Nonparametric inference of quantile curves for nonstationary time series

The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results. In particular, our results can be used to test the trends of extremes of climate variables, an important problem in understanding climate change. Our methodology is applied to the analysis of the maximum speed of tropical cyclone winds. It was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values. However, there is no trend in the mean lifetime-maximum wind speed. This example shows the effectiveness of the quantile regression technique.Comment: Published in at http://dx.doi.org/10.1214/09-AOS769 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electrical Neutrality and Symmetry Restoring Phase Transitions at High Density in a Two-Flavor Nambu-Jona-Lasinio Model

A general research on chiral symmetry restoring phase transitions at zero temperature and finite chemical potentials under electrical neutrality condition has been conducted in a Nambu-Jona-Lasinio model to describe two-flavor normal quark matter. Depending on that $m_0/\Lambda$, the ratio of dynamical quark mass in vacuum and the 3D momentum cutoff in the loop integrals, is less or greater than 0.413, the phase transition will be second or first order. A complete phase diagram of $u$ quark chemical potential versus $m_0$ is given. With the electrical neutrality constraint, the region where second order phase transition happens will be wider than the one without electrical neutrality limitation. The results also show that, for the value of $m_0/\Lambda$ from QCD phenomenology, the phase transition must be first order.Comment: 9 pages, 1 figur

On a Stopping Game in continuous time

We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.Comment: To appear in the Proceedings of the AMS. Final versio

Stimulus-responsive Injectable Polysaccharide Scaffolds for Soft Tissue Engineering Prepared by O/W High Internal Phase Emulsion

This thesis describes work on the development of several novel stimuli-responsive porous hydrogels prepared from oil-in-water (o/w) high internal phase emulsion (HIPE) as injectable scaffolds for soft tissue engineering. Firstly, by copolymerising glycidyl methacrylate (GMA) derivatised dextran and N-isopropylacrylamide (NIPAAm) in the aqueous phase of a toluene-in-water HIPE, thermo-responsive polyHIPE hydrogels were obtained. The temperature depended modulus of these porous hydrogels, as revealed by oscillatory mechanical measurements, indicated improvements of the mechanical properties of these hydrogels when heated from room temperature to human body temperature, as the polyNIPAAm copolymer segments starts to phase separate from the aqueous phase and causes the hydrogel to form a more compact structure within the aqueous phase of the polyHIPE. Secondly ion responsive methacrylate modified alginate polyHIPE hydrogels were prepared. The physical dimensions, pore and pore throat sizes as well as water uptakes of these ion responsive hydrogels can be controllably decreased in the presence of Ca2+ ions and are fully recovered after disruption of the ionic crosslinking using a chelating agent (sodium citrate). These ion-responsive polyHIPE hydrogels also possess good mechanical properties (modulus up to 20 kPa). Both of these polyHIPE hydrogels could be easily extruded through a hypodermic needle while breaking into small fragments (about 0.5 to 3.0 mm in diameter), but the interconnected porous morphology was maintained after injection as revealed by SEM characterisation. Furthermore, the hydrogel fragments produced during injection can be crosslinked into a coherent scaffold under very mild condition using Ca2+ salts and alginate aqueous solution as the ionically crosslinkable adhesive. In order to increase the pore size of these covalently crosslinked polyHIPE hydrogels and also find a biocompatible nontoxic emulsifier as substitution to traditional surfactants, methyl myristate-in-water and soybean oil-in-water HIPEs solely stabilised by hydroxyapatite (HAp) nanoparticle were prepared. These Pickering- HIPEs were used as template to prepare polyHIPE hydrogels. Dextran-GMA, a water soluble monomer, was polymerised in the continuous phase of the HAp Pickering HIPEs leading to porous hydrogels with a tunable pore size varying from 1.5 μm to 41.0 μm. HAp is a nontoxic biocompatible emulsifier, which potentially provides extra functions, such as promoting hard tissue cell proliferation. HIPE-templated materials whose porous structure is maintained solely by the reversible physical aggregation between thermo-responsive dextran-b-polyNIPAAm block polymer chains in an aqueous environment (for this type of HIPE templated material we coined the name thermo-HIPEs) were prepared. No chemical reaction is required for the solidification of this porous material. This particular feature should provide a safer route to injectable scaffolds as issues of polymerisation/crosslinking chemistry or residual initiator fragments or monomers potentially being cytotoxic do not arise in our case, as all components are purified polymers prior to HIPE formation. Thermo-HIPEs with soybean oil or squalene as dispersed oil phase were prepared. Also in this HIPE system it was possible to replace the original surfactant Triton X405 with colloidal HAp nanoparticles or pH/thermo-responsive polyNIPAAm-co- AA microgel particles. The pore sizes and the mechanical properties of colloidal particles stabilised thermo-HIPEs showed improvement compared with thermo-HIPEs stabilised by Triton X405. In summary new injectable polyHIPEs have been prepared which retain their pore morphology during injection and can be solidified by either a thermal or ion (Ca2+) or chelating ion (Ca2+) stimulus. The materials used are intrinsically biocompatible and thus makes these porous injectable scaffolds excellent candidates for soft tissue engineering