We consider column-sparse positive covering integer programs, which generalize set cover and which have attracted a long line of research developing (randomized) approximation algorithms. We develop a new rounding scheme based on the Partial Resampling variant of the Lovász Local Lemma developed by Harris & Srinivasan (2013). This achieves an approximation ratio of 1 + ln(∆1+1) amin +O( √ log(∆...

Batch gradient descent, ~w(t) = -7JdE/dw(t) , conver~es to a minimum of quadratic form with a time constant no better than '4Amax/ Amin where Amin and Amax are the minimum and maximum eigenvalues of the Hessian matrix of E with respect to w. It was recently shown that adding a momentum term ~w(t) = -7JdE/dw(t) + Q'~w(t 1) improves this to ~ VAmax/ Amin, although only in the batch case. Here we ...

The Amin and Bodurtha (1995) framework, building on a discrete-time version of the Heath, Jarrow, and Morton (1992) term structure model and the binomial model of Cox, Ross, and Rubinstein (1979), allows a consistent valuation of instruments driven by three sources of uncertainty: domestic interest rate risk, foreign interest rate risk and exchange rate risk. This makes the framework applicable...