Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Increasing incidence of Epstein‐Barr virus–related nasopharyngeal carcinoma in the United States

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152902/1/cncr32517_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152902/2/cncr32517.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152902/3/cncr32517-sup-0001-FigS1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152902/4/cncr32517-sup-0002-FigS2.pd

Prostaglandin E2 Promotes Endothelial Differentiation from Bone Marrow-Derived Cells through AMPK Activation

Prostaglandin E2 (PGE2) has been reported to modulate angiogenesis, the process of new blood vessel formation, by promoting proliferation, migration and tube formation of endothelial cells. Endothelial progenitor cells are known as a subset of circulating bone marrow mononuclear cells that have the capacity to differentiate into endothelial cells. However, the mechanism underlying the stimulatory effects of PGE2 and its specific receptors on bone marrow-derived cells (BMCs) in angiogenesis has not been fully characterized. Treatment with PGE2 significantly increased the differentiation and migration of BMCs. Also, the markers of differentiation to endothelial cells, CD31 and von Willebrand factor, and the genes associated with migration, matrix metalloproteinases 2 and 9, were significantly upregulated. This upregulation was abolished by dominant-negative AMP-activated protein kinase (AMPK) and AMPK inhibitor but not protein kinase, a inhibitor. As a functional consequence of differentiation and migration, the tube formation of BMCs was reinforced. Along with altered BMCs functions, phosphorylation and activation of AMPK and endothelial nitric oxide synthase, the target of activated AMPK, were both increased which could be blocked by EP4 blocking peptide and simulated by the agonist of EP4 but not EP1, EP2 or EP3. The pro-angiogenic role of PGE2 could be repressed by EP4 blocking peptide and retarded in EP4+/− mice. Therefore, by promoting the differentiation and migration of BMCs, PGE2 reinforced their neovascularization by binding to the receptor of EP4 in an AMPK-dependent manner. PGE2 may have clinical value in ischemic heart disease

BMC Cancer

BACKGROUND: Although some countries have observed a stabilization in the incidence of CNS, an increasing incidence has been reported from multiple studies. Recent observations point out to the heterogeneity of incidence trends according to histological subtypes, gender and age-groups. Using a high-quality regional CNS tumor registry, this article describes the trends of CNS tumor incidence for main histological subtypes, including benign and malignant tumors, in the French department of Gironde from 2000 to 2012. METHODS: Crude and age-standardized incidence rates were calculated globally, by histological subtypes, malignant status, gender and age groups. For trends, annual percent changes (APC) were obtained from a piecewise log-linear model. RESULTS: A total of 3515 CNS tumors was registered during the period. The incidence of overall CNS tumors was 19/100000 person-years (8.3/100000 for neuroepithelial tumors and 7.3/100000 for meningeal tumors). An increased incidence of overall CNS tumors was observed from 2000 to 2012 (APC = + 2.7%; 95%-confidence interval (CI): 1.8-3.7). This trend was mainly explained by an increase in the incidence of meningiomas over the period (APC = + 5.4%, 95%-CI: 3.8-7.0). The increased incidence rate of CNS tumors was more pronounced in female and in older patients even though the incidence rate increased in all age groups. CONCLUSIONS: Part of the temporal variation may be attributed to improvement in registration, diagnosis and clinical practices but also to changes in potential risk factors. Thus, etiological studies on CNS tumors are needed to clarify this rising trend