Construction of topological representation of geometric patterns using Cantor self-similar set

Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any patterns can be represented by a specific topological space, a construction of topological representation of patterns using Cantor set is shown. The obtained topological representations are then demonstrated by the contractions that characterize the self-similarity of Cantor set. For some practical geometric patterns, e.g., network, dendritic, and clusterized patterns, their topological representations are focused on

Angiomatous Nasal Polyp Diagnosed by Preoperative Imaging and Successfully Resected by Endonasal Endoscopic Surgery: A Case Report

Angiomatous polyp is a benign, nonneoplastic nasal polyp that accounts for 4-5% of all inflammatory nasal polyps but is rarely reported in the literature. It can grow rapidly and exhibit an aggressive clinical behavior that can simulate malignant sinonasal tumor. We herein report a case of a 13-year-old boy with a rapidly growing angiomatous polyp in the nasal cavity. We had followed up the patient without significant changes for two years, but the tumor had rapidly grown in the last six months. At first, the rapid growth of the tumor and the bone erosion of the maxilla were suggestive of a malignant tumor. However, with preoperative magnetic resonance imaging (MRI) and [18F]-2-fluoro-2-deoxy-D-glucose positron emission tomography imaging findings, we established the corrective diagnosis of an angiomatous polyp. After the diagnostic imaging, we performed an endoscopic endonasal surgery and totally resected the tumor without unnecessary excessive surgery. Recognition of this disease that can mimic malignancy is important to avoid excessive surgery such as en bloc resection by craniofacial approach, and we believe that MRI findings can be helpful for the imaging diagnosis