CONTROL LIE ALGEBRAS OF SEMI-DISCRETIZAT IONS OF THE SCHROEDINGER EQUATION

ABSTRACT We consider control of the one-dimensional Schroedinger equation via a time-dependent rectangular potential. We discretize the equation in the space variable, obtaining a system of ODEs in which the control is bilinear. We find Control Lie Algebras for several cases, including single point and full width potentials. We use full discretizations, in space and time, to examine the effect of the number of inputs

Data Use in the Measurement of Systemic Risk in Financial Systems

The financial crisis of 2008 led to an increase in research on the subject of systemic risk in various financial systems--broadly speaking, the possibility that losses experienced by one participant in the system would start a cascade of losses in part or all of the rest of the system. While many papers are theoretical in nature and do not use actual data sets, others do. In this talk we will give a partial survey of empirical studies and the data sets used, for example Furfine\u27s use of payment flow data from the Federal Reserve\u27s large-value transfer system, Fedwlre, and the use of the Mexican interbank exposures market and the Mexican Large Value Payments System by Martinez-Jaramillo et al. We will discuss proposed systemic risk measures, by Bisias et al, and by the Federal Reserve