M. Rauf Ahmad

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In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. The estimation of parameters using a flip-flop algorithm is also briefly discussed.
The plant specific Dof (DNA Binding with One Zinc Finger) transcription factors (TFs) perform many different functions, and some members of this family appear to play an important role in the evolution of the vascular system characteristic of land plants. Here we report the functional characterization of a Dof TF from Arabidopsis (At4g00940-AtDof4.1).(More)
Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. The test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly(More)
Soft computing approach like swarm optimization can be used in the software development environment also for developing effective software. Software development and testing cost must be reduced and optimized so that companies can survive and sustain in the market. Object oriented analysis and design is used for developing complex real time software systems.(More)
A study was carried out to asses the phytosocology and structures of National Park. For tree species, point center quarter method (PCQ) and understorey vegetation, 1.5m circular plot at each PCQ point, while for bushes 20 quadrats 3x5 m were used. Five stands dominated by trees and eight stands of bushes were recorded. Picea smithiana and Pinus wallichiana(More)
New sets of parameters (" tunes ") for the underlying-event (UE) modelling of the pythia8, pythia6 and herwig++ Monte Carlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton–proton (pp) data at √ s = 7 TeV and to UE proton–antiproton (pp) data from the CDF experiment at lower √ s, are used to(More)