320 research outputs found

    Horospherical surfaces of curves in hyperbolic space

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    We consider the contact between curves and horospheres in Hyperbolic 3-space as an application of singularity theory of functions. We define the osculating horosphere of the curve. We also define the horospherical surface of the curve whose singular points correspond to the locus of polar vectors of osculating horospheres of the curve. One of the main results is to give a generic classification of singularities of horospherical surface of curves

    The rectifying developable and the spherical Darboux image of a space curve

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    In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices

    Singularities of hyperbolic Gauss maps

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    In this paper we adopt the Hyperboloid in Minkowski space as the model of Hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in Hyperbolic space. The hyperbolic Gauss map has been introduced by Epstein[7] in the Poincare ball model which is very useful for the study of constant mean curvature ·surfaces. However, it is very hard to proceed the calculation because it has an intrinsic form. Here, we give an extrinsic definition and we study singularities of these. In the study of singularities of the hyperbolic Gauss map (indicatrix), we understand that the hyperbolic Gauss indicatrix is much easier to proceed the calculation. We introduce the notion of hyperbolic Gauss-Kronecker curvature whose zero sets correspond to the singular set of the hyperbolic Gauss map (indicatrix). We also develop a local differential geometry of hypersurfaces concerning on contact with hyperhorospheres

    Topological classification of black Hole: Generic Maxwell set and crease set of horizon

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    The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

    Endothelial Cells Regulate Physiological Cardiomyocyte Growth via VEGFR2-Mediated Paracrine Signaling

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    Background: Heart failure, which is a major global health problem, is often preceded by pathological cardiac hypertrophy. The expansion of the cardiac vasculature, to maintain adequate supply of oxygen and nutrients, is a key determinant of whether the heart grows in a physiological compensated manner or a pathological decompensated manner. Bidirectional endothelial cell (EC)-cardiomyocyte (CMC) cross talk via cardiokine and angiocrine signaling plays an essential role in the regulation of cardiac growth and homeostasis. Currently, the mechanisms involved in the EC-CMC interaction are not fully understood, and very little is known about the EC-derived signals involved. Understanding how an excess of angiogenesis induces cardiac hypertrophy and how ECs regulate CMC homeostasis could provide novel therapeutic targets for heart failure. Methods: Genetic mouse models were used to delete vascular endothelial growth factor (VEGF) receptors, adeno-associated viral vectors to transduce the myocardium, and pharmacological inhibitors to block VEGF and ErbB signaling in vivo. Cell culture experiments were used for mechanistic studies, and quantitative polymerase chain reaction, microarrays, ELISA, and immunohistochemistry were used to analyze the cardiac phenotypes. Results: Both EC deletion of VEGF receptor (VEGFR)-1 and adeno-associated viral vector-mediated delivery of the VEGFR1-specific ligands VEGF-B or placental growth factor into the myocardium increased the coronary vasculature and induced CMC hypertrophy in adult mice. The resulting cardiac hypertrophy was physiological, as indicated by preserved cardiac function and exercise capacity and lack of pathological gene activation. These changes were mediated by increased VEGF signaling via endothelial VEGFR2, because the effects of VEGF-B and placental growth factor on both angiogenesis and CMC growth were fully inhibited by treatment with antibodies blocking VEGFR2 or by endothelial deletion of VEGFR2. To identify activated pathways downstream of VEGFR2, whole-genome transcriptomics and secretome analyses were performed, and the Notch and ErbB pathways were shown to be involved in transducing signals for EC-CMC cross talk in response to angiogenesis. Pharmacological or genetic blocking of ErbB signaling also inhibited part of the VEGF-B-induced effects in the heart. Conclusions: This study reveals that cross talk between the EC VEGFR2 and CMC ErbB signaling pathways coordinates CMC hypertrophy with angiogenesis, contributing to physiological cardiac growth.</div

    Circulating Fibroblast Growth Factor 21 Levels Are Closely Associated with Hepatic Fat Content: A Cross-Sectional Study

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    BACKGROUND AND AIMS: Fibroblasts growth factor 21 (FGF21), a liver-secreted endocrine factor involved in regulating glucose and lipid metabolism, has been shown to be elevated in patients with non-alcoholic fatty liver disease (NAFLD). This study aimed to evaluate the quantitative correlation between serum FGF21 level and hepatic fat content. METHODS: A total of 138 subjects (72 male and 66 female) aged from 18 to 65 years with abnormal glucose metabolism and B-ultrasonography diagnosed fatty liver were enrolled in the study. Serum FGF21 levels were determined by an in-house chemiluminescence immunoassay and hepatic fat contents were measured by proton magnetic resonance spectroscopy. RESULTS: Serum FGF21 increased progressively with the increase of hepatic fat content, but when hepatic fat content increased to the fourth quartile, FGF21 tended to decline. Serum FGF21 concentrations were positively correlated with hepatic fat content especially in subjects with mild/moderate hepatic steatosis (r = 0.276, p = 0.009). Within the range of hepatic steatosis from the first to third quartile, FGF21 was superior to any other traditional clinical markers including ALT to reflect hepatic fat content. When the patients with severe hepatic steatosis (the fourth quartile) were included, the quantitative correlation between FGF21 and hepatic fat content was weakened. CONCLUSIONS: Serum FGF21 was a potential biomarker to reflect the hepatic fat content in patients with mild or moderate NAFLD. In severe NAFLD patients, FGF21 concentration might decrease due to liver inflammation or injury

    VEGF attenuates development from cardiac hypertrophy to heart failure after aortic stenosis through mitochondrial mediated apoptosis and cardiomyocyte proliferation

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    <p>Abstract</p> <p>Background</p> <p>Aortic stenosis (AS) affects 3 percent of persons older than 65 years and leads to greater morbidity and mortality than other cardiac valve diseases. Surgery with aortic valve replacement (AVR) for severe symptomatic AS is currently the only treatment option. Unfortunately, in patients with poor ventricular function, the mortality and long-term outcome is unsatisfied, and only a minority of these patients could bear surgery. Our previous studies demonstrated that vascular endothelial growth factor (VEGF) protects cardiac function in myocardial infarction model through classic VEGF-PI3k-Akt and unclear mitochondrial anti-apoptosis pathways; promoting cardiomyocyte (CM) proliferation as well. The present study was designed to test whether pre-operative treatment with VEGF improves AS-induced cardiac dysfunction, to be better suitable for AVR, and its potential mechanism.</p> <p>Methods</p> <p>Adult male mice were subjected to AS or sham operation. Two weeks later, adenoviral VEGF (Ad-VEGF), enhanced green fluorescence protein (Ad-EGFP, as a parallel control) or saline was injected into left ventricle free wall. Two weeks after delivery, all mice were measured by echocardiography and harvested for further detection.</p> <p>Results</p> <p>AS for four weeks caused cardiac hypertrophy and left ventricular dysfunction. VEGF treatment increased capillary density, protected mitochondrial function, reduced CMs apoptosis, promoted CMs proliferation and eventually preserved cardiac function.</p> <p>Conclusions</p> <p>Our findings indicate that VEGF could repair AS-induced transition from compensatory cardiac hypertrophy to heart failure.</p

    Factory outbreak of Escherichia coli O157:H7 infection in Japan.

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    To determine the cause of a July 1996 outbreak of Escherichia coli O157:H7 among factory workers in Kyoto, Japan, we conducted cohort and case-control studies. Eating radish sprout salad during lunch at the factory cafeteria had been linked to illness. The sprouts were traced to four growers in Japan; one had been associated with an outbreak of E. coli O157:H7 among 6,000 schoolchildren in Sakai earlier in July
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