State estimation for partially observed Markov chains

Recursive equations are derived for the conditional distribution of the state of a Markov chain, given observations of a function of the state. Mainly continuous time chains are considered. The equations for the conditional distribution are given in matrix form and in differential equation form. The conditional distribution itself forms a Markov process. Special cases considered are doubly stochastic Poisson processes with a Markovian intensity, Markov chains with a random time, and Markovian approximations of semi-Markov processes. Further the results are used to compute the Radon-Nikodym derivative for two probability measures for a Markov chain, when a function of the state is observed.     

Performance Analysis with Truncated Heavy-Tailed Distributions

This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form U ∧ K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than . We study the compound Poisson ruin probability ψ(u) or, equivalently, the tail of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of ψ(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times, and compare the results to different approximations of ψ(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we investigate the asymptotics as K → ∞ of the asymptotic exponential decay rate γ = γ ^(K) in a more general truncated Lévy process setting, and give a discussion of some of the implications for the approximations. AMS 2000 Subject Classification Primary 68M20, Secondary 60K25 †Partially supported by MaPhySto—A Network in Mathematical Physics and Stochastics, founded by the Danish National Research Foundation. An erratum to this article is available at .     

Alkaloids ofDelphinium grandiflorum

Chemistry of Natural Compounds -     

Bacteria counting with impedance spectroscopy in a micro probe station

A method to quantify the density of viable biological cells in suspensions is presented. The method is implemented by low-frequency impedance spectroscopy and based on the finding that immobilized ions are released to move freely in the surrounding suspension when viable Escherichia coli cells are killed by a heat shock. The presented results show that an amount of ions corresponding to approximately 2 x 10(8) unit charges are released per viable bacterium killed. A micro probe station with coplanar Ti electrodes was electrically characterized and used as a measuring unit for the impedance spectroscopy recordings. This unit is compatible with common microfabrication techniques and should enable the presented method to be employed using a flow-cell device for viable bacteria counting in miniaturized on-line monitoring systems.     

Solvent effects on the redox properties of Cu complexes used as mediators in atom transfer radical polymerization

Solvent effects on the redox properties of six Cu(I) complexes used as mediators in atom transfer radical polymerization (ATRP) have been studied using cyclic voltammetry. The six ligands used were tris[2-(dimethylamino)ethyl]amine, N-(n-propyl)-2-pyridylmethanimine, N,N,N',N',N'-pentamethyldiethylenetriamine, 1,1,4,7,10,10-hexamethyl-triethylenetetramine, 2,2'-bipyridine, and 1,4,8,11-tetraaza-1,4,8,11-tetramethylcyclotetradecan. The solvents used were DMSO, DMF, MeCN, MeOH, IP, and BuOH. Significant solvent effects were observed and quantitatively analyzed in terms of Kamlet-Taft relationships. The resulting Kamlet-Taft equations were found to successfully describe the solvent effects and could thus be used as tools for the design of ATRP in new solvents. The solvent sensitivity of the different ligands and the nature of the solvent effects are also discussed to some extent.     

Reversible bond formation in a gold-atom-organic-molecule complex as a molecular switch

We report on the formation of a metal-molecule complex that can be used as a molecular switch. Using a cryogenic scanning tunneling microscope, a covalent bond was formed reversibly between a gold atom and a perylene-3,4,9,10-tetracarboxylic dianhydride molecule supported by a thin insulating film. The bonded and the nonbonded state of the complex were found to be associated with different charge states, and the switching between the two states was accompanied by a considerable change in the tunneling current. Atomic force microscopy molecular imaging was employed to determine precisely the atomic structure of the complex, and the experimental results were corroborated by density functional theory calculations.     

ChemInform Abstract: Nickel Vanadium Tellurium Oxide,NiV2Te2O10.

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