43,570 research outputs found
Oscillations in the Primordial Bispectrum: Mode Expansion
We consider the presence of oscillations in the primordial bispectrum,
inspired by three different cosmological models; features in the primordial
potential, resonant type non-Gaussianities and deviation from the standard
Bunch Davies vacuum. In order to put constraints on their bispectra, a logical
first step is to put these into factorized form which can be achieved via the
recently proposed method of polynomial basis expansion on the tetrahedral
domain. We investigate the viability of such an expansion for the oscillatory
bispectra and find that one needs an increasing number of orthonormal mode
functions to achieve significant correlation between the expansion and the
original spectrum as a function of their frequency. To reduce the number of
modes required, we propose a basis consisting of Fourier functions
orthonormalized on the tetrahedral domain. We show that the use of Fourier mode
functions instead of polynomial mode functions can lead to the necessary
factorizability with the use of only 1/5 of the total number of modes required
to reconstruct the bispectra with polynomial mode functions. Moreover, from an
observational perspective, the expansion has unique signatures depending on the
orientation of the oscillation due to a resonance effect between the mode
functions and the original spectrum. This effect opens the possibility to
extract informa- tion about both the frequency of the bispectrum as well as its
shape while considering only a limited number of modes. The resonance effect is
independent of the phase of the reconstructed bispectrum suggesting Fourier
mode extraction could be an efficient way to detect oscillatory bispectra in
the data.Comment: 17 pages, 12 figures. Matches published versio
The Effects of Malpractice Pressure and Liability Reforms on Physicians’ Perceptions of Medical Care
Considerable evidence suggests that the medical malpractice liability system neither provides compensation to patients who suffer negligent medical injury nor seeks to penalize physicians whose negligence causes patient injury. The relationship between liability reforms, malpractice pressure and physician perceptions of medical care is examined
Quantifying the Statistical Impact of GRAPPA in fcMRI Data with a Real-Valued Isomorphism
The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed on the effects that the GRAPPA operation has on reconstructed voxel means and correlations. The interpolation of missing spatial frequencies with the GRAPPA model is shown to result in an artificial correlation induced between voxels in the reconstructed images, and these artificial correlations are shown to reside in the low temporal frequency spectrum commonly associated with functional connectivity. Through a real-valued isomorphism, such as the one outlined in this manuscript, the exact artificial correlations induced by the GRAPPA model are not simply estimated, as they would be with simulations, but are precisely quantified. If these correlations are unaccounted for, they can incur an increase in false positives in functional connectivity studies
Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture
We determine the correlation between Polyakov loops in three dimensional
SU(3) gauge theory in the confined region at finite temperature. For this
purpose we perform lattice calculations for the number of steps in the
temperature direction equal to six. This is expected to be in the scaling
region of the lattice theory. We compare the results to the bosonic string
model. The agreement is very good for temperatures T<0.7T_c, where T_c is the
critical temperature. In the region 0.7T_c<T<T_c we enter the critical region,
where the critical properties of the correlations are fixed by universality to
be those of the two dimensional three state Potts model. Nevertheless, by
calculating the critical lattice coupling, we show that the ratio of the
critical temperature to the square root of the zero temperature string tension,
where the latter is taken from the literature, remains very near to the string
model prediction.Comment: 11 pages, 1 figure, 1 tabl
Incorporating Relaxivities to More Accurately Reconstruct MR Images
Purpose
To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.
Materials and methods
In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T2⁎, T1, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted by image warping, blurring, and loss in image intensity. Although T1 on tissue relaxation time provides valuable quantitative information on tissue characteristics, the T1 recovery term is typically neglected by assuming a long repetition time. In this study, the linear framework presented in the work of Rowe et al., 2007, and of Nencka et al., 2009 is extended to develop a Fourier reconstruction operation in terms of a real-valued isomorphism that incorporates the effects of T2⁎, ∆B, and T1. This framework provides a way to precisely quantify the statistical properties of the corrected image-space data by offering a linear relationship between the observed frequency space measurements and reconstructed corrected image-space measurements. The model is illustrated both on theoretical data generated by considering T2⁎, T1, and/or ∆B effects, and on experimentally acquired fMRI data by focusing on the incorporation of T1. A comparison is also made between the activation statistics computed from the reconstructed data with and without the incorporation of T1 effects.
Result
Accounting for T1 effects in image reconstruction is shown to recover image contrast that exists prior to T1 equilibrium. The incorporation of T1 is also shown to induce negligible correlation in reconstructed images and preserve functional activations.
Conclusion
With the use of the proposed method, the effects of T2⁎ and ∆B can be corrected, and T1 can be incorporated into the time series image-space data during image reconstruction in a single step. Incorporation of T1 provides improved tissue segmentation over the course of time series and therefore can improve the precision of motion correction and image registration
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