An explicit lifting construction of CAP forms on O(1, 5) (Automorphic form, automorphic LL-functions and related topics)

This article is the write-up of what the fist named author presented on January 25th in 2022 during the RJMS workshop. We explicitly construct non-tempered cusp forms on the orthogonal group O(1, 5) of signature (1+, 5-). Given a definite quaternion algebra B over ℚ, the orthogonal group is attached to the indefinite quadratic space of rank 6 with the anisotropic part defined by the reduced norm of B. As well as the explicit construction we study the cuspidal representations generated by our cusp forms in detail. We determine all local components of the cuspidal representations and show that our cusp forms are CAP forms. Our construction can be viewed as a generalization of [8]to the case of any definite quaternion algebras, for which we note that [8] takes up the case where the discriminant of B is two. Unlike [8] the method of the construction is to consider the theta lifting from Maass cusp forms to O(1, 5), following the formulation by Borcherds

Semantic Segmentation of Smartphone Wound Images: Comparative Analysis of AHRF and CNN-Based Approaches

Smartphone wound image analysis has recently emerged as a viable way to assess healing progress and provide actionable feedback to patients and caregivers between hospital appointments. Segmentation is a key image analysis step, after which attributes of the wound segment (e.g. wound area and tissue composition) can be analyzed. The Associated Hierarchical Random Field (AHRF) formulates the image segmentation problem as a graph optimization problem. Handcrafted features are extracted, which are then classified using machine learning classifiers. More recently deep learning approaches have emerged and demonstrated superior performance for a wide range of image analysis tasks. FCN, U-Net and DeepLabV3 are Convolutional Neural Networks used for semantic segmentation. While in separate experiments each of these methods have shown promising results, no prior work has comprehensively and systematically compared the approaches on the same large wound image dataset, or more generally compared deep learning vs non-deep learning wound image segmentation approaches. In this paper, we compare the segmentation performance of AHRF and CNN approaches (FCN, U-Net, DeepLabV3) using various metrics including segmentation accuracy (dice score), inference time, amount of training data required and performance on diverse wound sizes and tissue types. Improvements possible using various image pre- and post-processing techniques are also explored. As access to adequate medical images/data is a common constraint, we explore the sensitivity of the approaches to the size of the wound dataset. We found that for small datasets ( \u3c 300 images), AHRF is more accurate than U-Net but not as accurate as FCN and DeepLabV3. AHRF is also over 1000x slower. For larger datasets ( \u3e 300 images), AHRF saturates quickly, and all CNN approaches (FCN, U-Net and DeepLabV3) are significantly more accurate than AHRF

Long Term Outcome of Patients with Penile Fracture Undergoing Delayed Repair

Introduction: Fracture of the penis is a rare urological emergency which occurs as a result of abrupt trauma to an erect penis. Immediate surgical repair is the standard of care and is superior to nonoperative management due to excellent long term outcomes. A large percentage of the patients present late for treatment out of fear or embarrassment. We report our series of patients who presented&nbsp;&nbsp; late and underwent delayed repair. We also report the long term outcome in these patients.Materials &amp; Methods: The data was retrospectively collected from hospital records, which included: detailed history, symptoms, type of relationship, mechanism of trauma, sexual position, clinical fi ndings at physical examination, imaging results, presence of urethral injury, outcomes, and long-term complications regarding sexual and voiding functions.Results: Twenty two patients presented to our hospital casualty/emergency services following penile fracture and underwent delayed surgical repair. Heterosexual inter- course was the most common cause&nbsp; of fracture (18 patients, 81.81%). The mean time duration between injury and presentation was 48.77±33.56 hours. The mean time duration between presentation and surgical intervention was&nbsp; 4.31±1.37 hours. MRI was done in 6 cases with positive predictive value of 100%. Seventeen (77.27%)&nbsp; patients experienced erections during the post-operative period in the hospital. At the end of 1 year&nbsp; follow-up all the 22 patients had been having sexual intercourse. Conclusions: Our data suggests that, patients with penile fractures undergoing delayed repair have preservation of erectile potency and overall&nbsp; sexual function is maintained.</p