Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better representation. However, current NMF methods do not always generate sparse solutions. In this paper, we propose new method log-norm imposed on the factor matrices enhance sparseness. Mor...

An exponential representation of the S-matrix provides a natural framework for understanding semi-classical limit scattering amplitudes. While sharing some similarities with eikonal formalism it differs from in details. Computationally, rules are simple because pieces that must be subtracted given by combinations unitarity cuts. Analyzing classical gravitational to third Post-Minkowskian order ...