Trending Research
A type theory for synthetic $\infty$-categories
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
Implementing Hadamard Matrices in SageMath
The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$.
Combinatorics
Estimation of the lead-lag parameter from non-synchronous data
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
Kangaroo Methods for Solving the Interval Discrete Logarithm Problem
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
Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation
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
Optimization-Based Autonomous Racing of 1:43 Scale RC Cars
This paper describes autonomous racing of RC race cars based on mathematical optimization.
Optimization and Control Robotics Systems and Control
Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization
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
Multirate Partitioned Runge-Kutta Methods for Coupled Navier-Stokes Equations
caidao22/pnode
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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
Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
These methods use random sampling to identify a subspace that captures most of the action of a matrix.
Numerical Analysis Probability
Universal Average-Case Optimality of Polyak Momentum
d2l-ai/d2l-en
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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
