Towards the total synthesis of Calyculin C: preparation of the C13-C25 spirocyclic core

A stereoselective synthesis of the C₁₃-C₂₅ of Calyculin C is described. Key steps involve the coupling of a terminal acetylene with a thiol ester and subsequent spirocyclisation using a double intramolecular hetero-Michael addition.     

Structure determination of slowly exchanging conformers in solution using high‐resolution NMR,computational modeling and DFT‐GIAO chemical shielding: application to an erythronolide A derivative

We discuss and demonstrate the potential of HSQC‐TOCSY and HSQC‐NOESY experiments to offer solutions for overlap problems in COSY and NOESY spectra, leading to improved signals that can be unambiguously assigned to individual carbons. Direct comparison of experimental ¹H and ¹³C chemical shielding with density functional theory (DFT)‐calculated values are uninformative; in contrast, the relative differences in experimental shielding between pairs of molecules correlates well with the relative differences in DFT‐GIAO shielding for the computed lowest energy conformers. A detailed application of both experimental and theoretical techniques is illustrated for slowly exchanging conformers of an erythronolide A derivative, which demonstrates that structure determination can strongly benefit from the interplay between experiment and theory. Copyright © 2009 John Wiley & Sons, Ltd.     

Reactivity of methacrylates in insertion polymerization

Polymerization of ethylene by complexes [{(P^O)PdMe(L)}] (P^O = κ(2)-(P,O)-2-(2-MeOC(6)H(4))(2)PC(6)H(4)SO(3))) affords homopolyethylene free of any methyl methacrylate (MMA)-derived units, even in the presence of substantial concentrations of MMA. In stoichiometric studies, reactive {(P^O)Pd(Me)L} fragments generated by halide abstraction from [({(P^O)Pd(Me)Cl}μ-Na)(2)] insert MMA in a 1,2- as well as 2,1-mode. The 1,2-insertion product forms a stable five-membered chelate by coordination of the carbonyl group. Thermodynamic parameters for MMA insertion are ΔH(++) = 69.0(3.1) kJ mol(-1) and ΔS(++) = -103(10) J mol(-1) K(-1) (total average for 1,2- and 2,1-insertion), in comparison to ΔH(++) = 48.5(3.0) kJ mol(-1) and ΔS(++) = -138(7) J mol(-1) K(-1) for methyl acrylate (MA) insertion. These data agree with an observed at least 10(2)-fold preference for MA incorporation vs MMA incorporation (not detected) under polymerization conditions. Copolymerization of ethylene with a bifunctional acrylate-methacrylate monomer yields linear polyethylenes with intact methacrylate substituents. Post-polymerization modification of the latter was exemplified by free-radical thiol addition and by cross-metathesis.     

Memory of chirality in cascade rearrangements of enediynes

The cascade rearrangement of chiral enediynes 1c-e, involving successively 1,3-proton shift, Saito-Myers cyclization, 1,5-hydrogen atom transfer, and intramolecular coupling of the resulting biradical, proceeded at 80 °C to form tri- and tetracyclic heterocycles possessing a quaternary stereogenic center with a very high level of memory of chirality.     

Π‐Stacking Functionalization of Carbon Nanotubes through Micelle Swelling

We report on a new, original and efficient method for π‐stacking functionalization of single‐wall carbon nanotubes. This method is applied to the synthesis of a high‐yield light‐harvesting system combining single‐wall carbon nanotubes and porphyrin molecules. We developed a micelle‐swelling technique that leads to controlled and stable complexes presenting an efficient energy transfer. We demonstrate the key role of the organic solvent in the functionalization mechanism. By swelling the micelles, the solvent helps the non‐water‐soluble porphyrins to reach the micelle core and allows a strong enhancement of the interaction between porphyrins and nanotubes. This technique opens new avenues for the functionalization of carbon nanostructures.     

Heralding two-photon and four-photon path entanglement on a chip

Generating quantum entanglement is not only an important scientific endeavor, but will be essential to realizing quantum-enhanced technologies, in particular, quantum-enhanced measurements with precision beyond classical limits. We investigate the heralded generation of multiphoton entanglement for quantum metrology using a reconfigurable integrated waveguide device in which projective measurement of auxiliary photons heralds the generation of path-entangled states. We use four and six-photon inputs, to analyze the heralding process of two- and four-photon NOON states-a superposition of N photons in two paths, capable of enabling phase supersensitive measurements at the Heisenberg limit. Realistic devices will include imperfections; as part of the heralded state preparation, we demonstrate phase superresolution within our chip with a state that is more robust to photon loss.     

Polarization control in spun and telecommunication optical fibers

We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are determined by the polarization state of the injected backward pump. In randomly birefringent telecommunication fibers, we show that an unpolarized signal beam can be repolarized into any particular polarization state, without loss of energy.     

Dynamics of the infinitely-thin kink

We consider the dynamics of the domain-wall kink soliton, in particular we study the zero mode of translation. In the infinitely-thin kink limit, we show that the zero mode is almost completely frozen out, the only remnant being a dynamically constrained four-dimensional mode of a single but arbitrary frequency. In relation to this result, we show that the usual mode expansion for dealing with zero modes - implicit collective coordinates - is not in fact a completely general expansion, and that one must use instead a traditional generalised Fourier analysis.     

How Fast Is the Bandit?

Abstract

In this article we investigate the rate of convergence of the so-called two-armed bandit algorithm. The behavior of the algorithm turns out to be highly non standard: no central limit theorem, possible occurrence of two different rates of convergence with positive probability.