Computational optimal transport: With applications to data science

G Peyré, M Cuturi - Foundations and Trends® in Machine …, 2019‏ - nowpublishers.com
Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Volume-law entanglement entropy of typical pure quantum states

E Bianchi, L Hackl, M Kieburg, M Rigol, L Vidmar - PRX Quantum, 2022‏ - APS
The entanglement entropy of subsystems of typical eigenstates of quantum many-body
Hamiltonians has recently been conjectured to be a diagnostic of quantum chaos and …

Three-dimensional virtual histology of the human hippocampus based on phase-contrast computed tomography

M Eckermann, B Schmitzer, F van der Meer… - Proceedings of the …, 2021‏ - pnas.org
We have studied the three-dimensional (3D) cytoarchitecture of the human hippocampus in
neuropathologically healthy and Alzheimer's disease (AD) individuals, based on phase …

[كتاب][B] Progress on the Study of the Ginibre Ensembles

SS Byun, PJ Forrester - 2025‏ - library.oapen.org
This open access book focuses on the Ginibre ensembles that are non-Hermitian random
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …

[HTML][HTML] 3d virtual histology reveals pathological alterations of cerebellar granule cells in multiple sclerosis

J Frost, B Schmitzer, M Töpperwien, M Eckermann… - Neuroscience, 2023‏ - Elsevier
We investigate structural properties of neurons in the granular layer of human cerebellum
with respect to their involvement in multiple sclerosis (MS). To this end we analyze data …

Singular value statistics of matrix products with truncated unitary matrices

M Kieburg, ABJ Kuijlaars… - International Mathematics …, 2016‏ - academic.oup.com
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a
Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is …

Convolution Monge Map** Normalization for learning on sleep data

T Gnassounou, R Flamary… - Advances in Neural …, 2023‏ - proceedings.neurips.cc
In many machine learning applications on signals and biomedical data, especially
electroencephalogram (EEG), one major challenge is the variability of the data across …

Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions

XK Chang, Y He, XB Hu, SH Li - Communications in Mathematical Physics, 2018‏ - Springer
Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for
orthogonal and symplectic random matrix ensembles. Motivated by the average of …

Products of independent Gaussian random matrices

JR Ipsen - arxiv preprint arxiv:1510.06128, 2015‏ - arxiv.org
This thesis reviews recent progress on products of random matrices from the perspective of
exactly solved Gaussian random matrix models. We derive exact formulae for the correlation …

[HTML][HTML] Random density matrices: Closed form expressions for the variance of squared Hilbert-Schmidt distance

A Laha, S Kumar - Physics Letters A, 2024‏ - Elsevier
One of the fundamental aspects of quantum information theory is the study of distance
measures between quantum states. Hilbert-Schmidt distance serves as a convenient choice …