An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models

Citation: Gonalves, M. A. D., Bello, N. M., Dritz, S. S., Tokach, M. D., DeRouchey, J. M., Woodworth, J. C., & Goodband, R. D. (2016). An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models. Journal of Animal Science, 94(5), 1940-1950. doi:10.2527/jas2015-0106Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp: Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G: F relative to Trp: Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G: F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G: F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp: Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with the estimation process rendered results from the BLQ model questionable. Importantly, accounting for heterogeneous variance enhanced inferential precision as the breadth of the confidence interval for the mean breakpoint decreased by approximately 44%. In summary, the article illustrates the use of linear and nonlinear mixed models for dose-response relationships accounting for heterogeneous residual variances, discusses important diagnostics and their implications for inference, and provides practical recommendations for computational troubleshooting

Seletividade inicial de mesotrione em função de modalidades de aplicação na cultura do milho doce.

No Brasil, o controle químico de plantas daninhas em milho doce baseia-se em herbicidas registrados para milho comum. Objetivou-se com este trabalho avaliar, por meio de curvas de dosagem-reposta, a seletividade inicial do herbicida mesotrione ao milho doce em função de modalidades de aplicação. O experimento foi conduzido em casa de vegetação, utilizando-se delineamento experimental em blocos casualizados em esquema fatorial 5x3, com cinco repetições. Foram avaliadas cinco dosagens de mesotrione (0, 72, 144, 288 e 576 g ha-1) e três épocas de aplicação do herbicida (pré-emergência em pós-semeadura, pós-emergência em estádio V3 e pós-emergência em estádio V6), totalizando 15 tratamentos. As avaliações foram realizadas de forma a estudar os efeitos de mesotrione relacionados a intoxicação, índice SPAD, crescimento e massa seca de parte aérea das plantas. Não foi observada interação significativa (p<0,05) entre os fatores avaliados (épocas de aplicação e dosagens do herbicida) no presente estudo. O mesotrione apresenta seletividade à cultura do milho doce híbrido Tropical Plus até quatro vezes a dosagem recomendada do herbicida (4 x 144 g ha-1) ou (576 g ha-1) tanto em aplicações em pré-emergência quanto em pósemergência (estádios V3 e V6)

Solving Fuzzy Job-Shop Scheduling Problems with a Multiobjective Optimizer

International audienceIn real-world manufacturing environments, it is common to face a job-shop scheduling problem (JSP) with uncertainty. Among different sources of uncertainty, processing times uncertainty is the most common. In this paper, we investigate the use of a multiobjective genetic algorithm to address JSPs with uncertain durations. Uncertain durations in a JSP are expressed by means of triangular fuzzy numbers (TFNs). Instead of using expected values as in other work, we consider all vertices of the TFN representing the overall completion time. As a consequence, the proposed approach tries to obtain a schedule that optimizes the three component scheduling problems (corresponding to the lowest, most probable, and largest durations) all at the same time. In order to verify the quality of solutions found by the proposed approach, an experimental study was carried out across different benchmark instances. In all experiments, comparisons with previous approaches that are based on a single-objective genetic algorithm were also performed

Modeling the adoption of innovations in the presence of geographic and media influences

While there has been much work examining the affects of social network structure on innovation adoption, models to date have lacked important features such as meta-populations reflecting real geography or influence from mass media forces. In this article, we show these are features crucial to producing more accurate predictions of a social contagion and technology adoption at the city level. Using data from the adoption of the popular micro-blogging platform, Twitter, we present a model of adoption on a network that places friendships in real geographic space and exposes individuals to mass media influence. We show that homopholy both amongst individuals with similar propensities to adopt a technology and geographic location are critical to reproduce features of real spatiotemporal adoption. Furthermore, we estimate that mass media was responsible for increasing Twitter's user base two to four fold. To reflect this strength, we extend traditional contagion models to include an endogenous mass media agent that responds to those adopting an innovation as well as influencing agents to adopt themselves

Thermally Induced Nano-Structural and Optical Changes of nc-Si:H Deposited by Hot-Wire CVD

We report on the thermally induced changes of the nano-structural and optical properties of hydrogenated nanocrystalline silicon in the temperature range 200–700 °C. The as-deposited sample has a high crystalline volume fraction of 53% with an average crystallite size of ~3.9 nm, where 66% of the total hydrogen is bonded as ≡Si–H monohydrides on the nano-crystallite surface. A growth in the native crystallite size and crystalline volume fraction occurs at annealing temperatures ≥400 °C, where hydrogen is initially removed from the crystallite grain boundaries followed by its removal from the amorphous network. The nucleation of smaller nano-crystallites at higher temperatures accounts for the enhanced porous structure and the increase in the optical band gap and average gap

The role of ETG modes in JET-ILW pedestals with varying levels of power and fuelling

