A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean

Phase-type distributions represent the time to absorption for a finite state Markov chain in continuous time, generalising the exponential distribution and providing a flexible and useful modelling tool. We present a new reversible jump Markov chain Monte Carlo scheme for performing a fully Bayesian analysis of the popular Coxian subclass of phase-type models; the convenient Coxian representation involves fewer parameters than a more general phase-type model. The key novelty of our approach is that we model covariate dependence in the mean whilst using the Coxian phase-type model as a very general residual distribution. Such incorporation of covariates into the model has not previously been attempted in the Bayesian literature. A further novelty is that we also propose a reversible jump scheme for investigating structural changes to the model brought about by the introduction of Erlang phases. Our approach addresses more questions of inference than previous Bayesian treatments of this model and is automatic in nature. We analyse an example dataset comprising lengths of hospital stays of a sample of patients collected from two Australian hospitals to produce a model for a patient's expected length of stay which incorporates the effects of several covariates. This leads to interesting conclusions about what contributes to length of hospital stay with implications for hospital planning. We compare our results with an alternative classical analysis of these data.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

Vapour phase assembly of a halogen bonded complex of an isoindoline nitroxide and 1,2-diiodotetrafluorobenzene

Vapour phase assembly has been used for the first time to prepare co-crystals in which the primary intermolecular interaction is halogen bonding. Co-crystals of the nitroxide 1,1,3,3-tetramethylisoindolin-2-yloxyl (TMIO) and 1,2-diiodotetrafluorobenzene (1,2-DITFB) are readily formed under standard sublimation conditions. Single crystal X-ray diffraction confirmed the structure of a 2:2 cyclic tetramer, (TMIO)2·(1,2-DITFB)2, which exhibits a new halogen bonding motif, with each nitroxide oxygen atom accepting two halogen bonds. Powder X-ray diffraction confirmed the homogeneity of the bulk sample. The crystalline complex was further characterized in the solid state using thermal analysis and vibrational spectroscopy (infrared and Raman). Density functional theory calculations were also used to evaluate the enthalpy of formation, electrostatic potential and unpaired electron density of the complex. These findings illustrate the preparation of co-crystals where solution state methodology is problematic and the potential of this approach for the formation of novel organic spin systems.

A dual-scale modelling approach for drying hygroscopic porous media

A new dualscale modelling approach is presented for simulating the drying of a wet hygroscopic porous material that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of wood at low temperatures and is valid in the so-called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradients of moisture content and temperature on the microscopic field using suitably-defined periodic boundary conditions, which allows the macroscopic mass and thermal fluxes to be defined as averages of the microscopic fluxes over the unit cell. This novel formulation accounts for the intricate coupling of heat and mass transfer at the microscopic scale but reduces to a classical homogenisation approach if a linear relationship is assumed between the microscopic gradient and flux. Simulation results for a sample of spruce wood highlight the potential and flexibility of the new dual-scale approach. In particular, for a given unit cell configuration it is not necessary to propose the form of the macroscopic fluxes prior to the simulations because these are determined as a direct result of the dual-scale formulation.

Synthesis of CuTCNQ/Au microrods by galvanic replacement of semiconducting phase I CuTCNQ with KAuBr4 in aqueous medium

