Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Schiffer variation of complex structure and coordinates for Teichmüller spaces

Schiffer variation of complex structure on a Riemann surfaceX ₀ is achieved by punching out a parametric disc \(\bar D\) fromX ₀ and replacing it by another Jordan domain whose boundary curve is a holomorphic image of \(\partial \bar D\) . This change of structure depends on a complex parameter ε which determines the holomorphic mapping function around \(\partial \bar D\) . It is very natural to look for conditions under which these ε-parameters provide local coordinates for Teichmüller spaceT(X ₀), (or reduced Teichmüller spaceT ^#(X₀)). For compactX ₀ this problem was first solved by Patt [8] using a complicated analysis of periods and Ahlfors' [2] τ-coordinates. Using Gardiner's [6], [7] technique, (independently discovered by the present author), of interpreting Schiffer variation as a quasi conformal deformation of structure, we greatly simplify and generalize Patt's result. Theorems 1 and 2 below take care of all the finitedimensional Teichmüller spaces. In Theorem 3 we are able to analyse the situation for infinite dimensionalT(X ₀) also. Variational formulae for the dependence of classical moduli parameters on the ε's follow painlessly.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

A study on anomalous yield drop behaviour in modified beta titanium alloys

ABSTRACT

The yield drop phenomenon observed in the Ti–15V-3Al–3Sn-3Cr (Ti–15–3) beta-titanium alloy and its anomalous behaviour in the boron and carbon added Ti–15–3 alloys have been studied. While the base and the carbon containing alloys exhibit yield drop, the boron containing alloy with smaller grain size than base alloy does not appear to show this phenomenon. Tensile tests were interrupted at different stress levels followed by analyses of slip lines and sub-structural characteristics using scanning and transmission electron microscopes to understand this anomalous yield point phenomenon. Infrared thermal imaging technique was used to map the strain localisation and the spatiotemporal evolution of deformation along the gauge length of the specimens during the tensile tests. Deformation in these alloys initiates only in a few grains. Pile-up of dislocations in these grains subsequently triggers the formation of dislocations in other grains and their rapid multiplications. The spreading of deformation by the generation of dislocations from pile up dislocations in one grain to neighbouring un-deformed grains and their rapid multiplication to new regions influence the yield drop phenomenon and its characteristics. It is shown in this study that microscopic instability in the grain level is a necessary, but not the sufficient condition for the manifestation of macroscopic instability during tensile deformation in polycrystalline materials. The presence of boride particles at grain boundaries restricts the slip transfer across the grains as well as the spreading of deformation to new regions, which causes the suppression of yield drop in the boron containing alloy.     

Synthesis and characterization of water-soluble carbon nanotubes from mustard soot

Carbon nanotubes (CNT) has been synthesized by pyrolysing mustard oil using an oil lamp. It was made water-soluble (wsCNT) through oxidative treatment by dilute nitric acid and was characterized by SEM, AFM, XRD, Raman and FTIR spectroscopy. The synthesized wsCNT showed the presence of several junctions and defects in it. The presence of curved graphene structure (sp²) with frequent sp³ hybridized carbon is found to be responsible for the observed defects. These defects along with the presence of di- and tri-podal junctions showed interesting magnetic properties of carbon radicals formed by spin frustration. This trapped carbon radical showed ESR signal in aqueous solution and was very stable even under drastic treatment by strong oxidizing or reducing agents. Oxidative acid treatment of CNT introduced several carboxylic acid group functionalities in wsCNT along with the nicking of the CNT at different lengths with varied molecular weight. To evaluate molecular weights of these wsCNTs, an innovative method like gel electrophoresis using high molecular weight DNA as marker was introduced.     

Cu (II) and Co (II/III) complexes of N,O‐chelated Schiff base ligands: DNA interaction,protein binding,cytotoxicity, cell death mechanism and reactive oxygen species generation studies

A series of copper (II) ( 1 and 3 ) and cobalt (II/III) ( 2 , 4 and 5 ) complexes comprising different imino‐phenolate ligands DCH , DTH and DBH ₂ (where DCH = 2,4‐dichloro‐6‐((mesitylimino)methyl)phenol, DTH = 2,4‐di‐tert‐butyl‐6‐((mesitylimino)methyl) phenol and DBH ₂ = 2,4‐dibromo‐6‐((mesitylimino)methyl)phenol) have been prepared with excellent yield and high purity. By utilizing different spectroscopic tools such as UV–visible, electrospray ionization (ESI)‐mass, Fourier‐transform infrared (FTIR) spectrometry and elemental analysis, the prepared complexes ( 1 – 5 ) were thoroughly characterized. The molecular structure of the synthesized complexes was ascertained by using single‐crystal X‐ray diffraction studies (SCXRDs). The experiment reveals that Complexes 1 – 5 bind to calf thymus DNA (CT‐DNA) through non‐intercalative way with good interacting abilities. However, 1 – 5 are excellent quenchers of the fluorescence intensity of bovine serum albumin (BSA) following the static pathway. Additionally, they had shown remarkable cytotoxic potential against MCF‐7 (mammary gland adenocarcinoma) and A549 (lung adenocarcinoma) cell lines. The IC₅₀ values associated with these complexes were much lower than the conventional drug cisplatin. Apoptosis‐induced cell death was confirmed from the DNA fragmentation studies and Hoechst 33342 staining. The 2′,7′‐dichlorofluorescein diacetate (DCFDA) assay indicates that the complex mediated reactive oxygen species (ROS) generation is accountable for governing the apoptosis mechanism via oxidative cell distress. Apart from these studies, by carrying out density functional theory (DFT) method, highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gap calculations and optimized structures of the synthesized complexes were accomplished.     

Synergic effect of multi-walled carbon nanotubes and gold nanoparticles towards immunosensing of ricin with carbon nanotube-gold nanoparticles-chitosan modified screen printed electrode

An amperometric immunosensor for the specific detection of Ricinus communis is reported. Screen printed electrodes (SPEs) were modified with gold nanoparticles (GNPs) loaded multiwalled carbon nanotubes (MWCNTs)-chitosan (Ch) film. The ratio of MWCNT and GNP was optimised to get best electrochemically active electrode. Sandwich immunoassay format was used for the immunosensing of ricin. The revealing antibodies tagged with the enzyme alkaline phosphatase (ALP) converts the substrate 1-naphthyl phosphate into 1-naphthol that was determined with the amperometric technique. The amperometric current obtained was correlated with the concentration of ricin. The prepared GNP-MWCNT-Ch-SPE showed high stability due to the Ch film, short response time with good reproducibility and increased shelf life of the electrodes immobilised with antibodies. The electrochemical activity of the electrode improved because of optimization of composition of CNTs and gold nanoparticles. Under the optimal conditions, the modified electrode showed a wide linear response to the concentration of ricin in the range of 2.5-25 ng mL(-1) with a limit of detection of 2.1 ng mL(-1) and with a relative standard deviation of 5.1% and storage life of 32 days.