Linear Toric Fibrations

These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations. Polarized toric varieties which are birationally equivalent to projective toric bundles are associated to a class of polytopes called Cayley polytopes. Their geometry and combinatorics have a fruitful interplay leading to fundamental insight in both directions. These notes will illustrate geometrical phenomena, in algebraic geometry and neighboring fields, which are characterized by a Cayley structure. Examples are projective duality of toric varieties and polyhedral adjunction theory

A Frobenius variant of Seshadri constants

We define and study a version of Seshadri constant for ample line bundles in positive characteristic. We prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle. As a consequence, we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual Seshadri constants holds also in positive characteristic.Comment: 16 page

Enhancement of photoacoustic detection of inhomogeneities in polymers

We report a series of experiments on laser pulsed photoacoustic excitationin turbid polymer samples addressed to evaluate the sound speed in the samples and the presence of inhomogeneities in the bulk. We describe a system which allows the direct measurement of the speed of the detected waves by engraving the surface of the piece under study with a fiduciary pattern of black lines. We also describe how this pattern helps to enhance the sensitivity for the detection of an inhomogeneity in the bulk. These two facts are useful for studies in soft matter systems including, perhaps, biological samples. We have performed an experimental analysis on Grilon(R) samples in different situations and we show the limitations of the method.Comment: 8 pages, 7 figure

MR Imaging Findings in 2 Cases of Late Infantile GM1 Gangliosidosis

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Hydrogen Peroxide Induces Heme Degradation and Protein Aggregation in Human Neuroglobin: Roles of the Disulfide Bridge and the H-bonding in the Distal Heme Cavity

In this study, human neuroglobin (hNgb) was found to undergo H2O2-induced breakdown of the heme center at a much slower rate than other globins, namely in the timescale of hours against minutes. We studied how the rate of the process is affected by the Cys46/Cys55 disulfide bond and the network of noncovalent interactions in the distal heme side involving Tyr44, Lys67, the His64 heme iron axial ligand and the heme propionate-7. The rate is increased by the Tyr44 to Ala and Phe mutations, however the rate is lowered by Lys67 to Ala swapping. The absence of the disulfide bridge slows down the reaction further. Therefore, the disulfide bond-controlled accessibility of the heme site and the residues at position 44 and 67 affect the activation barrier of the reaction. Wild-type and mutated species form -amyloid aggregates in the presence of H2O2 producing globular structures. Furthermore, the C46A/C55A, Y44A, Y44F and Y44F/C46A/C55A variants yield potentially harmful fibrils. Finally, the nucleation and growth kinetics for the aggregation of the amyloid structures can be successfully described by the Finke-Watzky model