The Experts below are selected from a list of 3381 Experts worldwide ranked by ideXlab platform
Peter C.m. Van Zijl - One of the best experts on this subject based on the ideXlab platform.
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effects of signal to noise ratio on the accuracy and reproducibility of diffusion tensor imaging derived fractional anisotropy mean diffusivity and Principal Eigenvector measurements at 1 5t
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van ZijlAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of signal‐to‐noise ratio on the accuracy and reproducibility of diffusion tensor imaging–derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van Zijl, Susumu MoriAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
Craig K. Jones - One of the best experts on this subject based on the ideXlab platform.
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effects of signal to noise ratio on the accuracy and reproducibility of diffusion tensor imaging derived fractional anisotropy mean diffusivity and Principal Eigenvector measurements at 1 5t
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van ZijlAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of signal‐to‐noise ratio on the accuracy and reproducibility of diffusion tensor imaging–derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van Zijl, Susumu MoriAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T.
NeuroImage, 2007Co-Authors: Bennett A. Landman, Jonathan A.d. Farrell, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Susumu MoriAbstract:Diffusion tensor imaging (DTI) is used to study tissue composition and architecture in vivo. To increase the signal to noise ratio (SNR) of DTI contrasts, studies typically use more than the minimum of 6 diffusion weighting (DW) directions or acquire repeated observations of the same set of DW directions. Simulation-based studies have sought to optimize DTI acquisitions and suggest that increasing the directional resolution of a DTI dataset (i.e., the number of distinct directions) is preferable to repeating observations, in an equal scan time comparison. However, it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability. Furthermore, the effect of different DW schemes on in vivo DTI findings is not fully understood. This study characterizes how the makeup of a DW scheme, in terms of the number of directions, impacts the precision and accuracy of in vivo fractional anisotropy (FA), mean diffusivity (MD), and Principal Eigenvector (PEV) findings. Orientation dependence of DTI reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results. As long as sampling orientations are well balanced, differences in DTI contrasts due to different DW schemes are shown to be small relative to intra-session variability. These differences are accentuated at low SNR, while minimized at high SNR. This result suggests that typical clinical studies, which use similar protocols but different well-balanced DW schemes, are readily comparable within the experimental precision.
Seth A. Smith - One of the best experts on this subject based on the ideXlab platform.
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effects of signal to noise ratio on the accuracy and reproducibility of diffusion tensor imaging derived fractional anisotropy mean diffusivity and Principal Eigenvector measurements at 1 5t
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van ZijlAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of signal‐to‐noise ratio on the accuracy and reproducibility of diffusion tensor imaging–derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van Zijl, Susumu MoriAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T.
NeuroImage, 2007Co-Authors: Bennett A. Landman, Jonathan A.d. Farrell, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Susumu MoriAbstract:Diffusion tensor imaging (DTI) is used to study tissue composition and architecture in vivo. To increase the signal to noise ratio (SNR) of DTI contrasts, studies typically use more than the minimum of 6 diffusion weighting (DW) directions or acquire repeated observations of the same set of DW directions. Simulation-based studies have sought to optimize DTI acquisitions and suggest that increasing the directional resolution of a DTI dataset (i.e., the number of distinct directions) is preferable to repeating observations, in an equal scan time comparison. However, it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability. Furthermore, the effect of different DW schemes on in vivo DTI findings is not fully understood. This study characterizes how the makeup of a DW scheme, in terms of the number of directions, impacts the precision and accuracy of in vivo fractional anisotropy (FA), mean diffusivity (MD), and Principal Eigenvector (PEV) findings. Orientation dependence of DTI reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results. As long as sampling orientations are well balanced, differences in DTI contrasts due to different DW schemes are shown to be small relative to intra-session variability. These differences are accentuated at low SNR, while minimized at high SNR. This result suggests that typical clinical studies, which use similar protocols but different well-balanced DW schemes, are readily comparable within the experimental precision.
Jerry L. Prince - One of the best experts on this subject based on the ideXlab platform.
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effects of signal to noise ratio on the accuracy and reproducibility of diffusion tensor imaging derived fractional anisotropy mean diffusivity and Principal Eigenvector measurements at 1 5t
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van ZijlAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of signal‐to‐noise ratio on the accuracy and reproducibility of diffusion tensor imaging–derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T
Journal of Magnetic Resonance Imaging, 2007Co-Authors: Jonathan A.d. Farrell, Bennett A. Landman, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Peter C.m. Van Zijl, Susumu MoriAbstract:Purpose To develop an experimental protocol to calculate the precision and accuracy of fractional anisotropy (FA), mean diffusivity (MD), and the orientation of the Principal Eigenvector (PEV) as a function of the signal to noise ratio (SNR) in vivo.
