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Artifacts and Pitfalls in Diffusion MRI
Published in Ioannis Tsougos, Advanced MR Neuroimaging, 2018
A typical workflow analysis begins with the input of a T1-weighted MR image and a DW image. Mitigation of both eddy current distortions and subject motion is achieved by registering the B0 image to the T1-weighted MRI scan and to a common atlas (Yendiki et al., 2011). Subsequently, using the T1 image data, FreeSurfer performs a subcortical segmentation and a cortical parcellation. The aforementioned atlas includes 18 white matter pathways; therefore, the reconstruction of volumetric distribution is atlas-based. The final output of the whole procedure is a file with exact statistics on many diffusion measures (e.g., FA or MD) for all reconstructed pathways. Weblink: https://surfer.nmr.mgh.harvard.edu/fswiki/Tracula.
Coding
Published in Goff Hill, The Cable and Telecommunications Professionals' Reference, 2012
A decoding error occurs when the path through the trellis selected by the decoder is not the correct path. The result will almost always be a burst error; it is even possible, for some codes, for the worst error to be infinite in extent. Such codes are clearly unusable. Analysis of the exact statistics of the error bursts (their probability as a function of their duration) is very complex; approximations can, however, be derived using the minimum free distance of the code. This is obtained by considering all possible error paths—that is, incorrect paths that depart from the correct path at one symbol time and rejoin it later. The minimum free distance is the minimum number of symbol differences between any of these error paths and the correct path. Note, however, that calculation of the true error rates involves analysis of many other interacting effects.
Methods for Analysis of Solid Samples
Published in Somenath Mitra, Pradyot Patnaik, Barbara B. Kebbekus, Environmental Chemical Analysis, 2018
Somenath Mitra, Pradyot Patnaik, Barbara B. Kebbekus
The basic rule of sampling for solids is that the variability due to sampling becomes greater as the particle size of the material becomes greater, as the sample size becomes smaller, and as the concentration of the analyte becomes more variable from particle to particle. By applying statistics to the sampling process, the variability due to sampling can be determined and controlled. In environmental samples, the statistical information required for such a treatment may not be readily available. However, even if the exact statistics of a given sampling task cannot be calculated, knowledge of basic sampling theory will assist us in obtaining the most representative samples possible.
Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts
Published in Molecular Physics, 2020
J. Finkelstein, G. Fiorin, B. Seibold
BBK has been a well-known Langevin discretisation method for the last three decades and is the default Langevin integrator in the popular MD suite, NAMD [31]. Similar to BAOAB, BBK is also a splitting method. It is weakly first-order accurate [10] and in the free particle case reproduces the Einstein relation. However, exact statistics are not recovered in the case of the harmonic oscillator, in sharp contrast to G-JF and BAOAB. Equation (1) is often re-formulated in terms of position and velocity, instead of momentum: This form will serve as the governing equation for our forthcoming analysis and discussion. Set and , with h being the time step used for discretisation. Note that, for sufficiently small, one has which leads to when nh=t. The quantities a and appear several times in the subsequent paragraphs and sections.
Influence of the exposure scenario and spatial correlation on the probabilistic life-cycle seismic performance of deteriorating RC frames
Published in Structure and Infrastructure Engineering, 2018
Andrea Titi, Silvia Bianchi, Fabio Biondini, Dan M. Frangopol
Monte Carlo simulation based on LHS with a sample size N = 200 usually provides good accuracy in terms of convergence of the statistical parameters of base shear capacities of RC frames (Dolšek, 2009). In this application, the comparison among exact statistics and numerical estimates of mean value and coefficient of variation of the random variables indicates very good accuracy with negligible error over the entire 50-year lifetime for all the exposure scenarios and correlation levels investigated.