Decoherence-induced conductivity in the discrete 1D Anderson model: A novel approach to even-order generalized Lyapunov exponents

A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent $\xi^{-1}$. We determine the exact value of $\xi^{-1}$ of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance $T$. This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center.Comment: 12 pages, 5 figure

Multidataset Incremental Training for Optic Disc Segmentation

When convolutional neural networks are applied to image segmentation results depend greatly on the data sets used to train the networks. Cloud providers support multi GPU and TPU virtual machines making the idea of cloud-based segmentation as service attractive. In this paper we study the problem of building a segmentation service, where images would come from different acquisition instruments, by training a generalized U-Net with images from a single or several datasets. We also study the possibility of training with a single instrument and perform quick retrains when more data is available. As our example we perform segmentation of Optic Disc in fundus images which is useful for glau coma diagnosis. We use two publicly available data sets (RIM-One V3, DRISHTI) for individual, mixed or incremental training. We show that multidataset or incremental training can produce results that are simi lar to those published by researchers who use the same dataset for both training and validation