On the mean value of probability measures on circular graphs

We introduce and discuss a class of difference equations motivated by a problem from combinatorial optimization on graphs. The local behavior at stationary points is investigated in detail, and in the course of this investigation we prove a stability result for certain types of non-isolated stationary points. Results include a complete characterization of the behavior on chain graphs, and a characterization of the local behavior for circular graphs.     

Simultaneous Credible Regions for Multiple Changepoint Locations

Within a Bayesian retrospective framework, we present a way of examining the distribution of changepoints through a novel set estimator. For a given level, α, we aim at smallest sets that cover all changepoints with a probability of at least 1 ? α. These so-called smallest simultaneous credible regions, computed for certain values of α, provide parsimonious representations of the possible changepoint locations. In addition, combining them for a range of different α’s enables very informative yet condensed visualizations. Therewith we allow for the evaluation of model choices and the analysis of changepoint data to an unprecedented degree. This approach exhibits superior sensitivity, specificity, and interpretability in comparison with highest density regions, marginal inclusion probabilities, and confidence intervals inferred by stepR. While their direct construction is usually intractable, asymptotically correct solutions can be derived from posterior samples. This leads to a novel NP-complete problem. Through reformulations into an Integer Linear Program we show empirically that a fast greedy heuristic computes virtually exact solutions. Supplementary material for this article is available online.     

Peculiarities of the regulation of fermentation and respiration in the crabtree-negative,xylose-fermenting yeastPichia stipitis

Applied Biochemistry and Biotechnology - The respiration ofPichia stipitis was not repressed by either high concentrations of fermentable sugars or oxygen limitation. Fermentation was not induced...     

Silver residues as a possible key to a remarkable oxidative catalytic activity of nanoporous gold

Recently, several forms of unsupported gold were shown to display a remarkable activity to catalyze oxidation reactions. Experimental evidence points to the crucial role of residual silver present in very small concentrations in these novel catalysts. We focus on the catalytic properties of nanoporous gold (np-Au) foams probed via CO and oxygen adsorption/co-adsorption. Experimental results are analyzed using theoretical models represented by the flat Au(111) and the kinked Au(321) slabs with Ag impurities. We show that Ag atoms incorporated into gold surfaces can facilitate the adsorption and dissociation of molecular oxygen on them. CO adsorbed on top of 6-fold coordinated Au atoms can in turn be stabilized by co-adsorbed atomic oxygen by up to 0.2 eV with respect to the clean unsubstituted gold surface. Our experiments suggest a linking of that most strongly bound CO adsorption state to the catalytic activity of np-Au. Thus, our results shed light on the role of silver admixtures in the striking catalytic activity of unsupported gold nanostructures.     

On sequentially Cohen-Macaulay complexes and posets

The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for posets is given. Finally, in an appendix we outline connections with ring-theory and survey some uses of sequential Cohen-Macaulayness in commutative algebra. Supported in part by National Science Foundation grants DMS 0302310 and DMS 0604562. Supported by Deutsche Forschungsgemeinschaft (DFG)     

Buchsbaum* complexes

A class of finite simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial homology are given. It is proved that Buchsbaum* complexes are doubly Buchsbaum. Various constructions, among them one which generalizes convex ear decompositions, are shown to yield Buchsbaum* simplicial complexes. Graph theoretic and enumerative properties of Buchsbaum* complexes are investigated.