This paper studies a fundamental problem that arises in sparse representation and compressed sensing community: can greedy algorithms give us a stable recovery from incomplete and contaminated observations ? Using the Regularized Orthogonal Matching Pursuit (ROMP) algorithm, a modified version of Orthogonal Matching Pursuit (OMP) [1], which was recently introduced by D.Needell and R.Vershynin [...

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...

The ring-opening metathesis polymerization (ROMP) of apopinene is reported. We find that apopinene reacts with Rubased metathesis catalysts to provide an all trans-polymer with a polydispersity index (PDI) as low as 1.6 and molecular weights in the 1100 to 15 600 g·mol−1 range (9−127 monomer units). Because apopinene is readily prepared in one-step from myrtenal or two-steps from α-pinene, both...

The incorporation of main group elements into polymers allows for the generation new functional materials with hitherto-unattainable physical and chemical properties through unique molecular geometries, electronic structures, reactivities element-based groups. synthesis these novel requires highly controllable polymerizations which are tolerant diverse functionalized monomers. In this review, w...

We study the Reconstruction-of-the-Measure Problem (ROMP) for commuting 2-variable weighted shifts $$W_{(\alpha ,\beta )}$$ , when initial data are given as Berger measure of restriction to a canonical invariant subspace, together with marginal measures 0–th row and column in weight diagram . prove that natural necessary conditions indeed sufficient. When correspond soluble problem, we give con...

A straightforward synthesis utilizing the ring-opening metathesis polymerization (ROMP) reaction is described for acid-triggered N,O-chelating ruthenium-based pre-catalysts bearing one or two 8-quinolinolate ligands. The innovative pre-catalysts were tested regarding their behavior in ROMP and especially for their use in the synthesis of poly(dicyclopentadiene) (pDCPD). Bearing either the commo...

This article reviews the development of catalysts for ring-opening metathesis polymerization (ROMP), synthesis of polymers bearing amino acids and peptides by ROMP of functionalized norbornenes, formation of aggregates and micelles, and applications of the polymers to medical materials. It also describes the control of monomer unit sequences, that is, living polymerization to synthesize block c...

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...

The potency, selectivity, and decreased side effects of bioactive peptides have propelled these agents to the forefront of pharmacological research. Peptides are especially promising for the treatment of neurological disorders and pain. However, delivery of peptide therapeutics often requires invasive techniques, which is a major obstacle to their widespread application. We have developed a tai...