We propose the use of the Extended Kalman Filter (EKF) for online data assimilation and update of a dynamic model, preliminary identified through the Sparse Identification of Nonlinear Dynamics (SINDy).

Dynamical Systems

We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry.

Differential Geometry Algebraic Topology

We prove that the solution to the linear flow relaxation on exact decision diagrams determines the fractional chromatic number of a graph.

Combinatorics Discrete Mathematics 05C15 G.2.2

Under the same assumptions on the shift, the analysis of the algorithm for the shifted and inverted problem leads to useful error bounds for the original problem, including a bound that shows how a single shift that is of moderate size in a scaled sense can be chosen so that every computed generalized eigenvalue corresponds to a generalized eigenvalue of a pair of matrices close to $A$ and $B$.

Numerical Analysis Numerical Analysis 65F15 (Primary), 15A22, 15A22, 15A23, 15A42 (Secondary)

We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions.

Optimization and Control 65K10, 35Q93, 90C56

We demonstrate that automatic differentiation, which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and affine super-resolution problems.

Optimization and Control

Primality testing is an especially useful topic for public-key cryptography.

Number Theory

Continuation techniques generate continuous families of such solutions in the combined state and parameter space, e. g., curves (branches) of periodic orbits or surfaces of equilibria.

Dynamical Systems

The order of floating-point summation is a key factor in numerical reproducibility.

Numerical Analysis Numerical Analysis Software Engineering

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines.

Numerical Analysis Numerical Analysis 65M60, 15A12, 65L60, 15B05