Trending Research
The Complex Gradient Operator and the CR-Calculus
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
Optimistix: modular optimisation in JAX and Equinox
We introduce Optimistix: a nonlinear optimisation library built in JAX and Equinox.
Optimization and Control Mathematical Software
A formal system for Euclid's Elements
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
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
A Wasserstein-type distance in the space of Gaussian Mixture Models
rflamary/POT
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In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models.
Optimization and Control
Construction of the Kolmogorov-Arnold representation using the Newton-Kaczmarz method
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
Tulipa Energy Model: Mathematical Formulation
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
Computation of 2D Stokes flows via lightning and AAA rational approximation
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
Formalization of Algorithms for Optimization with Block Structures
Block-structured problems are central to advances in numerical optimization and machine learning.
Optimization and Control G.1.6
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
