Spectral graph fractional Fourier transform for directed graphs and its application

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs

Coherent heteronuclear spin dynamics in an ultracold spin-1 mixture

We report the observation of coherent heteronuclear spin dynamics driven by inter-species spin-spin interaction in an ultracold spinor mixture, which manifests as periodical and well correlated spin oscillations between two atomic species. In particular, we investigate the magnetic field dependence of the oscillations and find a resonance behavior which depends on {\em both} the linear and quadratic Zeeman effects and the spin-dependent interaction. We also demonstrate a unique knob for controlling the spin dynamics in the spinor mixture with species-dependent vector light shifts. Our finds are in agreement with theoretical simulations without any fitting parameters.Comment: 13 pages including the supplementary materia