Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes

The aim of this paper is to define and study the 3-category of extensions of Picard 2-stacks over a site S and to furnish a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves. More precisely, our main Theorem furnishes (1) a parametrization of the equivalence classes of objects, 1-arrows, 2-arrows, and 3-arrows of the 3-category of extensions of Picard 2-stacks by the cohomology groups Ext^i, and (2) a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves via extensions of Picard 2-stacks. To this end, we use the triequivalence between the 3-category of Picard 2-stacks and the tricategory T^[-2,0](S) of length 3 complexes of abelian sheaves over S introduced by the second author in arXiv:0906.2393, and we define the notion of extension in this tricategory T^[-2,0](S), getting a pure algebraic analogue of the 3-category of extensions of Picard 2-stacks. The calculus of fractions that we use to define extensions in the tricategory T^[-2,0](S) plays a central role in the proof of our Main Theorem.Comment: 2 New Appendix: in the first Appendix we compute a long exact sequence involving the homotopy groups of an extension of Picard 2-stacks, and in the second Appendix we sketch the proof that the fibered sum of Picard 2-stacks satisfies the universal propert

Evaluation of vertebral artery dominance, hypoplasia and variations in the origin: angiographic study in 254 patients

Background: The aim of this study was to determine the dimensional characteristics and variations in the origin of vertebral arteries (VA). Materials and methods: We retrospectively reviewed angiographic studies in 254 patients (133 males, 121 females) for the evaluation of diameter differences in VA. We examined different criteria from the literature (difference of ≥ 0.3 mm, ≥ 0.8 mm, ≥ 1 mm between the widths of two VA and diameter ratio more than 1.4) to find out the dominant VA, rate of co-dominance and hypoplasia. The differences among groups were analysed using the c2 and Kruskal-Wallis test. Also concordance analysis test was used to determine correspondence between the tests. We also noticed the variations in the origin of VA. Results: The average diameter of VA in 254 patients was 3.21 ± 0.7 mm on the right, and 3.16 ± 0.7 mm on the left. The average diameter difference was found 0.88 ± 0.7 mm. The rate of hypoplasia was found 7.1% on the right and 9.4% on the left. Among 254 patients according to the criterion of any diameter difference; right side was found wider in 126 (49.6%) patients and left side was found wider in 120 (47.2%) patients. The criterion of 0.3 mm or greater difference showed right VA dominance in 107 (42.1%) patients, left VA dominance in 99 (39%) patients. Co-dominance was mainly observed when we used the criteria of 0.8 mm and 1 mm or greater difference and diameter ratio more than 1.4. We found out harmony of two criterion of difference of ≥ 0.8 mm and ≥ 1 mm (concordance analysis test, 76.1%). There was no statistically significant relation between age, gender and any dominance criteria (p > 0.05). The majority of VA showed classical origin arising from both subclavian arteries with a rate of 94.9%. Conclusions: The most striking result we have found is the dominance of the right VA in diameter by using all different criteria unlike with previous reports in the literature.

de Sitter Vacua in Type IIB String Theory: Classical Solutions and Quantum Corrections

We revisit the classical theory of ten-dimensional two-derivative gravity coupled to fluxes, scalar fields, D-branes, anti D-branes and Orientifold-planes. We show that such set-ups do not give rise to a four-dimensional positive curvature spacetime with the isometries of de Sitter spacetime. We further argue that a de Sitter solution in type IIB theory may still be achieved if the higher-order curvature corrections are carefully controlled. Our analysis relies on the derivation of the de Sitter condition from an explicit background solution by going beyond the supergravity limit of type IIB theory. As such this also tells us how the background supersymmetry should be broken and under what conditions D-term uplifting can be realized with non self-dual fluxes

The evolution of bits and bottlenecks in a scientific workflow trying to keep up with technology: Accelerating 4D image segmentation applied to nasa data

In 2016, a team of earth scientists directly engaged a team of computer scientists to identify cyberinfrastructure (CI) approaches that would speed up an earth science workflow. This paper describes the evolution of that workflow as the two teams bridged CI and an image segmentation algorithm to do large scale earth science research. The Pacific Research Platform (PRP) and The Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI) resources were used to significantly decreased the earth science workflow's wall-clock time from 19.5 days to 53 minutes. The improvement in wall-clock time comes from the use of network appliances, improved image segmentation, deployment of a containerized workflow, and the increase in CI experience and training for the earth scientists. This paper presents a description of the evolving innovations used to improve the workflow, bottlenecks identified within each workflow version, and improvements made within each version of the workflow, over a three-year time period

Flavor Structure in F-theory Compactifications

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there is a geometry with only one E_6 type point and one D_6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N_gen x N_gen CKM matrix is predicted to have only N_gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. We also obtained a precise description of zero mode wavefunctions near the E_6 type singularity points, where the up-type Yukawa couplings are generated.Comment: 148 page

Phase Structure of a Brane/Anti-Brane System at Large N

We further analyze a class of recently studied metastable string vacua obtained by wrapping D5-branes and anti-D5-branes over rigid homologous S^2's of a non-compact Calabi-Yau threefold. The large N dual description is characterized by a potential for the glueball fields which is determined by an auxiliary matrix model. The higher order corrections to this potential produce a suprisingly rich phase structure. In particular, at sufficiently large 't Hooft coupling the metastable vacua present at weak coupling cease to exist. This instability can already be seen by an open string two loop contribution to the glueball potential. The glueball potential also lifts some of the degeneracy in the vacua characterized by the phases of the glueball fields. This generates an exactly computable non-vanishing axion potential at large N.Comment: v3: 55 pages, 11 figures, typos correcte

Blow up for the wave equation with a fractional damping

Abstract. We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time