Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

Unbiased Bayes estimates and improper priors

Given two random variables (X, Y) the condition of unbiasedness states that:E(X |Y=y)=y andE(Y |X=x)=x both almost surely (a.s.). If the prior onY is proper and has finite expectation or non-negative support, unbiasedness impliesX=Y a.s. This paper examines the implications of unbiasedness when the prior onY is improper. Since the improper case can be meaningfully analysed in a finitely additive framework, we revisit the whole issue of unbiasedness from this perspective. First we argue that a notion weaker than equality a.s., named coincidence, is more appropriate in a finitely additive setting. Next we discuss the meaning of unbiasedness from a Bayesian and fiducial perspective. We then show that unbiasedness and finite expectation ofY imply coincidence betweenX andY, while a weaker conclusion follows if the improper prior onY is only assumed to have positive support. We illustrate our approach throughout the paper by revisiting some examples discussed in the recent literature.This work was partially supported by C.N.R. grant N.80.02970.10 (G.C.) and by C.N.R. grant altri interventi (P.V.). A preliminary draft was written while the Authors were visiting the Department of Statistics at Carnegie Mellon University.The paper is the result of close cooperation between the two authors. However subsections 3.1 and 3.3 are mainly due to G.C. while subsection 3.2 and section 4 are mainly due to P.V.     

Two-step upflow anaerobic sludge bed system for sewage treatment under subtropical conditions with posttreatment in waste stabilization ponds

A pilot-scale sewage treatment system consisting of two upflow anaerobic sludge bed (UASB) reactors followed by five waste stabilization ponds (WSPs) in series was studied under subtropical conditions. The first UASB reactor started up in only 1 mo (stable operation, high chemical oxygen demand [COD] removal efficiency, low volatile fatty acids concentration in the effluent, alkalinity ratio above 0.7, biogas production above 0.1 Nm3/kg of CODremoved). Removal efficiencies up to 90% were obtained in the anaerobic steps at a hydraulic retention time of 6 + 4 h (80% removal in the first step). Fecal coliform removal in the whole system was 99.9999% (99.94% in anaerobic steps and 99.98% in WSPs). COD balances over UASB reactors are provided. A minimum set of data necessary to build COD balances is proposed. Intermittent sludge washout was detected in the reactors with the COD balances. Sludge washout from single-step UASB reactors should be monitored and minimized in order to ensure constant compliance with discharge standards, especially when no posttreatment is provided. The system combined high COD and fecal coliform removal efficiency with an extremely low effluent concentration, complying with discharge standards, and making it an attractive option for sewage treatment in subtropical regions.     

Reactivity of 2-methyl-4-(1-pyrrolidinyl)-2H-1,2-benzothiazine 1,1-dioxide towards p-toluenesulphonyl azide

The 2-methyl-2H-1,2-benzothiazin-4-(3H)-one 1,1 dioxide ( 2 ), obtained according to a new, one-pot method, is transformed into the pyrrolidino enamine 3 . Reaction of p-toluenesulphonyl azide with 3 gives, via an unstable triazoline adduct which loses nitrogen, the two isomeric tosylamino derivatives 4 and 5 . The structures have been assigned by exhaustive nmr analysis and some aspects on their formation and chemical behaviour are discussed.     

The synthesis of 1,3,4,5-tetrahydro-2,3-benzoxazepines and 1,2,4,5-tetrahydro-3,2-benzoxazepines

Condensation of o-bromomethylphenethyl bromide with potassium salt of N-hydroxyurethan afforded 3-earbethoxy-1,3,4,5-tetrahydro-2,3-benzoxazepine, which was hydrolyzed to 1,3,4,5-tetrahydro-2,3-benxoxazepine (III). The reaction of o-aeetoxymethylphenethyl bromide (VIb) with potassium salt of N-hydroxyurethan in DMF, gave a complex mixture, from which O-[2-(o-acetoxymethylphenyl)(ethyl]-N-earbethoxyhydroxylamine (VIIa) was separated. Subsequent desacetylation to VIIb and halogenation yielded O-[2-(o-bromomethylphenyl)ethyl]-N-carbethoxyhydroxylamine (VIIc). By treatment of VIIc with potassium hydroxide, 2-carbethoxy-1,2,4,5-tetrahydro-3,2-benzoxazepine (X) was obtained together with small amounts of 6,15-diearbethoxy-5,6,8,9,14,15,17, 18-octahy drodibe nzo[d,I]-1,8-dioxa-2,9-diazaeyclotetradec in e (XI). Hydrolysis of X with potassium hydroxide gave 1,2,4,5-tetrahydro-3,2-benzoxazepine (XII). N-Alkyl and N-acyl derivatives of III and XII were also prepared.     

Separation of oligonucleotides and DNA fragments by capillary electrophoresis in dynamically and permanently coated capillaries,using a copolymer of acrylamide and β-D-glucopyranoside as a new low viscosity matrix with high sieving capacity

New copolymers of acrylamide and β-D -glucopyranoside were synthesized and characterized. The different reactivity of the two monomers towards radical polymerization meant we could control the growth of the polymer chains whose length was inversely related to the number of glucose residues incorporated in the copolymers. The properties of these polymers were investigated in the separation of oligonucleotides and double-stranded DNA by capillary electrophoresis (CE) in coated and uncoated capillaries. The new copolymers were a suitable matrix for CE due to their high-resolving capacity and low viscosity. We also looked into the advantages of a new method of dynamic suppression of electroosmotic flow based on the addition of small amounts (0.03–0.05%) of dimethylacrylamide to the sieving and to the running buffer. A complete test was run on the reproducibility and efficiency of separations carried out in a permanently and dynamically coated capillary, and the advantages and disadvantages of the two methods were compared.     

Diffeomorphism-invariant properties for quasi-linear elliptic operators

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and nondegenerate coerciveness.     

Ionic electroactive polymer metal composites: Fabricating,modeling, and applications of postsilicon smart devices

Smart systems adapt to the surrounding environments in a number of ways. They are capable to scavenge energy from available sources, sense and elaborate external stimuli and adequately react. Electro Active Polymers are playing a main role in the realization of smart systems for applications if fields such as bio inspired and autonomous robotics, medicine, and aerospace. This paper focus on the possibility to use Ionic Polymer Metal Composites as a class of materials relevant to the realization of post silicon smart systems. The three main aspects of this new technology, i.e., fabrication methods, modeling, and applications are described with emphasis to most recent results. Attention is given to main challenges and shortcomings to be solved for technology, modelling, and control of IPMC based devices that need to be solved before this new technology can be fully exploited in real world applications. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013     

Synthesis of aggregation pheromone components of cerambycid species through α-hydroxylation of alkylketones

The synthesis of 3-hydroxy-2-hexanone and 2,3-hexanediol, two components of the aggregation pheromone of several cerambycid species, is disclosed in here. Starting from 2-hexanone, through an α-hydroxylation using (diacetoxyiodo)benzene, 3-hydroxy-2-hexanone is obtained in good yield. Further reduction of this compound, gives 2,3-hexanediol in excellent yield. A study of the α-hydroxylation reaction of several alkylketones using an hypervalent iodine reagent is also disclosed in here. The synthesis of optically active compounds (R)- and (S)-3-hydroxy-2-hexanone was achieved starting from 2-hexanone with nitrosobenzene and l- and d-proline respectively, in several reaction media.