Equivariance and Invariance for Optimal Designs in Generalized Linear Models Exemplified by a Class of Gamma Models

The main intention of the present work is to outline the concept of equivariance and invariance in the design of experiments for generalized linear models and to demonstrate its usefulness. In contrast with linear models, pairs of transformations have to be employed for generalized linear models. These transformations act simultaneously on the experimental settings and on the location parameters in the linear component. Then, the concept of equivariance provides a tool to transfer locally optimal designs from one experimental region to another when the nominal values of the parameters are changed accordingly. The stronger concept of invariance requires a whole group of equivariant transformations. It can be used to characterize optimal designs which reflect the symmetries resulting from the group actions. The general concepts are illustrated by models with gamma distributed response and a canonical link. There, for a given transformation of the experimental settings, the transformation of the parameters is not unique and may be chosen to be nonlinear in order to fully exploit the model structure. In this case, we can derive invariant maximin efficient designs for the D- and the IMSE-criterion.

Electricity consumption forecasting using DFT decomposition based hybrid ARIMA-DLSTM model

Forecasting electricity consumption is vital, it guides policy makers and electricity distribution companies in formulating policies to manage production and curb pilfering. Accurately forecasting electricity consumption is a challenging task. Relying on a single model to forecast electricity consumption data which comprises both linear and nonlinear components produces inaccurate results. In this paper, a hybrid model using autoregressive integrated moving average (ARIMA) and deep long short-term memory (DLSTM) model based on discrete fourier transform (DFT) decomposition is presented. Aided by its superior decomposition capability, filtering using DFT can efficiently decompose the data into linear and nonlinear components. ARIMA is employed to model the linear component, while DLSTM is applied on the nonlinear component; the two predictions are then combined to obtain the final predicted consumption. The proposed techniques are applied on the household electricity consumption data of France to obtain forecasts for one day, one week and ten days ahead consumption. The results reveal that the proposed model outperforms other benchmark models considered in this investigation as it attained lower error values. The proposed model could accurately decompose time series data without exhibiting a performance degradation, thereby enhancing prediction accuracy.

Stability Analysis for Yield and it’s Related Characters in Linseed (Linum usitatissimum L.)

Thirty-six genotypes including eight parents and their 28 crosses developed in diallel fashion excluding reciprocals were used to studied their stability performance over six contrasting environments viz., early, normal and late sown under rainfed and irrigated conditions for seed yield and its contributing characters. Genotype x Environment interaction and Linear component of G x E interaction were showed significant for all the characters except plant height, secondary branches per plant and biological yield per plant under study. The parents Meera and PA2 showed stable performance for two characters and rest of the genotypes showed stable performance for one character over a range of environments under study. The cross Meera x RL13161 and RL15583 x KBA3 showed stable performance for seed yield and two crosses RL13161 x KBA3 and RL15583 x KBA3 showed stable performance for oil content and rest of four crosses showed stable performance for other characters.

Latent Linear Adjustment Autoencoder v1.0: a novel method for estimating and emulating dynamic precipitation at high resolution

