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Concept

Symmetric group

Related publications (29)

Multiplicity-free Representations of Algebraic Groups

Donna Testerman

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

Academic Press Inc Elsevier Science2023

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

Adélie Eliane Garin

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 invol ...

EPFL2022

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

EPFL2022

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022

Subgroups of elliptic elements of the Cremona group

Christian Lucius Urech

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...

2021

Local 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

Optimal radial basis for density-based atomic representations

Michele Ceriotti, Félix Benedito Clément Musil, Jigyasa Nigam, Sergey Pozdnyakov, 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 ...

2021

High-order geometric integrators for representation-free Ehrenfest dynamics

Jiri Vanicek, Seonghoon Choi

Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equa ...

2021

A Chiral Naphthyridine Diimine Ligand Enables Nickel‐Catalyzed Asymmetric Alkylidenecyclopropanations

Nicolai Cramer, Elena Braconi

A novel class of chiral naphthyridine diimine ligands (NDI*) readily accessible from C2‐symmetric 2,6‐di‐(1‐arylethyl)anilines is described. The utility of these ligands, particularly one with fluorinated aryl side arms, is demonstrated by a reductive Ni‐c ...

Wiley-VCH Verlag GmbH2020

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. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

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

Frédéric Mila, Pierre Marcel Nataf, Samuel Gozel

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 ...

2020

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...

HEBREW UNIV MAGNES PRESS2020

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 powerful ...

2020

Generalization of the Haldane conjecture to SU(n) chains

Frédéric Mila, Miklos Lajko

Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-psymmetric ones with pnot a multiple of 3, it was argued that the ground state exhibits gap ...

2020

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

Yi-Chiang Sun, 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 ...

Nature Research2020

Overlapping Multi-Bandit Best Arm Identification

Volkan Cevher, Jonathan Mark Scarlett, Ilija Bogunovic

In the multi-armed bandit literature, the multi-bandit best-arm identification problem consists of determining each best arm in a number of disjoint groups of arms, with as few total arm pulls as possible. In this paper, we introduce a variant of the multi ...

IEEE2019

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Nicolas Monod

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation group ...

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2019

Generalized Optical Signal Processing Based on Multioperator Metasurfaces Synthesized by Susceptibility Tensors

Karim Achouri, Ali Momeni

This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling ...

American Physical Society (APS)2019