Universal convex covering problems under translation and discrete rotations

We consider the smallest-area universal covering of planar objects of perimeter 2 (or equivalently closed curves of length 2) allowing translation and discrete rotations. In particular, we show that the solution is an equilateral triangle of height 1 when translation and discrete rotation of $\pi$ are allowed. Our proof is purely geometric and elementary. We also give convex coverings of closed curves of length 2 under translation and discrete rotations of multiples of $\pi/2$ and $2\pi/3$. We show a minimality of the covering for discrete rotation of multiples of $\pi/2$, which is an equilateral triangle of height smaller than 1, and conjecture that the covering is the smallest-area convex covering. Finally, we give the smallest-area convex coverings of all unit segments under translation and discrete rotations $2\pi/k$ for all integers $k\ge 3$

Ruptured Medullary Hemangioblastoma Mimicking a Craniocervical Junction Dural Arteriovenous Fistula with a Pseudoaneurysm

Hemangioblastomas (HBMs) are rare vascular tumors commonly located in the posterior fossa of adults. A mid-50s patient presented with sudden unconsciousness. Computed tomography scans revealed acute hemorrhages around the posterior fossa, predominantly in the subarachnoid space. Digital subtraction angiography (DSA) revealed an 8-mm round lesion filled with contrast agent, fed by the C1 segmental artery of the left vertebral artery (VA), showing early venous drainage to the spinal cord and brainstem. Emergent embolization was attempted under suspicion of a ruptured dural arteriovenous fistula, resulting in parent artery occlusion due to feeder selection failure. Follow-up DSA after a month depicted a persistent aneurysm via collaterals from both VAs. Consequently, the decision was made to proceed with surgical intervention, leading to the resection of the lesion, confirming its diagnosis as a HBM through histological examination. This case underscores the potential for misdiagnosis when HBMs with an intratumoral shunt mimic vascular shunt lesions

Dual Effect of Chrysanthemum indicum

The risk of bone-related diseases increases due to the imbalance between bone resorption and bone formation by osteoclasts and osteoblasts, respectively. The goal in the development of antiosteoporotic treatments is an agent that will improve bone through simultaneous osteoblast stimulation and osteoclast inhibition without undesirable side effects. To achieve this goal, numerous studies have been performed to identify novel approaches using natural oriental herbs to treat bone metabolic diseases. In the present study, we investigated the effect of Chrysanthemum indicum extract (CIE) on the differentiation of osteoclastic and osteoblastic cells. CIE inhibited the formation of TRAP-positive mature osteoclasts and of filamentous-actin rings and disrupted the bone-resorbing activity of mature osteoclasts in a dose-dependent manner. CIE strongly inhibited Akt, GSK3β, and IκB phosphorylation in RANKL-stimulated bone marrow macrophages and did not show any effects on MAP kinases, including p38, ERK, and JNK. Interestingly, CIE also enhanced primary osteoblast differentiation via upregulation of the expression of alkaline phosphatase and the level of extracellular calcium concentrations during the early and terminal stages of differentiation, respectively. Our results revealed that CIE could have a potential therapeutic role in bone-related disorders through its dual effects on osteoclast and osteoblast differentiation

Clinical Characteristics and Management of Saccular Cysts: A Single Institute Experience

Objectives A saccular cyst is defined as a dilated saccule of the larynx, filled with mucus, and is located between the false vocal cords and the thyroid cartilage. Although this uncommon laryngeal condition is benign in nature, it could lead to dyspnea, stridor, and airway obstruction, depending on its size and location. Furthermore, some saccular cysts have been associated with laryngeal carcinoma. This study aimed to characterize this rather uncommon laryngeal condition to aid in determining the proper management of this pathology. Methods Medical records were retrospectively reviewed of all patients with saccular cysts diagnosed and treated between 2006 and 2017 at a tertiary otolaryngologic care center. Results Seven patients with saccular cysts were identified (male:female=2:5; mean age, 34.1 years); two were pediatric patients. Surgical intervention was performed in all patients by laryngo-microsurgery using CO2 laser. There was no recurrence after the initial surgical treatment. Conclusion Saccular cysts can be managed endoscopically using CO2 laser, without requiring an external approach. Therefore, an endoscopic approach should be actively considered for an optimal treatment outcome