Componentwise adaptation for high dimensional MCMC

Summary  We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.     

Die Kristallstrukturen der Monohydrate von Lithiumchlorid und Lithiumbromid

Crystal Structure of the Monohydrates of Lithium Chloride and Lithium Bromide Using single crystal analysis and powder diffraction data the crystal structures of the monohydrates of lithium chloride and lithium bromide were solved. Both compounds crystallise isotypic in the space group Cmcm (LiCl·H₂O: single crystal analysis; T = 100 K; a = 758, 35(2); b = 768, 07(2); c = 762, 35(2) pm; Z = 8; 1179 unique reflections; R₁ = 0, 0196. LiBr·H₂O: Rietveld‐refinement; T = 220 K; a = 806, 15(1); b = 799, 44(1) und c = 794, 61(1) pm; Z = 8; 157 unique reflections; R_p = 0, 0922; R_wp = 0, 0979; R_exp = 0, 0657). The structure derives from the perowskite structure according to the formula X(H₂O)Li□₂ (X = Cl, Br). The orientation of the water molecules is linked clearly to the distribution of the lithium cations and vice versa. The high level ionic conductivity in the cubic high temperature phase of LiBr·H₂O is related to the initial rotation of the water molecules during the phase transformation. This motion favours the lithium ion hopping and the melting of the lithium substructure respectively.     

Polynomial time approximation schemes for general multiprocessor job shop scheduling

We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule (preemptive or non-preemptive, depending on the model) with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for both preemptive and non-preemptive variants of this problem that compute approximate solutions of any positive ε accuracy and run in O(n) time for any fixed values of m, μ, and ε. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines, multiprocessor tasks, and classical open, flow and job shops.     

Untersuchungen an Natriumtrifluormethylsulfonat – Kristallstruktur und Phasenumwandlung des Monohydrats und Natriumionenleitfähigkeit des wasserfreien Salzes

Studies on Sodium Trifluormethanesulfonate – Crystal Structure and Phase Transition of Sodium Trifluormethanesulfonate Monohydrate and Sodium Ion Conductivity of Anhydrous Sodium Trifluormethanesulfonate According to the results of temperature dependent powder diffractometry (Guinier-Simon-technique) sodium trifluormethanesulfonate monohydrate is dimorphous. The phase transition occurs at ?35°C. The room-temperature modification crystallizes monoclinic in space group P2₁/c with the lattice parameters a = 941.6(5) pm, b = 654.3(2) pm, c = 1062.4(5) pm and β = 107.73(2)°. The crystal structure consists of double layers of trifluormethanesulfonate anions, the lipophilic CF₃-groups pointing at each other. Sodium is coordinated by four oxygen atoms from four different anions and by two molecules of crystal water. The resulting polyhedron may be addressed as a distorted octahedron. The low-temperature modification crystallizes orthorhombic in space group Pnma with the lattice parameters a = 645.31(9) pm, b = 538.03(9) pm, c = 1745.3(3) pm. The loss of crystal water occurs at 136°C. Anhydrous sodium trifluormethanesulfonate shows a phase transition at 252°C. The high-temperature modification is a good sodium ionic conductor (σ = 4.1 · 10^?1 Ω^?1 cm^?1 at 250°C).     

Intestinal absorption of drugs II. The effect of inclusion in cyclodextrins on the absorption of dantrolene

The inclusion of dantrolene sodium, a muscle relaxant with poor water-solubility, in-,- and-cyclodextrins was determined. Subsequently, the influence of the cyclodextrins on the absorption of the drug from aqueous solutions was investigated in a chronically isolated internal loop in the small intestine of the rat.A good correlation was found between the inclusion of dantrolene in the various cyclodextrins and the decrease in the absorption rate resulting from a reduction of the thermodynamically active dantrolene according to the phase-separation model. It was concluded that the cyclodextrins do not have a significant influence on the passage of dantrolene across the absorption barrier. Furthermore, experimental evidence was collected to support the fact that-cyclodextrin was absorbed to a limited, if not negligible, extent in the small intestine of the rat.