The spontaneous reaction between microrods of an organic semiconductor molecule, copper 7,7,8,8-tetracyanoquinodimethane (CuTCNQ) with [AuBr4]− ions in an aqueous environment is reported. The reaction is found to be redox in nature which proceeds via a complex galvanic replacement mechanism, wherein the surface of the CuTCNQ microrods is replaced with metallic gold nanoparticles. Unlike previous reactions reported in acetonitrile, the galvanic replacement reaction in aqueous solution proceeds via an entirely different reaction mechanism, wherein a cyclical reaction mechanism involving continuous regeneration of CuTCNQ consumed during the galvanic replacement reaction occurs in parallel with the galvanic replacement reaction. This results in the driving force of the galvanic replacement reaction in aqueous medium being largely dependent on the availability of [AuBr4]− ions during the reaction. Therefore, this study highlights the importance of the choice of an appropriate solvent during galvanic replacement reactions, which can significantly impact upon the reaction mechanism. The reaction progress with respect to different gold salt concentration was monitored using Fourier transform infrared (FT-IR), Raman, and X-ray photoelectron spectroscopy (XPS), as well as XRD and EDX analysis, and SEM imaging. The CuTCNQ/Au nanocomposites were also investigated for their potential photocatalytic properties, wherein the destruction of the organic dye, Congo red, in a simulated solar light environment was found to be largely dependent on the degree of gold nanoparticle surface coverage. The approach reported here opens up new possibilities of decorating metal–organic charge transfer complexes with a host of metals, leading to potentially novel applications in catalysis and sensing.

A new approach to prepare ZVI and its application in removal of Cr(VI) from aqueous solution

Zero valent iron (ZVI) was prepared by reducing natural goethite (NG-ZVI) and synthetic goethite (SG-ZVI) in hydrogen at 550 °C. XRD, TEM, FESEM/EDS and specific surface area (SSA) and pore analyser were used to characterize goethites and reduced goethites. Both NG-ZVI and SG-ZVI with a size of nanoscale to several hundreds of nanometers were obtained by reducing goethites at 550 °C. The reductive capacity of the ZVIs was assessed by removal of Cr(VI) at ambient temperature in comparison with that of commercial iron powder (CIP). The effect of contact time, initial concentration and reaction temperature on Cr(VI) removal was investigated. Furthermore, the uptake mechanism was discussed according to isotherms, thermodynamic analysis and the results of XPS. The results showed that SG-ZVI had the best reductive capacity to Cr(VI) and reduced Cr(VI) to Cr(III). The results suggest that hydrogen reduction is a good approach to prepare ZVI and this type of ZVI is potentially useful in remediating heavy metals as a material of permeable reaction barrier.

Direct observation of the gas phase reaction of the cyclohexyl radical with dioxygen using a distonic radical ion approach

Alkylperoxyl radicals are intermediates in the oxidation Of hydrocarbons. The reactive nature of these intermediates, however, has made therin elusive to direct observation and isolation. We have employed ion trap mass spectrometry to synthesize and characterize 4-carboxylatocyclohexyl radical anions ((center dot)C(6)H(10)-CO(2)(-)) and observe their reactivity in the presence of dioxygen. The resulting reaction is facile (k = 1.8 x 10(-10) cm(3) molecule(-1) s(-1) or 30% of calculated collision rate) and results in (i) the addition Of O(2) to form stabilized 4-carboxylatocyclohexylperoxyl radical anions ((center dot)OO-C(6)H(10)-CO(2)(-)), providing the first direct observation of a cyclohexylperoxyl radical, and (ii) elimination of HO(2)(center dot) and HO(center dot) radicals consistent with recent laser-induced fluorescence studies of the reaction of neutral cyclohexyl radicals with O(2). Electronic structure calculations at the B3LYP/6-31+G(d) level of theory reveal viable pathways for the observed reactions showing that formation of the peroxyl radical is exothermic by 37 kcal mol(-1) with subsequent transition states its low as -6.6 kcal mol(-1) (formation of HO(2)(center dot)) and -9.1 kcal mol(-1) (formation of HO(center dot)) with respect to the entrance channel. The combined computational and experimental data Suggest that the structures of the reaction products correspond to cyclohexenes and epoxides from HO(2)(center dot) and HO(center dot) loss, respectively, while alternative pathways leading to cyclohexanone or ring-opened isomers ate not observed, Activation of the charged peroxyl radical (center dot)OO-C(6)H(10)-CO(2)(-) by collision induced disassociation also results in the loss Of HO(2)(center dot) and HO(center dot) radicals confirming that these products are directly connected to the peroxyl radical intermediate.

