Plenary talks

The best rate for a noisy (communication) channel to transmit data nearly perfectly is called the capacity.  The best error correction strategy is optimized over an unbounded domain as the blocklength diverges, yet the capacity for a classical channel to transmit classical data has a surprisingly simple expression, and there is no capacity gain by coding two channels jointly.  This talk will focus on how the capacity of a quantum channel to transmit quantum data deviates from most of the classical counterpart.  Most notably, we describe how two quantum channels used jointly can have combined capacity much higher than the sum of the capacities of the constituent channels. 

An electroretinogram (ERG) is a diagnostic test that measures the electrical activity of the neuronal cells of the retina. A light stimulus causes transmembrane currents in the photoreceptors (the rods and cones) and in the other retinal neurons via synaptic connections with the photorecpetors. These currents are detected by electrodes on the surface of the eye. We use an extended bidomain framework to model the whole-tissue electrical activity of the retina. Detailed ionic current models of the rods, cones, and bipolar cells, including the phototransduction pathway and the neuronal connectivity of the retina, are coupled to an elliptic PDE for the electrostatic potential inside the interior of the eye. To numerically integrate the stiff dynamics, we employ an adaptive time-stepping routine, a Newton iteration, and an efficient spatial discretization of the PDE. The simulation provides a physical basis for the a waves in ERG recordings used by ophthalmologists to diagnose disease. For ERG recordings indicative of disease, we solve an inverse problem to infer a biophysical basis of the retinal disease. We solve a numerical optimal control problem to design a light stimulus to produce an efficient, patient-specific, and adaptive diagnosis procedure.