Concept
Hermitian symmetric space
Related publications (45)
Optimal denoising of rotationally invariant rectangular matrices
Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba
In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...
2022From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem
In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...
EPFL2022The cohomology of semi-simple Lie groups, viewed from infinity
We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...
2022Robust Differentiable SVD
Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu
Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...
2021Spherical birational sheets in reductive groups
We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2021Local invertibility and sensitivity of atomic structure-feature mappings
Michele Ceriotti, Sergey Pozdnyakov
Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...
2021