Topological quantum field theories and Markovian random fields

We discuss an analogy between topological quantum field theories and the theory of Markov processes, which both rely on the combination of a notion of transition and a notion of locality. We assume no prior knowledge of topological quantum field theory (TQFT) and devote the first section to a motivation of its definition, which was originally given by M. Atiyah. We then discuss 1- and 2-dimensional TQFT?s, and a mild generalization of them which incorporates a notion of time and is suited to the parallel with Markov processes.This text is a written version of a talk whose emphasis was on explaining and illustrating ideas. There are few rigorous statements in it, and no proof.     

Collisions of Particles in Locally AdS Spacetimes II Moduli of Globally Hyperbolic Spaces

We investigate globally hyperbolic 3-dimensional AdS manifolds containing “particles”, i.e., cone singularities of angles less than 2π along a time-like graph Γ. To each such space (equipped with a time-like vector field satisfying some additional properties) we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.     

Variable-range hopping and quantum creep in one dimension

We study the quantum nonlinear response to an applied electric field E of a one-dimensional pinned charge-density wave or Luttinger liquid in the presence of disorder. From an explicit construction of low-lying metastable states and of bounce instanton solutions between them, we demonstrate quantum creep v=e(-c/E(1/2)) as well as a sharp crossover at E=E(*) towards a linear response form consistent with variable-range hopping arguments, but dependent only on electronic degrees of freedom.     

General linear formulations of stochastic dominance criteria

We develop and implement linear formulations of general Nth order stochastic dominance criteria for discrete probability distributions. Our approach is based on a piece-wise polynomial representation of utility and its derivatives and can be implemented by solving a relatively small system of linear inequalities. This approach allows for comparing a given prospect with a discrete set of alternative prospects as well as for comparison with a polyhedral set of linear combinations of prospects. We also derive a linear dual formulation in terms of lower partial moments and co-lower partial moments. An empirical application to historical stock market data suggests that the passive stock market portfolio is highly inefficient relative to actively managed portfolios for all investment horizons and for nearly all investors. The results also illustrate that the mean–variance rule and second-order stochastic dominance rule may not detect market portfolio inefficiency because of non-trivial violations of non-satiation and prudence.     

Mechanistic study of the electrodeposition of nanoporous self-assembled ZnO/Eosin Y hybrid thin films: effect of eosin concentration

ZnO films prepared by one-step electrodeposition in the presence of dissolved eosin molecules present an internal nanoporous hybrid structure resulting from self-assembling processes occurring in solution between ZnO and eosin components. This study aims to better understand the underlying growth mechanism, which is still unexplained. The films were deposited by cathodic electrodeposition from an oxygen-saturated aqueous zinc chloride solution. The effects of the addition of 10 to 100 micromol.L(-1) eosin Y, as a sodium salt, on the growth rate and film properties, were systematically studied while all other parameters remained constant (concentrations of zinc salt and supporting electrolyte, applied potential of -1.4 V versus the mercurous sulfate electrode (MSE), temperature of 70 degrees C, rotating disk electrode at 300 rotations per min, and a glass-coated tin oxide electrode). It is shown that the addition of eosin provokes the formation of a nanoporous "cauliflower" structure whose nodule size and composition depend on the eosin concentration in the bath. The growth rate of the hybrid films increases markedly with the eosin concentration. The ZnO and eosin contents of the films are determined for each concentration by chemical analysis. Comparing with thickness determinations, it is shown that the total porosity increases up to 60-65% in volume fraction toward an eosin concentration of 100 micromol.L(-1). The empty pore volume fraction increases up to about 30% at an eosin concentration of about 20 micromol.L(-1) and then decreases. These correlations have been precisely established for the first time. It is shown that the global composition is fixed by the relative rate of deposition for zinc oxide, which is constant, and for the relative rate of eosin inclusion, which is proportional to the concentration in solution. This is explained on the basis of different steps in the growth mechanism, in particular, a diffusion effect limitation for both oxygen and eosin. This variation explains part of the increase in the growth rate. Another contribution is related by the structural effect on the nanoscale leading to the formation of the interpenetrated porous network. Competition between empty and eosin-filled parts of the pore network is evidenced. The formation of the porous network structure could be governed by a diffusion-limited aggregation mechanism. The system may represent a reference case of competing reactions in the electrochemical self-assembly of hybrid nanostructures.     

Diastereocontrolled addition of organometallic reagents to S-chiral N-(tert-butanesulfinyl)-α-fluoroenimines

Grignard and organolithium reagents efficiently react with (S)-N-(tert-butanesulfinyl)-α-fluoroenimines to provide chiral allylamines in excellent yields and with diastereomeric ratios of up to 96:4. Acidic removal of the sulfinyl group and simple functional group transformations allow to get enantiopure fluoroolefin dipeptide mimics.     

Electronic structure of Li-intercalated oligopyridines: a comparative study by photoelectron spectroscopy

The role of nitrogen in the charge transfer and storage capacity of lithium-intercalated heterocyclic oligophenylenes was investigated using photoelectron spectroscopy. The development of new occupied states at low binding energies in the valence band region, as well as core level chemical shifts at both carbon and nitrogen sites, demonstrates partial charge transfer from lithium atoms to the organic component during formation of the intercalated compound. In small compounds, i.e., biphenyl and bipyridine derivatives, the position of the nitrogen heteroatom significantly affects the spacing between gap states in the Li-intercalated film; yet it has minimal effects on the charge storage capacity. In larger, branched systems, the presence of nitrogen in the aromatic system significantly enhances the charge storage capacity while the Li-N bond strength at high intercalation levels is significantly weakened relative to the nitrogen-free derivative. These observations have strong implications towards improved deintercalation processes in organic electrodes in lithium-ion batteries.     

Synthesis of trifluoromethyl cyclohexyl, cyclohexenyl and aryl compounds via stepwise Robinson annulation

The diketone 2-fluoro-2-(trifluoromethyl)-1-phenylhexane-1,5-dione 3 was synthesized by a Mukaiyama Michael type reaction from the corresponding tetrafluoroenol silyl ether prepared from pentafluoropropiophenone. This diketone was treated under basic conditions and was converted, depending on the stoichiometry of the base, into the surprisingly stable ketol 4-fluoro-4-(trifluoromethyl)-3-hydroxy-3-phenylcyclohexanone 4 as a single diastereomer (catalytic KOH) or to the biphenylol 6-(trifluoromethyl)biphenyl-3-ol (excess KOH, THF) 5. Solvolysis of the trifluoromethyl group (anionic activation) occurred using excess KOH in alcohol. The corresponding cyclohexenone derivative 7, the usual product of Robinson annulation, might be prepared in good yield via mesylation of the ketol. Thus various unprecedented fluorinated cyclohexane and aromatic derivatives were achieved in a few steps from the commercially available pentafluoropropiophenone.     

Regioselective remote CH fluoroalkylselenolation of 8-aminoquinolines

Herein, the direct C-5 fluoroalkylselenolation of 8-aminoquinolines is described. The Pd-catalyzed reaction is performed with the in situ generated fluoroalkylselenyl chloride and various 8-aminoquinoline amides or sulfonamides. The desired products were formed in moderate to excellent yields.