Aniline accelerates hydrazone formation and transimination through nucleophilic catalysis. To demonstrate the method, unprotected peptides are reacted and then scrambled using a hydrazone reaction under conditions relevant for biological applications. The strong enhancement in the rate of hydrazone equilibration broadens the scope of this stable imine in the field of dynamic covalent chemistry.

We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.

Abstract. We present a theory for Euclidean dimensionality reduction with subgaussian matrices which unifies several restricted isometry property and Johnson-Lindenstrauss type results obtained earlier for specific data sets. In particular, we recover and, in several cases, improve results for sets of sparse and structured sparse vectors, low-rank matrices and tensors, and smooth manifolds. In addition, we establish a new Johnson-Lindenstrauss embedding for data sets taking the form of an infinite union of subspaces of a Hilbert space.

Let Φ ∈ R m×n be a sparse Johnson-Lindenstrauss transform (Kane and Nelson in J ACM 61(1):4, 2014) with s non-zeroes per column. For a subset T of the unit sphere, ε ∈ (0, 1/2) given, we study settings for m, s required to ensurei.e. so that Φ preserves the norm of every x ∈ T simultaneously and multiplicatively up to 1 + ε. We introduce a new complexity parameter, which depends on the geometry of T , and show that it suffices to choose s and m such that this parameter is small. Our result is a sparse analog of Gordon's theorem, which was concerned with a dense Φ having i.i.d. Gaussian entries. We qualitatively unify several results related to the Johnson-Lindenstrauss lemma, subspace embeddings, and Fourierbased restricted isometries. Our work also implies new results in using the sparse Johnson-Lindenstrauss transform in numerical linear algebra, classical and modelbased compressed sensing, manifold learning, and constrained least squares problems such as the Lasso.