Perfect simulation with exponential tails on the running time

Monte Carlo algorithms typically need to generate random variates from a probability distribution described by an unnormalized density or probability mass function. Perfect simulation algorithms generate random variates exactly from these distributions, but have a running time T that is itself an unbounded random variable. This article shows that commonly used protocols for creating perfect simulation algorithms, such as Coupling From the Past can be used in such a fashion that the running time is unlikely to be very much larger than the expected running time. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Complex network approach for recurrence analysis of time series

We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.     

<Superscript>27</Superscript>Al NMR Study of the Metal Cluster Compound Al<Subscript>50</Subscript>C<Subscript>120</Subscript>H<Subscript>180</Subscript>

We present an ²⁷Al NMR study of the metal cluster compound Al₅₀Cp*₁₂ which is composed of (identical) Al₅₀ clusters, each surrounded by a Cp* ligand shell, and arranged in a crystalline 3D array (here Cp* = pentamethylcyclopentadienyl = C₅(CH₃)₅). The compound is found to be non-conducting, the nuclear spin-lattice relaxation in the temperature range 100–300 K being predominantly due to reorientational motions of the Cp* rings. These lead to a pronounced maximum in the relaxation rate at T ∼ 170 K, corresponding to an activation energy of about 850 K. Data for the related compound Al₄Cp*₄, containing very much smaller Al₄ clusters are also presented. A comparison is drawn with the quadrupolar relaxation recently observed for the non-conducting fraction of Ga₈₄ molecules in the metal cluster compound Ga₈₄[N(SiMe₃)₂]₂₀-Li₆Br₂(thf)₂₀·2toluene. It is our pleasure to dedicate this paper to our colleague professor Günter Schmid at the occasion of his 70th birthday.     

Geometric Heat Comparison Criteria for Riemannian Manifolds

The main results of this paper are small-time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustrate them by examples. Mathematics subject classifications (2000): 58J35, 35K05     

I/O-efficient algorithms for computing planar geometric spanners

We present I/O-efficient algorithms for computing planar Steiner spanners for point sets and sets of polygonal obstacles in the plane.     

Die Struktur des Iod‐Adduktes von 2,3‐Dihydro‐1,3,4,5‐tetramethyl‐2‐methylenimidazol: Schwache Wechselwirkungen in einem linearen CI2‐Fragment [1]

The Structure of the Iodine Adduct of 2,3‐Dihydro‐1,3,4,5‐tetramethyl‐2‐methylenimidazole: Weak Interactions in a Linear CI₂‐Fragment [1] Crystals of C₃₆H₆₉Cl₂I₇N₈ ( 7 ) consisting of 3 equivalents of 6 , one equivalent of pentamethylimidazolium iodide and one equivalent of dichloromethane are obtained through the crystallisation of the iodine adduct of 2,3‐dihydro‐1,3,4,5‐tetramethyl‐2‐methylenimidazole (C₈H₁₄I₂N₂, 6 ). The crystal structure analysis of 7 reveals the presence of weak I–I bond and a nearly linear C–I–I arrangement for 6 indicating an interionic charge transfer interaction between iodomethylimidazolium and iodide ions.