We present the results of GENE gyrokinetic calculations based on a series of JET-ITER-like-wall (ILW) type I ELMy H-mode discharges operating with similar experimental inputs but at different levels of power and gas fuelling. We show that turbulence due to electron-temperature-gradient (ETGs) modes produces a significant amount of heat flux in four JET-ILW discharges, and, when combined with neoclassical simulations, is able to reproduce the experimental heat flux for the two low gas pulses. The simulations plausibly reproduce the high-gas heat fluxes as well, although power balance analysis is complicated by short ELM cycles. By independently varying the normalised temperature gradients (omega(T)(e)) and normalised density gradients (omega(ne )) around their experimental values, we demonstrate that it is the ratio of these two quantities eta(e) = omega(Te)/omega(ne) that determines the location of the peak in the ETG growth rate and heat flux spectra. The heat flux increases rapidly as eta(e) increases above the experimental point, suggesting that ETGs limit the temperature gradient in these pulses. When quantities are normalised using the minor radius, only increases in omega(Te) produce appreciable increases in the ETG growth rates, as well as the largest increases in turbulent heat flux which follow scalings similar to that of critical balance theory. However, when the heat flux is normalised to the electron gyro-Bohm heat flux using the temperature gradient scale length L-Te, it follows a linear trend in correspondence with previous work by different authors

Predictive JET current ramp-up modelling using QuaLiKiz-neural-network

This work applies the coupled JINTRAC and QuaLiKiz-neural-network (QLKNN) model on the ohmic current ramp-up phase of a JET D discharge. The chosen scenario exhibits a hollow T-e profile attributed to core impurity accumulation, which is observed to worsen with the increasing fuel ion mass from D to T. A dynamic D simulation was validated, evolving j, n(e), T-e, T-i, n(Be), n(Ni), and n(W) for 7.25 s along with self-consistent equilibrium calculations, and was consequently extended to simulate a pure T plasma in a predict-first exercise. The light impurity (Be) accounted for Z(eff) while the heavy impurities (Ni, W) accounted for Prad. This study reveals the role of transport on the Te hollowing, which originates from the isotope effect on the electron-ion energy exchange affecting T-i. This exercise successfully affirmed isotopic trends from previous H experiments and provided engineering targets used to recreate the D q-profile in T experiments, demonstrating the potential of neural network surrogates for fast routine analysis and discharge design. However, discrepancies were found between the impurity transport behaviour of QuaLiKiz and QLKNN, which lead to notable T-e hollowing differences. Further investigation into the turbulent component of heavy impurity transport is recommended

Shattered pellet injection experiments at JET in support of the ITER disruption mitigation system design

A series of experiments have been executed at JET to assess the efficacy of the newly installed shattered pellet injection (SPI) system in mitigating the effects of disruptions. Issues, important for the ITER disruption mitigation system, such as thermal load mitigation, avoidance of runaway electron (RE) formation, radiation asymmetries during thermal quench mitigation, electromagnetic load control and RE energy dissipation have been addressed over a large parameter range. The efficiency of the mitigation has been examined for the various SPI injection strategies. The paper summarises the results from these JET SPI experiments and discusses their implications for the ITER disruption mitigation scheme

New H-mode regimes with small ELMs and high thermal confinement in the Joint European Torus

New H-mode regimes with high confinement, low core impurity accumulation, and small edge-localized mode perturbations have been obtained in magnetically confined plasmas at the Joint European Torus tokamak. Such regimes are achieved by means of optimized particle fueling conditions at high input power, current, and magnetic field, which lead to a self-organized state with a strong increase in rotation and ion temperature and a decrease in the edge density. An interplay between core and edge plasma regions leads to reduced turbulence levels and outward impurity convection. These results pave the way to an attractive alternative to the standard plasmas considered for fusion energy generation in a tokamak with a metallic wall environment such as the ones expected in ITER.&amp; nbsp;Published under an exclusive license by AIP Publishing

Disruption prediction at JET through deep convolutional neural networks using spatiotemporal information from plasma profiles

In view of the future high power nuclear fusion experiments, the early identification of disruptions is a mandatory requirement, and presently the main goal is moving from the disruption mitigation to disruption avoidance and control. In this work, a deep-convolutional neural network (CNN) is proposed to provide early detection of disruptive events at JET. The CNN ability to learn relevant features, avoiding hand-engineered feature extraction, has been exploited to extract the spatiotemporal information from 1D plasma profiles. The model is trained with regularly terminated discharges and automatically selected disruptive phase of disruptions, coming from the recent ITER-like-wall experiments. The prediction performance is evaluated using a set of discharges representative of different operating scenarios, and an in-depth analysis is made to evaluate the performance evolution with respect to the considered experimental conditions. Finally, as real-time triggers and termination schemes are being developed at JET, the proposed model has been tested on a set of recent experiments dedicated to plasma termination for disruption avoidance and mitigation. The CNN model demonstrates very high performance, and the exploitation of 1D plasma profiles as model input allows us to understand the underlying physical phenomena behind the predictor decision