Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone

By using a suitable triple cover we show how to possibly model the construction of a minimal surface with positive genus spanning all six edges of a tetrahedron, working in the space of BV functions and interpreting the film as the boundary of a Caccioppoli set in the covering space. After a question raised by R. Hardt in the late 1980's, it seems common opinion that an area-minimizing surface of this sort does not exist for a regular tetrahedron, although a proof of this fact is still missing. In this paper we show that there exists a surface of positive genus spanning the boundary of an elongated tetrahedron and having area strictly less than the area of the conic surface.Comment: Expanding on the previous version with additional lower bounds, new images, corrections and improvements. Comparison with Reifenberg approac

A table of n-component handlebody links of genus n+1 up to six crossings

A handlebody link is a union of handlebodies of positive genus embedded in 3-space, which generalises the notion of links in classical knot theory. In this paper, we consider handlebody links with a genus two handlebody and n - 1 solid tori, n > 1. Our main result is the classification of such handlebody links with six crossings or less, up to ambient isotopy

Intradural angiomatous meningioma arising from a thoracic nerve root

BACKGROUND: Spinal intradural meningiomas that arise purely from a nerve root without dural attachments are extremely rare. Spinal meningiomas arise from arachnoidal cap cells in the spinal canal, and growth of these tumors exerts pressure on the spinal cord and nerve roots. CASE DESCRIPTION: A patient presented with a lesion at the T3-T4 level that resembled a schwannoma on magnetic resonance imaging. During surgery, the tumor originated from a spinal nerve root. Pathologically, it was an angiomatous meningioma (AM). CONCLUSIONS: In a review of the literature, we discuss the pathogenesis and surgical strategy for diagnosing and treating these extremely rare AM lesions

On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions

In this paper we estimate from above the area of the graph of a singular map $u$ taking a disk to three vectors, the vertices of a triangle, and jumping along three $\mathcal{C}^2-$ embedded curves that meet transversely at only one point of the disk. We show that the relaxed area can be estimated from above by the solution of a Plateau-type problem involving three entangled nonparametric area-minimizing surfaces. The idea is to "fill the hole" in the graph of the singular map with a sequence of approximating smooth two-codimensional surfaces of graph-type, by imagining three minimal surfaces, placed vertically over the jump of $u$, coupled together via a triple point in the target triangle. Such a construction depends on the choice of a target triple point, and on a connection passing through it, which dictate the boundary condition for the three minimal surfaces. We show that the singular part of the relaxed area of $u$ cannot be larger than what we obtain by minimizing over all possible target triple points and all corresponding connections.Comment: 35 pages and 15 figure

Emergency decompressive craniectomy after removal of convexity meningiomas

BACKGROUND: Convexity meningiomas are benign brain tumors that are amenable to complete surgical resection and are associated with a low complication rate. The aim of this study was to identify factors that result in acute postoperative neurological worsening after the removal of convexity meningiomas. METHODS: Clinical evaluation and neuroradiological analysis of patients who underwent removal of a supratentorial convexity meningioma were reviewed. Patients were selected when their postoperative course was complicated by acute neurological deterioration requiring decompressive craniectomy. RESULTS: Six patients (mean age: 43.3 years) underwent surgical removal of a supratentorial convexity meningioma. Brain shift (mean: 9.9 mm) was evident on preoperative imaging due to lesions of varying size and perilesional edema. At various times postoperatively, patient consciousness worsened (up to decerebrate posture) with contralateral paresis and pupillary anisocoria. Computed tomography revealed no postoperative hematoma, however, did indicate increased brain edema and ventricular shift (mean: 12 mm). Emergency decompressive craniectomy and brief ventilator assistance were performed in all patients. Ischemia of the ipsilateral posterior cerebral artery occurred in 3 patients and hydrocephalus occurred in 2 patients. Outcome was good in 2, fair in 2, 1 patient had severe disability, and 1 patient died after 8 months. CONCLUSIONS: Brain shift on preoperative imaging is a substantial risk factor for postoperative neurological worsening in young adult patients after the removal of convexity meningiomas. Emergency decompressive craniectomy must be considered because it is effective in most cases. Other than consciousness impairment, there is no reliable clinical landmark to guide the decision to perform decompressive craniectomy; however, brain ischemia may have already occurred

Fine-needle aspiration accuracy in the diagnosis of primary epithelioid angiosarcoma of the adrenal gland: a case report and review of the literature

Primary epithelioid angiosarcoma of the adrenal gland is extremely rare. Only 37 cases have been reported in the scientific literature.Here we describe the case of a 55-year-old woman affected by metastatic angiosarcoma in the right adrenal gland, who died few days after the histological diagnosis made by fine-needle aspiration (FNA). This is the second case of primary epithelioid angiosarcoma diagnosed by FNA among scientific articles published in English in PubMed. Microscopically, the tumor showed a predominant epithelioid differentiation, thus making the diagnostic process more difficult than usual. Immunohistochemical examination revealed positive reactivity for cytokeratin, CD31, and CD34. The literature shows that epithelioid adrenal angiosarcoma has poor clinical outcome, especially when metastatic at presentation

NMR as evaluation strategy for cellular uptake of nanoparticles

Advanced nanostructured materials, such as gold nanoparticles, magnetic nanoparticles, and multifunctional materials, are nowadays used in many state-of-the-art biomedical application. However, although the engineering in this field is very advanced, there remain some fundamental problems involving the interaction mechanisms between nanostructures and cells or tissues. Here we show the potential of 1H NMR in the investigation of the uptake of two different kinds of nanostructures, that is, maghemite and gold nanoparticles, and of a chemotherapy drug (Temozolomide) in glioblastoma tumor cells. The proposed experimental protocol provides a new way to investigate the general problem of cellular uptake for a variety of biocompatible nanostructures and drugs. © 2014 American Chemical Society