Renormalization Analysis of Resonance Structure in 2-D Symplectic Map

A symplecticity-preserving RG analysis is carried out to study a resonance structure near an elliptic fixed point of a proto-type symplectic map in two dimensions. Through analyzing fixed points of a reduced RG map, a topology of the resonance structure such as a chain of resonant islands can be determined analytically. An application of this analysis to the Henon map is also presented.Comment: 10 page

Laparoscopic Partial Hepatectomy of Focal Nodular Hyperplasia

Focal nodular hyperplasia is a benign liver lesion incidentally discovered with increasing frequency because of the proliferation of imaging studies. Radiographic characterization can diagnose this pathologic lesion and nonoperative therapy is the standard of care. However, surgical resection may be required for diagnostic reasons or symptomatic patients. Depending on the anatomic location of the lesion, biopsy and/or resection can be performed laparoscopically. We herein report the case of a 26-year-old Japanese woman with a hepatic tumor who required a medical examination. Her medical history was negative for alcohol abuse, oral contraceptive administration and trauma. Clinical examination showed no significant symptoms. Ultrasonography, computed tomography and magnetic resonance imaging showed a mass located in the left lateral segment of the liver with a diameter of about 40 mm. It was difficult to diagnose the tumor definitively from these imaging studies, so we performed laparoscopic partial hepatectomy with successive firing of endoscopic staplers. The histopathological diagnosis was focal nodular hyperplasia. Surgical procedures and postoperative course were uneventful and the patient was discharged from the hospital on postoperative day 5

The immunoreactivity for mir-424 in senile hemangioma.

<p>In situ detection of mir-424 in paraffin-embedded, formalin-fixed tissues of normal skin (a) and senile hemangioma (SH, b). Nucleus was counterstained with nuclear fast red (magnification, ×200). The immunoreactivity for mir-424 (blue) is indicated by arrows. Results are representative of 3 normal skins and 3 SH.</p

The expression of angiogenic factors or the structure of vessels.

<p>(a) Mean relative transcript levels of HIF-1α, VEGFR1 or VEGFR2 (normalized to GAPDH) in tissues from 7 normal skin (normal) or vascular anomalies such as 7 senile hemangioma (SH), 3 vascular malformation (VM), 4 angiosarcoma (AS), 4 venous lake (VL) and 3 infantile hemangioma (IH) by real-time quantitative PCR. The transcript levels in samples of normal skin were set at 1. Error bars represent SD of +1. (b) The expression of α-smooth muscle actin (SMA) or type IV collagen (COL4) in the affected vessels of senile hemangioma (SH), vascular malformation (VM) and venous lake (VL). Paraffin sections were subjected to immunohistochemical analysis with antibodies against α-SMA or COL4 as described in ‘<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0014334#s2" target="_blank">Materials and Methods</a>’. Results are representative of several cases.</p