Advances towards Cell-Specific Gene Transfection: A Small-Molecule Approach Allows Order-of-Magnitude Selectivity

A transfection vector that can home in on tumors is reported. Whereas previous vectors that allow moderately cell selective gene transfection used larger systems, this small-molecule approach paved the way for precise structure-activity relationship optimization. For this, biotin, which mediates cell selectivity, was combined with the potent DNA-binding motif tetralysine-guanidinocarbonypyrrol via a hydrophilic linker, thus enabling SAR-based optimization. The new vector mediated biotin receptor (BR)-selective transfection of cell lines with different BR expression levels. Computer-based analyses of microscopy images revealed a preference of one order of magnitude for the BR-positive cell lines over the BR-negative controls.     

Mixing time of an unaligned Gibbs sampler on the square

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square ${[0,1]}^2$ to approach a stationary distribution with density proportional to $exp(?A^2{(u?v)}^2)$ for $(u,v)\in {[0,1]}^2$ with some large parameter $A$.Diaconis conjectured the mixing time of this process to be $O\left(A^2\right)$ which we confirm in this paper. This improves on the currently known $O(exp\left(A^2\right))$ estimate.     

Separation technique based on electrophoresis,chromatography and magnetism phenomena: the migration time and peak broadening

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Pericyclic reactions in the synthesis of new 5-aryl-5,6-dihydroquinolino[2,1-b]quinazolin-12-ones

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Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

‐Theory for Schrödinger systems

In this article, we study for the ‐realization of the vector‐valued Schrödinger operator . Using a noncommutative version of the Dore–Venni theorem due to Monniaux and Prüss, we prove that the ‐realization of , defined on the intersection of the natural domains of the differential and multiplication operators which form , generates a strongly continuous contraction semigroup on . We also study additional properties of the semigroup such as extension to L¹, positivity, ultracontractivity and prove that the generator has compact resolvent.     

Embedding Banach spaces into the space of bounded functions with countable support

We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ).