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One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the simplest representation (i.e. the smallest amount of terms). One such approach is the sparse identification of nonlinear dynamics framework [6] which uses a sparsity-promoting algorithm that iterates between a partial least-squares fit and a thresholding (sparsity-promoting) step. In this work, we provide some theoretical results on the behavior and convergence of the algorithm proposed in [6]. In particular, we prove that the algorithm approximates local minimizers of an unconstrained 0 -penalized leastsquares problem. From this, we provide sufficient conditions for general convergence, rate of convergence, and conditions for one-step recovery. Examples illustrate that the rates of convergence are sharp. In addition, our results extend to other algorithms related to the algorithm in [6], and provide theoretical verification to several observed phenomena.

Ammonia synthesis is one of the most studied reactions in heterogeneous catalysis. To date, however, electrochemical N reduction in aqueous systems has proven to be extremely difficult, mainly due to the competing hydrogen evolution reaction (HER). Recently, it has been shown that transition metal complexes based on molybdenum can reduce N to ammonia at room temperature and ambient pressure in a non-aqueous system, with a relatively small amount of hydrogen output. We demonstrate that the non-aqueous proton donor they have chosen, 2,6-lutidinium (LutH), is a viable substitute for hydronium in the electrochemical process at a solid surface, since this donor can suppress the HER rate. We also show that the presence of LutH can selectively stabilize the *NNH intermediate relative to *NH or *NHvia the formation of hydrogen bonds, indicating that the use of non-aqueous solvents can break the scaling relationship between limiting potential and binding energies.