Results 41 to 50 of about 249 (128)

Equal area partitions of the sphere with diameter bounds, via optimal transport

Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1524-1538, May 2025.
Abstract We prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge–Kantorovich distances. This can be used to obtain bounds on the expectation of the maximum diameter of partition sets, when points are uniformly sampled from the sphere.
Jun Kitagawa, Asuka Takatsu
wiley   +1 more source

Low Dimensional Representation of Multi‐Patient Flow Cytometry Datasets Using Optimal Transport for Measurable Residual Disease Detection in Leukemia

Cytometry Part A, Volume 107, Issue 2, Page 126-139, February 2025.
ABSTRACT Representing and quantifying Measurable Residual Disease (MRD) in Acute Myeloid Leukemia (AML), a type of cancer that affects the blood and bone marrow, is essential in the prognosis and follow‐up of AML patients. As traditional cytological analysis cannot detect leukemia cells below 5%, the analysis of flow cytometry datasets is expected to ...
Erell Gachon, Jérémie Bigot, Elsa Cazelles, Audrey Bidet, Jean‐Philippe Vial, Pierre‐Yves Dumas, Aguirre Mimoun   +6 more
wiley   +1 more source

A new Kantorovich-type theorem for Newton's method [PDF]

Applicationes Mathematicae, 1999
Summary: A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation \(F(x) =0\) defined on a Banach space. It is assumed that the operator \(F\) is twice Fréchet differentiable, and that \(F'\), \(F''\) satisfy Lipschitz conditions.
openaire   +1 more source

Fine Properties of Geodesics and Geodesic λ-Convexity for the Hellinger-Kantorovich Distance. [PDF]

Arch Ration Mech Anal, 2023
Liero M, Mielke A, Savaré G.
europepmc   +1 more source

The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities. [PDF]

Calc Var Partial Differ Equ, 2023
Sodini GE.
europepmc   +1 more source

On a theorem of L.V. Kantorovich concerning Newton's method

Journal of Computational and Applied Mathematics, 2003
The author proves the local and semilocal convergence of the Newton method assuming the Fréchet differentiability only at a point. A numerical example shows the potentials of the new theorem.
openaire   +1 more source

Homogenisation of dynamical optimal transport on periodic graphs. [PDF]

Calc Var Partial Differ Equ, 2023
Gladbach P, Kopfer E, Maas J, Portinale L.   +3 more
europepmc   +1 more source

To the generalization of the Newton-Kantorovich theorem.

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2017
Constructive conditions for solvability are obtained, as well as an iterative scheme for finding solutions of the nonlinear equation that generalize the well-known Newton-Kantorovich theorem. The case of a nonlinear equation whose dimension does not coincide with the dimension of the unknown has been researched.
openaire   +3 more sources

Efficient Discrete Optimal Transport Algorithm by Accelerated Gradient Descent. [PDF]

Proc AAAI Conf Artif Intell, 2022
An D, Lei N, Xu X, Gu X.
europepmc   +1 more source

First Order Expansion in the Semiclassical Limit of the Levy-Lieb Functional. [PDF]

Arch Ration Mech Anal
Colombo M, Di Marino S, Stra F.
europepmc   +1 more source