In this work, explicit models of grid-following and grid-forming virtual inertia (VI) devices are developed for inertia emulation in low-inertia systems.

Optimization and Control

The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$.

Combinatorics

These methods use random sampling to identify a subspace that captures most of the action of a matrix.

Numerical Analysis Probability

One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces.

Numerical Analysis Numerical Analysis Computational Physics

Stein's unbiased risk estimate (SURE) gives an unbiased estimate of the $\ell_2$ risk of any estimator of the mean of a Gaussian random vector.

Statistics Theory Optimization and Control Computation Statistics Theory

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems.

Optimization and Control Systems and Control Systems and Control

Students started using the specific formulations of proof steps from the custom proof language in their handwritten proofs; the explicit phrasing of these sentences helped to clarify the logical structure of their arguments.

History and Overview

We introduce structured decompositions: category-theoretic generalizations of many combinatorial invariants -- including tree-width, layered tree-width, co-tree-width and graph decomposition width -- which have played a central role in the study of structural and algorithmic compositionality in both graph theory and parameterized complexity.

Category Theory Data Structures and Algorithms Combinatorics 18B10, 05C75 (Primary) 68W40 (Secondary) F.2.m; G.0

We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency.

Optimization and Control Systems and Control

We propose and experimentally demonstrate a feedback control method that allows synchronizing the motion of a chain of several coupled nonlinear oscillators actuated through one end of the chain.

Optimization and Control Dynamical Systems