Using a time-gated dual quadrature spectral interferometry technique, for the first time we demonstrate single-shot characterization of both spectral amplitude and phase of approximately 1THz bandwidth optical arbitrary waveforms generated from a 10 GHz frequency comb. Our measurements provide a temporal resolution of 1ps over a record length of 100ps. Singleshot characterization becomes partic...

The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained in a wide context from a local point of view, so giving a characterization of the so-called pseudo-distanceregularity aro...

In this work, we investigate several natural computational problems related to identifying symmetric signings of symmetric matrices with specific spectral properties. We show NP-completeness for verifying whether an arbitrary matrix has a symmetric signing that is positive semi-definite, is singular, or has bounded eigenvalues. We exhibit a stark contrast between invertibility and the above-men...