The two major approaches to sparse recovery are L1-minimization and greedy methods. Recently, Needell and Vershynin developed Regularized Orthogonal Matching Pursuit (ROMP) that has bridged the gap between these two approaches. ROMP is the first stable greedy algorithm providing uniform guarantees. Even more recently, Needell and Tropp developed the stable greedy algorithm Compressive Sampling Matching Pursuit (CoSaMP). CoSaMP provides uniform guarantees and improves upon the stability bounds and RIC requirements of ROMP. CoSaMP offers rigorous bounds on computational cost and storage. In many cases, the running time is just O(NlogN), where N is the ambient dimension of the signal. This review summarizes these major advances.

Interest in high-spin organic materials is driven by opportunities to enable far-reaching fundamental science and develop technologies that integrate light element spin, magnetic, and quantum functionalities. Although extensively studied, the intrinsic instability of these materials complicates synthesis and precludes an understanding of how fundamental properties associated with the nature of the chemical bond and electron pairing in organic materials systems manifest in practical applications. Here, we demonstrate a conjugated polymer semiconductor, based on alternating cyclopentadithiophene and thiadiazoloquinoxaline units, that is a ground-state triplet in its neutral form. Electron paramagnetic resonance and magnetic susceptibility measurements are consistent with a high-to-low spin energy gap of 9.30 × 10^-3 kcal mol^-1. The strongly correlated electronic structure, very narrow bandgap, intramolecular ferromagnetic coupling, high electrical conductivity, solution processability, and robust stability open access to a broad variety of technologically relevant applications once thought of as beyond the current scope of organic semiconductors.