The Conjugacy Problem is Solvable in Free-By-Cyclic Groups

We show that the conjugacy problem is solvable in [finitelygenerated free]-by-cyclic groups, by using a result of O. Maslakovathat one can algorithmically find generating sets for the fixedsubgroups of free group automorphisms, and one of P. Brinkmannthat one can determine whether two cyclic words in a free groupare mapped to each other by some power of a given automorphism.We also solve the power conjugacy problem, and give an algorithmto recognize whether two given elements of a finitely generatedfree group are twisted conjugated to each other with respectto a given automorphism. 2000 Mathematics Subject Classification20F10, 20E05.     

Stereoselective alkylation of tartrate derivatives. A concise route to (+)-O-methylpiscidic acid and natural analogues

The lithium enolate of (2S,3S,5S,6S)-dimethoxy-2,3-dimethyl-1,4-dioxane-5,6-dithiocarboxylate undergoes stereoselective mono- and/or dialkylations to afford two new stereogenic centers. The alkylation products obtained possessed a cis stereochemistry, which was confirmed by the synthesis of natural 4'-O-methylpiscidic acid dimethyl ester .     

Organocatalytic regioselective Michael additions of cyclic enones via asymmetric phase transfer catalysis

Cyclohexanone and cycloheptanone can be enantioselectively functionalized in the 3-position with up to 92% ee and 87% ee, respectively, by the base-promoted dimerization of the corresponding enones using 3,4,5-tribenzyloxybenzyl cinchoninium bromide, as a new effective catalyst.     

Monitoring of fluid motion in a micromixer by dynamic NMR microscopy

The velocity distribution of liquid flowing in a commercial micromixer has been determined directly by using pulsed-field gradient NMR. Velocity maps with a spatial resolution of 29 microm x 43 microm were obtained by combining standard imaging gradient units with a homebuilt rectangular surface coil matching the mixer geometry. The technique provides access to mixers and reactors of arbitrary shape regardless of optical transparency. Local heterogeneities in the signal intensity and the velocity pattern were found and serve to investigate the quality and functionality of a micromixer, revealing clogging and inhomogeneous flow distributions.     

A new approach to center conditions for simple analytic monodromic singularities

In this paper we present an alternative algorithm for computing Poincaré-Lyapunov constants of simple monodromic singularities of planar analytic vector fields based on the concept of inverse integrating factor. Simple monodromic singular points are those for which after performing the first (generalized) polar blow-up, there appear no singular points. In other words, the associated Poincaré return map is analytic. An improvement of the method determines a priori the minimum number of Poincaré-Lyapunov constants which must cancel to ensure that the monodromic singularity is in fact a center when the explicit Laurent series of an inverse integrating factor is known in (generalized) polar coordinates. Several examples show the usefulness of the method.     

PopGen: population-based recruitment of patients and controls for the analysis of complex genotype-phenotype relationships

OBJECTIVE: Patient samples used for mapping complex human disease genes are unlikely to be representative of the phenotype spectrum of the respective population as a whole. On the other hand, most ongoing prospective studies are probably too small for evaluating polygenic disease markers. DESIGN: Precise estimates of population-specific genotypic risks can be obtained efficiently through the complete ascertainment of patients in a geographically confined area. The PopGen project uses the most northern part of Germany as a target region for such a pursuit. RESULTS: PopGen currently pursues recruitment, sampling and processing activities in close collaboration with a multitude of clinical partners, covering cardiovascular, neuropsychiatric and environmental diseases. CONCLUSION: PopGen has successfully established itself as a large-scale genetic epidemiological project of international recognition.     

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so‐called word‐based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k ‐tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so‐called graph‐based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph‐based distribution, while they are exponentially generic in the word‐based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

A note on approximate Bayesian credible sets based on modified loglikelihood ratios

Higher-order asymptotic arguments for a scalar parameter of interest have been widely investigated for Bayesian inference. In this paper the theory of asymptotic expansions is discussed for a vector parameter of interest. A modified loglikelihood ratio is suggested, which can be used to derive approximate Bayesian credible sets with accurate frequentist coverage. Three examples are illustrated.