Stable systolic category of the product of spheres

The stable systolic category of a closed manifold M indicates the complexity in the sense of volume. This is a homotopy invariant, even though it is defined by some relations between homological volumes on M. We show an equality of the stable systolic category and the real cup-length for the product of arbitrary finite dimensional real homology spheres. Also we prove the invariance of the stable systolic category under the rational equivalences for orientable 0-universal manifolds

Design for Testability in a SerDes System

Testing an IC after fabrication helps ensure chip functionality. The techniques that consider the creation and utilization of tests inside the design flow are called Design for Testability. The present work evaluates and improves the test modules implementing BIST techniques created by César Limones 2016 thesis. It is important to mention that this work reports the first effort to make the full SerDes analog and digital module integration at ITESO. It required all the designers to work together in order to complete the SerDes chip design flow. In particular, the comparison data module design structure was redefined after the data flow was analyzed. The test modules simulation demonstrated the correct functionality while the timing reports with a 156.25MHz clock frequency, showed that the design is timing compliant. The SerDes final layout, which also integrated the test modules, was created with the analog modules placement and routing. However, there were issues with the routing over the analog modules, which produced an overlap on the internal metal layers. For this reason, it is encouraged to further research about the association and outcomes between the layout of the analog modules, the LEF file generation, and the analog module routing in the design flowRealizar pruebas en un chip luego de ser fabricado asegura la funcionalidad del circuito integrado. Las técnicas que contemplan la creación y aplicación de pruebas dentro del flujo de diseño del chip se llaman design for testability (diseño testable). Esta tesina evalúa y mejora los módulos de prueba que implementan técnicas de BIST, los cuales fueron creados por César Limones en la tesina del 2016. Es importante mencionar que este trabajo reporta los primeros esfuerzos realizados en el ITESO en integrar los módulos análogos y digitales que componen el SerDes. Se requirió del trabajo conjunto de todos los diseñadores para completar el flujo de diseño del chip del SerDes. En particular, la estructura del módulo de comparación fue totalmente modificada luego de que el flujo de datos fue analizado. Mediante la simulación de los módulos pruebas se demostró su correcto funcionamiento y los reportes de análisis de tiempo aplicados con un reloj a una frecuencia de 156.25MHz, mostraron que el diseño cumple con las restricciones de tiempo. El layout (diseño) final del SerDes, que integra también los módulos de pruebas, fue creado con la colocación y enrutamiento de los módulos análogos. Sin embargo, se presentaron problemas con el enrutamiento creado sobre el módulo análogo lo cual provocó un solapamiento con las capas de metal internas. Por esta razón, se exhorta a investigar sobre la asociación y resultados entre el layout de los módulos análogos, la generación del archivo LEF y el enrutamiento de los módulos análogos en el flujo de diseño.ITESO, A. C.Consejo Nacional de Ciencia y Tecnologí

Branes at \C^4/\Ga Singularity from Toric Geometry

We study toric singularities of the form of \C^4/\Ga for finite abelian groups \Ga \subset SU(4). In particular, we consider the simplest case \Ga=\Z_2 \times \Z_2 \times \Z_2 and find explicitly charge matrices for partial resolutions of this orbifold by extending the method by Morrison and Plesser. We obtain three kinds of algebraic equations, $z_1 z_2 z_3 z_4=z_5^2, z_1 z_2 z_3=z_4^2 z_5$ and $z_1 z_2 z_5 = z_3 z_4$ where $z_i$'s parametrize \C^5. When we put $N$ D1 branes at this singularity, it is known that the field theory on the worldvolume of $N$ D1 branes is T-dual to $2 \times 2 \times 2$ brane cub model. We analyze geometric interpretation for field theory parameters and moduli space.Comment: 1 figure, 4 tables, latex file and 26 pages:v1 added mathematical results on projective crepant resolutions by Dais et al and refs added:v2 typos corrected and the beginning paragrphs in section 3 clarifie

Symmetry of Quantum Torus with Crossed Product Algebra

In this paper, we study the symmetry of quantum torus with the concept of crossed product algebra. As a classical counterpart, we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function. An invariant function under the group action is constructed as a variant of the classical theta function. Then our main issue, the crossed product algebra representation of quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding. We perform this analysis with Manin's so-called model II quantum theta function approach. The symplectic group Sp(2n,Z) satisfies the consistency condition of crossed product algebra representation. However, only a subgroup of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr