The Zakai Equation of Nonlinear Filtering for Jump-Diffusion Observations: Existence and Uniqueness

In this paper we study a nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t∈[0,T], the σ-algebra $\mathcal{F}^{Y}_{t}:= \sigma\{ Y_{s}: s\leq t\}$ provides all the available information about the signal X _t . The central goal of stochastic filtering is to characterize the filter, π _t , which is the conditional distribution of X _t , given the observed data $\mathcal{F}^{Y}_{t}$ . In Ceci and Colaneri (Adv. Appl. Probab. 44(3):678–701, 2012) it is proved that π is the unique probability measure-valued process satisfying a nonlinear stochastic equation, the so-called Kushner-Stratonovich equation (in short KS equation). In this paper the aim is to improve the hypotheses to obtain the KS equation and describe the filter π in terms of the unnormalized filter ?, which is solution of a linear stochastic differential equation, the so-called Zakai equation. We prove the equivalence between strong uniqueness of the solution of the KS equation and strong uniqueness of the solution of the Zakai one and, as a consequence, we deduce pathwise uniqueness of the solution of the Zakai equation by applying the Filtered Martingale Problem approach (Kurtz and Ocone in Ann. Probab. 16:80–107, 1988; Ceci and Colaneri in Adv. Appl. Probab. 44(3):678–701, 2012). To conclude, we discuss some particular models.     

A condition of indecomposability for Butler \mathrm B (n)-groups

We give a manageable sufficient condition for indecomposability of Butler \(\mathrm B (n)\) -groups, allowing the easy construction of a big family of indecomposable torsionfree Abelian groups of finite rank.     

Biosprayed spleen cells integrate and function in mouse models

Bio-electrospraying (BES) and aerodynamically assisted bio-jetting (AABJ), two non-contact direct cell handling approaches, have recently undergone rigorous scientific testing to assess whether cells retain chemical, physical and more importantly biological functions similarly to their unmanipulated counterparts. Previous in vitro validation of these two approaches has shown that they are inert for the direct handling and distributing of cells with great accuracy. In the present investigation we aim to validate, in vivo, that the spray techniques do not functionally or phenotypically alter splenic cells. By taking advantage of an adoptive transfer mouse model we demonstrated that the in vivo behaviour of treated cells is indistinguishable from unmanipulated cells following adoptive transfer into C57/BL6 mice. Indeed, sprayed cells survived and proliferated in response to antigen activation to similar levels observed in unmanipulated cells. In addition, in vivo sprayed cells displayed identical migratory characteristics to those observed in unmanipulated cells. Thus, demonstrating the inertness of these biosprays. Hence these biotechniques hold great potential for use in the development of three-dimensional cultures, tracking and monitoring cell-interactions and in vitro modelling of disease-states and therapeutics.     

Inhibitory activities on mammalian central nervous system receptors and computational studies of three sesquiterpene lactones from Coriaria ruscifolia subsp. ruscifolia

The electrophysiological characterization of sesquiterpene lactones from Coriaria ruscifolia subsp. ruscifolia has been tested on hippocampal neurons. The results for glycinergic rat hippocampal transmission and native γ-aminobutyric acid (GABA)ergic transmission on neurons (13DIV) are remarkably different for tutin, coriamyrtin, and dihydrotutin, being tutin the most potent inhibitor and dihydrotutin the least potent one. To understand the applied mechanism of action, we discuss the structural and electronic requirements for inhibitory activity by these sesquiterpene lactones when modulating receptors of the central nervous system. The structural and electrostatic properties of these compounds were compared to those of more active metabolites like picrotoxins. The minimal energy level of these structures was calculated and then optimized at the ab initio B3LYP/DGDZVP level of theory using Gaussian 03W software. This allowed calculation of the corresponding vibrational circular dichroism spectrum of coriamyrtin which rendered the molecular absolute configuration after comparison with an experimental spectrum. These results are consistent with those from studies of other models that provide the basis for the activity on the presence of the lactone at carbons 3 and 5, the presence of the hydroxyl group at position 6, and the different electronic distributions observed in tutin and coriamyrtin. The latter has an isopropenyl moiety at carbon 4 in contrast to the dihydrotutin isopropyl group at the same position, which could explain the difference in activity between dihydrotutin and tutin or coriamyrtin. The presence of the hydroxyl group at carbon 2 is not decisive since this functionality is present in tutin, the most active compound, and in dihydrotutin, the less active one.     

Rheological Behavior and Wear Abrasion Resistance of Polyethylene Oxide/Laponite Nanocomposites

Polymer/layered silicate nanocomposite thin films were developed as clear, transparent coatings. Laponite‐S, which is a synthetic layered clay, was dispersed in a polyethylene oxide matrix and solution cast onto glass slides for further testing. Rheological properties, wear abrasion resistance, and scratch resistance were tested for each sample to examine the nanoparticle dispersion effects on the materials' properties. In this study, we identify and characterize the materials to be used, establish the appropriate conditions for the preparation of polymer/Laponite nanocomposite dispersions, illustrate methods for the development of PEO/Laponite‐S films, and characterize the films. Results on the rheological behavior of PEO‐silicate nanocomposites as a function of Laponite solids loading and PEO concentration, as well as some preliminary wear abrasion properties of the films are presented in this study.     

