An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed

Proximity effect in granular superconductor-normal metal structures

We fabricated three-dimensional disordered Pb-Cu granular structures, with various metal compositions. The typical grain size of both metals is smaller than the superconductor and normal metal coherence lengths, thus satisfying the Cooper limit. The critical temperature of the samples was measured and compared with the critical temperature of bilayers. We show how the proximity effect theories, developed for bilayers, can be modified for random mixtures and we demonstrate that our experimental data fit well the de Gennes weak coupling limit theory in the Cooper limit. Our results indicate that, in granular structures, the Cooper limit can be satisfied over a wide range of concentrations.Comment: 15 pages, 4 figure

Proteomic identification of heterogeneous nuclear ribonucleoprotein L as a novel component of SLM/Sam68 nuclear bodies

Background: Active pre-mRNA splicing occurs co-transcriptionally, and takes place throughout the nucleoplasm of eukaryotic cells. Splicing decisions are controlled by networks of nuclear RNA-binding proteins and their target sequences, sometimes in response to signalling pathways. Sam68 (Src-associated in mitosis 68 kDa) is the prototypic member of the STAR (Signal Transduction and Activation of RNA) family of RNA-binding proteins, which regulate splicing in response to signalling cascades. Nuclear Sam68 protein is concentrated within subnuclear organelles called SLM/Sam68 Nuclear Bodies (SNBs), which also contain some other splicing regulators, signalling components and nucleic acids. Results: We used proteomics to search for the major interacting protein partners of nuclear Sam68. In addition to Sam68 itself and known Sam68-associated proteins (heterogeneous nuclear ribonucleoproteins hnRNP A1, A2/B1 and G), we identified hnRNP L as a novel Sam68-interacting protein partner. hnRNP L protein was predominantly present within small nuclear protein complexes approximating to the expected size of monomers and dimers, and was quantitatively associated with nucleic acids. hnRNP L spatially co-localised with Sam68 as a novel component of SNBs and was also observed within the general nucleoplasm. Localisation within SNBs was highly specific to hnRNP L and was not shared by the closely-related hnRNP LL protein, nor any of the other Sam68-interacting proteins we identified by proteomics. The interaction between Sam68 and hnRNP L proteins was observed in a cell line which exhibits low frequency of SNBs suggesting that this association also takes place outside SNBs. Although ectopic expression of hnRNP L and Sam68 proteins independently affected splicing of CD44 variable exon v5 and TJP1 exon 20 minigenes, these proteins did not, however, co-operate with each other in splicing regulation of these target exons. Conclusion: Here we identify hnRNP L as a novel SNB component. We show that, compared with other identified Sam68-associated hnRNP proteins and hnRNP LL, this co-localisation within SNBs is specific to hnRNP L. Our data suggest that the novel Sam68-hnRNP L protein interaction may have a distinct role within SNBs

Parameterized Algorithms for Graph Partitioning Problems

We study a broad class of graph partitioning problems, where each problem is specified by a graph $G=(V,E)$, and parameters $k$ and $p$. We seek a subset $U\subseteq V$ of size $k$, such that $\alpha_1m_1 + \alpha_2m_2$ is at most (or at least) $p$, where $\alpha_1,\alpha_2\in\mathbb{R}$ are constants defining the problem, and $m_1, m_2$ are the cardinalities of the edge sets having both endpoints, and exactly one endpoint, in $U$, respectively. This class of fixed cardinality graph partitioning problems (FGPP) encompasses Max $(k,n-k)$-Cut, Min $k$-Vertex Cover, $k$-Densest Subgraph, and $k$-Sparsest Subgraph. Our main result is an $O^*(4^{k+o(k)}\Delta^k)$ algorithm for any problem in this class, where $\Delta \geq 1$ is the maximum degree in the input graph. This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain faster algorithms for certain subclasses of FGPPs, parameterized by $p$, or by $(k+p)$. In particular, we give an $O^*(4^{p+o(p)})$ time algorithm for Max $(k,n-k)$-Cut, thus improving significantly the best known $O^*(p^p)$ time algorithm