Architecture of Computing Systems - ARCS 2011

Architecture of Computing Systems - ARCS 2011, 24th International Conference, Como, Italy, February 24-25, 2011. Proceeding

On the Cauchy problem for the debar operator

We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.Comment: This is the final version, which is appearing in Arkiv foer Mathemati

Alternative splicing regulates stochastic NLRP3 activity

Leucine-rich repeat (LRR) domains are evolutionarily conserved in proteins that function in development and immunity. Here we report strict exonic modularity of LRR domains of several human gene families, which is a precondition for alternative splicing (AS). We provide evidence for AS of LRR domain within several Nod-like receptors, most prominently the inflammasome sensor NLRP3. Human NLRP3, but not mouse NLRP3, is expressed as two major isoforms, the full-length variant and a variant lacking exon 5. Moreover, NLRP3 AS is stochastically regulated, with NLRP3. exon 5 lacking the interaction surface for NEK7 and hence loss of activity. Our data thus reveals unexpected regulatory roles of AS through differential utilization of LRRs modules in vertebrate innate immunity

Malgrange's vanishing theorem for weakly pseudoconcave CR manifolds

The authors prove the following CR version of Malgrange's theorem: Assume $M$M is a smooth, non-compact, weakly pseudoconcave CR manifold of type $(n,k)$(n,k) of finite kind. Then the highest $\overline{\partial}_M$∂−M cohomology $H^{p,n}_{\overline{\partial}_M}(M)$Hp,n∂−M(M) vanishes for $0\le p\le n+k$0≤p≤n+k. This generalises a similar result for real analytic CR manifolds by the third author [in Hyperbolic problems and regularity questions, 137--150, Birkhäuser, Basel, 2007; MR2298789 (2008d:32034)]. Furthermore, they prove the following approximation theorem: If $M$M is as above and $U\subset\subset V \subset\subset M$U⊂⊂V⊂⊂M are two open sets such that V\sbs UV∖U has no compact connected component then for $0\le p\le n+k$0≤p≤n+k the restriction map $Z^{p,n-1}(\overline{V})\to Z^{p,n-1}(U)$Zp,n−1(V−)→Zp,n−1(U) has dense image, with respect to the \scr C^\inftyC∞ topology on $U$U. The authors prove the following CR version of Malgrange's theorem: Assume $M$M is a smooth, non-compact, weakly pseudoconcave CR manifold of type $(n,k)$(n,k) of finite kind. Then the highest $\overline{\partial}_M$∂−M cohomology $H^{p,n}_{\overline{\partial}_M}(M)$Hp,n∂−M(M) vanishes for $0\le p\le n+k$0≤p≤n+k. This generalises a similar result for real analytic CR manifolds by the third author [in Hyperbolic problems and regularity questions, 137--150, Birkhäuser, Basel, 2007; MR2298789 (2008d:32034)]. Furthermore, they prove the following approximation theorem: If $M$M is as above and $U\subset\subset V \subset\subset M$U⊂⊂V⊂⊂M are two open sets such that V\sbs UV∖U has no compact connected component then for $0\le p\le n+k$0≤p≤n+k the restriction map $Z^{p,n-1}(\overline{V})\to Z^{p,n-1}(U)$Zp,n−1(V−)→Zp,n−1(U) has dense image, with respect to the \scr C^\inftyC∞ topology on $U$U. The authors prove the following CR version of Malgrange's theorem: Assume $M$M is a smooth, non-compact, weakly pseudoconcave CR manifold of type $(n,k)$(n,k) of finite kind. Then the highest $\overline{\partial}_M$∂−M cohomology $H^{p,n}_{\overline{\partial}_M}(M)$Hp,n∂−M(M) vanishes for $0\le p\le n+k$0≤p≤n+k. This generalises a similar result for real analytic CR manifolds by the third author [in Hyperbolic problems and regularity questions, 137--150, Birkhäuser, Basel, 2007; MR2298789 (2008d:32034)]. Furthermore, they prove the following approximation theorem: If $M$M is as above and $U\subset\subset V \subset\subset M$U⊂⊂V⊂⊂M are two open sets such that V\sbs UV∖U has no compact connected component then for $0\le p\le n+k$0≤p≤n+k the restriction map $Z^{p,n-1}(\overline{V})\to Z^{p,n-1}(U)$Zp,n−1(V−)→Zp,n−1(U) has dense image, with respect to the \scr C^\inftyC∞ topology on $U$U