Polynomial combinatorial algorithms for skew-bisubmodular function minimization

Mathematical Programming - Huber et al. (SIAM J Comput 43:1064–1084, 2014) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy...     

Linear response theory in stochastic many-body systems revisited

The Green–Kubo relation, the Einstein relation, and the fluctuation–response relation are representative universal relations among measurable quantities that are valid in the linear response regime. We provide pedagogical proofs of these universal relations for stochastic many-body systems. Through these simple proofs, we characterize the three relations as follows. The Green–Kubo relation is a direct result of the local detailed balance condition, the fluctuation–response relation represents the dynamic extension of both the Green–Kubo relation and the fluctuation relation in equilibrium statistical mechanics, and the Einstein relation can be understood by considering thermodynamics. We also clarify the interrelationships among the universal relations.     

On coarse geometric aspects of Hilbert geometry

We begin a coarse geometric study of Hilbert geometry. Actually we give a necessary and sufficient condition for the natural boundary of a Hilbert geometry to be a corona, which is a nice boundary in coarse geometry. In addition, we show that any Hilbert geometry is uniformly contractible and with coarse bounded geometry. As a consequence of these we see that the coarse Novikov conjecture holds for a Hilbert geometry with a mild condition. Also we show that the asymptotic dimension of any two-dimensional Hilbert geometry is just two. This implies that the coarse Baum–Connes conjecture holds for any two-dimensional Hilbert geometry via Yu’s theorem.

     

Acylhydrazone Subunits as a Proton Cargo Delivery System in 7-Hydroxyquinoline

The reimagined concept of long-range tautomeric proton transfer using crane subunits is shown by designing and synthesising two new acylhydrazones containing a 7-hydroxyquinoline (7-OHQ) platform. The acylhydrazone subunits attached to the 7-OHQ at the 8th position act as crane arms for delivering proton cargo to the quinoline nitrogen. Light-induced tautomerization to their keto forms leads to Z/E isomerization of the C=C axle bond, followed by proton delivery to the quinoline nitrogen by the formation of covalent or hydrogen bonds. The axle‘s being either an imine or ketimine bond is the structural difference between the studied compounds. The −CH₃ group in the latter provides steric strain, resulting in different proton transport pathways. Both compounds show long thermal stability in the switched state, which creates a tuneable action of bidirectional proton cargo transport by using different wavelengths of irradiation. Upon the addition of acid, the quinoline nitrogen is protonated; this results in E/Z configuration switching of the acylhydrazone subunits. This was proven by single-crystal X-ray structure analysis and NMR spectroscopy.     

Cell specific peptide-conjugated polysaccharide nanogels for protein delivery

A cell specific peptide (Arg‐Gly‐Asp; RGD)‐modified nanogel was prepared and evaluated for its potential to act as a protein delivery carrier. A bovine serum albumin (BSA)/RGD‐modified nanogel complex was efficiently internalized into cells through integrin‐mediated endocytosis. Endosomal escape of the RGD‐modified nanogel was observed after 24 h incubation. The nanogel proved useful for targeted protein delivery.

     

Nickel-catalyzed regio- and stereoselective reductive coupling between methylenecyclopropanes, aldehydes, and triethylborane with retention of the cyclopropane ring

Running rings: The first regio- and stereoselective reductive coupling between methylenecyclopropanes, aldehydes, and triethylborane with retention of the cyclopropane ring was achieved using a nickel-phosphine catalyst (see scheme). The reductive coupling reaction constructed a stereo-defined cyclopropane ring with formation of a quaternary stereogenic carbon center.     

A polyoxometalate-cyanometalate multilayered coordination network

The reaction of the ε-Keggin polyoxometalate (POM) [PMo(12)O(36)(OH)(4){La(H(2)O)(4)}(4)](5+) with Fe(II)(CN)(6)(4-) under typical bench conditions at room temperature and ambient pressure has afforded the novel [ε-PMo(12)O(37)(OH)(3){La(H(2)O)(5)(Fe(CN)(6))(0.25)}(4)] network, which exhibits a three-dimensional multilayered structure. The compound has been fully characterized by synchrotron-radiation X-ray crystallography, IR spectroscopy, elemental analysis, and thermogravimetric analysis. This coordination network constitutes the first example of a cyanometalate bonded to a POM unit.     

A convenient synthesis of 1,3-dimethyl(5h,7h)imidazo(4,5-dpyrimidine-2,4,6-trithione and its unusual character

1,3-Diemthyl(5H,7H)imidazo(4,5-$\text{d}$pyrimidine-2,4,6-trithione ($\text{1}$) was synthesized by the reaction of carbon disulfide with 1,3-dimethyl-4-cyano-5-aminoimidazolidine-2-thione ($\text{3}$) which was produced by reacting trimethylsilyl cyanide with methyl isothiocyanate followed by methanolysis. An unusual reversible formation of the dimethylamine salt of $\text{1}$ is also described.