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Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magnetic Resonance in Medicine
, 2004
"... In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is t ..."
Abstract

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In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the thus obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This paper addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the Maximum Likelihood method. As a performance criterion, the meansquared error (MSE) is used. 1
Theory of Natural Selection, 1
, 2003
"... I was among the last of RA Fisher’s students and disciples and, as a result, he had an enormous influence both on my career and on my attitudes to science and scientific research. In the summer before I started taking Fisher’s lecture courses in statistical and mathematical population genetics, I wa ..."
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I was among the last of RA Fisher’s students and disciples and, as a result, he had an enormous influence both on my career and on my attitudes to science and scientific research. In the summer before I started taking Fisher’s lecture courses in statistical and mathematical population genetics, I was given a reading list that included Fisher’s three outstanding books, The Genetical
RA Fisher, statistician and geneticist extraordinary: a personal view
, 2003
"... I was among the last of RA Fisher’s students and disciples and, as a result, he had an enormous influence both on my career and on my attitudes to science and scientific research. In the summer before I started taking Fisher’s lecture courses in statistical and mathematical population genetics, I wa ..."
Abstract
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I was among the last of RA Fisher’s students and disciples and, as a result, he had an enormous influence both on my career and on my attitudes to science and scientific research. In the summer before I started taking Fisher’s lecture courses in statistical and mathematical population genetics, I was given a reading list that included Fisher’s three outstanding books, The Genetical
Maximum Likelihood estimation of signal
 Magn Reson Med
, 2004
"... In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is ..."
Abstract
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In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the thus obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets.
ClujNapoca An Analysis of the Distribution of Seed Size: A Case Study of the Gymnosperms
"... Seed morphology is one of the most addressed issues in seeding plants studies due to its importance in the propagation of seeding plants, which can be related to the influence of the environment of the genetic structure in plant populations. A distribution analysis was conducted on extreme values (m ..."
Abstract
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Seed morphology is one of the most addressed issues in seeding plants studies due to its importance in the propagation of seeding plants, which can be related to the influence of the environment of the genetic structure in plant populations. A distribution analysis was conducted on extreme values (minimum and maximum) of seed width and length for gymnosperms spread within the Carpathian Mountains region. Combining the probabilities from independent tests successfully limited the bestfit distribution to a small number of distribution laws. Analyses revealed that the extreme values of investigated seed width and length best fit a loglogistic distribution or one of its generalised forms. The leftweighting of the distribution (to small sizes) revealed a better adaptation of smallsized seeding species. The extreme values of seed dimensions could be used to predict the dimension of a random observation, while the composition of the seeds, which is related to dimension, could provide phylogenetic information.