Optimal rates of convergence for estimating Toeplitz covariance matrices

Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm. The properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound. The results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces. The minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent Gaussian scale model and through a careful selection of a finite collection of least favorable parameters. In addition, optimal rate of convergence for estimating the inverse of a Toeplitz covariance matrix is also established.     

The Milstein Scheme for Stochastic Delay Differential Equations Without Using Anticipative Calculus

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delay differential equations but the analysis of the convergence is technically complicated due to anticipative integrals in the remainder terms. This article employs an elementary method to derive the Milstein scheme and its first order strong rate of convergence for stochastic delay differential equations.     

Aberration-free optical refocusing in high numerical aperture microscopy

We describe a method of optical refocusing for high numerical aperture (NA) systems that is particularly relevant for confocal and multiphoton microscopy. This method avoids the spherical aberration that is common to other optical refocusing systems. We show that aberration-free images can be obtained over an axial scan range of 70 mum for a 1.4 NA objective lens. As refocusing is implemented remotely from the specimen, this method will enable high axial scan speeds without mechanical interference between the objective lens and the specimen.     

CARS methane spectra: Experiments and simulations for temperature diagnostic purposes

CARS laboratory experiments were done in the 2905–2925 cm⁻¹ range, in the vicinity of the ν₁ band of the methane molecule, for pressures ranging from 1 to 50 bar, and temperatures up to 1100 K. These experiments were carried out in order to retrieve the pressure evolution of the CH₄ spectrum, as well as to confirm its temperature dependance. After a brief recall on the theory used to compute pressure broadening coefficients and relaxation rates, we consider the ν₃ and ν₄ infrared bands of methane for benchmark calculations purposes. Next, we present recent experimental CARS spectra and calculated ones. Lastly, we discuss flame experiments as well as comparisons of temperature retrieval using N₂ and CH₄ as probe molecules.     

Order-preserving representations of the partitions on the finite set

A partial ordering is defined for monotone projections f: N → N, N = {1, 2,…, n}, such that the class of these mappings is a lattice which is isomorphic to the partition lattice. Thus a partition can be uniquely represented by an element of this class of mappings and the partial ordering of partitions is preserved. Algorithms for computing the join and meet of given partitions are presented.     

A new reactivity-based one-pot synthesis of N-acetyllactosamine oligomers

Poly-N-acetyllactosamine oligomer is a type-2 glycan core from which a number of important bioactive glycoconjugates are assembled in vivo. Development of an effective synthesis of N-acetyllactosamine oligomers will therefore provide a new chemoenzymatic entry to this class of complex saccharides. This paper describes the design and synthesis of thioglycoside building blocks, determination of their relative reactivity values, and demonstration of their use in the programmable one-pot synthesis of various N-acetyllactosamine oligomers. Through a combination of segment condensation, the strategy allows for the preparation of larger oligosaccharides with minimal protecting group manipulation, as illustrated in the synthesis of an octasaccharide in a very short period of time.     

Mutagenicity and DNA damage studies of N-acyloxy-N-alkoxyamides--the role of electrophilic nitrogen

N-Acyloxy-N-alkoxyamides are anomeric amides that are direct-acting mutagens. They have been shown to damage DNA in the major and the minor grooves in a pH and sequence-selective manner. In acidic media, they damage adenines at N3 in the minor groove but above neutral pH, only guanine is damaged at N7 in the major groove. Both the acyloxy leaving group and the alkoxy group at the amide nitrogen are responsible for their electrophilicity and Salmonella mutagenicities in TA 100 and DNA damage data confirm that the mutagens react with DNA in an intact form, rather than by solvolysis to electrophilic nitrenium ions in the cytosol, or in vitro, prior to reacting with DNA. Hydrophobicity plays a role in both mutagenicity and DNA damage.     

Photochemical free radical formation from aliphatic dicarboxylic acids in solution as studied by electron spin resonance spectroscopy

Various free radicals formed during UV.-irradiation of aliphatic dicarboxylic acids in aqueous and methanolic solution are identified by ESR.-spectroscopy. Their structures point to α-cleavage and photoreduction as the dominant primary photochemical decay processes. The relative contributions of these reactions to the overall photodecomposition depend on solvent and degree of α-alkylation of the acid. Emission ESR.-spectra are found for radicals formed by C, CO-bond cleavage of α-dimethyl substituted acids. The polarization is referred to the triplet mechanism of CIDEP. and indicates this cleavage reaction occurs from a triplet molecular state.