Matrices with positive principal minors

AbstractA new necessary and sufficient condition is given for all principal minors of a square matrix to be positive. A special subclass of such matrices, called quasidominant matrices, is also examined

Functional programming framework for GRworkbench

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional programming techniques. By allowing functions to be directly represented as program variables in C++ code, the functional framework enables the mathematical formalism of Differential Geometry to be more closely reflected in GRworkbench . The powerful technique of `automatic differentiation' has replaced numerical differentiation of the metric components, resulting in more accurate derivatives and an order-of-magnitude performance increase for operations relying on differentiation

Numerical wave optics and the lensing of gravitational waves by globular clusters

We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.Comment: To appear in: Proceedings of the Eleventh Marcel Grossmann Meetin

Commercial Bank Small Business Lending Pre and Post Crisis

We analyze small business lending at U.S. commercial banks, how it has changed over time and how it differs by bank size. Specifically, we examine the impact of government policy intervention on small business lending in the aftermath of the financial crisis. We find several important results. First, we find that the Troubled-Asset Relief Program’s (TARP) $200 billion Capital Purchase Program (CPP) had little impact on the banks that received capital injections’ small business lending. Second, the Small Business Loan Fund (SBLF) lending program appears to have been a success as banks participating in the loan fund increased their lending to small businesses. Finally, we find that financial turmoil had a substantial negative impact on lending to small businesses at community banks but not their large bank counterparts. This result suggests that the larger banks may have behaved in a manner consistent with too big to fail. Collectively, these results provide important insights for policy makers as they continue to deal with the credit access issues of small firms