled data set containing both strains and sexes. To assess the model performance, three different criteria are used. Further, a growth-simulation was performed to evaluate the shape of the generated curve. This way we could assess the capability of the models to predict future growth. The 3-parametric Gompertz model achieved the best fit in 42.9% of all cases tested and the lowest Bayesian information criterion in 100% of cases. The model produced realistically shaped curves and asymptotic values matching the biological attributes of the species. In contrast, 5-parametric functions projected unrealistically shaped curves and predicted improbable mature sizes. Our results show that increasing number of parameters do not lead to increasing goodness of fit, but tend to result in overfitting, and demonstrate the advantages of the 3-parametric Gompertz model for describing the growth of turbot.

Openness, growth convergence and China’s development prospects

ABSTRACTThis paper examines China’s long-term growth prospects and the potential drivers of future growth, based on cross-country productivity convergence and China’s featured demographic evolution. In a nonlinear open economy catch-up growth model, per capital GDP growth of the followers depend on that of the leading economy and time varying convergence of the relative per capita GDP. Comparable open economies of China are identified in terms of relative per capita GDP and the historical data of which are used to project China’s trajectory of productivity convergence and then the growth of per capita GDP. Projection shows China’s future GDP growth will gradually descend from 6.6–6.7% (2016–2020) to 2.6–2.7% (2046–2050) in low variant. Predictions under medium and high variants are provided as well. The importance of further opening-up domestic markets, elimination of birth control policies and accumulation of human capital in the process of promoting urbanization are highlighted and have significant implications for the economic restructuring and transformation of China.Abbreviations: ICRG: International Country Risk Guide; IMF: International Monetary Fund

Modeling the individual height and volume of two integrated crop-livestock-forest systems of &lt;i&gt;Eucalyptus&lt;/i&gt; spp. in the Brazilian Savannah

The aim of this study was to model the individual height and volume of eucalyptus wood in two integrated crop-livestock-forest systems (ICLF1 and ICLF2) in Campo Grande, a city in the state of Mato Grosso do Sul, Brazil. Classic nonlinear growth models were adjusted for height (Logistic, Gompertz, Richards, Weibull, Van Bertalanffy, Brody, Mitscherlich, and Chapman and Richards) and volume (Shumacher-hall nonlinear, Takata, Honner, Logistic, Gompertz, and Weibull) in two structural arrangements: ICLF1, with a spacing of 14 x 2 m and density of 357 trees ha-1, and ICLF2, with a spacing of 22 x 2 m and density of 227 trees ha-1. Diameter at Breast Height (DBH) measurements were performed in 100% of trees, with measurements of the total height of some individuals and a rigorous scaling procedure in diameter classes. According to the calculated value of Student's t-test, there was no significant evidence that DBH and the average height of the trees were different between ICLF1 and ICLF2. Based on the Akaike information criterion (AIC), the corrected Akaike information criterion (AICC) and the Bayesian information criterion (BIC), the Richards model was selected to estimate heights and the Takata model was selected to estimate the volume.

Estimating Complex Measurement and Growth Models Using the R Package PLmixed

Measurement models, such as factor analysis and item response theory models, are commonly implemented within educational, psychological, and behavioral science research to mitigate the negative effects of measurement error. These models can be formulated as an extension of generalized linear mixed models within a unifying framework that encompasses various kinds of multilevel models and longitudinal models, such as partially nonlinear latent growth models. We introduce the R package PLmixed, which implements profile maximum likelihood estimation to estimate complex measurement and growth models that can be formulated within the general modeling framework using the existing R package lme4 and function optim. We demonstrate the use of PLmixed through two examples before concluding with a brief overview of other possible models.