Introduction: Multi-environmental trials (METs) and analysis of genotype-by-environment (GE) interaction have a critical role in breeding programs related to the release of high-yielding cultivars with high yield satbility for cultivation across different environments. Different statistical and graphical methods have been proposed to evaluate the GE interaction effects. In the present study, the effect of GE interaction on grain yield in set of new promising lines of barley was evaluated using the additive main effect and multiplicative interaction (AMMI) model. Materials and methods: A set of promising lines of barley including 18 new advanced lines along with two commercial cultivars (cv. Golchin and cv. Oxin) as reference checks were evaluated in the multi-environment trials. Experiments were carried out in five geographical regions in the warm agro-climatic of Iran which included Ahvaz (E1 and E2), Darab (E3 and E4), Gonbad (E5 and E6), Zabol (E7 and E8), and Moghan (E9 and E10) for two consecutive cropping seasons (2021-2022 and 2022-2023). The AMMI model and some stability and adaptability statistics were used to evaluate the effect of GE interaction on grain yield and identify the high yielding with yield stability promising lines. Results: The results indicated that grain yield was significantly affected by environments (E), genotypes (G), and their interaction (GEI). Environments and GE interaction effect explained the highest portion of observed variation of grain yield. Moreover, the GEI effect was further divided into three principal components (IPCAs) and accounted for 68.99 of the total GE interaction variation. Mean comparison showed that promising lines 14, 3, 10, and 17 had higher grain yield (4960, 4920, 4750, and 4670 kg.ha-1, respectively) when compared to the other promising lines and check cultivars. According to the AMMI-based stability statistics, promising lines 17 had the highest yield stability. Moreover, this genotype along with promising lines 1, 3, 10, and 14 were selected as superior promising lines based on the BLUP-based stability and adaptability statistics. Principle components analyisis based on biplot rendered using the WAASB index and grain yield clustered all studied promising lines and experimental environments into four quadrants. Accordingly, promising lines 3, 10, and 17 were placed into the highest yield stability group. Conclusion: The results of this research revealed that promising lines 4 and 14 had specific adaptability to the northern regions (Moghan and Gonbad), and promising lines 3 and 10 showed specific adaptability to the southern regions (Ahvaz, Darab, and Zabol). Therefore, further evaluation of these promising lines, for selection and releasing some of them as new commercial cultivars as well as using them as parents in the national barley breeding programs, is required.

The principal component analysis (PCA) is one of the procedures that have been a successful performance in signal processing and dimension reduction of the signals. However, a requirement in applying PCA to the images is converting images into a vector.This process leads to loss spatial locality information. To solve this problem, the two-dimensional PCA was proposed. Also, most recently the sparse principal component was introduced that not only keep the properties of standard PCA but also try to make a lot of elements of the basis vectors to zero. In this paper, inspired by the above two ideas, the two-dimensional sparse principal component analysis (2-D. SPCA) is proposed.In this paper, the Least Angle Regression- Elastic Net formula, in addition, using l1 and l2 constraints is extended to two-dimensional model with a few minor changes in its input to approach 2-D. SPCA.The two-dimensional sparse principal component analysis is evaluated in image compression. Before applying the algorithm, the image is divided into several blocks with resolution 8×8 and a database of these blocks is formed. Comparison the performance of 2-D. SPCA and Discrete Cosine transform, for the same number of elements that are necessary to save the image after the conversion shows the good performance of the proposed algorithm. In addition, the proposed algorithm is applied to 8×8 blocks of 60 images with different textures, and the resulted two-dimensional sparse principal components could be used for other test images with a suitable performance.

In this study, PC technique was used to reduce the number of spectral bands or spatial variables in a data set by finding their linear combinations. To apply the PCA for spectral/spatial data set, Landsat TM data recorded from 5 different areas in Central Iran, and 18 soil varaibales were used. The result of PCA transformation for TM bands revealed the importance of PC1 in soil studies, PC2 and or PC3 for vegetation investigations. The results of PCA for Landsat TM and soil data showed that the TM data of 7 bands and 18 soil variables v/ere mainly compressed to just three PCs that describe more than 90% and 55% of spectral and spatial information respectively. Based on the obtained results we may conclude that PCA can be applied to different sources of spectral/spatial data, for a better establishment of sampling plan and save in money and time.

It is the purpose of this paper to contribute to the discussion initiated by Wachter about the parallelism between principal component (PC) and a typological grade of membership (Go M) analysis. The author tested empirically the close relationship between both analysis in a low dimensional framework comprising up to nine dichotomous variables and two typologies.Our contribution to the subject is also empirical. It relies on a dataset from a survey which was especially designed to study the reward of skills in the banking sector in Portugal. The statistical data comprise thirty polythomous variables and were decomposed in four typologies using an optimality criterion. The empirical evidence shows a high correlation between the first PC scores and individual Go M scores. No correlation with the remaining PCs was found, however. In addtion to that, the first PC also proved effective to rank individuals by skill following the particularity of data distribution meanwhile unveiled in Go M analysis.