A type theory for synthetic $\infty$-categories

rzk-lang/rzk 21 May 2017

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

0.42 stars / hour

Implementing Hadamard Matrices in SageMath

sagemath/sage 29 Jun 2023

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


0.04 stars / hour

Estimation of the lead-lag parameter from non-synchronous data

philipperemy/lead-lag 20 Mar 2013

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

0.04 stars / hour

Kangaroo Methods for Solving the Interval Discrete Logarithm Problem

jeanlucpons/kangaroo 28 Jan 2015

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

0.03 stars / hour

Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation

Willcox-Research-Group/rom-operator-inference-Python3 28 Jul 2020

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

0.03 stars / hour

Optimization-Based Autonomous Racing of 1:43 Scale RC Cars

alexliniger/MPCC 20 Nov 2017

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

Optimization and Control Robotics Systems and Control

0.03 stars / hour

Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization

kul-optec/alpaqa 4 Dec 2021

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

0.02 stars / hour

Multirate Partitioned Runge-Kutta Methods for Coupled Navier-Stokes Equations

caidao22/pnode 24 Feb 2022

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

0.02 stars / hour

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

maxhalford/prince 22 Sep 2009

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

Numerical Analysis Probability

0.02 stars / hour

Universal Average-Case Optimality of Polyak Momentum

d2l-ai/d2l-en 19 Aug 2020

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

0.02 stars / hour