General model selection estimation of a periodic regression with a Gaussian noise

This paper considers the problem of estimating a periodic function in a continuous time regression model with an additive stationary Gaussian noise having unknown correlation function. A general model selection procedure on the basis of arbitrary projective estimates, which does not need the knowledge of the noise correlation function, is proposed. A non-asymptotic upper bound for L₂{\mathcal{L}_2} -risk (oracle inequality) has been derived under mild conditions on the noise. For the Ornstein–Uhlenbeck noise the risk upper bound is shown to be uniform in the nuisance parameter. In the case of Gaussian white noise the constructed procedure has some advantages as compared with the procedure based on the least squares estimates (LSE). The asymptotic minimaxity of the estimates has been proved. The proposed model selection scheme is extended also to the estimation problem based on the discrete data applicably to the situation when high frequency sampling can not be provided.     

Noncommutative Batalin–Vilkovisky geometry and matrix integrals

I study the new type of supersymmetric matrix models associated with any solution to the quantum master equation of the noncommutative Batalin–Vilkovisky geometry. The asymptotic expansion of the matrix integrals gives homology classes in the Kontsevich compactification of the moduli spaces, which I associated with the solutions to the quantum master equation in my previous paper. I associate with the Bernstein–Leites matrix superalgebra equipped with an odd differentiation, whose square is nonzero, the family of cohomology classes of the compactification. This family is the generating function for the products of the tautological classes. The simplest example of my matrix integrals in the case of dimension zero is a supersymmetric extension of the Kontsevich model of 2-dimensional gravity.     

Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment

We consider a one-dimensional random walk in random environment in the Sinai's regime. Our main result is that logarithms of the transition probabilities, after a suitable rescaling, converge in distribution as time tends to infinity, to some functional of the Brownian motion. We compute the law of this functional when the initial and final points agree. Also, among other things, we estimate the probability of being at time t at distance at least z from the initial position, when z is larger than ln²t, but still of logarithmic order in time.Partially supported by CNRS (UMR 7599 ``Probabilités et Modéles Aléatoires'), and by the ``Réseau Mathématique France-Brésil'Partially supported by CNPq (300676/00–0 and 302981/02–0), COFECUB, and by the ``Rede Matemática Brasil-França'     

Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

 We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr?dinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamiltonian. Received: 5 June 2002 / Accepted: 20 January 2003 Published online: 28 March 2003 RID="⋆" ID="⋆" D.D. was supported in part by NSF Grant No. DMS–0227289 Communicated by M. Aizenman     

Failure of immunocompetitive capillary electrophoresis assay to detect disease-specific prion protein in buffy coat from humans and chimpanzees with Creutzfeldt-Jakob disease

The emergence of a new environmentally caused variant of Creutzfeldt-Jakob disease (vCJD), the result of food-born infection by the causative agent of bovine spongiform encephalopathy (BSE), has stimulated research on a practical diagnostic screening test. The immunocompetitive capillary electrophoresis (ICCE) assay has been reported to detect disease-specific, proteinase-resistant prion protein (PrPres) in the blood of scrapie-infected sheep. We have applied this method to blood from CJD-infected chimpanzees and humans. The threshold of detection achieved with our ICCE was 0.6 nM of synthetic peptide corresponding to the prion protein (PrP) C-terminus, and 2 nM of recombinant human PrP at the optimized conditions. However, the test was unable to distinguish between extracts of leucocytes from healthy and CJD-infected chimpanzees, and from healthy human donors and patients affected with various forms of CJD. Thus, the ICCE assay as presently performed is not suitable for use as a screening test in human transmissible spongiform encephalopathies (TSEs).     

5-Exo-dig radical cyclization of enediynes: the first synthesis of tin-substituted benzofulvenes

[reaction: see text] Bu(3)Sn-mediated 5-exo-dig radical cyclization of diaryl enediynes provides a mild and efficient approach to tin-substituted fulvenes. Further synthetic opportunities opened by this process and general factors responsible for the observed regio- and stereoselectivity are outlined.     

Collision Energetics in a Tandem Time-of-Flight (TOF/TOF) Mass Spectrometer with a Curved-Field Reflectron

Collisions of fullerene ions (C(60) (+)) with helium and neon were carried out over a range of laboratory energies (3-20 keV) on a unique tandem time-of-flight (TOF/TOF) mass spectrometer equipped with a curved-field reflectron (CFR). The CFR enables focusing of product ions over a wide kinetic energy range. Thus, ions extracted from a laser desorption/ionization (LDI) source are not decelerated prior to collision, and collision energies in the laboratory frame are determined by the source extraction voltages. Comparison of product ion mass spectra obtained following collisions with inert gases show a time (and apparent mass) shift for product ions relative to those observed in spectra obtained by metastable dissociation (unimolecular decay), consistent with impulse collision models, in which interactions of helium with fullerene in the high energy range are primarily with a single carbon atom. In addition, within a narrow range of kinetic energies an additional peak corresponding to the capture of helium is observed for fragment ions C(50) (+), C(52) (+), C(54) (+), C(56) (+) and C(58) (+).     

Hot recombination of photogenerated ion pairs

The recombination dynamics of ion pairs generated upon electron transfer quenching of perylene in the first singlet excited state by tetracyanoethylene in acetonitrile is quantitatively described by the extended unified theory of photoionization/recombination. The extension incorporates the hot recombination of the ion pair passing through the level-crossing point during its diffusive motion along the reaction coordinate down to the equilibrium state. The ultrafast hot recombination vastly reduces the yield of equilibrated ion pairs subjected to subsequent thermal charge recombination and separation into free ions. The relatively successful fit of the theory to the experimentally measured kinetics of ion accumulation/recombination and free ion yield represents a firm justification of hot recombination of about 90% of primary generated ion pairs.     

Molecular modelling of hyperbranched polyacetylene

Ab initio and density functional theory calculations carried out on linear and dendritic polyacetylenic (PA) oligomers of different size showed that acetylenic dendrimers are less stable than trans‐PA oligomers and that the instability increases with molecular weight reflecting the strain in crowded hyperbranched structures. However, the energy difference between linear and dendritic structure is rather small and tends to a limit with molecular weight. Twisting of the double bonds decreases the conjugation in hyperbranched PA compared to linear trans‐PA. However, the conjugation though less effective than in trans‐PA is extended up to the 4^th or 5^th generation of dendrimers. It was shown that bromine end groups strongly affect the electronic properties of acetylenic dendrimers decreasing even more the conjugation due to the sterical hindrances, however, highly polarizable bromine atoms reduced significantly the adiabatic potentials of ionization to be very close to that for trans‐PA oligomers.     

Hydrogel composites of neutral and slightly charged poly (acrylamide) gels with incorporated bentonite. Interaction with salt,linear polyelectrolytes and ionic surfactants

The swelling behavior in the solutions of sodium chloride, linear polyelectrolytes and ionic surfactants of the composites based on clay mineral bentonite (BENT) embedded in neutral and slightly charged poly(acrylamide) (PAAm) gels is studied. Negatively charged flat clay particles incorporated into polymer gel adsorb oppositely charged surfactant and linear polyelectrolyte and attract the charged chains of cationic polymer matrix. The results of SAXS study manifest the formation of lamella structure of the cationic surfactant adsorbed by the clay plates. The gels loaded with the clay show a strong response to changes in the nature and the composition of the ionic environment.