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

Means of payment, the unbanked, and EFT '99

Electronic funds transfers ; Checks ; Social security

Introducing Latent Timbre Synthesis

We present the Latent Timbre Synthesis (LTS), a new audio synthesis method using Deep Learning. The synthesis method allows composers and sound designers to interpolate and extrapolate between the timbre of multiple sounds using the latent space of audio frames. We provide the details of two Variational Autoencoder architectures for LTS, and compare their advantages and drawbacks. The implementation includes a fully working application with graphical user interface, called \textit{interpolate\_two}, which enables practitioners to explore the timbre between two audio excerpts of their selection using interpolation and extrapolation in the latent space of audio frames. Our implementation is open-source, and we aim to improve the accessibility of this technology by providing a guide for users with any technical background

Orientifold, Geometric Transition and Large N Duality for SO/Sp Gauge Theories

We extend the large N duality of four dimensional N=1 supersymmetric Yang-Mills theory with additional chiral fields and arbitrary superpotential recently proposed by Cachazo, Intriligator and Vafa to the case of SO/Sp gauge groups. By orientifolding the geometric transition, we investigate a large N duality between N=1, SO/Sp supersymmetric theories with arbitrary superpotential and an Abelian N=2 theory with supersymmetry broken to N=1 by electric and magnetic Fayet-Iliopoulos terms.Comment: 20 pages, LaTeX, no figure

The triticeous cartilage — redefining of morphology, prevalence and function

Background: Triticeous cartilage is a small cartilaginous component of the laryngeal skeleton. This cartilage, located in posterior end of the thyrohyoid ligament, presents in different shapes. Radiological studies indicate clinical and anatomical importance of the triticeous cartilage but these studies have limited information due to inadequate inspection method. Computed tomographic angiography is able to evaluate the triticeous cartilage with using three-dimensional images in more detail. The aim of this study is to describe prevalence and morphological properties of the triticeous cartilage. Materials and methods: We examined computed tomographic angiography images of 746 patients (368 women, 378 men) retrospectively. Shapes, calcification degrees, volumes, lengths and wideness of the triticeous cartilage were evaluated by OsiriX-Lite software. Results: According to our results, triticeous cartilage presents common in the examined population (68.1%). The prevalence of the triticeous cartilage was higher in men than in women. We also found that the degree of calcification was not related with age and gender. Conclusions: Clinical importance of the triticeous cartilage is that it could be misdiagnosed with atherosclerosis in common carotid artery because the triticeous cartilage is located almost at same level as the bifurcation of the common carotid artery. Therefore, clinicians should be aware about the triticeous cartilage

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