MPS-FFA: A multiplane and multiscale feature fusion attention network for Alzheimer's disease prediction with structural MRI.

Structural magnetic resonance imaging (sMRI) is a popular technique that is widely applied in Alzheimer's disease (AD) diagnosis. However, only a few structural atrophy areas in sMRI scans are highly associated with AD. The degree of atrophy in patients' brain tissues and the distribution of lesion areas differ among patients.

Newtonian versus special-relativistic statistical predictions for low-speed scattering.

The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected.

Statistical predictions for the dynamics of a low-speed system: Newtonian versus special-relativistic mechanics.

The newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic.

Comparison of newtonian and special-relativistic trajectories with the general-relativistic trajectory for a low-speed weak-gravity system.

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the system is non-dissipative, the breakdown of agreement occurs for chaotic trajectories and non-chaotic trajectories.