[1] Knowledge about the properties of silicate melts is needed by volcanologists and petrologists to evaluate the dynamics of volcanic eruptions and magmatic processes. These properties include the solubility and diffusivity of volatile components in silicate melts, silicate melt viscosity, and the fragmentation condition. Data and models of each property are reviewed and assessed. For rhyolitic melts many properties are sufficiently well known to allow realistic modeling of volcanic and magmatic processes. One interesting example is the role of speciation in the solubility and diffusivity of H 2 O and CO 2 . Even though both H 2 O and CO 2 are present in silicate melts as at least two species, the complexity in the solubility and diffusion behavior of H 2 O and the simplicity of CO 2 are due to differences in the speciation reaction: For the H 2 O component the stoichiometric coefficient is one for one hydrous species (molecular H 2 O) but is two for the other hydrous species (OH) in the species interconversion reaction, whereas for CO 2 the stoichiometric coefficients for all carbon species are one. The investigation of the species reaction not only helps in understanding the solubility and diffusion behavior, but the reaction among the hydrous species also serves as a geospeedometer (cooling rate indicator) for hydrous rhyolitic pyroclasts and glass and provides a method to infer viscosity. For melts other than rhyolite, a preliminary description of their properties is also available, but much more experimental and modeling work is necessary to quantify these properties more accurately.

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This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex functions: the first function is smooth with up to the dth-order derivative information available, and the second function is possibly nonsmooth, but its proximal tensor mappings can be computed approximately in an efficient manner. The problem is to find—in that setting—the best possible (optimal) iteration complexity for convex optimization. Along that line, for the smooth case (without the second nonsmooth part in the objective), Nesterov proposed an optimal algorithm for the first-order methods ([Formula: see text]) with iteration complexity [Formula: see text], whereas high-order tensor algorithms (using up to general dth-order tensor information) with iteration complexity [Formula: see text] were recently established. In this paper, we propose a new high-order tensor algorithm for the general composite case, with the iteration complexity of [Formula: see text], which matches the lower bound for the dth-order methods as previously established and hence is optimal. Our approach is based on the accelerated hybrid proximal extragradient (A-HPE) framework proposed by Monteiro and Svaiter, where a bisection procedure is installed for each A-HPE iteration. At each bisection step, a proximal tensor subproblem is approximately solved, and the total number of bisection steps per A-HPE iteration is shown to be bounded by a logarithmic factor in the precision required.

Secondary impairment of blood-brain barrier (BBB) occurs in the remote thalamus after ischemic stroke. Netrin-1, an axonal guidance molecule, presents bifunctional effects on blood vessels through receptor-dependent pathways. This study investigates whether netrin-1 protects BBB against secondary injury. Netrin-1 (600 ng/d for 7 days) was intracerebroventricularly infused 24 h after middle cerebral artery occlusion (MCAO) in hypertensive rats. Neurological function was assessed 8 and 14 days after MCAO, and the permeability of BBB in the ipsilateral thalamus was detected. The viability of brain microvascular endothelial cells was determined after being disposed with netrin-1 (50 ng/mL) before oxygen-glucose deprivation (OGD). The role of netrin-1 was further explored by examining its receptors and their function. We found that netrin-1 infusion improved neurological function, attenuated secondary impairment of BBB by up-regulating the levels of tight junction proteins and diminishing extravasation of albumin, with autophagy activation 14 days after MCAO. Netrin-1 also enhanced cell survival and autophagy activity in OGD-treated cells, inhibited by UNC5H2 siRNA transfection. Furthermore, the beneficial effects of netrin-1 were suppressed by PI3K inhibitors 3-Methyladenine and LY294002. Our results showed that netrin-1 ameliorated BBB impairment secondary to ischemic stroke by promoting tight junction function and endothelial survival. PI3K-mediated autophagy activation depending on UNC5H2 receptor could be an underlying mechanism.