Redox evolution of a degassing magma rising to the surface.

Volatiles carried by magmas, either dissolved or exsolved, have a fundamental effect on a variety of geological phenomena, such as magma dynamics1–5 and the composition of the Earth's atmosphere 6. In particular, the redox state of volcanic gases emanating at the Earth's surface is widely believed to mirror that of the magma source, and is thought to have exerted a first-order control on the secular evolution of atmospheric oxygen6,7. Oxygen fugacity (fO2 ) estimated from lava or related gas chemistry, however, may vary by as much as one log unit8–10, and the reason for such differences remains obscure. Here we use a coupled chemical–physical model of conduit flow to show that the redox state evolution of an ascending magma, and thus of its coexisting gas phase, is strongly dependent on both the composition and the amount of gas in the reservoir. Magmas with no sulphur show a systematic fO2 increase during ascent, by as much as 2 log units. Magmas with sulphur show also a change of redox state during ascent, but the direction of change depends on the initial fO2 in the reservoir. Our calculations closely reproduce the H2S/SO2 ratios of volcanic gases observed at convergent settings, yet the difference between fO2 in the reservoir and that at the exit of the volcanic conduit may be as much as 1.5 log units. Thus, the redox state of erupted magmas is not necessarily a good proxy of the redox state of the gases they emit. Our findings may require re-evaluation of models aimed at quantifying the role of magmatic volatiles in geological processes

Geometric methods on low-rank matrix and tensor manifolds

In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors

Significance of vascular endothelial growth factor in growth and peritoneal dissemination of ovarian cancer

Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis which drives endothelial cell survival, proliferation, and migration while increasing vascular permeability. Playing an important role in the physiology of normal ovaries, VEGF has also been implicated in the pathogenesis of ovarian cancer. Essentially by promoting tumor angiogenesis and enhancing vascular permeability, VEGF contributes to the development of peritoneal carcinomatosis associated with malignant ascites formation, the characteristic feature of advanced ovarian cancer at diagnosis. In both experimental and clinical studies, VEGF levels have been inversely correlated with survival. Moreover, VEGF inhibition has been shown to inhibit tumor growth and ascites production and to suppress tumor invasion and metastasis. These findings have laid the basis for the clinical evaluation of agents targeting VEGF signaling pathway in patients with ovarian cancer. In this review, we will focus on VEGF involvement in the pathophysiology of ovarian cancer and its contribution to the disease progression and dissemination