Consistency of Markov chain quasi-Monte Carlo on continuous state spaces

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than i.i.d. U(0,1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Specificity and Kinetics of Haloalkane Dehalogenase

Haloalkane dehalogenase converts halogenated alkanes to their corresponding alcohols. The active site is buried inside the protein and lined with hydrophobic residues. The reaction proceeds via a covalent substrate-enzyme complex. This paper describes a steady-state and pre-steady-state kinetic analysis of the conversion of a number of substrates of the dehalogenase. The kinetic mechanism for the “natural” substrate 1,2-dichloroethane and for the brominated analog and nematocide 1,2-dibromoethane are given. In general, brominated substrates had a lower Km, but a similar kcat than the chlorinated analogs. The rate of C-Br bond cleavage was higher than the rate of C-Cl bond cleavage, which is in agreement with the leaving group abilities of these halogens. The lower Km for brominated compounds therefore originates both from the higher rate of C-Br bond cleavage and from a lower Ks for bromo-compounds. However, the rate-determining step in the conversion (kcat) of 1,2-dibromoethane and 1,2-dichloroethane was found to be release of the charged halide ion out of the active site cavity, explaining the different Km but similar kcat values for these compounds. The study provides a basis for the analysis of rate-determining steps in the hydrolysis of various environmentally important substrates.

Absorption and emission spectroscopies of homogeneous and inhomogeneously broadened multilevel systems in strong light fields

A method is introduced to calc., for a model set of mol. levels, the spectral line shapes expected for a variety of conventional laser expts. including absorption, hole burning, fluorescence line narrowing, and Raman scattering. The method allows the incident laser field to have arbitrary intensity. Furthermore, the effects of model gaussian or lorenzian inhomogeneous distributions are readily incorporated. Earlier results for a 2-level system are easily obtained and new results are presented for inhomogeneously broadened 2- and 3-level systems, and for the effects of pure dephasing on the strong field spectra. The differences between fluorescence and Raman in strong fields, and the effect of strong fields on the spontaneous emission of inhomogeneously broadened transitions were described. Some predictions are made regarding line narrowing expts. in the strong-field limit

Influence of mutations of Val226 on the catalytic rate of haloalkane dehalogenase

Haloalkane dehalogenase converts haloalkanes to their corresponding alcohols. The 3D structure, reaction mechanism and kinetic mechanism have been studied. The steady state kcat with 1,2-dichloroethane and 1,2-dibromoethane is limited mainly by the rate of release of the halide ion from the buried active-site cavity. During catalysis, the halogen that is cleaved off (Clα) from 1,2-dichloroethane interacts with Trp125 and the Clβ interacts with Phe172. Both these residues have van der Waals contacts with Val226. To establish the effect of these interactions on catalysis, and in an attempt to change enzyme activity without directly mutating residues involved in catalysis, we mutated Val226 to Gly, Ala and Leu. The Val226Ala and Val226Leu mutants had a 2.5-fold higher catalytic rate for 1,2-dibromoethane than the wild-type enzyme. A pre-steady state kinetic analysis of the Val226Ala mutant enzyme showed that the increase in kcat could be attributed to an increase in the rate of a conformational change that precedes halide release, causing a faster overall rate of halide dissociation. The kcat for 1,2-dichloroethane conversion was not elevated, although the rate of chloride release was also faster than in the wild-type enzyme. This was caused by a 3-fold decrease in the rate of formation of the alkyl-enzyme intermediate for 1,2-dichloroethane. Val226 seems to contribute to leaving group (Clα or Brα) stabilization via Trp125, and can influence halide release and substrate binding via an interaction with Phe172. These studies indicate that wild-type haloalkane dehalogenase is optimized for 1,2-dichloroethane, although 1,2-dibromoethane is a better substrate.

Linking theory and practice in using action-oriented methods

We felt that there is a great opportunity for PM researchers to use dialectical approaches such as action research, action learning and action science to link theory and practice. The aim of this chapter to provide doctoral students a practical way to use action-oriented methods – action research, action learning and action science – to carry out research in and about projects while making a theoretical contribution to the field. After briefly explaining each of these methods the chapter discusses ways in which these methods can be combined to provide synergy. The chapter discusses some common data collection strategies used with these methods, also pointing out that other methods of data collection are welcome if the research project requires such data. Action research is often criticised for not being scientific and therefore a discussion on how it can be made rigorous and valid at both data collection and data analysis stages is discussed. Action researchers often do not write up their research using the conventions used in conventional quantitative and qualitative research theses or dissertations. A section is therefore devoted to discussing how to write up action research in novel ways. The chapter includes several reflective exercises to guide the reader (student or researcher) as well as some tips for supervisors of action research projects. At the end of this chapter, the reader can: • understand the basics of action-oriented methods and how they can be used in a research project; • justify adequately why action-oriented methods are applicable to your research project; • establish a model/process to carry out your research applying action-oriented methods

Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed