Light Spanners

A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality -- in this work we focus on the latter. Specifically, it is shown that for any parameters $k\ge 1$ and $\epsilon>0$, any weighted graph $G$ on $n$ vertices admits a $(2k-1)\cdot(1+\epsilon)$-stretch spanner of weight at most $w(MST(G))\cdot O_\epsilon(kn^{1/k}/\log k)$, where $w(MST(G))$ is the weight of a minimum spanning tree of $G$. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of $O(\log k)$.Comment: 10 pages, 1 figure, to appear in ICALP 201

Systematic Approach to Conformational Sampling for Assigning Absolute Configuration Using Vibrational Circular Dichroism

Systematic methods that speed-up the assignment of absolute configuration using vibrational circular dichrosim (VCD) and simplify its usage will advance this technique into a robust platform technology. Applying VCD to pharmaceutically relevant compounds has been handled in an ad hoc fashion, relying on fragment analysis and technical shortcuts to reduce the computational time required. We leverage a large computational infrastructure to provide adequate conformational exploration which enables an accurate assignment of absolute configuration. We describe a systematic approach for rapid calculation of VCD/IR spectra and comparison with corresponding measured spectra and apply this approach to assign the correct stereochemistry of nine test cases. We suggest moving away from the fragment approach when making VCD assignments. In addition to enabling faster and more reliable VCD assignments of absolute configuration, the ability to rapidly explore conformational space and sample conformations of complex molecules will have applicability in other areas of drug discovery

Recruitment of mRNA cleavage/polyadenylation machinery by the yeast chromatin protein Sin1p/Spt2p

The yeast chromatin protein Sin1p/Spt2p has long been studied, but the understanding of its function has remained elusive. The protein has sequence similarity to HMG1, specifically binds crossing DNA structures, and serves as a negative transcriptional regulator of a small family of genes that are activated by the SWI/SNF chromatin-remodeling complex. Recently, it has been implicated in maintaining the integrity of chromatin during transcription elongation. Here we present experiments whose results indicate that Sin1p/Spt2 is required for, and is directly involved in, the efficient recruitment of the mRNA cleavage/polyadenylation complex. This conclusion is based on the following findings: Sin1p/Spt2 frequently binds specifically downstream of many ORFs but almost always upstream of the first polyadenylation site. It directly interacts with Fir1p, a component of the cleavage/polyadenylation complex. Disruption of Sin1p/Spt2p results in foreshortened poly(A) tracts on mRNA. It is synthetically lethal with Cdc73p, which is involved in the recruitment of the complex. This report shows that a chromatin component is involved in 3′ end processing of RNA