Publications related to Symmetric space

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 ...

2022

Optimal radial basis for density-based atomic representations

Michele Ceriotti, Sergey Pozdnyakov, Jigyasa Nigam, Félix Benedito Clément Musil, Alexander Jan Goscinski

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

AIP Publishing2021

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. First, we show that a symmetric set S subset of Z(q)(n) containing vertical bar S vertical bar = mu . q(n) elements must contain at leas ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Samuel Gozel, Pierre Marcel Nataf

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

AMER PHYSICAL SOC2020

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerfu ...

2020

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

Roland Widmer, Yi-Chiang Sun, Timur Kim, Samuel Thomas Stolz

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use sca ...

2020

A General Theory of Equivariant CNNs on Homogeneous Spaces

Mario Geiger

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Perfect soliton crystals in optical microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Hairun Guo, Martin Hubert Peter Pfeiffer, Wenle Weng

We demonstrate the existence of perfect soliton crystal states and develop the deterministic procedure for their excitation in Si3N4 microresonators. We show that despite exceptional symmetrical properties, their behavior is strongly linked to the chaotic ...

IEEE2019

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Symmetric space

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Optimal denoising of rotationally invariant rectangular matrices

Optimal radial basis for density-based atomic representations

On arithmetic progressions in symmetric sets in finite field model

Haldane Gap of the Three-Box Symmetric SU(3) Chain

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

A General Theory of Equivariant CNNs on Homogeneous Spaces

Computationally Efficient Estimation of the Electric-Field Maximums for the MFT Insulation Coordination

Perfect soliton crystals in optical microresonators

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Chat with Graph Search

Optimal radial basis for density-based atomic representations

On arithmetic progressions in symmetric sets in finite field model

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

From Trees to Barcodes and Back Again:A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Perfect soliton crystals in optical microresonators

Computationally Efficient Estimation of the Electric-Field Maximums for the MFT Insulation Coordination

Optimal denoising of rotationally invariant rectangular matrices

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa

A General Theory of Equivariant CNNs on Homogeneous Spaces