A key challenge in climate science is to quantify the forced response in impact-relevant variables such as precipitation against the background of internal variability, both in models and observations. Dynamical adjustment techniques aim to remove unforced variability from a target variable by identifying patterns associated with circulation, thus effectively acting as a filter for dynamically induced variability. The forced contributions are interpreted as the variation that is unexplained by circulation. However, dynamical adjustment of precipitation at local scales remains challenging because of large natural variability and the complex, nonlinear relationship between precipitation and circulation particularly in heterogeneous terrain. Building on variational autoencoders, we introduce a novel statistical model – the Latent Linear Adjustment Autoencoder (LLAAE) – that enables estimation of the contribution of a coarse-scale atmospheric circulation proxy to daily precipitation at high resolution and in a spatially coherent manner. To predict circulation-induced precipitation, the Latent Linear Adjustment Autoencoder combines a linear component, which models the relationship between circulation and the latent space of an autoencoder, with the autoencoder's nonlinear decoder. The combination is achieved by imposing an additional penalty in the cost function that encourages linearity between the circulation field and the autoencoder's latent space, hence leveraging robustness advantages of linear models as well as the flexibility of deep neural networks. We show that our model predicts realistic daily winter precipitation fields at high resolution based on a 50-member ensemble of the Canadian Regional Climate Model at 12 km resolution over Europe, capturing, for instance, key orographic features and geographical gradients. Using the Latent Linear Adjustment Autoencoder to remove the dynamic component of precipitation variability, forced thermodynamic components are expected to remain in the residual, which enables the uncovering of forced precipitation patterns of change from just a few ensemble members. We extend this to quantify the forced pattern of change conditional on specific circulation regimes. Future applications could include, for instance, weather generators emulating climate model simulations of regional precipitation, detection and attribution at subcontinental scales, or statistical downscaling and transfer learning between models and observations to exploit the typically much larger sample size in models compared to observations.

Evaluation of genotype by environment interaction and adaptability in lowland irrigated rice hybrids for grain yield under high temperature

Recent predictions on climate change indicate that high temperature episodes are expected to impact rice production and productivity worldwide. The present investigation was undertaken to assess the yield stability of 72 rice hybrids and their parental lines across three temperature regimes over two consecutive dry seasons using the additive main effect and multiplicative interaction (AMMI), genotype and genotype × environment interaction (GGE) stability model analysis. The combined ANOVA revealed that genotype × environment interaction (GEI) were significant due to the linear component for most of the traits studied. The AMMI and GGE biplot explained 57.2% and 69% of the observed genotypic variation for grain yield, respectively. Spikelet fertility was the most affected yield contributing trait and in contrast, plant height and tiller numbers were the least affected traits. In case of spikelet fertility, grain yield and other yield contributing traits, male parent contributed towards heat tolerance of the hybrids compared to the female parent. The parental lines G74 (IR58025B), G83 (IR40750R), G85 (C20R) and hybrids [G21 (IR58025A × KMR3); G3 (APMS6A × KMR3); G57 (IR68897A × KMR3) and G41 (IR79156A × RPHR1005)] were the most stable across the environments for grain yield. They can be considered as potential genotypes for cultivation under high temperature stress after evaluating under multi location trials.

Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

Biological features of blood lymphocytes of the primary patients with endometrial cancer

The aim: to examine the radiosensitivity of chromosomes of T-lymphocytes in the blood of primary patients with endometrial cancer depending on the radiation dose. It was expected that the investigations would reveal a cytogenetic parameter as a predictor of radiosensitivity in non-malignant cells of patients exposed to curative irradiation. Materials and methods. Blood samples from 20 primary patients and 30 conditionally healthy donors were examined. Peripheral blood T-lymphocytes culture test system with metaphase chromosome aberration analysis was used. X-ray test-irradiation was performed at G0-stage of the cell cycle in the dose range of 0.5–3.0 Gy. Results. It was shown that the spontaneous level of chromosome aberrations in lymphocytes of primary patients before anti-tumour therapy is 7,82±0,33 aberrations/100 metaphases. This is more than 2-fold higher than the upper limit of average population index and approximately 6-fold higher than the data of own control. In our study during X-ray irradiation of cells cultures of patients, it was found for the first time that the total frequency of radiation-induced chromosome aberrations obeys the classical linear quadratic dose dependence with a predominance of linear component values; the frequency of radiation markers – also linear quadratic dose dependence, but with a predominance of quadratic component. Conclusions. High specificity of T-lymphocyte chromosomes to exposure to ionizing radiation as well as strict dependence of chromosome aberration yield on exposure dose justify their use as predictors of radiosensitivity of healthy cells from the tumour environment. The revealed dependences of induction of chromosomal damage in T-lymphocytes of patients with endometrial cancer prove the need for a personalized approach to plan the course of radiation therapy