Abstract:The leaf area density (LAD) within a tree canopy is very important for the understanding and modeling of photosynthetic studies of the tree. Terrestrial light detection and ranging (LiDAR) has been applied to obtain the three-dimensional structural properties of vegetation and estimate the LAD. However, there is concern about the efficiency of available approaches. Thus, the objective of this study was to develop an effective means for the LAD estimation of the canopy of individual magnolia trees using high-resolution terrestrial LiDAR data. The normal difference method based on the differences in the structures of the leaf and non-leaf components of trees was proposed and used to segment leaf point clouds. The vertical LAD profiles were estimated using the voxel-based canopy profiling (VCP) model. The influence of voxel size on the LAD estimation was analyzed. The leaf point cloud's extraction accuracy for two magnolia trees was 86.53% and 84.63%, respectively. Compared with the ground measured leaf area index (LAI), the retrieved accuracy was 99.9% and 90.7%, respectively. The LAD (as well as LAI) was highly sensitive to the voxel size. The spatial resolution of point clouds should be the appropriate estimator for the voxel size in the VCP model.

Accurate estimation and monitoring of rice phenology is necessary for the management and yield prediction of rice. The radar backscattering coefficient, one of the most direct and accessible parameters has been proved to be capable of retrieving rice growth parameters. This paper aims to investigate the possibility of monitoring the rice phenology (i.e., transplanting, vegetative, reproductive, and maturity) using the backscattering coefficients or their simple combinations of multi-temporal RADARSAT-2 datasets only. Four RADARSAT-2 datasets were analyzed at 30 sample plots in Meishan City, Sichuan Province, China. By exploiting the relationships of the backscattering coefficients and their combinations versus the phenology of rice, HH/VV, VV/VH, and HH/VH ratios were found to have the greatest potential for phenology monitoring. A decision tree classifier was applied to distinguish the four phenological phases, and the classifier was effective. The validation of the classifier indicated an overall accuracy level of 86.2%. Most of the errors occurred in the vegetative and reproductive phases. The corresponding errors were 21.4% and 16.7%, respectively.

We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius-Perron dimension p n m, where p is a prime number, m is a square-free natural number and gcd(p, m) = 1. We prove that if n ≤ 5 or m is prime with m < p then they are group-theoretical. This generalizes several results in the literature and gives a partial answer to the question posed by the first author and H. Tucker. As an application, we prove that an integral modular category whose Frobenius-Perron dimensions is odd and less than 1125 is group-theoretical.

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Abstract. Let q be a prime number, k an algebraically closed field of characteristic 0, and H a semisimple Hopf algebra of dimension 2q3 . This paper proves that H is always semisolvable. That is, such Hopf algebras can be obtained by (a number of) extensions from group algebras or duals of group algebras.