Publications related to Frobenius techniques in birational geometry

Unlabeled Principal Component Analysis and Matrix Completion

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Microtome Publ2024

Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures

Marianne Liebi, Manuel Guizar Sicairos

The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural symmetries. For s ...

Chester2023

On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

MATHEMATICAL SCIENCE PUBL2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories.We introduce the notion of tame spectra and show it has a concrete algebraic description.We then carry out a study of

\infty

-operads and ...

EPFL2022

Algebraic Homotopy Interleaving Distance

Nicolas Michel Berkouk

The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients requires solving loc ...

EPFL2020

Adaptive Gradient Descent without Descent

Konstantin Mishchenko

We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don’t increase the stepsize too fast and 2) don’t overstep the local curvature. No need for functional values, no line search, no information about the func ...

2020

Open and Closed Radicals: Local Geometry around Unpaired Electrons Governs Magic-Angle Spinning Dynamic Nuclear Polarization Performance

David Lyndon Emsley, Yu Rao, Dominik Józef Kubicki, Moreno Lelli, Gabriele Stevanato, Manuel Cordova, Georges Guévork Jean-Jacques Menzildjian

The development of magic-angle spinning dynamic nuclear polarization (MAS DNP) has allowed atomic-level characterization of materials for which conventional solid-state NMR is impractical due to the lack of sensitivity. The rapid progress of MAS DNP has be ...

2020

Neuron Geometry Underlies Universal Network Features in Cortical Microcircuits

Henry Markram, Rodrigo de Campos Perin, Idan Segev, Eyal Gal, Michael London

Why do cortical microcircuits in a variety of brain regions express similar, highly nonrandom, network motifs? To what extent this structure is innate and how much of it is molded by plasticity and learning processes? To address these questions, we develop ...

2020

A Learned Shape-Adaptive Subsurface Scattering Model

Wenzel Alban Jakob, Delio Aleardo Vicini

Subsurface scattering, in which light refracts into a translucent material to interact with its interior, is the dominant mode of light transport in many types of organic materials. Accounting for this phenomenon is thus crucial for visual realism, but exp ...

ASSOC COMPUTING MACHINERY2019

Frobenius techniques in birational geometry

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Unlabeled Principal Component Analysis and Matrix Completion

Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures

On rationally connected varieties over C1 fields of characteristic 0

A Hopf algebra model for Dwyer's tame spaces

Algebraic Homotopy Interleaving Distance

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Adaptive Gradient Descent without Descent

Open and Closed Radicals: Local Geometry around Unpaired Electrons Governs Magic-Angle Spinning Dynamic Nuclear Polarization Performance

Neuron Geometry Underlies Universal Network Features in Cortical Microcircuits

A Learned Shape-Adaptive Subsurface Scattering Model

On rationally connected varieties over C1 fields of characteristic 0

Small-angle scattering tensor tomography algorithm for robust reconstruction of complex textures

Unlabeled Principal Component Analysis and Matrix Completion

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Open and Closed Radicals: Local Geometry around Unpaired Electrons Governs Magic-Angle Spinning Dynamic Nuclear Polarization Performance

A Hopf algebra model for Dwyer's tame spaces

Algebraic Homotopy Interleaving Distance

Neuron Geometry Underlies Universal Network Features in Cortical Microcircuits

Adaptive Gradient Descent without Descent

A Learned Shape-Adaptive Subsurface Scattering Model