Trending Research

The Complex Gradient Operator and the CR-Calculus

mitmath/matrixcalc 26 Jun 2009

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus.

Optimization and Control Complex Variables

474
0.08 stars / hour

Optimistix: modular optimisation in JAX and Equinox

patrick-kidger/optimistix 15 Feb 2024

We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox.

Optimization and Control Mathematical Software

408
0.05 stars / hour

A formal system for Euclid's Elements

loganrjmurphy/leaneuclid 23 Oct 2008

We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

Logic 03B30, 51M05, 03B35

98
0.03 stars / hour

A type theory for synthetic $\infty$-categories

fizruk/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

222
0.03 stars / hour

A Wasserstein-type distance in the space of Gaussian Mixture Models

rflamary/POT 11 Jun 2020

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models.

Optimization and Control

2,524
0.03 stars / hour

Construction of the Kolmogorov-Arnold representation using the Newton-Kaczmarz method

mpoluektov/kan-polar 14 May 2023

It is known that any continuous multivariate function can be represented exactly by a composition functions of a single variable - the so-called Kolmogorov-Arnold representation.

Numerical Analysis Numerical Analysis 26B40, 41A99, 65D15

44
0.02 stars / hour

Tulipa Energy Model: Mathematical Formulation

tulipaenergy/tulipaenergymodel.jl 14 Sep 2023

Tulipa Energy Model aims to optimise the investment and operation of the electricity market, considering its coupling with other sectors, such as hydrogen and heat, that can also be electrified.

Optimization and Control 90C90 G.1.6

39
0.02 stars / hour

Computation of 2D Stokes flows via lightning and AAA rational approximation

yidanxue/lars 23 Jun 2023

Brubeck and Trefethen (2022) recently introduced a lightning Stokes solver that uses rational functions to approximate the Goursat functions in polygonal domains.

Numerical Analysis Numerical Analysis Fluid Dynamics 41A20, 65N35, 76D07

14
0.02 stars / hour

Formalization of Algorithms for Optimization with Block Structures

optsuite/optlib 24 Mar 2025

Block-structured problems are central to advances in numerical optimization and machine learning.

Optimization and Control G.1.6

50
0.02 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 $4$.

Combinatorics

1,720
0.02 stars / hour