A pixel-based segmentation method was demonstrated to be confounded by developmental stage in estimation of flowering of mango. Categorization of panicles into three developmental stages was undertaken with a single and a two-stage deep learning framework (YOLO and R2CNN), using either upright or rotated bounding boxes. For a validation image set and for total panicle count, the models MangoYOLO(-upright), MangoYOLO-rotated, YOLOv3-rotated, R2CNN(-rotated) and R2CNN-upright achieved: (i) RMSEs of 25.6, 16.0, 15.4, 25.8 and 32.3 panicles per tree image, (ii) Mean average precision (mAP) scores of 72.2, 69.1, 65.0, 62.5 and 70.9% and (iii) weighted F1-scores of 76.5, 76.1, 74.9, 74.0 and 82.0, respectively. For a test set of images involving a different orchard and cultivar and use of a different camera, the R2 for machine vision to human count of panicles per tree was 0.86, 0.80, 0.83, 0.81 and 0.76 for the same models, respectively. Thus, models generalised well, but with no consistent benefit from use of rotated over upright bounding boxes. While the YOLOv3-rotated model was superior in terms of total panicle count, the R2CNN-upright model was more accurate for panicle stage classification. To demonstrate practical application, panicle counts were made weekly for an orchard of 994 trees, with a peak detection routine applied to document multiple flowering events.

Lunar grabens are the largest tensional linear structures on the Moon. In this paper, 17 grabens were selected to investigate the dips and displacement-length ratios (γ) of graben-bounding faults. Several topographic profiles were generated from selected grabens to measure their rim elevation, width and depth through SLDEM2015 (+LOLA) data. The differences in rim elevation (∆h) and width (∆W) between two topographic profiles on each graben were calculated, yielding 146 sets of data. We plotted ∆h versus ∆W for each and calculated the dip angle (α) of graben-bounding faults. A dip of 39.9° was obtained using the standard linear regression method. In order to improve accuracy, large error data was removed based on error analysis. The results 49.4° and 52.5° were derived by the standard linear regression and mean methods, respectively. Based on the depth and length of grabens, the γ value of the graben-bounding normal fault is also studied in this paper. The γ value is 3.6×10-3 for lunar normal faults according to the study of grabens and the Rupes Recta normal fault. After obtaining the values of α and γ, the increase in lunar radius caused by the formation of grabens was estimated. We suggest that the lunar radius has increased by around 130 m owing to the formation of grabens. This study could aid in the understanding of normal fault growth and provide important constraints on the thermal evolution of the Moon.

In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the \v{C}ech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system.

This paper introduces extensions H4,p and X8,p of Horn’s double hypergeometric function H4 and Exton’s triple hypergeometric function X8, taking into account recent extensions of Euler’s beta function, hypergeometric function, and confluent hypergeometric function. Among the numerous extended hypergeometric functions, the primary rationale for choosing H4 and X8 is their comparable extension type. Next, we present various integral representations of Euler and Laplace type, Mellin and inverse Mellin transforms, Laguerre polynomial representation, transformation formulae and a recurrence relation for the extended functions. In particular, we provide a generating function for the X8,p and several bounding inequalities for the H4,p and X8,p.