String Creation and Monodromy from Fractional D-branes on ALE spaces

We investigate the anomalous creation of fundamental strings using the boundary state formalism of fractional D-branes on ALE spaces in the orbifold limit. The open string Witten index plays a crucial role in this calculation and so the result remains unchanged even if we blow up the orbifold geometrically, matching the anomaly inflow argument. Further we consider the quiver gauge theories on such fractional D3-branes and see that the string creation mechanism determines 1-loop logarithmic monodromy of these gauge theories. Also we comment on the relation of D(-1)-D3 amplitude to the 1-loop beta function.Comment: Latex,20 pages,minor changes and reference adde

Average Stopping Set Weight Distribution of Redundant Random Matrix Ensembles

In this paper, redundant random matrix ensembles (abbreviated as redundant random ensembles) are defined and their stopping set (SS) weight distributions are analyzed. A redundant random ensemble consists of a set of binary matrices with linearly dependent rows. These linearly dependent rows (redundant rows) significantly reduce the number of stopping sets of small size. An upper and lower bound on the average SS weight distribution of the redundant random ensembles are shown. From these bounds, the trade-off between the number of redundant rows (corresponding to decoding complexity of BP on BEC) and the critical exponent of the asymptotic growth rate of SS weight distribution (corresponding to decoding performance) can be derived. It is shown that, in some cases, a dense matrix with linearly dependent rows yields asymptotically (i.e., in the regime of small erasure probability) better performance than regular LDPC matrices with comparable parameters.Comment: 14 pages, 7 figures, Conference version to appear at the 2007 IEEE International Symposium on Information Theory, Nice, France, June 200