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

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

Combinatorics

A two-dimensional process $(X_t, Y_t)$ reproduces a lead-lag effect if, for some time shift $\vartheta\in \mathbb{R}$, the process $(X_t, Y_{t+\vartheta})$ is a semi-martingale with respect to a certain filtration.

Statistics Theory Statistics Theory

In this thesis, I improve the running time of methods that use more than four kangaroos significantly, and almost beat the fastest kangaroo algorithm, by presenting a seven kangaroo method with an expected average running time of $\big(1. 7195 + o(1)\big)\sqrt{N} \pm O(1)$ group operations.

Number Theory Data Structures and Algorithms

This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation.

Numerical Analysis Numerical Analysis

This paper describes autonomous racing of RC race cars based on mathematical optimization.

Optimization and Control Robotics Systems and Control

This paper presents alpaqa, an open-source C++ implementation of an augmented Lagrangian method for nonconvex constrained numerical optimization, using the first-order PANOC algorithm as inner solver.

Optimization and Control Systems and Control Systems and Control 65K05, 49M37, 90C30

Earth system models are complex integrated models of atmosphere, ocean, sea ice, and land surface.

Numerical Analysis Numerical Analysis Computational Physics Fluid Dynamics 76N06, 65M08, 65L04

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

Numerical Analysis Probability

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