Convergence rate for the Bayesian inversion theory

Recently, the metrics of Ky Fan and Prokhorov were introduced as a tool for studying convergence of regularization methods for stochastic ill-posed problems. In this work, we examine the Bayesian approach to linear inverse problems in this new framework. We consider the finite-dimensional case where the measurements are disturbed by an additive normal noise and the prior distribution is normal. A convergence rate result for the posterior distribution is obtained when the covariance matrices are proportional to the identity matrix. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Living Free Radical Polymerization of Cyclodextrin Host‐Guest Complexes of Styrene via the Reversible Addition Fragmentation Chain Transfer (RAFT) Process in Aqueous Solution

Summary: Host‐guest complexes of styrene and randomly methylated β‐cyclodextrin (m‐β‐CD) were polymerized in aqueous medium via the reversible addition fragmentation chain transfer (RAFT) process. 3‐Benzylsulfanylthiocarbonylsulfanylpropionic acid (TTC) was used as trithiocarbonate‐type RAFT agent. The results indicate a controlled character of the polymerization of the styrene complexes as the number‐average molecular weight, , increases linearly with monomer to polymer conversion; however, the molecular weights of the obtained polystyrenes deviate to higher values than those theoretically predicted. Nevertheless, the molecular weights can be controlled by variation of the initial RAFT agent concentration. The polystyrenes produced in this system exhibited narrower polydispersities (1.23 < < 2.36) than those produced without RAFT agent (5.24 < < 9.21) under similar conditions. The present contribution represents the first example of RAFT polymerization of a m‐β‐CD‐complexed hydrophobic vinylmonomer (styrene) from homogenous aqueous solution.

Schematic presentation of complexation and RAFT polymerization of m‐β‐CD‐complexed styrene with TTC as RAFT agent and evolution of the full molecular weight distributions in the CD‐mediated styrene free radical RAFT polymerization.     

Error Analysis of the Symplectic Lanczos Method for the Symplectic Eigenvalue Problem

A rounding error analysis of the symplectic Lanczos algorithm for the symplectic eigenvalue problem is given. It is applicable when no break down occurs and shows that the restriction of preserving the symplectic structure does not destroy the characteristic feature of nonsymmetric Lanczos processes. An analog of Paige's theory on the relationship between the loss of orthogonality among the Lanczos vectors and the convergence of Ritz values in the symmetric Lanczos algorithm is discussed. As to be expected, it follows that (under certain assumptions) the computed J-orthogonal Lanczos vectors loose J-orthogonality when some Ritz values begin to converge.     

Di­methyl­phenyl­sulfonium tri­fluoro­methane­sulfonate and methyl­di­phenyl­sulfonium tri­fluoro­methane­sulfonate

The bonding geometry of sulfur in the cations of the title compounds, C₈H₁₁S⁺·CF₃SO₃^? and C₁₃H₁₃S⁺·CF₃SO₃^?, respectively, is similar and is independent of the ratio of the Me/Ph substituents. As expected, in both cations, the S—Ph bonds are somewhat shorter than the S—Me bonds. In both crystal structures, the interaction between cations and anions is similar.     

Indium solubility in iron studied with perturbed angular correlations

Segregation of In in Fe-based alloys containing 0.11–2.12 at.% In has been studied by measuring the perturbed angular correlations of γ-rays emitted in the nuclear decay of ¹¹¹In. The probe atoms were introduced into the alloys by either adding the carrier-free ¹¹¹In during melting or via ion implantation. Ageing of the samples at elevated temperatures followed by a slow cooling to room temperature allowed us to determine the upper limit of the solubility at room temperature, S(300 K)≤ 30 at. ppm. This value is far below the one reported in the published phase diagram. Quenching of the samples in water from 973–1373 K resulted in the determination of the indium solubility in iron at these elevated temperatures. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonlinear analysis of irregular animal vocalizations

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.     

Zur Spektraltheorie in lokalkonvexen Algebren

Ohne ZusammenfassungDer größte Teil der vorliegenden Arbeit wurde bei der Naturwissenschaftlich-Mathematischen Fakultät der Ruprecht-Karl-Universität zu Heidelberg als Dissertation eingereicht.     

Einige Bemerkungen zur Theorie der maximalen Ideale

Ohne ZusammenfassungHerrnFriedrich Karl Schmidt zum 60. Geburtstag am 22. 9. 1961 gewidmet