We analyze the stability properties of the Synchrosqueezing transform, a time-frequency signal analysis method that can identify and extract oscillatory components with time-varying frequency and amplitude.
Classical Analysis and ODEs Computational Engineering, Finance, and Science Numerical Analysis Data Analysis, Statistics and Probability 42C40, 65T99, 62M15, 86A04
To make the bookkeeping in such proofs manageable, we use a three-layered type theory with shapes, whose contexts are extended by polytopes within directed cubes, which can be abstracted over using "extension types" that generalize the path-types of cubical type theory.
Category Theory Logic 03G30, 18G55, 55U40
Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives.
Optimization and Control
PySINDy is a Python package for the discovery of governing dynamical systems models from data.
Dynamical Systems Computational Physics
The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB.
Optimization and Control Numerical Analysis Programming Languages
We introduce Fireshape, an open-source and automated shape optimization toolbox for the finite element software Firedrake.
Optimization and Control Numerical Analysis Numerical Analysis
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the degree of dependence between the variables, which is 0 if and only if the variables are independent and 1 if and only if one is a measurable function of the other, and (c) has a simple asymptotic theory under the hypothesis of independence, like the classical coefficients?
Statistics Theory Probability Statistics Theory 62H20, 62H15