There are various ways to impose a potential variation in time, and subsequently a series of voltammetric methods. Cyclic voltammetry relies on linearly scanning the potential in time, observing a triangular waveform variation [1-3]. Differential pulse voltammetry is based on two samplings of the current intensity for each potential pulse: one measurement before applying the pulse, and the seco...

This dissertation consists of two independent parts: oscillatory data analysis (Part I) and fast algorithms for integral operators in computational harmonic analysis (Part II). The first part concentrates on developing theory and efficient tools in applied and computational harmonic analysis for oscillatory data analysis. In modern data science, oscillatory data analysis aims at identifying and...

Despite the ubiquitous use of distance transforms in the shape analysis literature and the popularity of fast marching and fast sweeping methods—essentially HamiltonJacobi solvers, there is very little recent work leveraging the Hamilton-Jacobi to Schrödinger connection for representational and computational purposes. In this work, we exploit the linearity of the Schrödinger equation to (i) des...