Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure

Brain Microstructure assessed by CHARMED and NODDI in the newborn

DTI, may be the only feasible technique to study micorstructural changes occurring during the brain development. The main aims of this study was to design a complete new pipeline to perform micro-structural diffusion analysis in neonatal brain and to compare DTI to CHARMED and NODDI, which provides new microstructural metrics such as the intra-cellular volume fraction (nic) and the orientation dispersion index (ODI). High quality subject template was generated using DTI-TK tensor registration tools, which allows the accurate definitions of 13 ROIs. FA, nic and ODI were able to depict fine microstructural differences in early maturation fiber tracts