Ricci flow on quasiprojective manifolds

We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in terms of cohomological data on X. We also give a sufficient condition for the singularity, if there is one, to be type-II.Comment: final versio

Novel Cell type-specific aptamer-siRNA delivery system for HIV-1 therapy

The successful use of small interfering RNAs (siRNAs) for therapeutic purposes requires safe and efficient delivery to specific cells and tissues. Here we demonstrate cell type-specific delivery of anti-HIV siRNAs via fusion to an anti-gp120 aptamer. The envelope glycoprotein is expressed on the surface of HIV-1 infected cells, allowing binding and interalization of the aptamer-siRNA chimeric molecules. We demonstrate that the anti-gp120 aptamer-siRNA chimera is specifically taken up by cells expressing HIV-1 gp120, and the appended siRNA is processed by Dicer, releasing an anti-tat/rev siRNA which in turn inhibits HIV replication. We show for the first time a dual functioning aptamer-siRNA chimera in which both the aptamer and the siRNA portions have potent anti-HIV activities and that gp120 expressed on the surface of HIV infected cells can be used for aptamer mediated delivery of anti-HIV siRNAs

Compressed Regression

Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized least squares regression can accurately estimate a sparse linear model from $n$ noisy examples in $p$ dimensions, even if $p$ is much larger than $n$. In this paper we study a variant of this problem where the original $n$ input variables are compressed by a random linear transformation to $m \ll n$ examples in $p$ dimensions, and establish conditions under which a sparse linear model can be successfully recovered from the compressed data. A primary motivation for this compression procedure is to anonymize the data and preserve privacy by revealing little information about the original data. We characterize the number of random projections that are required for $\ell_1$-regularized compressed regression to identify the nonzero coefficients in the true model with probability approaching one, a property called ``sparsistence.'' In addition, we show that $\ell_1$-regularized compressed regression asymptotically predicts as well as an oracle linear model, a property called ``persistence.'' Finally, we characterize the privacy properties of the compression procedure in information-theoretic terms, establishing upper bounds on the mutual information between the compressed and uncompressed data that decay to zero.Comment: 59 pages, 5 figure, Submitted for revie