Zero skew clock routing for fast clock tree generation

A Zero Skew Clock Routing Methodology has been developed to help design team speed up their clock tree generation process. The methodology works by breaking up the clock net into smaller partitions, then inserting clock buffers to drive each portion, and lastly, routing the connection from original clock source to each newly inserted clock buffers with zero skew. A few Perl scripts and a new Visual Basic based routing tool have been developed to support the methodology implementation. The routing algorithm used in this tool is based on the Exact Zero Skew Routing Algorithm. The methodology has been tested using a real design database and resulting in a significant improvement in the through put time required to complete the clock tree generation. This improvement is attributed to the ability to generate clock tree on much smaller portions of clock nets that supports of speeding up the clock tree generation process in IC design

Exact Simulation of One-dimensional Stochastic Differential Equations involving the local time at zero of the unknown process

In this article we extend the exact simulation methods of Beskos et al. to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case where the solution of the SDE with local time corresponds to a divergence form operator with a discontinuous coefficient at zero. Numerical examples are shown to illustrate the method and the performances are compared with more traditional discretization schemes.Comment: 21 pages r\'ef\'erences comprise

Fast clock tree generation using exact zero skew clock routing algorithm

A Zero Skew clock routing methodology has been developed to help design team speed up their clock tree generation process. The methodology works by breaking up the clock net into smaller partitions, then inserting clock buffers to drive each portion and lastly, routing the connection from original clock source to each newly inserted clock buffers with zero skew. A few Perl scripts and a new visual basic based routing tool have been developed to support the methodology implementation. The routing algorithm used in this tool is based on the Exact Zero Skew Routing Algorithm. The methodology has been tested using a real design database and resulting in a significant improvement in the through put time required to complete the clock tree generation. This improvement is attributed to the ability to generate clock tree on much smaller portions of clock nets that supports of speeding up the clock tree generation process in IC design

Skew group algebras, invariants and Weyl Algebras

The aim of this paper is two fold: First to study finite groups $G$ of automorphisms of the homogenized Weyl algebra $B_{n}$, the skew group algebra $B_{n}\ast G$, the ring of invariants $B_{n}^{G}$, and the relations of these algebras with the Weyl algebra $A_{n}$, with the skew group algebra $A_{n}\ast G$, and with the ring of invariants $A_{n}^{G}$. Of particular interest is the case $n=1$. In the on the other hand, we consider the invariant ring \QTR{sl}{C}[X]^{G} of the polynomial ring $K[X]$ in $n$ generators, where $G$ is a finite subgroup of Gl(n,\QTR{sl}{C}) such that any element in $G$ different from the identity does not have one as an eigenvalue. We study the relations between the category of finitely generated modules over \QTR{sl}{C}[X]^{G} and the corresponding category over the skew group algebra \QTR{sl}{C}% [X]\ast G. We obtain a generalization of known results for $n=2$ and $G$ a finite subgroup of $Sl(2,C)$. In the last part of the paper we extend the results for the polynomial algebra $C[X]$ to the homogenized Weyl algebra $B_{n}$

Linear spaces of matrices of constant rank and instanton bundles

We present a new method to study 4-dimensional linear spaces of skew-symmetric matrices of constant co-rank 2, based on rank 2 vector bundles on P^3 and derived category tools. The method allows one to prove the existence of new examples of size 10x10 and 14x14 via instanton bundles of charge 2 and 4 respectively, and provides an explanation for what used to be the only known example (Westwick 1996). We also give an algorithm to construct explicitly a matrix of size 14 of this type.Comment: Revised version, 22 pages. Brief intro to derived category tools and details to proof of Lemma 3.5 added, some typos correcte