Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

Polynomial modeling and reduction of RF body coil spatial inhomogeneity in MRI

The usefulness of statistical clustering algorithms developed for automatic segmentation of lesions and organs in magnetic resonance imaging (MRI) intensity data sets suffers from spatial nonstationarities introduced into the data sets by the acquisition instrumentation. The major intensity inhomogeneity in MRI is caused by variations in the B1-field of the radio frequency (RF) coil. A three-step method was developed to model and then reduce the effect. Using a least squares formulation, the inhomogeneity is modeled as a maximum variation order two polynomial. In the log domain the polynomial model is subtracted from the actual patient data set resulting in a compensated data set. The compensated data set is exponentiated and rescaled. Statistical comparisons indicate volumes of significant corruption undergo a large reduction in the inhomogeneity, whereas volumes of minimal corruption are not significantly changed. Acting as a preprocessor, the proposed technique can enhance the role of statistical segmentation algorithms in body MRI data sets.     

Validation of LC/MS electrospray ionisation method for the estimation of ursodiol in human plasma and its application in bioequivalence study

A novel High Performance Liquid Chromatography-electrospray mass spectrometric method has been developed for the estimation of Ursodiol (Ursodeoxycholic acid)--a bile acid, in human plasma using Ornidazole as internal standard. The methodology involved solid phase extraction of the analyte from human plasma matrix. The chromatographic separation was achieved within seven minutes by an isocratic mobile phase containing 1.0 mM ammonium acetate and Acetonitrile (65:35, v/v), flowing through XTerra MS C18, 100 x 2.1, 3.5 microm analytical column, at a flow rate of 0.2 ml/min. Ion signals were measured in negative mode for Ursodiol and internal standard at m/z 391.3 and 278.1, respectively. A detailed validation of the method was performed as per USFDA guidelines and the standard curves were found to be linear in the range 50.0 ng/ml to 3000.0 ng/ml with the mean correlation coefficient more than 0.99. The absolute recovery was more than 54.90% for Ursodiol and 76.51% for internal standard. Ursodiol was stable for sixty-nine days at -70 degrees C and for eight hours at ambient temperature. After extraction from plasma, the reconstituted samples of Ursodiol were stable in autosampler at 10 degrees C for forty-eight hours. Upon subjecting to three freeze thaw cycles, there was no change in the recovery of the analyte. The integrity of the plasma samples remained unaffected even upon four-fold dilution with drug free human plasma. The method was simple, specific, sensitive, precise, accurate and suitable for bioequivalence and pharmacokinetic studies. It was successfully applied to the pilot bioequivalence study of Ursodiol in male human subjects.