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Effects of diffusion weighting schemes on the reproducibility of DTI-derived fractional anisotropy, mean diffusivity, and Principal Eigenvector measurements at 1.5T.
NeuroImage, 2007Co-Authors: Bennett A. Landman, Jonathan A.d. Farrell, Craig K. Jones, Seth A. Smith, Jerry L. Prince, Susumu MoriAbstract:Diffusion tensor imaging (DTI) is used to study tissue composition and architecture in vivo. To increase the signal to noise ratio (SNR) of DTI contrasts, studies typically use more than the minimum of 6 diffusion weighting (DW) directions or acquire repeated observations of the same set of DW directions. Simulation-based studies have sought to optimize DTI acquisitions and suggest that increasing the directional resolution of a DTI dataset (i.e., the number of distinct directions) is preferable to repeating observations, in an equal scan time comparison. However, it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability. Furthermore, the effect of different DW schemes on in vivo DTI findings is not fully understood. This study characterizes how the makeup of a DW scheme, in terms of the number of directions, impacts the precision and accuracy of in vivo fractional anisotropy (FA), mean diffusivity (MD), and Principal Eigenvector (PEV) findings. Orientation dependence of DTI reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results. As long as sampling orientations are well balanced, differences in DTI contrasts due to different DW schemes are shown to be small relative to intra-session variability. These differences are accentuated at low SNR, while minimized at high SNR. This result suggests that typical clinical studies, which use similar protocols but different well-balanced DW schemes, are readily comparable within the experimental precision.
Thomas L Saaty - One of the best experts on this subject based on the ideXlab platform.
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THE ANALYTIC HIERARCHY PROCESS WITHOUT THE THEORY OF OSKAR PERRON
International Journal of the Analytic Hierarchy Process, 2014Co-Authors: Thomas L SaatyAbstract:It is known and has been mathematically proven that the Principal Eigenvector is necessary for deriving priorities from judgments in the Analytic Hierarchy Process (AHP). According to the work of Oskar Perron, the Principal Eigenvector can be obtained as the limiting power of a positive matrix. In this paper we show that the Principal Eigenvector does not need the theory of Perron for its existence based on the fact that the Principal eigenvalue and corresponding Principal Eigenvector are transparently obtained for a consistent matrix. By perturbation theory the result is obtained for a near consistent matrix. http://dx.doi.org/10.13033/ijahp.v5i2.191
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Why is the Principal Eigenvector Necessary
International Series in Operations Research & Management Science, 2012Co-Authors: Thomas L Saaty, Luis G. VargasAbstract:In the field of decision-making, the concept of priority is quintessential and how priorities are derived influences the choices one makes. Priorities should be unique and not one of many possibilities, they must also capture the dominance of the order expressed in the judgments of the pairwise comparison matrix.
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decision making with the ahp why is the Principal Eigenvector necessary
European Journal of Operational Research, 2003Co-Authors: Thomas L SaatyAbstract:In this paper it is shown that the Principal Eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A=(aij) when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained, it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision.
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Decision Aiding Decision-making with the AHP: Why is the Principal Eigenvector necessary
2003Co-Authors: Thomas L SaatyAbstract:In this paper it is shown that the Principal Eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix A ¼ð aijÞ when A is a small perturbation of a consistent matrix. When providing numerical judgments, an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios. Near consistent matrices are essential because when dealing with intangibles, human judgment is of necessity inconsistent, and if with new information one is able to improve inconsistency to near consistency, then that could improve the validity of the priorities of a decision. In addition, judgment is much more sensitive and responsive to large rather than to small perturbations, and hence once near consistency is attained, it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one. If such perturbations were forced, they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision. 2002 Elsevier Science B.V. All rights reserved.
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PRIORITY AS DOMINANCE IN DERIVED MEASUREMENT: INVARIANCE OF THE Principal Eigenvector
International Journal of Information Technology & Decision Making, 2003Co-Authors: Thomas L Saaty, Mujgan OzdemirAbstract:Ranking is a process of prioritization. Priorities, as measurement rather than pure guessing, can be derived from paired comparison judgments that generalize on ratios of actual measurements. Paired comparisons involve the selection of the smaller of the two objects being compared as the unit and estimating how many multiples of that unit the larger object is with respect to an attribute they share. In this paper, it is shown how priorities are derived as the Principal right Eigenvector of a pairwise comparison matrix and several examples are given to illustrate how the process works.