Environmental dose rate distribution along the Romanian Black Sea Shore

The ambient dose rate distribution, measured along the Southern sector of Romanian Black Sea shore, between Vama Veche in South and Chituc sandbank in North gave, with some notable exception, values between 34 and 54 nSv/h, lower than the 90 nSv/h, the average value for Romania. The experimental dose rates increase northward, reaching a maximum in the vicinity the Chituc sandbank, i.e. at the Vadu and Corbu beaches. According to gamma ray measurements performed in the Slanic-Prahova Low-Background Radiation Laboratory on the sand collected from the same location, the natural radionuclides have a major contribution to observes dose rate while the contribution of the anthropogenic ¹³⁷Cs, 26 years after Chernobyl accident, remains almost negligible. By taking into account both activity concentrations of radionuclides and the contribution of cosmic rays, we have calculated the local values of dose rate, which showed to be, within experimental uncertainties, coincident with the experimental ones. Moreover, on Chituc sandbank, we have noticed the presence of some local maxima, two to three times higher than the average ones. Further investigations showed an increased content of natural radionuclides, most probably accumulated in the heavy minerals fraction—a common occurrence in the vicinity of Danube Delta.     

Leaching Studies of Inorganic and Organic Compounds from Fly Ash

Fly ash is produced in massive quantities by fossil fuel based power plants and waste incinerators, and contains high levels of potentially toxic chemicals. Various leaching tests exist to determine the available fractions, but the outcome is strongly dependent on the experimental conditions, and these have not yet been harmonised at the international level. In order to test existing protocols for heavy metals, several intercomparisons were organised within the framework of an EU-INCO project "ANALEACH", in which seven institutes from five countries participated. Two existing reference materials were made available for the project and test batches of two new fly ash reference materials were produced. Availability tests, leaching tests and pH-stat tests were studied and critical steps in the procedures were identified. Fly ashes can also contain large amounts of inorganic sulphur and nitrogen compounds, and the determination and leaching behaviour of these compounds were also studied. In one intercomparison for metals, inorganic S and N-compounds were also included. A five-step leaching test was optimised for fly ash in order to link metal fractions to different types of binding. Column leaching experiments were carried out to investigate leaching from fly ash into soil, mimicking the effects of (acid) rain on fly ash deposited on topsoil after atmospheric transport. The major fraction of the leached metal ions was retained by the soil. Also large numbers of organic compounds (including many toxic ones) were identified in fly ash extracts, especially in city waste incinerator ash. Leaching procedures based on ultrasonic extraction were developed for organic compounds and an intercomparison exercise was organised. In a field study at the river Nitra(Slovakia) numerous organic pollutants were found at elevated levels downstream from a major fly ash dump site.     

Enantioselective Total Synthesis of (−)‐Diversonol

For the synthesis of (?)‐diversonol (ent‐ 1 ), an enantioselective domino‐Wacker/carbonylation/methoxylation reaction and an enantioselective Wacker oxidation were used to give the chroman in high yield and 96 % and 93 % ee, respectively. Dihydroxylation at the vinyl moiety using the Sharpless procedure and a Wittig–Horner reaction followed by hydrogenation, benzylic oxidation, and an intramolecular acylation provided the tetrahydroxanthenone, from which ent‐ 1 is accessible in a few steps. Furthermore, the synthesis of the diastereomeric diversonol rac‐1,9 a‐epi‐diversonol (rac‐ 41 ) is also described.     

Photochemical- and pH-switching Properties of a New Photoelastic Ligand Based Upon Azobenzene. Basicity and Anion Binding

Abstract

The synthesis of a new cylindrical macrotricyclic ligand (L) based upon two 1,4,7,13-tetramethyl-1,4,7,10,13,16-hexaazacyclooctadecane rings connected via two azobenzene pillars is described. The ligands displays photoelastic properties: light absorption at 366 nm produces trans→cis isomerization of the azobenzene moieties with formation of trans-cis (L _E-Z ) and cis-cis (L _Z-Z ) isomers. Recovery of the thermodynamically more stable trans-trans (L _E-E ) isomer can be obtained by thermal back-isomerization or visible light (430 nm) absorption. The isomeric composition of L solution depends upon pH: for pH < 5.5 the L _E-E form is the unique species in solution, while increasing amounts of Z species are formed at increasing pH. The protonation constants of L _E-E have been determined in 0.1 mol dm^?3 Me₄NNO₃ solution at 298.1 ± 0.1 K. The protonated species of L form stable inclusion complexes with anionic species such as [Co(CN)₆]^3?.     

Identification and quantification of different species in animal fibres by LC/ESI‐MS analysis of keratin‐derived proteolytic peptides

In the present paper, a proteomic method for species determination in fibres has been developed. Keratin was extracted from yak, wool and cashmere fibres and digested by trypsin, providing peptide mixtures that were analyzed by liquid chromatography coupled with electrospray mass spectrometry (LC/ESI‐MS) in order to identify peptidic species‐specific markers able to differentiate the fibres. Several suitable peptide markers were identified and validated in different fibres of different origin and having undergone different technological treatments, showing 100% specificity and 100% selectivity. Most of the peptide markers were also identified by means of high‐resolution mass spectrometry, confirming the origin from species‐specific keratin sequences. Some peptides were also used for the quantification of the different species in mixed fibres by LC/ESI‐MS. Validation experiments and blind tests confirmed their ability to act as very specific quantitative and qualitative markers. The method here developed is a valid complement to the standard benchmark methods for fibre identification and quantification and will be very useful for assessing the authenticity of textile products. Copyright © 2013 John Wiley & Sons, Ltd.