Publications associées à Ring of symmetric functions

A Determinantal Identity for the Permanent of a Rank 2 Matrix

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

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

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 ...

2021

Interacting with Explanations through Critiquing

Boi Faltings, Claudiu-Cristian Musat, Diego Matteo Antognini

Using personalized explanations to support recommendations has been shown to increase trust and perceived quality. However, to actually obtain better recommendations, there needs to be a means for users to modify the recommendation criteria by interacting ...

2021

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

Principal Component Analysis By Optimization Of Symmetric Functions Has No Spurious Local Optima

Armin Eftekhari

Principal component analysis (PCA) finds the best linear representation of data and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that preserve most of its "e ...

SIAM PUBLICATIONS2020

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

Polynomial Evaluation on Superscalar Architecture, Applied to the Elementary Function e(x)

Felix Schürmann, Francesco Cremonesi, Timothée Ewart, Fabien Jonathan Delalondre

The evaluation of small degree polynomials is critical for the computation of elementary functions. It has been extensively studied and is well documented. In this article, we evaluate existing methods for polynomial evaluation on superscalar architecture. ...

2020

Quasi-Rayleigh model for modeling hysteresis of piezoelectric actuators

Dragan Damjanovic, Meng Zhang

Piezoelectric actuators (PEAs) have been widely used in nano-positioning applications for their high resolution of displacement. However, hysteresis, which is an inherent property of ferroelectric PEAs has been shown to significantly degrade the system per ...

2020

Sum-Rate Capacity for Symmetric Gaussian Multiple Access Channels With Feedback

Michael Christoph Gastpar, Erixhen Sula

The feedback sum-rate capacity is established for the symmetric

J

-user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the f ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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

Twisting structures and morphisms up to strong homotopy

Kathryn Hess Bellwald

We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...

2020

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to for ...

OXFORD UNIV PRESS2018

Simplified Modal Expansion to Analyze Frequency-Selective Surfaces: An Equivalent Circuit Approach

Juan Ramon Mosig, Maria Garcia Vigueras

This communication extends a previously reported analytical circuit that models the plane wave scattering by 2-D arrays of planar patches/apertures embedded in a layered media. In this extension, it is assumed that the current/electric field spatial profil ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Exact diagonalization of HeisenbergSU(N)chains in the fully symmetric and antisymmetric representations

Frédéric Mila, Pierre Marcel Nataf

Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have developed a method to exactly diagonalize the Heisenberg SU(N) Hamiltonian with several particles per site living in a fully symme ...

2016

A Dichotomy for Real Weighted Holant Problems

Sangxia Huang

Holant is a framework of counting characterized by local constraints. It is closely related to other well-studied frameworks such as the counting constraint satisfaction problem (#CSP) and graph homomorphism. An effective dichotomy for such frameworks can ...

Springer Basel Ag2016

Trace maps for Mackey algebras

Baptiste Thierry Pierre Rognerud

Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...

Elsevier2015

Function Computation over Networks : Efficient Information Processing for Cache and Sensor Applications

Chien-Yi Wang

This thesis looks at efficient information processing for two network applications: content delivery with caching and collecting summary statistics in wireless sensor networks. Both applications are studied under the same paradigm: function computation ove ...

EPFL2015

Maximizing Symmetric Submodular Functions

Moran Feldman

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. In this work, we identify submodular maximization problems for which one can get a better app ...

Springer Int Publishing Ag2015

Computing in social networks

Rachid Guerraoui, Anne-Marie Kermarrec, Kévin Clément Huguenin, Andrei Giurgiu

This paper defines the problem of Scalable Secure computing in a Social network: we call it the S-3 problem. In short, nodes, directly reflecting on associated users, need to compute a symmetric function f : V-n -> U of their inputs in a set of constant si ...

Elsevier2014