The relation between isoperimetric properties and Laplacian spectra of weighted graphs is investigated. The vertices are classified into k clusters with „few" inter-cluster edges of „small" weights (area) and „similar" cluster sizes (volumes). For k=2 the Cheeger constant represents the minimum requirement for the area/volume ratio and it is estimated from above by v?1(2-?1), where ?1 is the smallest positive eigenvalue of the weighted Laplacian. For k?2 we define the k-density of a weighted graph that is a generalization of the Cheeger constant and estimated from below by Si=1k-1?i and from above by c2 Si=1k-1 ?i, where 0<?1=…=Sk-1 are the smallest Laplacian eigenvalues and the constant c?1 depends on the metric classification properties of the corresponding eigenvectors. Laplacian spectra are also related to canonical correlations in a probabilistic setup.
Understanding the relationship between root system and yield related traits is an important objective in crop breeding programs. Canonical correlation analysis has been adopted to study the strength of association between the root morphological traits and grain yield components under low-moisture stress and well-watered conditions and to find the root morphological characters that have the largest influence on grain yield and its components under the two conditions. This study revealed that root to shoot length and weight ratios and root dry weight were had the largest effect on plant height, shoot dry weight and grain yield under well-watered condition. Under low moisture stress, maximum root length and root number were also important for improving grain yield and panicle length. The interrelationships clearly identified the importance of root to shoot length and weight ratios and root dry weight under well-watered condition. While, maximum root length and root number are a better combination under low moisture stress condition.
To determine the effect of tree canopy composition on understory species abundance, three-hundred 2 m × 2-m quadrats from 30 high-latitude boreal forest stands were sampled. In addition, all trees within a 3mradius of each quadrat center and ≥1 m tall were also measured for height, basal diameter, and canopy width (n = 3130). Stands were 33–178 years old, with canopies of Populus tremuloides (trembling aspen) and Picea spp. (spruce) in varying proportions. Arctostaphylos uva-ursi, Calamagrostis purpurascens, Chamerion angustifolium, Shepherdia canadensis, and Hylocomium splendens were the most frequent understory species among quadrats. Scatterplots of P. tremuloides and individual vascular understory species cover values lacked bivariate trends, but the understory species had distinct maxima that ranged from 20 to 90%. A moderately strong correlation (r = 0.52, P <0.001) occurred between P. tremuloides canopy and total vascular understory plant covers, but weak individual species correlations (r = 0.22–0.35, P <0.001), suggested understory species variation was primarily determined by factors other than the amount of immediately overhead canopy cover. Canonical correlation analysis (R = 0.82, P <0.001) indicated that greater vascular understory plant cover occurred when forest stands consisted of P. tremuloides with large canopies and large basal diameters, and lacked Picea. Maximum cover for vascular understory species declined when Picea cover exceeded 7–10%. In combination, P. tremuloides stem densities or a metric based on summed canopy areas converted to a diameter value (canopy-area diameter), and the vertical silhouette area of Picea canopies (canopy profile area), as independent linear regression variables, explained ∼79% of the variance in total vascular understory plant cover. Several Picea basal areaderived metrics were strongly and positively associated with increasing H. splendens cover, but canopy profile area was more informative. Populus tremuloides canopy area and Picea canopy profile area, as indicators of shading, may be important determinants of vascular understory vegetation abundance in stands where solar radiation enters at angles of up to 52° during the summer.
thermogenic curves of B. subtilis growth with and without CUR were calculated using the cosine method [ 37 ].
Canonicalcorrelation analysis (CCA)
The typical use for CCA in the experimental context is to take two sets of
Authors:Aidin Pahlavan, Mohammad Hassan Kamani, Amir Hossein Elhamirad, Zahra Sheikholeslami, Mohammad Armin, and Hanieh Amani
regression models and canonicalcorrelation. Although several attempts have been made on the quality assessment of bread attributes in various wheat varieties, no comprehensive method has yet introduced to estimate the quality properties of bread from the raw