Wavelets and Wavelet Packets on Quantum Computers

We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.Comment: 11 pages, 10 postscript figure, to appear in Proc. of Wavelet Applications in Signal and Image Processing VI

Primal-Dual Rates and Certificates

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in particular in machine learning applications. We obtain new primal-dual convergence rates, e.g., for the Lasso as well as many L1, Elastic Net, group Lasso and TV-regularized problems. The theory applies to any norm-regularized generalized linear model. Our approach provides efficiently computable duality gaps which are globally defined, without modifying the original problems in the region of interest.Comment: appearing at ICML 2016 - Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 2016. JMLR: W&CP volume 4

On next-to-eikonal exponentiation

The eikonal approximation is at the heart of many theoretical and phenomenological studies involving multiple soft gauge boson emissions in high energy physics. We describe our efforts towards the extension of the eikonal approximation for scattering amplitudes to the first subleading power in the soft momentum.Comment: Proc. of "Loops and Legs in Quantum Field Theory", April, 2010, W\"orlitz, German