Investigation of the gas phase reactivity of the 1-adamantyl radical using a distonic radical anion approach

The gas phase reactions of the bridgehead 3-carboxylato-1-adamantyl radical anion were observed with a series of neutral reagents using a modified electrospray ionisation linear ion trap mass spectrometer. This distonic radical anion was observed to undergo processes suggestive of radical reactivity including radical-radical combination reactions, substitution reactions and addition to carbon-carbon double bonds. The rate constants for reactions of the 3-carboxylato-1-adamantyl radical anion with the following reagents were measured ( in units 10(-12) cm(3) molecule(-1) s(-1)): O-18(2) ( 85 +/- 4), NO ( 38.4 +/- 0.4), I-2 ( 50 +/- 50), Br-2 ( 8 +/- 2), CH3SSCH3 ( 12 +/- 2), styrene ( 1.20 +/- 0.03), CHCl3 ( H abstraction 0.41 +/- 0.06, Cl abstraction 0.65 +/- 0.1), CDCl3 ( D abstraction 0.035 +/- 0.01, Cl abstraction 0.723 +/- 0.005), allyl bromide (Br abstraction 0.53 +/- 0.04, allylation 0.25 +/- 0.01). Collision rates were calculated and reaction efficiencies are also reported. This study represents the first quantitative measurement of the gas phase reactivity of a bridgehead radical and suggests that distonic radical anions are good models for the study of their elusive uncharged analogues.

‘Click’ functionalised polymer resins : a new approach to the synthesis of surface attached bipyridinium and naphthalene diimide [2]rotaxanes

Herein we describe the design and synthesis of a series of solid-tethered [2]rotaxanes utilising crown ether-naphthalene diimide or crown ether- bipyridinium host guest interactions. TentaGel polystyrene resins were initially modified in a two-stage procedure to azide functionalised beads before the target supramolecular architectures were attached using a copper catalysed “click” procedure. The final assembly was examined using IR spectroscopy and gel-phase 1H High Resolution Magic Angle Spinning (HR MAS) NMR spectroscopy. The HR MAS technique enabled a direct comparison between the solid-tethered architectures and the synthesis and characterisation of analogous solution-based [2]rotaxanes to be made.

Synthesis of novel interlocked architectures in solution and solid phase

Mechanically interlocked molecules, such as catenanes and rotaxanes, are fascinating due to their unique sensing and catalytic properties and their potential to act as molecular motors or switches. Traditionally their synthesis has been laborious and expensive, however this research project endeavoured to overcome this challenge by exploring novel ways of preparing mechanically interlocked molecules both in solution and on surfaces. A series of disulfide-linked macrocycles, [2]catenanes and [2]rotaxanes were synthesised in solution using reversible dynamic covalent chemistry. Subsequently, the interlocked architectures were adapted into solid-tethered systems via attachment to swelling polystyrene resins.

2.5-dimensional solution of the advective accretion disk:a self-similar approach

We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion- induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Use of a volatile buffer at ambient temperature *1: Versatile approach to the purification of self-complementary synthetic deoxyoligonucleotides by reversed-phase high-performance liquid chromatography

Abstract is not available.

A unified approach to the solution of plane problems of Magneto-elasticity with special reference to a hole in a thin infinite conducting plate

Under certain specific assumption it has been observed that the basic equations of magneto-elasticity in the case of plane deformation lead to a biharmonic equation, as in the case of the classical plane theory of elasticity. The method of solving boundary value problems has been properly modified and a unified approach in solving such problems has been suggested with special reference to problems relating thin infinite plates with a hole. Closed form expressions have been obtained for the stresses due to a uniform magnetic field present in the plane of deformation of a thin infinite conducting plate with a circular hole, the plate being deformed by a tension acting parallel to the direction of the magnetic field.